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L-type CA2+ channel mediated CA2+ transient discriminates different firing patterns in hippocampal CA1… Ren, Jihong 2000

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L - T Y P E C A 2 + C H A N N E L M E D I A T E D C A 2 + TRANSIENT DISCRIMINATES DIFFERENT FIRING PATTERNS IN H I P P O C A M P A L CA1 NEURONS: A M O D E L I N G STUDY. by J I H O N G R E N B . E . , Huazhong University of Science and Technology, 1995 M . E . , Huazhong University of Science and Technology, 1998 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U R E M E N T S F O R T H E D E G R E E O F Master of Science in T H E F A C U L T Y O F G R A D U A T E S T U D I E S Graduate program in neuroscience We accept this thesis as conforming to the required standards The University of British Columbia July 2000 © Jihong Ren, 2000 In p resen t ing this thesis in partial fu l f i lment of the requ i remen ts for an a d v a n c e d d e g r e e at the Univers i ty of Brit ish C o l u m b i a , I agree that the Library shall m a k e it f reely avai lable fo r re ference and s tudy. I fur ther agree that pe rm iss i on fo r ex tens ive c o p y i n g o f th is thesis fo r scho lar ly p u r p o s e s m a y b e g ran ted by the h e a d of my depa r tmen t o r by his o r her representa t ives . It is u n d e r s t o o d that c o p y i n g o r pub l i ca t i on of this thesis fo r f inancial ga in shal l no t be a l l o w e d w i t hou t m y wr i t ten p e r m i s s i o n . D e p a r t m e n t of A/^orpScvW^-The Univers i ty of Brit ish C o l u m b i a V a n c o u v e r , C a n a d a Da te D E - 6 (2/88) Abstract Evidence suggests an important role for L-type voltage sensitive Ca + channels (VSCCs) in activating immediate early genes (Murphy et al. 1991). To understand how L-type V S C C s regulate somatic and nuclear C a 2 + dynamics in response to different synaptic bursting waveforms that might be associated with unique forms of plasticity, we have modeled hippocampal C A 1 neuron electrophysiology and intracellular C a 2 + dynamics. The model reproduces most of the eletrophysiological properties of hippocampal C A 1 neurons, such as bursting vs. nonbursting behavior, A P frequency accommodation and A P back propagation. We examined C a 2 + influx through L-type V S C C s , and the resulting intracellular C a 2 + transient in response to simulated waveforms obtained with different presynaptic firing frequencies, active conductances and synaptic conductances. Simulation results suggest that L-type V S C C s prefer synaptic stimuli and conditions that result in a high depolarization plateau over other types of waveforms including repetitive APs , subthreshold EPSPs, or bursting firing. It was found that low activation potential and slow activation rate of L-type V S C C s contribute to the selective response of L-type V S C C s to firing patterns. Pharmacological experiments and simulation results suggest an important role of intracellular C a 2 + stores in nuclear C a 2 + elevation in response to either single A P or tetanic synaptic stimulus. Moreover, previous studies in muscle suggest a specific spatial relationship between the L-type V S C C s and the ryanodine receptor. Therefore, we sought to determine whether a similar coupling between C a 2 + channels and stores would facilitate Ca 2 + -induced C a 2 + release (CICR) action. Moving the C a 2 + stores away from the ii Ca + channels (from 50 nm to 2 )im) resulted in a large reduction in the elevation of Ca' transient. i i i TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii ACKNOWLEDGEMENT x CHAPTER 1 INTRODUCTION 1 1.1 Ca 2 + channels 6 1.2 Ca 2 + s tore 9 1.3 Co-localization of V S C C s with C a 2 + store 10 1.4 Research Hypothesis 11 CHAPTER 2 METHODS 14 2.1 Experimental procedure 14 2.2 Modeling hippocampal C A 1 neuron 15 2.2.1 Introduction to N E U R O N simulator 16 2.2.2 Modeling hippocampal C A 1 neuron eletrophysiology 17 2.2.2.1 Structure of model cell and electrotonic parameters 17 2.2.2.2 Ionic channel kinetics 19 2.2.3 Modeling intracellular C a 2 + dynamics 38 iv 2.2.3.1 Ca 2 + buffer ing 41 2.2.3.2 Diffusion of C a 2 + 42 2.2.3.3 Ca 2 + Sto re 44 2.2.3.4 C a 2 + pumps and leak channels 45 CHAPTER 3 RESULTS 47 3.1 Electrophysiological property reproduction 47 3.1.1 Bursting vs. Nonbursting behavior 47 3.1.2 A P backpropagation 49 3.1.3 Complex firing patterns in response to synaptic stimuli 52 3.2 Intracellular C a 2 + dynamics reproduction 55 3.2.1 Intracellular Ca 2 + dynamics in response to single A P 55 3.2.2 R o l e o f C I C R 57 3.3 Intracellular C a 2 + dynamics in response to different firing patterns 61 3.3.1 L-type V S C C s distinguish different firing patterns 61 3.4 What properties of L-type V S C C s are important for firing pattern selection 67 3.5 Critical role of coupling between V S C C s and C a 2 + store 71 CHAPTER 4 DISCUSSION 73 4.1 Significance of this study 73 v 4.2 Is the simple structure of our model enough to represent the complex propert of hippocampal C A 1 neurons? 4.3 Shortcomings of the intracellular C a 2 + model R E F E R E N C E S vi LIST OF TABLES Table 1 Distribution of ionic channels 20 Table 2 Intracellular C a 2 + dynamics model parameters 39 Table 3 Intracellular C a 2 + dynamics in response to single A P - Comparison of experimental data and simulation results 57 Table 4 Group data: single A P leads to cytoplasmic and nuclear C a 2 + elevation that is sensitive to agents that deplete C a 2 + stores - C P A 59 vii LIST OF FIGURES Figure 1 A model for the mechanism of L-type Ca + V S C C activation during synaptic stimulation. 13 Figure 2 Structure of N E U O R N simulation environment. 17 Figure 3 Physical structure of hippocampal C A 1 neuronal model. 19 Figure 4 Frequency dependent slow inactivation of sodium channels. 27 Figure 5 Properties of L-type V S C C model. 35 Figure 6 Intracellular C a 2 + dynamics model. 38 Figure 7 Simulated bursting vs. nonbursting behavior of hippocampal C A 1 pyramidal neurons. 48 Figure 8 A P backpropagation. 51 Figure 9 Percentage of A P spike attenuation vs. distance from the soma with the indicated amounts of IA for single or paired APs . 51 Figure 10 Complex firing patterns elicited by a 100 H z synaptic tetanus in hippocampal pyramidal neurons. 54 Figure 11 Intracellular C a 2 + dynamics in response to single A P at 34°C. 56 Figure 12 Nuclear C a 2 + dynamics in response to A P trains with different frequencies, with and without C I C R . 59 Figure 13 Role of C I C R in intracellular C a 2 + dynamics in response to tetanic synaptic stimulation. 60 Figure 14 C a 2 + influx through L-type V S C C s in response to different firing patterns. 63 Figure 15 C a 2 + influx through P/Q-type V S C C s in response to viii different firing patterns. 64 Figure 16 Nuclear C a 2 + dynamics in response to different firing patterns. 66 Figure 17 Impact of different half activation potentials on selective response of L-type V S C C s to different firing patterns. 68 Figure 18 10%-90% rise time of L-type C a 2 + current in response to different levels of step depolarization. 69 Figure 19 Impact of different opening rates on selective response of L-type V S C C s to different firing patterns. 70 Figure 20 Critical role of spatial coupling between V S C C s and C a 2 + stores. 72 ix Acknowledgement I would like to express my sincere appreciation to my supervisor, Dr. Timothy Murphy, for his inspiration, patience and guidance during my studies in the Neuroscience program. He allowed me the freedom to choose a topic most interesting to me and at the same time most suitable for my background. Without his encouragement and always-valuable advice, it is impossible for me, as a layman with little knowledge in neuroscience two years ago, to conduct the research in this thesis today. Also I would like to express my appreciation to Dr. Nicholas Swindale for his suggestions and help during the research and his time of reading my thesis and giving valuable suggestions. Also I would like to thank other members in my supervisory committee: Dr. Terry Snutch and Dr . Robert Miura, as well as Dr. Lynn Raymond and Dr . Nansheng Chen for their suggestions and enlightening discussions during the research. I thank Tao Luo, Jessica Y u , Sabrina Wang for their technical support. Thanks go out to many of my fellows at U B C , but especially to those with whom I shared the lab, not only for their day-to-day help in the lab but also good times outside the lab. Finally, I would like to thank my parents, Dehui W u and Xuemei Ren, who have always offered encouragement regardless of my choices. Chapter 1 Introduction Over the last several decades, neuroscientists have made considerable efforts to understand basic mechanisms underlying learning and memory. At the cellular level, one common hypothesis is that neuronal information critical for memory may be encoded via synaptic plasticity, activity-dependent changes in synaptic structure and strength. A persistent increase in synaptic strength commonly known as long-term potentiation (LTP) can be rapidly induced by brief neuronal activity. It has received extensive study during the last few decades as an in vitro model of activity-dependent synaptic plasticity. How does neuronal activity lead to lasting adaptive changes? One hypothesis is that it is activity-dependent regulation of gene expression that mediates long-lasting changes in neuronal structure and function (Pittenger and Kandel, 1998). Evidence from animal models that are deficient for the immediate-early genes (IEGs) c-fos and FosB suggest an important role of gene expression in the long-lasting functional changes that underlie some adaptive responses induced by neuronal activity (Brown et al., 1996; Finkbeiner and Greenberg, 1998; Watanabe et a l , 1996). Moreover, the role of activity-dependent gene expression in synaptic plasticity has been extensively studied in L T P . It was found that in the first few hours after L T P induction, there is increased gene expression activity. The early phase of L T P induced by brief tetanus appears resistant to inhibitors of protein synthesis and gene transcription (Sossin, 1997), whereas a longer lasting phase of L T P (> 3hr) is blocked (Frey et a l , 1988; Frey and Morris, 1998; Nguyen et al., 1994). These inhibitor studies suggest a two-phase model of L T P , in which the early phase of L T P is likely mediated by modifications to existing proteins, such as phosphorylation, whereas 1 the later phase requires new gene expression and protein synthesis (reviewed in Finkbeiner and Greenberg (1998)). H o w could various patterns of synaptic activity couple with the activation of nuclear transcription factors and thus regulate neuronal gene expression? There are a number of ways by which activated synapses might send signals to the nucleus (reviewed in Bito et al. (1997)). For example, microdomains of postsynaptic C a 2 + near the plasma membrane can activate type I adenylyl cyclase to produce cyclic A M P , which can either diffuse into the nucleus or can activate P K A , causing it to translocate into the nucleus (Bacskai et al., 1993). Moreover, C a 2 + can activate the r a s / M A P K cascade (Bading and Greenberg, 1991; Kawasaki et a l , 1997). (Martin et a l , 1997) showed that M A P kinase translocates into the nucleus during the induction of L T P in Aplysia . Deisseroth et al. (1996) have suggested that C a 2 + influx through N-Methyl-D-aspartate ( N M D A ) receptors or L-type voltage-sensitive C a 2 + channels (VSCCs) might activate co-localized calmodulin (CaM) and that the activated C a M translocates into the nucleus, resulting in c A M P responsive element-binding protein ( C R E B ) phosphorylation. In contrast to the studies of Deisseroth et al. (1996), Hardingham et al. (1997) have shown that, in order for C R E B to induce transcription, it is necessary for C a 2 + to invade the nucleus. Meberg et al. (1996) showed that Ca 2 +-sensitive transcriptional regulator NF-kappa B (NF-kB) mediated gene expression in the hippocampus is increased by augmented synaptic activity. N F - k B exists in cytoplasm as complex with the inhibitor I-kB. Cytoplasmic C a 2 + elevation may activate calcineurin which dephosphorylates the complex and induces its dissociation leading to translocation of the active subunits to the nucleus, resulting in gene expression (Meldolesi, 2 1998). Although this is an extensive network of interactions, it is clear that Ca + plays a critical role in neuronal gene transcription. Besides alterations in gene expression, intracellular C a 2 + elevation can trigger various processes including neurotransmitter release, modulation of synaptic transmission and excitotoxic cell death (Ghosh and Greenberg, 1995). Although the physiological concentration of extracellular C a 2 + is in the m M range, the resting intracellular C a 2 + concentration is around 50 - 100 n M . This huge concentration gradient across the plasma membrane is maintained by the following mechanisms (reviewed in Berridge (1998)). 1) Endogenous C a 2 + buffer in the form of C a 2 + binding proteins with various degrees of affinity, fixed or mobile. 2) Various C a 2 + transporters, such as C a 2 + pumps and N a + - C a 2 + exchangers, continuously extrude C a 2 + from the cytoplasm to extracellular space or into intracellular C a 2 + stores. The mechanisms described above lead to greatly restricted intracellular mobility of C a 2 + and make it an excellent local messenger (Llinas and Moreno, 1998). Intracellular C a 2 + concentration can be increased by C a 2 + influx through C a 2 + permeable ion channels, and by C a 2 + release from internal C a 2 + stores (Berridge, 1998). There are various types of C a 2 + channels with distinct electrophysiological and pharmacological properties and sub-cellular distribution (discussed below). The complex distribution profile of different types of C a 2 + channels, together with the restricted intracellular mobility of C a 2 + , achieves temporal and spatial compartmentalization of C a 2 + signaling during neuronal activity (Roberts, 1994). Plasma membrane C a 2 + permeable ion channels consist of two groups: voltage (VSCCs) and ligand-gated. V S C C s include high voltage-activated ( H V A ) C a 2 + channels, such as P /Q, L , R-type C a 2 + channels, and low voltage-activated ( L V A ) C a 2 + channels, 3 such as T-type Ca channels (Ertel et al., 2000). Ligand-gated Ca + channels include N M D A receptors, neuronal acetylcholine receptors (nAchRs), the type 3 serotonin receptors (5HT3Rs) and the C a 2 + permeable a-amino-3-hydroxy-5-methyl-4-isozazolepropionic acid ( A M P A ) and kainate glutamate receptors (Ghosh and Greenberg, 1995). Among these C a 2 + channels, evidence suggests an important role for both L-type V S C C s and N M D A receptors in activating IEGs (Bito et a l , 1997; Murphy et al., 1991). IEGs are rapidly and transiently transcribed in response to a variety of extracellular signals. Several IEGs, including c-fos, encode transcription factors and control secondary programs of gene expression that may ultimately result in functional and structural changes to neurons (Bading et al., 1993). Bading et al. (1993) reported that treatment of hippocampal neurons with glutamate caused a rapid increase in c-fos transcription and this increase can be blocked by selective N M D A receptor antagonist D(-)-2-amino-5-phosphonovalerate ( A P V ) or the addition of ethyleneglycol-bis-(P-amino-ethyl)-tetraacetic acid ( E G T A ) in bath solution, indicating important role of transmembrane C a 2 + through N M D A receptors. In addition, exposure to L-type V S C C antagonists or agonists rapidly suppresses or increases basal expression of several IEGs driven by spontaneous activity respectively (Murphy et al., 1991). Intuitively, it may be expected that the important role of L-type V S C C s in activity-dependent gene expression might be because they may be responsible for the intracellular C a 2 + elevation during synaptic or action potential (AP) stimuli. If so, the effect of L-type V S C C antagoinsts and agonists on basal expression of IEGs would be via suppressing and boosting intracellular C a 2 + elevation respectively. In contrast, most reports show a relatively small role for L-type V S C C s in mediating C a 2 + influx in response to synaptic or A P stimuli (Christie et a l , 1995; Regehr and Tank, 1992). 4 Besides extracellular C a 2 + , there is an intracellular supply of C a 2 + stored within the endoplasmic reticulum (ER) of neurons. Inositol 1,4,5-tris-phosphate receptors ( I P 3 R S ) and ryanodine receptors (RyRs) are two types of C a 2 + channels distributed on the E R that are responsible for releasing C a 2 + from this intracellular C a 2 + store. Intracellular C a 2 + stores play an important role in controlling the intracellular C a 2 + concentration and shaping intracellular C a 2 + dynamics (Jacobs and Meyer, 1997; Usachev and Thayer, 1997). Recently, it was reported that blocking intracellular C a 2 + release from C a 2 + stores decreases synaptic activity induced gene transcription activity by -50% (Hardingham et al., 1999). The downstream events after activation of L-type V S C C s leading to gene expression are still a compelling question. Contradictory conclusions have been reached by different studies regarding the role of nuclear C a 2 + transients in triggering gene expression (Deisseroth et al., 1996; Hardingham et a l , 1997). C R E B has been suggested to play a central and highly conserved role in the production of protein synthesis-dependent long-term changes in synaptic strength and neuronal structure (Mayford et al., 1995; Stevens, 1994). The abrupt change in phosphorylation level of C R E B serves as an early indicator of nuclear events that lead to gene expression. From the Deisseroth studies, it was suggested that C a 2 + influx through L-type V S C C s activates cytoplasmic C a 2 + targets such as C a M , the C a 2 + - C a M complex then translocates to the nucleus leading to C R E B phosphorylation and gene expression. In contrast, studies by Hardingham suggested that activation of L-type V S C C s produces an elevation of nuclear C a 2 + concentration that triggers gene expression by interaction with nuclear C a M kinase I V . In the present work, we are interested in nuclear C a 2 + dynamics during synaptic stimuli. For the following 5 reasons we argue against models suggesting that cytoplasmic C a z + elevation is critical for activity-dependent gene expression. 1) C a M is a large protein hence its translocation from cytoplasm to the nucleus is not a trivial issue for cell to manipulate. We believe that activated C a 2 + bound C a M would have a short half life preventing the intact complex from reaching the nucleus. 2) C a M already exists in the nucleus and would therefore not need to translocate (Santella and Carafoli, 1997). 3) Recently, it was reported by Hardingham et al 1999 that the presence of phosphorylated C R E B is not sufficient for transcriptional activation since additional steps are required. They proposed that the additional step is targeted at CREB-binding protein (CBP) , and CBP-dependent transcription is controlled by nuclear C a 2 + and C a 2 + / C a M dependent protein kinase I V . 4) There are also some nuclear transcription factors such as D R E A M which are themselves C a 2 + dependent (Carrion et al., 1999) which further supports the importance of nuclear C a 2 + flux in regulating gene expression. Therefore, in the present work, we are particularly interested in the role of L-type V S C C s as well as intracellular C a 2 + stores in nuclear C a 2 + dynamics during synaptic stimuli associated with plasticity. 1.1 Ca2+channels V S C C s are involved in the regulation of a variety of neuronal functions and neurotransmitter release (Sabria et al., 1995). Research in recent years has demonstrated numerous subtypes of V S C C s , which can be differentiated on the basis of their molecular, pharmacological and electrophysiological properties (Ertel et al., 2000). There are at least five types of high-threshold V S C C s (L, N , P, Q, and R) and one type of low-threshold V S C C s (T). 6 At the molecular level, they have the same configuration, composed of the main pore performing cti subunit, the accessory 0C2 and (3 subunits, and some optional subunits such as y, 8 subunit in cardiac L-type V S C C s . Eight distinct (Xi subunits are expressed in the mammalian C N S ( a u , OCIB, « I C , a m , CCIE, OCIG, a m and a n ) (Ertel et al., 2000). Functional expression and immunoprecipitation studies have demonstrated that a i c and a m encode L-type V S C C s (Hell et a l , 1993; Williams et a l , 1992), whereas a ^ encodes N-type V S C C s (Stea et al., 1993; Westenbroek et al., 1992). It is generally accepted that differentially spliced forms of a iA are components of P/Q-type V S C C s (Bourinet et al., 1999; Stea et al., 1994; Westenbroek et al., 1995). a m shows some features similar to R-type V S C C s (Westenbroek et al., 1998; Zhang et al., 1993). Channels containing a i c « IH, and a n are believed to mediate T-type C a 2 + currents (Ertel et al., 2000). In terms of pharmacological properties, N-type V S C C s are sensitive to 00-conotoxin G V I A ( G V I A ) (Tsien et al., 1988), whereas P/Q-type V S C C s are blocked by o> conotoxin M V I I C ( M V I I C ) (Randall and Tsien, 1995). P/Q-type V S C C s have different sensitivity to (O -Aga-IVA ( I C 5 0 S of ~1 n M for P-type and -0.1 p M for Q-type) (Randall and Tsien, 1995). L-type V S C C s preferentially bind 1,4-dihydropyridines (DHP) (Mori et al., 1991; Sabria et al., 1995; Tsien et al., 1988) and have unique electrophysiological properties. It was found that L-type V S C C s activate at more negative membrane potentials and more slowly than non-L-type H V A V S C C s (Mermelstein et al., 2000). L-type V S C C s show fairly little voltage-dependent inactivation which was shown by B a 2 + current experiments, but are profoundly sensitive to C a 2 + (Hofer et al., 1997). The Ca 2 +-dependent inactivation of L-type V S C C s is suppressed if current carrier is B a 2 + instead of C a 2 + (Brehm and Eckert, 1978). For molecular mechanisms that initiate Ca 2 +-dependent 7 inactivation, recent studies by (Peterson et a l , 1999; Zuhlke et al., 1999) suggest that C a M acts as both C a 2 + concentration sensor and the mediator of the feedback effects of C a 2 + influx on L-type V S C C function. In contrast, P/Q-type V S C C s show voltage-dependent inactivation as well as Ca 2 +-dependent inactivation (Forsythe et al., 1998; Lee et al., 1999). The Ca 2 +-dependent inactivation of P/Q-type V S C C s is different from that of L-type V S C C s since it shows little selectivity between different divalent cations (Forsythe et al., 1998). Besides kinetic properties of calcium channels, subcellular localization is another critical determinant of their physiological roles, such as whether they participate in regulation of gene expression, action potential generation, or neurotransmitter release, ccic and OCID which encode L-type V S C C s , have been shown to be localized predominantly in the soma and proximal dendrites of neurons throughout the brain (Hell et al., 1993; Will iams et al., 1992) where they may participate in regulation of activity-dependent gene expression (Murphy et al., 1991). (XIA is distributed mainly in presynaptic terminals and dendritic shafts in brain neurons. This distribution profile is also consistent with the role of P/Q-type V S C C s in triggering neurotransmitter release and activating C a 2 + dependent messengers in dendrites (Jun et a l , 1999). Immunochemical staining of OCIA extends along the entire length of the apical dendrites of C A 1 pyramidal neurons (Westenbroek et a l , 1998). 8 1.2 Ca 2 + store There is an elaborate endoplasmic reticulum that extends throughout the neuronal cell body. It appears to be a continuous membrane system, from outer nuclear membrane to axon terminal and dendrites (Martone et al., 1993). E R contains a relatively higher resting free C a 2 + concentration compared to the cytoplasm (Berridge, 1998; Verkhratsky and Petersen, 1998). The existence of this internal store of C a 2 + has a profound effect on shaping neuronal C a 2 + signals (Garaschuk et al., 1997). IP3RS and RyRs on this continuous network, responsible for C a 2 + release, are capable of regenerative C a 2 + release, which enables C a 2 + store to play an active role in neuronal C a 2 + signaling. They both are sensitive to C a 2 + and are capable of displaying the phenomenon of C a 2 + - induced C a 2 + release (CICR) (Berridge, 1998). IP 3 Rs, although gated by IP 3 , are also stimulated by C a 2 + (Bezprozvanny et al., 1991). IP3 responses wi l l thus in a crude way resemble that of RyRs. Thus, for simplicity, in the present work, only RyRs were taken into consideration. The basic idea is that intracellular C a 2 + elevation mediated by plasma membrane C a 2 + channels, subsequently activates C a 2 + channels on internal stores, resulting in an amplification of an influx signal by release of C a 2 + from internal stores. This allows information to spread long distances in spite of the existence of strong C a 2 + buffers in cytoplasm (Berridge, 1998). Pharmacological studies suggested a role of C a 2 + stores in mediating synaptic plasticity. It was concluded that the induction of L T D by low frequency stimulation depends on a C a 2 + influx via V S C C s , which is then augmented by C a 2 + release from the internal stores through the RyRs (Wang et al., 1997). Inhibitors of the C a 2 + pump on C a 2 + stores, such as thapsigargin, were found to inhibit the onset of both L T P (Wang et al., 1997) and L T D (Reyes and Stanton, 1996). Hardingham et al. (1999) 9 found that blocking C I C R reduced C R E B phosphorylation by -50%, which is possibly caused by reduction of nuclear C a 2 + elevation after blocking RyRs . 1.3 Co-localization of VSCCs with C a 2 + store It is well documented that L-type channels are coupled to RyRs. In skeletal muscle, L-type V S C C s act as voltage sensors to control RyRs on sarcoplasmic reticulum (Nakai et al., 1996) and in turn RyRs generate a retrograde signal that modifies L-type V S C C activity (Grabner et al., 1999; Nakai et al., 1998). In cardiac cells, there is cross signaling between L-type V S C C s and RyRs (Sham et al., 1995). This kind of functional coupling is also found in neurons (Chavis et al., 1996). Immunocytochemical and biochemical studies have demonstrated localization of RyRs in neuronal cell bodies, dendrites and axons (Padua et al., 1996). Although influx of extracellular C a 2 + triggers neurotransmitter release (Borst and Sakmann, 1996), several reports suggest intracellular C a 2 + release mediated by RyRs may play a major role in modulating neurotransmitter release (Peng, 1996; Smith and Cunnane, 1996) and the induction of both L T P and L T D (Wang et al., 1997; Wang et al., 1996). The localization of RyRs on terminal as well as V S C C s (N-type and P/Q type) and their important role in transmitter release implicate that there probably exists some kind of coupling between them. Recently, Sutton et al. (1999) have shown that selective influx of C a 2 + through P/Q-type V S C C s is responsible for activating expression of syntaxin-lA, a presynaptic protein that mediates vesicle docking, fusion and neurotransmitter release. Blocking C a 2 + release from intracellular C a 2 + store, blocks expression of syntaxin by P/Q -type V S C C s (Sutton 10 et al., 1999). Their data indicates that there may be a privileged close association between P/Q-type channels and C a 2 + stores. 1.4 Research Hypothesis Classical experimental methods of inducing long-term potentiation are high frequency trains of activity, while low frequency stimulation results in depression. This indicates that plastic stimuli that might trigger gene expression are inherently different from normal synaptic transmission. For example, Deisseroth et al. (1996) reported that LTP-inducing synaptic stimuli (high frequency synaptic input) but not action potential firing, produces nuclear C R E B phosphorylation. Interestingly, they found that the two types of input both resulted in comparable global increases in C a 2 + . Recent studies show that the contribution from L-type V S C C s to intracellular C a 2 + transient induced by EPSPs-like sustained depolarization is larger than that of A P s (Mermelstein et al., 1999; Nakazawa and Murphy, 1999). It is possible that stimulus paradigms, such as high frequency synaptic stimuli might result in synchronized activation of multiple neuronal inputs and thus bring neurons to a sustained depolarizing membrane potentials. F ig . 1 illustrates a model for signal transduction from the synapse to the nucleus. High frequency synaptic input causes synchronized activation of synaptic A M P A receptors causing depolarization and a reduction of N M D A receptor M g 2 + block. The slow decay kinetics of N M D A receptor cause sustained depolarization of dendrite. This strong and sustained depolarization in dendrites propagates to soma and provides sustained changes of membrane potential preferred by L-type V S C C activation. C a 2 + influx through L-type V S C C s efficiently causes C a 2 + release from C a 2 + store, resulting in large cytoplasmic C a 2 + 11 transient. Free C a 2 + in cytoplasm diffuses to the nucleus and causes nuclear C a z + elevation and nuclear C a M K I V activation leading to C R E B phosphorylation and gene expression. According to above model, in the present work, we sought to investigate the following hypotheses: 1) LTP-inducing stimulus patterns could result in sustained depolarization of the soma. 2) The specific kinetic properties of L-type V S C C s distinguish different firing patterns. 3) The coupling between C a 2 + channels and C a 2 + stores plays an important role in regulating nuclear C a 2 + concentration. To test these hypotheses, a hippocampal C A 1 neuron model was built with a detailed representation of intracellular C a 2 + dynamics. Key electrophysiological features of hippocampal C A 1 neurons and intracellular C a 2 + dynamics were reproduced. B y doing so, we were able to investigate the activation of L-type V S C C s and the resulting intracellular C a 2 + transients during plasticity inducing synaptic stimuli. Since we included C a 2 + stores in the intracellular C a 2 + dynamics model, we were able to study the role of physical coupling between C a 2 + channels and C a 2 + stores in regulating nuclear C a 2 + concentration. 12 Somatic L-type C a 2 + channel synaptic activity Q q 2 + Figure 1 A model for the mechanism of L-type C a 2 + V S C C activation during synaptic stimulation. Synaptic activity causes depolarization of dendrites which propagates to the soma, resulting in somatic membrane potential changes. Depolarization of the soma activates L-type C a 2 + V S C C s and causes C a 2 + influx into the cytoplasm. There may be three ways through which C a 2 + influx via L-type C a 2 + V S C C s may alternate gene expression activities in the nucleus. 1) C a 2 + activates some cytoplasmic C a 2 + targets such as C a M and activated C a 2 + targets tanslocate to the nucleus. 2) C a 2 + diffuses to nucleus directly and activates nuclear targets. 3) C a 2 + causes C a 2 + release from intracellular C a 2 + stores, resulting in mobilization of intracellular C a 2 + which finally causes C a 2 + elevation in the nucleus and activates nuclear targets. 13 Chapter 2 Methods 2.1 Experimental procedure Embryonic cortical neurons and glial cells (from day 18 rat fetuses) were grown 3-4 weeks in vitro on polylysine coated glass coverslips before use in imaging experiments (as in Nakazawa and Murphy, 1999). Confocal imaging with a B io Rad M R C 600 system attached to a Zeiss upright (Axioskop) microscope was used for all experiments. Two objectives were used, either a 0.9 N . A . Zeiss 63X water immersion or an Olympus 0.9 N . A . 6 0 X water immersion. The laser intensity was attenuated to 1% and the confocal pinhole was set to 3.5 (Bio Rad units). Images were acquired using the linescan mode (3.9 ms/line) in which a 1 pixel line across the soma and the nucleus is scanned repeatedly. For imaging of [Ca 2 + ] i neurons were loaded with 11 u M fluo-3 A M ( M I N T A E T A L . , 1989) for 50 min. To determine the position of the neuronal nucleus, images were also taken by scanning in both X and Y dimensions. The nucleus was readily identifiable since it accumulated more fluo-3 C a 2 + probe than the cytoplasm (Nakazawa and Murphy, 1999; OTVIalley, 1994). Using X , Y scanning the approximate center of the nucleus was identified and linescan images were taken across the cytoplasm and nucleus. Synaptic stimuli were delivered using pclamp6 software and constant current stimulation using platinum bath electrodes (1 ms duration (Ryan and Smith, 1995)). The intensity (stimulus current) of field stimulation was adjusted over a 30-90 m A range to produce APs , normally around 1.5 times the firing threshold. Three u M A P V and 60 uJVI C N Q X were added in bath solutions to reduce synaptic activity. To examine the role of C a 2 + store in intracellular C a 2 + dynamics, 30 | i M cyclopiazonic acid (CPA) , a C a 2 + pump inhibitor 14 which empties intracellular C a 2 + store by blocking its refilling, was included in the bath solution in some experiments. To synchronize delivery of field pulses with confocal image acquisition, a T T L signal from the confocal was used to trigger a second computer running pclamp6 software to produce synaptic stimuli. Confocal images were exported as byte arrays by removal of data headers and analyzed using routines written in I D L programming language (Research Systems Inc., Boulder, C O ) on a Pentium computer. Linescan data were analyzed by breaking the cytoplasmic and nuclear compartments of the cell into discrete regions by averaging the value of 5 adjacent pixels (1.1 urn). Off line averaging was done using floating point arrays to obtain additional precision over byte data (256 levels). Multiple 1.1 urn regions corresponding to cytoplasm and nucleus were averaged to improve the signal to noise ratio. The means of these adjacent pixels were plotted over time. In all o f our experiments, C a 2 + levels were reported as raw fluo-3 fluorescence intensity. Experiments performed on vehicle treated neurons indicated best stability of C a 2 + transients (over time) if C a 2 + transients were quantitated in this way (Nakazawa and Murphy, 1999). 2.2 Modeling hippocampal CA1 neuron The hippocampal C A 1 neuron model was built using N E U R O N simulator (Version 4.1.1) (Hines, 1999) on a PII-450 P C , using a 25-ns time step. 15 2.2.1 Introduction to NEURON simulator N E U R O N provides a powerful and flexible environment for implementing biologically realistic models of electrical and chemical signaling in neurons and networks of neurons. It is designed to address these problems by enabling both the convenient creation of biologically realistic quantitative models of brain mechanisms and the efficient simulation of the operation of these mechanisms. The structure of N E U R O N simulator written by Hines group is illustrated in F ig . 2. N E U R O N incorporates a programming language based on hoc, a floating point calculator with C-like syntax. With hoc one can quickly write short programs in terms that are familiar to neurophysiologists. The interpreter is used to define the morphology and membrane properties of neurons, establish graphical user interface, execute simulations, optimize parameters and analyze experimental data. It is suitable for biologists since it provides efficient mathematical tools and users can focus on biological mechanism instead of mathematical methods. It provides many ionic mechanisms, such as FLFf model for fast sodium channels and fast potassium channels that are responsible for A P firing. Moreover, it is especially convenient for investigating new kinds of membrane channels since they are described in a high level language ( N M O D L ) which allows the expression of models in terms of kinetic schemes or sets of simultaneous differential and algebraic equations (explained in detail later) (Hines and Carnevale, 2000). A l l user-defined mechanisms in N M O D L have .mod extension. To maintain efficiency, user defined mechanisms in N M O D L are automatically translated into C, compiled, and linked into the rest of N E U R O N . The mechanisms described below, including various kinds of ionic channels, 16 Ca buffer and Ca stores, were described with N M O D L and then compiled, linked to N E U R O N as a dynamic link library (Hines and Carnevale, 1997). hoc code hoc interpreter h nic mechanisms User-defined provided by ionic mechanmisms N E U R O N ' in N M O D L r Implemented Mathemutic tools Figure 2 Structure of N E U R O N simulation environment. A l l gray boxes are provided by N E U R O N . Morphological and ionic properties of neurons are described with hoc (file extension is .hoc also). Specific ionic mechanisms such as C a 2 + channel model are described in N M O D L , with file extension mod. 2.2.2 Modeling hippocampal CA1 neuron eletrophysiology 2.2.2.1 Structure of model cell and electrotonic parameters Studies by Mainen and Sejnowski (1996) and Pinsky and Rinzel (1994) indicate that the complex spiking behavior of pyramidal neurons can be modeled using relatively few compartments. For this hippocampal C A 1 neuron model, we have used four compartments that include a central soma as well as two dendrites and an axon (see F ig . 17 3). The dendrites and axon are each represented by a cylinder with different diameter (see F ig . 3). The model cell has the following passive membrane parameters: axial resistance R; = 200 Q-cm (for dendrites and soma, 50 0,-cm for axon), membrane resistance R m = 50,000 Sl-cm2, membrane capacitance C m = 1 uF/cm 2 (Spruston et a l , 1994). In N E U R O N , a continuous length of unbranched cable is denoted as a section. Thus, the above four compartments (2 dendrites, 1 soma and 1 axon) are four sections. To satisfy requirements for numerical accuracy, N E U R O N represents each section by one or more segments of equal length. The discretization method employed by N E U R O N makes the location of the second-order correct voltage at the center of a segment (Hines and Carnevale, 1997). The choice of segment size affects the accuracy of a compartmental simulation. There is a tradeoff between the computational complexity and accuracy. As long as the segment size is smaller than 5%X, where X is the electrotonic length, the numerical error in simulation is tolerable (Mainen and Sejnowski, 1998). In physical terms, X is the distance along an infinite cylinder (with same radius r, membrane resistance Rm and axial resistance Ri) over which a steady-state voltage decays e-fold. Since the cable is finite, the actual voltage decay is less than e-fold per X. The value of X is The passive membrane parameters described above together with structural parameters (diameter of each compartment), result in different X values for different sections. Among them, basal dendrite has the smallest X (0.196 cm). Thus, 50 | im, which is smaller than 5%*0.196 cm = 98 p.m, was chosen for dendrites and axon (X = 0.223 cm). The soma has (Spruston et al., 1994; Traub et al., 1991). 18 a very large X (50 cm). 5%X (2.5 cm) is still much larger than its length (30 pm). Thus, it is represented by single segment. L = 400 pm Dendrites Soma Axon Figure 3 Physical structure of hippocampal C A 1 neuronal model. The model cell contains 4 compartments with structural parameters shown in the figure. Each compartment is represented by a cylinder. A n axon hillock (not shown) is also included and placed between the soma and the axon. The axon hillock is 50 pm long and has the same diameter as the axon. 2.2.2.2 Ionic channel kinetics Twelve intrinsic membrane conductances gNa, gNaP, gKA, §KDR> gKM, gBK, gKsk, gsiAHP, gcaP, gCaL, N M D A and A M P A receptors are incorporated in the compartmental model in order to reproduce hippocampal C A 1 neuron electrophysiological properties as closely as possible. The distribution of these conductances is illustrated in Table 1. 19 Table 1 Distribution of ionic channels Dendrite (distal) Dendrite (proximal) Soma Hillock Axon Comments mS/cm 2 mS/cm 2 mS/cm 2 mS/cm 2 Na 15 mS/cm 2 15 15 300 15 Maximum conductance was from Destexhe 1994 and Mainen et al. 1998. Na conductance at hillock was adjusted to obtain A P backpropagation and A P spike amplitude at the soma -100 mV. NaP 0.02 mS/cm 2 0.05 0.1 0.1 From Lipowsky et al 1996. Maximum conductance on the dendrites was adjusted to obtain proper excitability of the model cell. Kdr 3 mS/cm 2 3 3 60 3 From Mainen et al. 1998 K A 7+ll*(distance from soma in u.m/100) (mS/cm2) 7 7 From Hoffman et al 1997 KM 0.2 mS/cm 2 0.2 0.2 0.4 Adjusted to balance NaP at resting membrane potential (Mainen et al. 1998). — 0.2 0.2 0.1 0.8 From Lipowsky et al 1996 SIAHP — 0.2 0.2 0.2 - Adjusted from Sah et al. 1996. KSK — 0.1 0.1 0.1 0.3 Lipowsky et al 1996 C a P 2.5 2.5 Maximum conductance was from Destexhe et al 1994. Distribution was based on Westenbroek et al. 1995. C a L — — 2.5 2.5 Maximum conductance was from Destexhe et al 1994. L-type VSCCs are distributed on the neuronal soma (Hell et al. 1993). VSCCs were put on the hillock in order to activate C a 2 + activated potassium channels. N M D A 0.002 mS (at synapse) Adjusted during simulation to give different levels of synaptic stimulation. A M P A 0.01 mS (at synapse) Adjusted during simulation to give different levels of synaptic stimulation. Note: 1) In most simulations, there are three synapses, two on distal dendrite, one on proximal dendrite. The synaptic conductances ( N M D A and A M P A ) are adjusted in simulations according to need. 2) Above distribution of ionic channels is for nonbursting cells. For bursting cell, there is more NaP (0.1 mS/cm 2 on proximal dendrites, 0.05 mS/cm on distal dendrites). 20 Most ionic channel models used are based on a Hodgkin-Huxley (HH) type formalism. In H H type formalism, an ionic channel is described with one or more gating particles. If x is a membrane state variable, corresponding to the probability of a gating particle in open state, then dx — = a(l - x) - fix dt where a and P are functions of voltage or ion concentration. The steady-state value of x, Xao = a/(a+ /3), and the time constant for relaxation to x„, T = l / ( a + J3). Sometimes, x<*> and rare given directly as functions of voltage or ion concentration. The macroscopic current / is the product of the maximum conductance gmax, probability of gating particles in open state xyxr-Xa, and the driving force across the membrane (the difference between membrane potential and the reversal potential of the ionic channel). Besides the above HH-type channel model, in the present work some channels such as N M D A receptors and g SAHP are described with a Markov kinetic scheme. A Markov kinetic scheme describes the movement between different conformational states of a protein. A simple Markov scheme containing only two states, an open state and a closing state, is shown below. a C^O 0 a and P are the forward and reverse reaction rates respectively. For a voltage-dependent channel, the reaction rates normally depend on the membrane potential. For a ligand-gated channel, normally at least the forward reaction rate depends on the ligand concentration. 21 A s described in the section "Introduction to N E U R O N simulator", it is quite convenient using N E U R O N to describe new ionic mechanisms in terms of sets of differential and algebraic equations or kinetic schemes. The following is an example of a user-defined membrane channel model used in the present work. ^ J H * * * * * * * * * * * * * * * * * * * * * * * mod ************************** : P o t a s s i u m IM current. :HH- type fo rma l i sm, with on ly one act ivat ion state var iab le m. I N D E P E N D E N T {t F R O M 0 T O 1 W I T H 1 (ms)} N E U R O N { S U F F I X IM U S E I O N k R E A D ek W R I T E ik R A N G E gkmbar , ik, gk :Spec i fy a dens i ty m e c h a n i s m with n a m e IM. : B y U S E I O N s ta tement , N E U R O N will keep track :the total outward current that is car r ied by an ion, :in th is c a s e , po tass i um . :gkmbar is the m a x i m u m m a c r o s c o p i c c o n d u c t a n c e whi le gk is the product of gkmba r :and the fract ion of c h a n n e l s that a re o p e n at any :moment . ik is the current that p a s s e s through gk. U N I T S { :Def ine new n a m e s for units in t e rms of ex is t ing (mA) = (mil l iamp) : n a m e s in the d a t a b a s e . (mV) = (millivolt) (S) = (Siemens) P A R A M E T E R { g k m b a r = 0.005 (S /cm2) ek = -90 (mV) dt (ms) v (mV) Ce ls ius (degC) :S imula t ion tempera ture , normal ly 36 °C . 22 t emp = 2 5 (degC) q10 = 3 } :Or ig inal tempera ture at wh i ch exper imen ts were c o n d u c t e d . :Tempera tu re sensi t iv i ty S T A T E { :Dec la re state va r i ab les wh ich are va r i ab les m :depend ing on differential equa t i ons or kinetic r e a c t i o n s c h e m e s . A S S I G N E D { :Var iab les w h o s e v a l u e s a re ca l cu la ted ik (mA/cm2) tadj } B R E A K P O I N T { :Ma in computa t ion b lock of the m e c h a n i s m . S O L V E s ta tes : B R E A K P O I N T b lock is usua l ly ca l l ed twice per gk = g k m b a r * m * m :t ime s tep. B y the e n d of th is b lock, all va r iab les ik = gk * (v - ek) :are cons is tent with the n e w t ime. } D E R I V A T I V E s ta tes { :Exac t H H equa t ions m' = (1 -m)*alpha(v) - m*beta(v) } INITIAL { i n i t i a l i ze state va r i ab les at t ime 0. m = alpha(v)/(alpha(v) + beta(v)) } F U N C T I O N a lpha(v(mV)) (/ms) { . . . Ca l cu l a t e a l p h a accord ing to m e m b r a n e potent ial v (mV) . } F U N C T I O N beIta(v(mV)) (/ms) { . . . C a l c u l a t e be ta acco rd ing to m e m b r a n e potent ial v (mV) . } mod ************************** 23 For Markov processes, N M O D L provides extremely convenient tool - kinetic scheme (Hines and Carnevale, 2000). For the simple two-state Markov model described above, the following K I N E T I C block can be used to substitute the D E R I V A T I V E block in IM.mod. K I N E T I C state { Rates(v ) :Rates(v) funct ion ca l cu la tes the react ion rates :a lpha and bel ta b a s e d on m e m b r a n e potential :v(mV) (or l igand concent ra t ion in the c a s e of : l igand-gated channe l ) , wh i ch n e e d s to be def ined . later a s a F U N C T I O N block (s imi lar to a lpha(v) :and belta(v) block in IM.mod) . ~ C <-> O (a lpha, belta) :K inet ic s c h e m e used to d e s c r i b e t ransi t ions :between c los ing a n d o p e n s ta tes. C and O :denote f ract ion of c h a n n e l s in c los ing and o p e n :state, respect ive ly . c o n s e r v e C + O = 1 :total channe l amoun t is c o n s e r v e d . } A l l user-defined channel models used in the present work were similarly implemented with N M O D L . Before illustrating those channel models, it is important to discuss the temperature dependence of channels and how it is treated in N E U R O N , since many physiological studies are performed at room temperature (22°C to 25°C) whereas we are trying to model neuronal behavior at physiological temperature (36°C). Temperature has been found to affect the kinetics of channels (Schwarz and Eikhof, 1987) and may also affect the channel conductance (Acerbo and Nobile, 1994). Although the effect of temperature on channel properties is significant, experimental data at physiological experiments and data on temperature dependence are still insufficient to construct accurate kinetic models of ionic channels at physiological temperature. In modeling studies, it is 24 normally assumed that steady state parameters are insensitive to temperature, which was implicated experimentally (Schwarz and Eikhof, 1987). Usually, to compensate for the effect of temperature, the temperature coefficient Qjo (fractional rate increase per 10°C temperature increase) is used to scale rate constants (Mainen and Sejnowski, 1996). For example, in the case of the relaxation time constant r of the activation variable x, after compensation for temperature dependence, T = l/(a + /3)/Qw(36-'emp)no°c where temp is the temperature at which experiments were performed. In the present work, Qio was assumed to be 3 for most channels, otherwise indicated (Destexhe et al., 1994). 1) Fast sodium channels It is well known that fast sodium channels are responsible for A P firing. Fast sodium channels have fast activation and inactivation kinetics. The classic HH-type sodium channel model describes its fast kinetics fairly well. Recently, it was found that in many kinds of neurons, including neocortical pyramidal neurons and hippocampal pyramidal neurons, there is slow cumulative sodium channel inactivation that is much slower than the fast, HH-type inactivation mentioned above (Fleidervish et al., 1996; Mickus et al., 1999; Mickus et al., 1999). This slow cumulative inactivation of sodium channel was found to contribute to the following phenomena: 1) Slow cumulative adaptation of spike firing which persists even after C o 2 + replaced C a 2 + in the bathing medium to block Ca 2 +-activated potassium channels (Fleidervish et al., 1996). This slow cumulative adaptation of spiking firing is associated with a gradual decrease in maximal rates of rise of action potentials, a slowing in the post-spike depolarization towards 25 threshold, and a positive shift in the threshold voltage for the next spike in the train. 2) Regulation of back-propagating A P amplitude and therefore dendritic excitation (Mickus et al., 1999). Here, the slow inactivation of sodium channels is taken into account by adding a slow variable into the classic HH-type model as the following. Parameter values for slow inactivation were adjusted according to experiments conducted by Mickus et al. (1999). Parameters for fast activation and inactivation were from Destexhe et al. (1994). ha = £ m a x -m3-h-s-(v-ENa) with am = 0 . 3 2 - ( 1 3 - v 2 ) / ( / 1 3 " V 2 ) / 4 - l ) Pm = 0.28-(v 2 - 4 0 ) / ( e ( V 2 _ 4 0 ) / 5 -1 ) ah = 0 . 1 2 8 e ( 1 7 - V 2 ) m fih = 4 / ( l + e ( 4 ° - V 2 ) / 5 ) where v 2 = Vm - Vlraub and Vtraub is the parameter controlling the A P firing threshold. a, = 0.005e (" 9 5~ v ) / 3 5 a n = 0 .0015e ( - 8 5 _ v ) / 6 5 Ps = 0 .017/(e ( - 1 7 - v ) / 7 +1) p„ = 0.034/(e ( - 1 4 ~ v ) / 9 +1) Fig . 4 A shows an example of simulated sodium current in response to 50 H z square pulses. The slow cumulative inactivation is apparent and the percentage of inactivation at different frequencies is similar to experimental data reported by Mickus et al. (1999) (see Fig. 4B). 26 A. t ( m s ) 1000 1500 2000 t ( m s ) B. © c « .2 q cs i % « i Comparison of sodium channel model with experimental data 50% -i 40% • 30% • 20% • 10% H 0% 10 Hz 20 Hz 50 Hz Stimulus frequency S experimental data • model results Figure 4 Frequency dependent slow inactivation of sodium channels, (a) Simulated sodium current in response to 2 ms 50 m V square pulses of 50 H z . (b) Percentage of inactivation (steady state) caused by 2 ms 50mV-step depolarization of different frequencies, compared with experimental data from (Mickus et al., 1999). 27 2) Persistent sodium channels Persistent sodium current has been found in various neurons including hippocampal C A 1 neurons (French et al., 1990; Mainen and Sejnowski, 1998). It activates below threshold and maybe boost the propagation of E P S P from dendrites to the soma. Since it has been suggested that the magnitude of persistent sodium currents J W is approximately 1% of the fast sodium current (Cri l l , 1996; Mainen and Sejnowski, 1998), we set the maximum conductance of the persistent sodium channels as - 1 % of the fast sodium conductance (see Table 1). The kinetic model of IN0P is from Lipowsky et al. (1996), which was based on experimental data on hippocampal neurons from French et al. (1990). hap = SNaP -m-(Vm -ENa) with am =-1.74 - (V m - i i ) / ( e ^ - n ) / ( - > 2 . 9 4 ) _ 1 } J3m =0.06-(Vm-5.9)/(e^+*9)K-5) +1) mm( = l / ( e ( ^ + 4 9 ) / ( - 5 ) + l ) 3) Delayed rectifier Potassium channels Model for delayed rectifier potassium channels, which are responsible for A P repolarization, is from Destexhe et al. (1994), described by the following HH-type equations. with 28 a„ = 0 . 0 3 2 - ( 1 5 - v 2 ) / ( e ( , 5 - V 2 ) / 5 - l ) ^ = 0 . 5 - e ( 1 0 - V 2 ) / 4 0 v = V -V, , 2 m traub where Vtraub is the parameter controlling the A P firing threshold. 4) A-type potassium channels Studies of Hoffman et al. (1997) on hippocampal C A 1 neuron revealed a very high density of transient A-type potassium channels and the density increases with distance from the soma. Their study suggested a very important role of this channel in limiting the excitability of C A 1 neuron dendrites. We have used their kinetic models for proximal and distal A-type potassium channels. iA = g K y - h - ( v m - E K ) with am = -0.0l(Vm +21 .3) / (e ( l / m + 2 I 3 , / " 3 5 -1 ) fim =0.01(Vm + 2 1 . 3 ) A > ° / m + 2 1 3 ) / 3 5 -1 ) for proximal channels am =-0.01(V m +34A)/(e(Vm+UA)'-21 -1 ) J3m = 0.01(Vm + 34 .4 ) / ( e ( l / m + 3 4 4 ) / 2 1 -1 ) for distal channels ah = -0M(Vm + 5 8 ) / ( e ( V m + 5 8 ) M i 2 - 1 ) fih = 0.01(V n + 58) / (e ( l / m + 5 8 ) / 8 2 - 1) for all channels 29 T = 0.2ms m th =5 + (2.6ms/mV)(Vm+20)/lO T. - 5ms h 5) M current IM is a slow, muscarine-sensitive, voltage-dependent potassium current. It partially activates at resting membrane potential. Together with persistent sodium currents, it gives rise to sub-threshold membrane potential oscillations (Gutfreund et a l , 1995). Together with Ca 2 +-dependent potassium channels, it is responsible for frequency accommodation in hippocampal neurons (Mainen and Sejnowski, 1998; Sah and Bekkers, 1996). The channels underlying this current have not yet been isolated and cloned. A model describing the kinetics of this current in hippocampal C A 1 neuron is given by Warman et al. (1994) which is based on the work of Hal l iwel l and Adams (1982) on guinea pig C A 1 neurons. lM=8Mn\Vm-EK) with an = 0 . 0 1 6 / e ( V m + 5 2 7 ) / - 2 3 PH= 0 . 0 1 6 / e ^ 5 2 1 ) n % i 6) Ca2+-dependent potassium channels (BK, SK, SIAHP) In hippocampal C A 1 pyramidal neurons, actually in many neurons of the central nervous system, APs are followed by a prolonged afterhyperpolarization (AHP) which is for V m > -20 m V for V m < -20 m V 30 caused by a rise in intracellular C a / + concentration. There are several groups of A H P according to their kinetic and pharmacological properties: I) AAHP is voltage-dependent and also C a 2 + dependent. It activates very rapidly and is presumably mediated by big conductance Ca 2 +-activated potassium channels (BK) (Davies et al., 1996; Storm, 1990; Yoshida et al., 1991). This current, designated Ic, contributes to A P repolarization (Poolos and Johnston, 1999; Shao et al., 1999). The following equations from Lipowsky et al. (1996) were used to describe the kinetics of this current. The difference between the Lipowsky Ic model and the model we used is the internal C a 2 + dynamics. In our model, we incorporated a detailed intracellular C a 2 + dynamics model. [Ca 2 +]j at the outermost sub-membrane shell (within 100 pm from the plasma membrane, see section 2.2.3), together with membrane potential, was used to activate this channel. There is evidence showing that C a 2 + dynamics rather than channel kinetics itself determine the kinetics of this current, as well as IAHP described later (Mainen and Sejnowski, 1998). Ic = 8B,-m2h-(Vm-EK) with V =-3 .781og 1 0 [Ca] , -11 .8 Tm = 1.1 ms m i n f =l/(e (-O.095VM+VSHIFL) + 1) ah = 1/e (Vm+79)/10 J3h=4/(e ,(Vm-82)/-27 + .1) 31 II) IAHP activates fast (<5 ms) after C a 2 + influx and decays with a time constant of hundred ms similar to that of the intracellular C a 2 + transient, and is apamin-sensitive and voltage independent (Kirkpatrick and Bourque, 1996; Mainen and Sejnowski, 1998; Neely and Lingle, 1992; Sacchi et al., 1995). The underlying channels are suggested to be SK-type Ca 2 +-activated potassium channels (Engel et al., 1999; Stocker et al., 1999; X i a et al., 1998). Together with IM, it is responsible for the medium-duration A H P and affects the instantaneous firing rate, contributing to the interval between A P s within a train (Storm, 1989). It is activated by submicromolar concentration of intracellular C a 2 + (EC50 = 0.4-0.7 u M ) in cultured rat hippocampal neurons (Hirschberg et al., 1998; Sah and Clements, 1999; Stocker et al., 1999). This current was modeled by the following equations modified from Destexhe et al. (1994), with the midpoint of the activation state variable m at 0.7 p M instead of 25 p M according to above experimental data in hippocampal neurons. =8sk-m2-(v-Ek) with m j n f = ( [Ca 2 + ] , . /0 .0007) 2 / ( l + ([Ca 2 +], . /0.0007) 2 ) T = 3 ms m III) SIAHP has much slower kinetics and is activated by intracellular C a 2 + with a time constant larger than 100 ms (Mainen and Sejnowski, 1998). It is voltage independent and apamin insensitive (Sah and Bekkers, 1996). Unlike IAHP, its kinetics is independent of the intracellular C a 2 + dynamics. It persists for seconds even after intracellular C a 2 + back to resting level (Sah and Clements, 1999). The underlying channel has not been identified but is suggested to have intrinsic slow kinetics and be gated by C a 2 + directly (Sah and 32 Clements, 1999). It is a key determinant of the repetitive firing properties of C A 1 pyramidal neurons and is modulated by second messenger systems (Pedarzani et al., 1998). It affects long-term changes of firing rate such as slow adaptation in C A 1 pyramidal neurons (Stocker et al., 1999). A modified version of the markov model of SIAHP given by Sah et al. (1999) was used. 4;jrCa],- 3/j[Ca]; 2^[Ca]; T,[Ca]; r„ Q O C 2 <^> C 3 <=> C 4 o C5<^0 ru 2ru 3ru Aru rc where r b = 10 /uM-s, r u = 0.5/s, r 0 = 600/s, and r c = 400/s. 7) L-type VSCCs L-type C a 2 + channels are modeled based on experimental data from Imredy and Yue (1994) and Mermelstein et al. (2000). A simple 3-state markov process, in which reaction rates are either voltage-dependent or Ca 2 +-dependent, was used. • O / , = 0.4/(1 + e - i w > " ) b, = 0.6/(1+ e ( v + 1 4 6 ) / 7 ) / 2 = 1 . 5 * [ C a 2 + ] , . b2 = 0.0045 / 3 = [Ca 2 +], . b3= 0.05/(1 + e(v+1-5)l2-5) 33 Among those rates, f\ and b\ is voltage-dependent, fi and are C a z + dependent. Initial parameter values for the voltage-dependent rates were from McDonald et al. (1994) in which experiments were conducted at 35°C on cardiac tissue, and were adjusted to give a rise time of approximately 8 ms at room temperature to match experimental results from Mermelstein et al. (2000). Initial parameter values for C a 2 + dependent rates were from Imredy and Yue (1994). f2 and b2 were adjusted to get a good match to fast inactivation time constant -40 ms at 0-10 mV. Recovery from the inactivation state was found to be voltage dependent. It was reported that the recovery rate is smaller than 0.005 ms at -5 -10 m V and increases steeply with hyperpolarization negative to -10 m V (Imredy and Yue, 1994). So the slope of the voltage-dependence of recovery rate b^ was chosen to be 2.5 m V . A simpler L-type V S C C model using HH-type formalism was also developed based on experimental data from Mermelstein et al. (2000). This L-type V S C C model has almost the same properties, such as the I V curve, as the one above. Most simulation results reported here were obtained with this L-type model, unless indicated otherwise. The C a 2 + -dependent inactivation time course was roughly chosen according to our own experimental data. The rise time of this model at 24°C is closer to what was reported (Mermelstein et al., 2000), and its rise time curve (rise time vs. voltage) is easier to change without changing the I V curve. ha = £ m a x ' m • f - (v - ECa) with ((v+14.6)/9.24) ) / (0.03(-v-14.6) •(! + «' ,((v+14.6)/9.24) )) (2.1) m„ = 1/(1 + e ,(-(v-v A a//)/3.24) ) (2.2) 34 Tj - 75 ms A = l / ( l + [Ca 2 + ] , /0 .001) where Vhaif = -18.6 m V for most simulations. The rise time of this model closely resembled what was reported by Mermelstein et al. (2000) at 24°C. The temperature dependence coefficient Qjo was assumed to be 2.5 (Acerbo and Nobile, 1994). 10-90% rise time of L-type C a 2 + current in response to different levels of voltage steps before and after temperature compensation is plotted in Fig . 5. Figure 5 Properties of L-type V S C C model using FfH-type formalism with Vhaif = -18.6 m V (see eq. 2.1, 2.2). Parameters for L-type V S C C model were adjusted based on experiments by Mermelstein et al. (2000), which were conducted at room temperature. A. I V curve, B. 10%-90% rise time of L-type C a 2 + current in response to different levels of step depolarization. Square indicates the rise time curve before temperature correction. Circle indicates the rise time curve at 36°C. 35 8) P/Q-type VSCCs The P/Q-type C a 2 + channel was modeled using HH-type of formalism, based on experimental data from Dove et al. (1998) on Purkinjie cells. In this model, voltage-dependent inactivation and Ca 2 +-dependent inactivation were taken in consideration. The middle point of Ca 2 +-dependent inactivation was set to 4 p M (Dove et al., 1998). lCa =Smax ' ™ " k ' / ' (V " ECa ) with T m = (1 - e ( - ( v + l 5 3 ) , 6 2 4 ) ) /(0.035 • (v +15.3) • (1 + e ^ + l 5 3 ) / 6 2 4 ) ) ) mM = l / ( l + e ( - ( v + 1 " ) / 3 - 5 ) ) =9/(0.0197 • e ( ^ 0 3 3 7 ' 0 0 3 3 7 ( v + 1 8 - 3 ) 2 ) +0.02) hmi = l / ( l + e « v + 2 l - 8 > ' 1 " ) ) = 10 ms / i D f =1/(1+[Ca],/0.004) 9) Synaptic conductances (NMDA receptor and AM PA receptor) A very simple model that approximates the kinetics of A M P A and N M D A receptors is used, which was provided in Destexhe (1997). The kinetics of A M P A and N M D A currents is modeled by the same scheme, except that there is a magnesium block of N M D A receptors, which is dependent on membrane potential. The following equations are used, I = G fB(V )(V - E ) 36 where r denotes N M D A or A M P A , / denotes the fraction of receptors in open state. For A M P A receptors, the term B(Vm) equals 1. In this model, the kinetics of these receptors are simply represented by a two-state markov process: a C+T&O P where a and P are voltage-dependent on- and off-binding rate. The values for these parameters are also from Destexhe et al. (1998). This is a simplification of the multi-state model in (Clements et al., 1992; Destexhe et al., 1994; Hessler et al., 1993), which contains two glutamate-binding sites and a desensitization state. Although the multi-state model more accurately represents the behavior of N M D A and A M P A receptors, the simplified model captured their basic properties, such as the time course of rise and decay, and their summation behavior (Destexhe et al., 1998). Since what we are interested in is somatic potential changes and nuclear C a 2 + dynamics, great details of synaptic activity are not very important. Moreover, this simplified model is more computationally efficient (Destexhe et al., 1998). Thus, in the present work, we used the simplified model of N M D A and A M P A receptors instead of the multi-state model. 10) Presynaptic cell and transmitter release The presynaptic cell contains fast sodium channels and delayed rectifier potassium channels that are responsible for A P firing and repolarization. A current injection mechanism was incorporated into the presynaptic cell to elicit APs . Different levels of current injection give different A P firing frequencies. The presynaptic glutamate release is simply modeled by brief pulse with a duration of 1 ms. Once there is an A P , there wi l l be a 37 1 ms, I m M pulse of glutamate present at the postsynaptic side (Clements et al., 1992; Destexhe et al., 1994). 2.2.3 Modeling intracellular Ca^+ dynamics The intracellular C a 2 + dynamics representation was placed in the soma and dendrites. Since what we are interested in is nuclear C a 2 + dynamics, somatic C a 2 + dynamics was described in great detail (see below). Dendritic C a 2 + dynamics was modeled much more simply with only C a 2 + diffusion and C a 2 + buffering mechanism, merely for activating Ca 2 +-activated potassium channels on dendrites. C a + buffer C a 2 + diffusion sC^ytoplasr Plasma membrane Soma C a 2 + buffer C a 2 + diffusion C a 2 + store: Ryanodine receptors, C a 2 + leak channels, and C a 2 + pumps •HVA C a 2 + channels C a 2 + pumps C a 2 + leak channels Figure 6 Intracellular C a 2 + dynamics model. In the compartmental model, the soma is represented by a cylinder with diameter of 30 um and length of 20 urn (see Fig . 3). It is divided into 50 concentric shells. The inner 35 shells are nucleus and outer 15 shells are cytoplasm. Mechanisms such as C a 2 + diffusion, C a 2 + stores, C a 2 + buffers and C a 2 + channels are placed in the nucleus, cytoplasm and plasma membrane according to literature. 38 Table 2 Intracellular Ca + dynamics model parameters Kinetic models Parameter values Comments C a 2 + Buffer Kon = 0.3 /mM-ms (Cyto) 0.05 /mM-ms (Nuclear) Totalbuffer concentration was derived from K j (Sinha et al. 1997) and C a 2 + binding ratio from Helmchen et al. 1996. Kon of C a 2 + buffer in cytoplasm was from Sala et al. 1992. Ko„ of C a 2 + buffer in nucleus was adjusted in order to obtain proper delay time between cytoplasmic C a 2 + transient and nuclear C a 2 + transient. K d = 400 n M Totalbuffer = 146 u M C a 2 + Diffusion Dca = 0.3 um 2/ms (Cyto) 0.05 p:m2/ms (Nuclear) D C a in cytoplasm is from De Schutter 1998 and Kargacin 1994. D C a in nucleus was adjusted to obtain proper delay time between cytoplasmic C a 2 + transient and nuclear C a 2 + transient and proper decay time constant of C a 2 + transient. Ryanodine Receptor Ko = 0.0001 x0ff was adjusted to match the decay time constant of the simulated cytoplasmic calcium transient to experimental data. x o n was set according to experimental data from Gyorke and Fi l l 1993. K 0 was adjusted to make cytoplasmic calcium transient peak value -300 nM (Helmchen et al. 1996). Ton = 1.2 ms x0ff = 40 ms C a 2 + pumps Vmax = 4.9e-13 mol/cm 2-s (for C a 2 + pumps on C a 2 + store) 9e-13 mol/cm 2-s (for C a 2 + pumps on plasma membrane) Parameters were from De Schutter 1998 and kargacin 1994. n = 2 K = 0.001 m M C a 2 + leak channels Kkak was chosen to balance calcium pump at the resting state. C a 2 + leak channels on plasma membrane were the same as those on ER (Girard et al. 1992; Goldbeter et al. 1990). 39 The soma is divided into 50 concentric shells around a cylindrical core (see Fig. 6). The thickness of the outermost shell is half of the others (200 nm). Concentration is second-order correct midway through the thickness of those shells and at the center of the core. These shells are divided into two compartments, cytoplasm and nucleus. The inner 35 shells are the nucleus (diameter = 14 pm). The remaining shells are the cytoplasm (thickness = 6 pm). Based on values found in the literature we have placed appropriate levels of C a 2 + handling mechanisms, such as C a 2 + buffer and C a 2 + stores, within the cytoplasm and the nucleus (See Fig . 6). C a 2 + buffering and C a 2 + diffusion were taken into consideration throughout the soma. It is well known that in cytoplasm, there is an elaborate E R system that can function as a C a 2 + store (reviewed in Verkhratsky and Petersen, 1998). I P 3 R S and RyRs distributed on E R are capable of releasing C a 2 + from this intracellular C a 2 + store (Berridge, 1998). Since they both are sensitive to C a 2 + and able to elicit C I C R (see Chapter 1), for simplicity, only RyRs are taken into account in present work. C a 2 + pumps on E R which are responsible for refilling this intracellular C a 2 + reservior, and also C a 2 + leak channels which balance C a 2 + pumps at resting C a 2 + level are also placed on the C a 2 + store. Unlike in cytoplasm, so far, no C a 2 + uptake or release mechanisms have been found in nuclear interior (Fox et al., 1997; Verkhratsky and Petersen, 1998). C a 2 + release only occurs at the nuclear envelope which is an extension of E R and contains several kinds of calcium release machinery (Lanini et a l , 1992; Petersen et al., 1998; Verkhratsky and Petersen, 1998). In this model, all properties of the nuclear envelope, such as the distribution of RyRs and C a 2 + pumps, are the same as the cytoplasmic C a 2 + store. For simplicity, the barrier effect of the E R to C a 2 + diffusion is not taken into consideration. This effect could be compensated by the adjustment of diffusion 40 constant of Ca . Moreover, the effect of the nuclear envelope on Ca diffusion is still a compelling question. The nuclear envelope is normally very permeable to C a 2 + because of the existence of large nuclear pores (Petersen et a l , 1998), although it seems that the permeability might be modulated (Badminton et al., 1998). 2.2.3.1 Ca 2 + buffer ing There is an elaborate C a 2 + buffering system within the cell, which contributes to achieve the temporal and spatial functional compartmentalization of C a 2 + signaling. A number of potential buffering systems for intracellular C a 2 + have been proposed (Kargacin, 1994; Naraghi and Neher, 1997; Neher and Augustine, 1992). Here, a non-mobile C a 2 + buffer is incorporated into the model. The following rate equation is used to describe the non-mobile C a 2 + buffer system. ^ = -Kon([Buffer]jree)(Ca) + Koff (Totalbuffer - [Buffer]free) at The coefficient K™ and are on and off-binding rate respectively, Totalbuffer is the total intracellular C a 2 + buffer concentration. The dissociation constant for C a 2 + binding to the intracellular C a 2 + buffer, ICj, which equals K ^ / K ^ w a s set as 400 n M (Kargacin, 1994; Sinha et al., 1997). Total C a 2 + buffer concentration is 146 p M which is estimated from ICj and C a 2 + binding ratio by the following equation (Helmchen et al., 1996). Totalbuffer-Kd KB=-([Ca]rest + Kd)([Ca]peak + Kd) KB (200) is the Ca 2 + -binding ratio of intracellular C a 2 + buffer (Helmchen et a l , 1996). Since peak C a 2 + concentration in response to single A P was suggested to be 150 ~ 300 41 n M (Helmchen et al., 1996). The total Ca buffer concentration was deduced from the resting C a 2 + level (50 nM) and peak C a 2 + concentration (250 nM). The on-binding rate used in the simulation was 0.3 / m M - m s for the cytoplasmic C a 2 + buffer and 0.05 /mM-ms for the nuclear C a 2 + buffer (see Table 2), which was adjusted to match the cytoplasmic and nuclear C a 2 + kinetics to experimental data (see Table 3). 2.2.3.2 Diffusion of C a 2 + A one-dimensional equation derived from Fick ' s law was used to describe C a 2 + diffusion in the radial direction within the cylindrical compartments (Crank, 1975). dCa I d , „dCa^ = (rD ) dt r dr dr D is the diffusion coefficient for C a 2 + within the cell and r is the radial distance variable. The diffusion coefficient used in the simulation was 0.3 u.m2/ms for the cytoplasm (De Schutter, 1998) and 0.05 |xm2/ms for the nucleus which was adjusted to match the simulated nuclear C a 2 + kinetics to experimental data (see Table 2). The explicit finite difference method (Crank, 1975) was used to solve the above equation. The cylindrical soma is divided into 50 shells. The index of the outmost shell is 49 and the index of the core is 0. The outermost shell and the inner core are half as thick as the others. The intervening 48 shells each have a thickness Ar which equals diam/(2*49) = 20/(2*49) = 0.204 UMn, where diam is the diameter of the segment. C a 2 + diffusion within dendrites and the axon was treated similarly. The only difference is the 42 number of shells because of the different diameters of these compartments. The cylindrical dendrites and axon were divided into 5 shells. Ca[i,t+At]-Ca[i,t}=_D ^2i+l)Ca[i+U]-4iCa[i]+(2i-l)Ca[i-l,t]) i±0 A t 2Ar2i Ca[0,t+At]-Ca[0,t] 4D r i . „ r . . . — — LJ_L=—~(Ca[ l , t ] -Ca[0 , t ] ) i=0 At Ar2 The diffusion coefficient D was set according to the location of the shell i (if it is in the nucleus, D is 0.05 u,m2/ms otherwise D is 0.3 u,m2/ms). Since the cytoplasmic and nuclear C a 2 + diffusion coefficients are different, diffusion between the nuclear envelope shell and the adjacent cytoplasmic shell was solved using a composite media approach described in Crank 1975. The diffusion problem in composite media was solved through the following steps. Imagining the nuclear boundary N to be extended one step (Ar) to the cytoplasm area, we can obtain: Ca\N,t+At]-Ca[N,t] Dn — — = ~—((2/V + l)Ca[N + l,t] - 4NCa[N,t] + (2N - l)Ca[N - U ] ) A ? 2ArZN where Dn is the nuclear C a 2 + diffusion coefficient, N is the index of the shell where nuclear boundary is. Also , imagining the cytoplasm boundary iV to be extended one step to the nucleus area, we can obtain: Ca[N,t+At]-Ca[N,t] Dc A t 2Ar2N ,2+ ((27V + \)Ca[N +1, t] - 4NCa[N, t] + (2N - l)Ca[N -1, t]) Dc is the cytoplasmic Ca diffusion coefficient. Let F(CaN,t) denote the flux across the interface. Since the diffusant enters one medium at the same rate as it leaves the other, the following condition should be satisfied. dCaN dCaN Dn — — = Dc—— = F(CaN,t) or or 43 Eliminating F term from the first and the second equation, we can get the final diffusion equation: A t 8N2 Ar2 8N2 Ar2 N represents where the nuclear envelope is. In all simulations, N is equal to 34. 2.2.3.3 C a 2 + Store C a 2 + stores were assumed as long tubes with diameter of 0.05 pm, occupying 20% of the volume of each cytoplasmic diffusion shell (De Schutter, 1998). The effect of stores on C a 2 + diffusion was not taken into consideration in this model. 100 m M of a non-mobile low-affinity (Ka 1 mM) C a 2 + buffer was placed in C a 2 + stores based on studies of De Schutter (1998). The resting level of free C a 2 + concentration in the stores was assumed to be 200 p M (Verkhratsky and Petersen, 1998). RyRs, C a 2 + pumps and C a 2 + leak channels were assumed to be evenly distributed on the surface of C a 2 + stores. 1) Ryanodine receptors The kinetics of C a 2 + release through RyRs is modeled by a permeability change of the C a 2 + store with an exponential increase process combined with a slower exponential decay (Backx et al., 1989; Kargacin, 1994). ^ = KQ (1 - <f"'» )(e-"T°« )(Cas - Ca) dt The activation time constant ron (1.2 ms) was set according to activation rate of RyRs (Gyorke and F i l l , 1993). The inactivation time constant Toff(40 ms) was adjusted to match the decay time constant of the simulated cytoplasmic C a 2 + transient to 44 experimental data (Helmchen et al., 1996). K0 was adjusted to make cytoplasmic Ca transient peak value -300 n M (Helmchen et a l , 1996). In neurons, all-or-none C I C R and a discrete threshold for C I C R activation that was subject to modulation has been reported (Usachev and Thayer, 1997). Then, the release kinetics responding to single C a 2 + influx was modeled by assuming above release kinetics combined with a fixed threshold. The threshold was set to 150nM for all simulations. Experiments conducted by Gyorke and F i l l (1993) revealed a mechanism of C a 2 + -dependent adaptation of RyRs that is distinct from conventional desensitization in that the channels adapt to a C a 2 + stimulus, but are still able to respond to new C a 2 + influx. In the present study, the adaptation only to maintained C a 2 + stimulus is taken into account and implemented by detecting the sign of the first derivative of C a 2 + transient. If the sign of the first derivative of C a 2 + transient is changed from minus to positive and the C a 2 + concentration level is above release threshold, a new C a 2 + release event is switched on. 2.2.3.4 C a 2 + pumps and leak channels Ca 2 + -ATPase pumps on C a 2 + stores continuously extrude cytoplasmic C a 2 + into C a 2 + stores. The pumps were modeled using H i l l ' s equation based on those of Goldbeter et al. (1990) and De Schutter (1998). dCa VmM(Cay dt Kn + Ca" The maximum pump velocity Vmax = 4.9e-14 mol/cm 2 • s), H i l l ' s coefficient n = 2, Kd = 0.001 m M . A n inward C a 2 + leakage was described by the equation 45 ^ = Kleak(Cas-Ca) which Kieak was adjusted to balance the pump efflux at the resting state. 46 Chapter 3 Results In the present work, a realistic model of a hippocampal C A 1 neuron with a detailed representation of intracellular C a 2 + dynamics, was built. Twelve kinds of ion channels found in hippocampal C A 1 neurons experimentally were included (see Chapter 2.1). When tested, this model reproduced many important features of hippocampal C A 1 neurons, including bursting vs. nonbursting behavior, A P backpropagation and A P frequency accommodation (Azouz et al., 1996; Cohen et al., 1999; Hoffman et al., 1997; Jensen et al., 1996; Johnston et al., 1999; Sah and Bekkers, 1996). Different firing patterns were obtained by adjusting ionic conductances and presynaptic firing frequencies. The intracellular C a 2 + dynamics model reproduces important features of C a 2 + transient kinetics in response to a single A P . Using the model we have predicted the cytoplasmic and nuclear C a 2 + transient in response to different firing patterns. 3.1 Electrophysiological property reproduction 3.1.1 Bursting vs. Nonbursting behavior Hippocampal C A 1 neurons although relatively homogenous do have different properties. For example, recordings by Jensen et al. (1996) have indicated that some hippocampal neurons exhibit burst-firing patterns in response to short depolarizing injections of current, while other C A 1 neurons exhibit a regular spiking pattern. The difference between these two types is thought to be due to the relative abundance of the persistent sodium current (INUP) (Lipowsky et al., 1996). B y only varying the amount of 47 I NaP on dendrites (see Table 1), we were able to model this essential feature of hippocampal C A 1 neurons. F ig . 7 shows different firing patterns, bursting and nonbursting, elicited by same amount of synaptic depolarization with two different parameter sets - one contains more INOP along dendrites than the other (0.1 mS/cm vs. 0.05 mS/cm 2 on proximal dendrites, 0.05 mS/cm 2 vs. 0.02 mS/cm 2 on distal dendrites). A n increase in the INap was found to be associated with bursting behavior. Less synaptic conductance was needed to bring the cell to its firing threshold, with larger amount of I N A P . In other words, INOP boosts synaptic currents in dendrites and contributes to bursting, which is consistent with what was suggested by experimental studies (Franceschetti et al., 1995; Lipowsky et al., 1996; Stuart and Sakmann, 1995). Nonbursting cell Bursting cell 20 m V 25 ms Figure 7 Simulated bursting vs. nonbursting behavior of hippocampal C A 1 pyramidal neurons, by varying the amount of persistent sodium current (INOP) (see Table 1). Both waveforms are postsynaptic potential recorded at the soma resulting from single presynaptic A P and same amount of synaptic conductances. Bursting cell contains more INap along dendrites than nonbursting cell (0.1 mS/cm 2 vs. 0.05 mS/cm 2 on proximal dendrites, 0.05 mS/cm 2 vs. 0.02 mS/cm 2 on distal dendrites). 48 3.1.2 AP backpropagation A notable feature of hippocampal C A 1 pyramidal neurons is the presence of backpropagating APs (Johnston et a l , 1999; Spruston et al., 1995; Stuart et al., 1997). The fact that APs are initiated in the axon suggests that this site has the lowest threshold for A P initiation. Both theoretical and experimental evidence suggests the axon contains a high sodium channel density (reviewed in Stuart and Sakmann, 1994)). To model this, we included a higher concentration of voltage-gated sodium conductance within the axon hillock region (Mainen and Sejnowski, 1998) (see Table 1). Recent data suggests that the dendritic A-type potassium current plays an important role in attenuating dendritic backpropagating APs in hippocampal C A 1 neurons (Hoffman et al., 1997). Along first three-fourths of apical dendrites, the density of A-type potassium channels increases five-fold (Hoffman et al., 1997). To model this we used a gradient of IA expression as in Hoffman et al (1997). Both these factors were critical for reproducing A P backpropagation features of hippocampal C A 1 pyramidal neurons. In Fig . 8 it is apparent that synaptically triggered APs are elicited in the somatic compartment before the dendrite, whereas with the same amount of voltage-gated sodium conductance within the axon hillock region as in other compartments, APs are elicited in dendrites following synaptic stimulation. The amount of A P spike attenuation at the dendrite 400 u,m from soma is -60% (see Fig . 9) which is quite similar to what was reported for hippocampal C A 1 neurons in Stuart and Sakmann (1994). Interestingly, the amount of A P spike attenuation along the dendrite for the first A P is different from the successive A P s (see Fig . 9). In Fig . 9 the diamond indicates the first A P in control condition (with the same amount IA as reported by Hoffman et al. 1997). The square indicates the amplitude of a 49 second A P in control condition. It is apparent that the amount of attenuation is smaller for the second A P , especially at the middle part of the dendrite (400 p m - 800 pm). This result is consistent with what was proposed by Hoffman et al. 1997 and is likely due to the inactivation of distal dendritic A-type potassium channels by depolarizing voltage, resulting in a smaller shunting current. This also could be verified by decreasing the amount of A-type potassium conductance to 10% of the original amount (see Table 1), which mimics pharmacological experiment condition. This results in a much smaller A P amplitude attenuation along the dendrite, and also a smaller difference between the first A P and the second one. The increasing density of A-type potassium channels is suggested to decrease the peak amplitude of backpropagating APs , to suppress the amplitude of EPSPs, and to limit the occurrence of dendritically initiated A P s (Johnston et al., 1999). The braking effect of A-type potassium channels for dendritic signal propagation can be modulated in a number of ways, including through voltage-dependent inactivation, and phosphorylation by protein kinases (Johnston et al., 1999). Experimental evidence shows that APs propagate actively into the dendrites in hippocampal pyramidal cells due to the existence of dendritic sodium channels (Stuart and Sakmann, 1994). The boosting effect of dendritic sodium channels on backpropagating A P s is demonstrated clearly by comparing backpropagation under the condition of a passive dendrite (star curve) with that of an active dendrite containing almost only sodium channels by reducing A-type potassium current to 10% of the original (triangle curve). The simulation result (Fig. 9) shows that the amplitude of a backpropagating A P is greatly reduced when dendritic sodium channels are not included (the passive dendrite case). 50 E P S P soma Figure 8 A P backpropagation. Dendritic membrane potential was recorded at 300 pm from the soma. The A P occurs within the soma before the dendrite. This suggests that suprathreshold synaptic stimulation leads to A P generation near the soma and subsequent propagation to the dendrites. 1 * x> 3 = 0.8 Q. Z 0-6 H < j8 0.4 H X • X X co E o z 0.2 A • • X X * A * X X x x X 400 800 1200 • Control (1st AP) Control (2nd AP) • 10% A-type potassium channel conductance (1st AP) • 10% A-type potassium channel conductance (2nd AP) X Passive Distance from the soma (pm) Figure 9 Percentage of A P spike attenuation vs. distance from the soma with the indicated amounts of l\ for single or paired APs . 51 3.1.3 Complex firing patterns in response to synaptic stimuli To study the activation of V S C C s during stimuli that are relevant to synaptic plasticity, we modeled high frequency presynaptic stimulation and its effect on the postsynaptic membrane potential and somatic cytoplasmic and nuclear C a 2 + dynamics. Notably, analysis of the literature and our own experimental data suggest that hippocampal C A 1 neurons exhibit a complex firing behavior in response to high frequency tetanic stimulation. The most notable features are A P frequency accommodation (Azouz et a l , 1997; Storm, 1990; Yoshida et al., 1991) and A P spike adaptation (Fleidervish et al., 1996; Mickus et al., 1999). These two phenomena lead to a slowing of A P frequency during the burst as well as a reduction in amplitude (Mickus et al., 1999). It has been reported that in hippocampal C A 1 neurons, one type of voltage-activated potassium channel and three types of Ca 2 +-activated potassium channels are responsible for spike frequency accommodation (Hirschberg et al., 1998; Sah and Bekkers, 1996; Sah and Clements, 1999; Stacker et al., 1999; Storm, 1990; Yoshida et a l , 1991). Voltage-activated potassium channels include IM and the Ca 2 +-activated potassium channels include B K , SIAHP, and S K . Among them, B K is voltage and C a 2 + activated, responsible for JTAHP and contributing to A P repolarization (Velumian and Carlen, 1999). S K together with IM, determines the interval between A P s (Hirschberg et al., 1998; Stacker et a l , 1999). Intracellular C a 2 + dynamics instead of intrinsic channel kinetics determines the S K current as well as the B K current (Mainen and Sejnowski, 1998). SIAHP has very slow kinetics (slow onset and slow closing), responsible for late phase of IAHP which lasts for seconds even after intracellular C a 2 + concentration returns 52 back to resting level (Sah and Clements, 1999). The kinetics of these potassium channels was modeled according to reported experimental data (see Chapter 2). To produce the voltage-dependent slow cumulative inactivation of sodium channels we added a slow variable s into the classical HH-type sodium channel model (see Chapter 2) and were able to obtain a frequency and voltage dependent inactivation of sodium channels during A P trains (see F ig . 4). B y reproducing the above features of hippocampal C A 1 neurons, we were able to obtain a complex firing behavior in response to high frequency tetanic stimulation, which qualitatively resembled that recorded experimentally (Fig. 10). The left panel of Fig . 10 shows some typical firing patterns recorded from rat hippocampal neurons in response to 100 H z synaptic tetanus stimulation. F ig . lOAa is A P bursting behavior superimposed on a big membrane potential oscillation. Instead of bursting, the second cell (Fig. 10A b) fires repetitive APs with decreasing frequency during the tetanic stimulation. The right panel shows simulation results obtained with different stimulus strength and parameter sets. F ig . lOBa was obtained with the parameter set for bursting cells (see Table 1), and 0.008 pS synaptic conductance and 100 H z presynaptic APs . This record is similar to the experimental result shown in F ig . lOAa. F ig . lOBb was obtained with the parameter set for nonbursting cells (see Table 1), and 0.008 pS synaptic conductance and 100 H z presynaptic APs . This cell fires repetitive APs with decreasing frequency similar to the one on the left. Moreover, i f we increase the synaptic conductance to 0.3 p:S, we can obtain a plateau waveform (a few APs followed by a high depolarized plateau), similar to what was recorded by Yeckel et al. (1995) on hippocampal neurons with tetanic stimulation. Comparison of simulated 100 H z synaptic stimulus trains to experimental 53 data from Yeckel et al. (1999) as well as our own experiments indicated good qualitative correspondence (see Fig . 10). A . E x p e r i m e n t a l data B . S i m u l a t i o n results Figure 10 Complex firing patterns elicited by a 100 H z synaptic tetanus in hippocampal pyramidal neurons, experimental data and simulation results. Left panel is experimental data. The first two were obtained in collaboration with Dr . S. Wang from rat hippocampal slices at -32 degrees in the presence of picrotoxin. They were two different cells. The data on the lower left is experimental data from Yeckel et al. 1995. Right panel is the simulation result obtained with different stimulus strength and parameter sets (see text for details). 54 3.2 Intracellular C a 2 + dynamics reproduction 3.2.1 Intracellular Ca2+ dynamics in response to single AP Analysis of experimental data indicated that somatic C a 2 + elevation attributed to V S C C s results in a delayed increase in intracellular C a 2 + levels within the nucleus (Nakazawa and Murphy, 1999). To better understand how synaptic stimuli might lead to nuclear elevations in C a 2 + we attempted to model this phenomenon. Several features are notable about the synaptically induced rise in nuclear C a 2 + levels. For example, there is a well-defined delay between the rise in cytoplasmic C a 2 + and nuclear C a 2 + of about 60 ms (Nakazawa and Murphy, 1999; O M a l l e y , 1994). In order to model this delay in nuclear C a 2 + elevation, we needed to reduce the C a 2 + diffusion constant within the nucleus to 0.05 um 2/s (0.3 um 2/s is the cytoplasmic value) (see Table 2). This also results in a slower decay time constant for the nuclear C a 2 + transient similar to what was obtained experimentally (Fig. 11; Table 3). The nuclear decay time constant obtained experimentally (Nakazawa and Murphy, 1999) is still larger than the simulation result (500 ms vs. 250.9 ms). This is probably because there was additional exogenous buffer ( C a 2 + indicator fluo-3) in the cell, especially there was a higher concentration of fluo-3 in nucleus (Nakazawa and Murphy, 1999). Fluo-3 binds to free C a 2 + when C a 2 + concentration goes high and release C a 2 + when C a 2 + concentration goes low, thus it influences intracellular C a 2 + kinetics by slowing down C a 2 + signal. 55 Experimental data Simulation results A B Cytoplasmic C a + transient Cytoplasmic C a + transient With C I C R 100 n M 100 ms Without C I C R Nuclear C a + transient d F 5 500 ms Nuclear C a 2 + transient Without C I C R 1 5 0 n M With C I C R 100 ms Figure 11 Intracellular C a 2 + dynamics in response to single A P at 34°C. A . Cytoplasmic and nuclear C a 2 + transients recorded from cortical neuron primary culture. C P A was used to block C a 2 + store refilling, and thus empty C a 2 + stores and block C a 2 + release mechanisms. To improve signal to noise ratio, all regions of the neuronal cytoplasm and the nucleus were averaged from the linescan data. Data were obtained with and without C P A perfusion. B. Simulated cytoplasmic and nuclear C a 2 + transients with and without C I C R mechanism in the cytoplasm. In order to be able to compare with experimental data, all regions of the neuronal cytoplasm and the nucleus were also averaged. Another important feature we produced in our model was the decay constant for cytoplasmic C a 2 + transient in response to a single A P stimulus (see Table 3). For determination of this value we could not rely on our previous experimental data since we did not correct for the presence of a C a 2 + indicator and its expected buffering. Therefore, we used data from Helmchen et al. (1996) that includes C a 2 + transient decay values extrapolated for conditions in which exogenous calcium buffers were absent. Adjustment of our model parameters (see Chapter 2.2) yielded a decay time constant for a single A P 56 stimulus that closely resembled that found in the Helmchen paper (Table 3). Furthermore, the peak value of the simulated cytoplasmic calcium transient in response to a single A P was around 300 n M , similar to what was reported for hippocampal C A 1 neuron (Helmchen et a l , 1996). Model Data Latency to peak nucleus versus cytoplasm 50 ms 60 ms Role of C a 2 + stores for nuclear elevation Almost complete partial Kinetics of nuclear C a 2 + transient decay (single A P ) 250.9 ms 506.4 ms (with exogenous C a 2 + buffer) Kinetics of cytoplasmic C a 2 + transient decay (single A P ) 84.2 ms 92 ms (without exogenous C a 2 + buffer) (Helmchen et al. 1996) 141.9 ms (with exogenous Ca2+ buffer) Table 3 Intracellular Ca dynamics in response to single A P - Comparison of experimental data and simulation results. 3.2.2 RoleofCICR Garaschuk et al. (1997) investigated the properties of ryanodine-sensitive C a 2 + stores in rat hippocampal C A 1 pyramidal neurons. Their study suggested an important role of C a 2 + stores in controlling the kinetics of C a 2 + signals in hippocampal C A 1 pyramidal neurons. Recently, it was reported that blocking C I C R decreases synaptic activity induced gene transcription activity by -50% (Hardingham et al., 1999). Thus, we sought to investigate the role of C a 2 + stores in nuclear C a 2 + elevation. Our 57 pharmacological experiments on cultured cortical neurons suggested an important role of C a 2 + stores in nuclear C a 2 + elevation (Fig. 11 A ) . Using C P A , a C a 2 + pump inhibitor (Garaschuk et al., 1997), we were able to empty C a 2 + stores by blocking C a 2 + store refilling. In F ig . 11 A , a single A P caused cytoplasmic and nuclear C a 2 + elevation, which is sensitive to C P A application. Table 4 shows the group data of the pharmacological experiments. Data are expressed in percent increase of raw fluorescence signal over basal fluorescence level. With C P A application, the cytoplasmic C a 2 + peak decreased by 32% and the nuclear C a 2 + peak decreased by 30.5%. Consistent with this, inclusion of cytoplasmic C a 2 + stores readily allowed C a 2 + levels to be elevated within the nuclear compartment, whereas removal of a C a 2 + store mechanism from the cytoplasm (Fig. 11 B) , greatly diminished the nuclear C a 2 + transient. This result suggested that propagation of C a 2 + signals to the nucleus was likely dependent on a store mechanism. Interestingly, simulation data suggested a much stronger role for C a 2 + stores than actual experiment (Table 3). This discrepancy may be caused by the fact that in the experimental conditions, there were several kinds of C a 2 + channels that mediate C a 2 + influx during an A P . It has been suggested that L-type V S C C s only mediate a small portion of total C a 2 + influx during an A P (Mermelstein et al., 2000), whereas in the simulation, only C a 2 + influx through L-type V S C C s was taken into consideration. Thus, under our experimental condition, C a 2 + influx itself resulted in significant intracellular C a 2 + elevation, while in the simulation, C a 2 + influx itself only resulted in a small intracellular C a 2 + elevation. Moreover, there may exist CPA-insensitive C a 2 + stores, that may further contribute to the discrepancy. 5 8 After establishing the role of C I C R in nuclear C a 2 + transients in response to single A P s (see F ig . 11), we examined its role in response to A P trains with different frequencies. Simulation results suggested that the existence of a C a 2 + store greatly differentiates high frequency stimuli from low frequency stimuli in terms of nuclear C a 2 + level (Fig. 12). Whereas, without the C a 2 + store, the relationship between nuclear C a 2 + peak value and A P frequency is linear. Ca 2 + transient j Control (AF/Fo) j CPA (AF/Fo) P value Nuclear j 2 8 . 1 % ± 0 . 1 % j Cytoplasmic I 3 3 . 6 % ± 1 . 1 % 19.0%±0.4% 23 .4%±1.0% 0.012783 0.016994 Table 4 Group data: single A P leads to cytoplasmic and nuclear C a 2 + elevation that is sensitive to agents that deplete C a 2 + stores - C P A 600 -I 500 • (Q 400 • V Q. + 300-O (0 200-o 100-0 • m —i— 20 • • • • 40 —i— 60 80 100 A P frequency (Hz) Figure 12 Nuclear C a 2 + dynamics in response to A P trains with different frequencies, with and without C I C R . Diamonds denote the nuclear C a 2 + peak in response to A P trains with the presence of C I C R . Squares denote that without the presence of C I C R . 59 A . B . Figure 13 Role of C I C R in intracellular Ca + dynamics in response to tetanic synaptic stimulation. A . Postsynaptic membrane potential at the soma obtained with 100 H Z presynaptic APs and gmax(NMDA, AMPA) = 0.3 u,S. B. Resulting intracellular C a 2 + transients with and without C I C R . Left panel is simulation results obtained with L-type V S C C s on the soma, while right panel shows simulation results with P/Q-type V S C C s on the soma. 60 Since previous modeling and experimental data suggested a critical role for Ca stores in nuclear C a 2 + elevation we also sought to examine their role in synaptic stimuli in tetanic synaptic stimulation. For both L-type and P/Q-type calcium channels we observed in the model that the C a 2 + stores had a substantial influence on the amplitude of the nuclear C a 2 + transient (Fig. 13). In contrast to that observed with the single A P stimulation (Fig. 11), in the absence of C a 2 + stores there was still a significant elevation of nuclear C a 2 + concentration, which was caused by the large amount of C a 2 + influx via V S C C s during the tetanic synaptic stimulation. 3.3 Intracellular C a 2 + dynamics in response to different firing patterns 3.3.1 L-type VSCCs distinguish different firing patterns After establishing a model of nuclear C a 2 + elevation that was in part dependent on calcium stores, we applied different synaptic membrane potential waveforms that might be associated with forms of plasticity (Deisseroth et al., 1996). Four classes of stimuli were chosen. The first was a subthreshold E P S P (Fig. 16A a). With larger synaptic conductances and the parameter set for bursting cells (increased INOP), we could produce a bursting waveform (Fig. 16A b). With the parameter set for a nonbursting cell and strong synaptic inputs, we could produce a repetitive firing waveform (Fig. 16A c). A very high level of synaptic stimulation (synaptic conductance is twenty times higher than above condition) produces a depolarized plateau (Fig. 16A d). We then examined the effects of these different stimuli on C a 2 + influx through L-type V S C C s . As recent experiments 61 suggest that the neuronal L-type calcium channels might have unique properties that allow them to distinguish between EPSPs and action potentials, we adjusted L-type current activation parameters to match that observed (Mermelstein et al., 2000) (see Chapter 2). The simulated C a 2 + currents in response to different firing patterns are shown in F ig . 14 A . The amount of C a 2 + influx in response to a firing pattern is represented by the integral of C a 2 + current over 1 s, designated as Ifiring pattern- J-Repetitive APS 2 is only 47% of the Ipiateau, although the repetitive A P pattern contains a large number of A P s (see F ig . 14 B) . This result is consistent with what was speculated in Mermelstein et al. (2000). In order to see whether this phenomenon is L-type V S C C s specific, P/Q-type V S C C s were put on the soma instead of L-type V S C C s . P/Q-type V S C C s and L-type V S C C s have different kinetics. Compared with L-type V S C C s , P/Q-type V S C C s activate at higher membrane potential and have faster kinetics (Mermelstein et al., 1999). Simulated C a 2 + currents are shown in F ig . 15 A and the integral of C a 2 + current in response to different firing patterns is compared in Fig . 15 B . The results show that in the case of P/Q-type V S C C s , there is little advantage of one waveform over another. Comparison of the C a 2 + current via L-type V S C C s with that of P/Q-type V S C C s in response to plateau waveform indicates that L-type V S C C s activate substantially during steady-state depolarization (~ -30 mV) whereas P/Q-type V S C C s mainly respond to the A P , which agrees with what was suggested by Mermelstein et al. (2000). 62 A. Repetitive APs 1 Repetitive APs 2 Plateau | o%-| 1 1 , 1 1 , 1 Repetitive APs 1 Repetitive APs 2 Plateau Firing patterns Figure 14 C a 2 + influx through L-type V S C C s in response to different firing patterns. A . C a 2 + current in response to different firing patterns. Repetitive A P s 1 is obtained with 100 H z presynaptic A P s and gmax(NMDA.AMPA) = 0.01 u,S, whereas, repetitive A P s 2 is obtained with gmax(NMDA,AMPA) = 0.015 uS. The synaptic conductance was set as 0.3 u,S for the plateau. B. Comparison of C a 2 + current integral over 1 s, normalized to the C a 2 + current integral in response to plateau waveform. 63 A. Repetitive A P s 1 Repetitive APs 2 Plateau B. c 3 U U D) -a H o c N — 15 E L_ o z 1 0 0 % -I 8 4 % 8 0 % • 6 0 % • 4 0 % • •IB Illll mm 2 0 % • 0 % • 1 0 2 % 1 0 0 % Repet i t i ve Repet i t i ve P l a t e a u A P s 1 A P s 2 Firing patterns Figure 15 C a 2 + influx through P/Q-type V S C C s in response to different firing patterns. A . C a 2 + current in response to different postsynaptic firing patterns. Repetitive APs 1 is obtained with 100 H z presynaptic APs and gmax(NMDA.AMPA) = 0.01 u,S, whereas, repetitive A P s 2 is obtained with gmax(NMDA, AMPA) = 0.015 uS. The synaptic conductance was set as 0.3 u,S for the plateau. B. Comparison of C a 2 + current integral over Is, normalized to the C a 2 + current integral in response to plateau waveform. 64 We then examined the effects of these different stimuli on nuclear C a / + transients produced by L-type V S C C s expressed on the neuronal soma. Simulated C a 2 + transients in response to different synaptic stimuli are shown in F ig . 16. Sub threshold EPSPs of -16 m V did not result in any detectable increase in C a 2 + in the soma or the nucleus. In contrast, bursting waveforms resulted in C a 2 + transients that were largely associated with the presence of APs . For repetitive firing waveforms we observed robust nuclear and cytoplasmic C a 2 + transients that seem to become attenuated with repetitive stimulation and associated voltage-dependent inactivation of the A P . Whereas the high depolarization plateau causes a sustained higher level of cytoplasmic and nuclear C a 2 + transient. The differential response to these firing patterns agrees with what was suggested by experimental data (Mermelstein et al., 2000; Nakazawa and Murphy, 1999). In order to know whether these results are L-type specific, we also examined the effects of these different stimuli on nuclear C a 2 + transient produced by P/Q-type V S C C s expressed on the neuronal soma (see F ig . 16 C) . The simulation results suggest that with P/Q-type V S C C s on the soma, C a 2 + transients in response to high depolarization plateau and repetitive APs are similar. The results suggest that L-type V S C C s have specific kinetic properties, together with their somatic distribution, making them be able to distinguish different types of synaptic stimuli in terms of nuclear C a 2 + transient. This may account for how normal synaptic activity is discriminated from activity that leads to gene expression. 65 a Figure 16 Nuclear C a 2 + dynamics in response to different firing patterns. A . Firing patterns obtained with different parameter sets. a. subthreshold E P S P , obtained with nonbursting cell parameter set (see table 2.1), 30 H z synaptic stimulus . and gmax (NMDA,AMPA) = 0.005 p,S. b. Bursting APs , obtained with bursting cell parameter set (see table 2.1), 100 H z synaptic stimulus and gmax (NMDA,AMPA) = 0.008 pS. c. Repetitive APs , obtained with nonbursting cell parameter set (see table 2.1), 100 H z presynaptic stimulus and gmax (NMDA,AMPA) = 0.01 pS. d. Plateau, obtained with nonbursting cell parameter set (see table 2.1), 100 H z synaptic stimulus and gmax(NMDA, A M P A > = 0.3 pS. B . Cytoplasmic and nuclear C a 2 + dynamics with L-type V S C C s on the soma in response to firing patterns shown on the left. C. Nuclear C a 2 + dynamics with P/Q-type V S C C s on the soma in response to firing patterns shown on the left. 66 3.4 What properties of L-type VSCCs are important for firing pattern selection After the observation that L-type V S C C s distinguish different firing patterns, we sought to investigate that what properties of L-type V S C C s are important for this selective response to different firing patterns. Half activation membrane potential (Vhaif) Since it was reported by Mermelstein et al. (2000) that L-type V S C C s respond to more negative potentials than non L-type V S C C s , we first investigated L-type V S C C models with different Vhaif. Fig . 17 A shows I V curves with different Vhaif Integral of C a 2 + current in response to different waveforms (repetitive firing and plateau) is compared in F ig . 17 B . When Vhaif is -18.6 m V (default), Repetitive APs/Ipiateau = 47%, whereas, when Vhaif is -12 mV, lRepetitive APs/Ipiateau = 65%. It is clear that Vhaif is very important to the selective response in terms of the amount of C a 2 + influx. Opening rate of L-type VSCCs Since Mermelstein et al. (2000) suggested that the slower opening rate of L-type V S C C s (as compared with non L-type V S C C s ) may contribute to distinguishing EPSPs over APs , we sought to change the opening rate of L-type V S C C s and see its influence on the amount of C a 2 + influx in response to different firing patterns (Ifmng pattern)- In order to change the opening rate independently, we changed the dependence of the L-type V S C C activation time constant on voltage from eq. 2.1 to eq. 3.1: rm = (1 - e«v+i4.6)/9.24)} / ( 0 . 0 3 ( - v -14.6) • (1 + g^ 1 4 - 6 " 9 - 2 4 ' ) ) (2.1) r m = (1 - e { v + u - 6 ) n 5 M ) ) /(OM • (-v -14.6) • (1 + e ( v + H - 6 ) ' r 2 4 ) ) ) (3.1) 67 A . B. 100% n 73 w> 80% H cu S3 Z 60% H fi cu u 40% H 3 A 20% H U 0% 47% 100% -18.6 46% 30° m Repeti tve APs • Plateau -12 Vm (mV) Figure 17 Impact of different half activation potentials on selective response of L -type V S C C s to different firing patterns. A . I V curves of L-type V S C C model with different Vhaif, B. Comparison of C a 2 + current integral in response to repetitive APs and plateau, with different Vhaif of L-type V S C C s . Repetitive APs and plateau were obtained with g m a x ( N M D A , A M P A > = 0.015 U.S and 0.3 u.S respectively, and both with 100 H z synaptic stimulus. 68 The resulting rise time vs. voltage curve is shown in Fig . 18. B y doing this, we changed the opening rate of L-type V S C C s while keeping the closing rate almost the same, and did not influence the I V curve. Simulated C a 2 + currents in response to different levels of synaptic stimuli are shown in Fig. 19 A . The upper panel shows simulated C a 2 + currents with eq. 2.1 (slower opening rate), while the lower panel is that with eq. 3.1 (faster opening rate). It is clear that the opening rate wi l l influence the amount of C a 2 + influx during each A P (peak current almost 2 times larger in faster opening rate case than the other). Ifiring pattern for each case is shown in F ig . 19 B . The faster opening rate results in a significant increase of C a 2 + influx during repetitive firing, whereas it has little influence on C a 2 + influx during plateau. lRepetitive Aps/Ipiateau increases from 47% with the slower opening rate (default) to 62% with the fast opening rate. From the above simulation results, it is clear that the slow opening rate of L-type V S C C s does contribute to distinguishing different firing patterns. Eq. 2.1 —A— Eq. 3.1 •a \ • V - A — A — A — A - 1 — -40 - | — -20 - 1 — 20 - 1 — 40 voltage (mV) Figure 18 10%-90% rise time of L-type C a 2 + current in response to different levels of step depolarization. Different rise time curves are achieved by changing the dependence of activation time constant ( r m ) of L-type V S C C model on membrane potential (eq. 2.1 (default) vs. eq. 3.1 (faster opening rate case)). 69 A. Repetitive A P s Plateau e q . 2.1 e q . 3.1 dependence of activation time constant xm on membrane potential Figure 19 Impact of different opening rates on selective response of L-type V S C C s to different firing patterns. Opening rate of L-type V S C C s is determined by the activation time constant x„„ which is set by eq. 2.1 in the default case. To achieve faster opening rate, eq. 3.1 is used. A . Simulated C a 2 + currents with different opening rate in response to different firing patterns. Repetitive APs and plateau were obtained with gmax(NMDA.AMPA) = 0.015 uS and 0.3 uS respectively, and both with 100 H z synaptic stimulus. B. Comparison of C a 2 + current integral in response to different firing patterns. 70 3.5 Critical role of coupling between VSCCs and Ca store Previous studies in muscle suggest a highly specific spatial relationship between the L-type V S C C s and the RyRs (Nakai et al., 1996). In neurons, it has been suggested that there is functional coupling between RyRs and L-type V S C C s (Chavis et al., 1996). The functional coupling between them was so tight that it even persisted in inside-out membrane patches (Chavis et al., 1996), which suggested a possibility that the co-localization between C a 2 + stores and L-type V S C C s may also happen in neurons. Besides the coupling between L-type V S C C s and C a 2 + stores, the distribution of C a 2 + stores on axon terminals as well as P/Q-type V S C C s , and their important role in transmitter release, implicate that there probably also exists similar coupling between them. Sutton et al. (1999) show that selective influx of C a 2 + through P/Q-type channels is responsible for activating expression of syntaxin-lA, while blockade C a 2 + release from intracellular C a 2 + store reduces syntaxin expression stimulated by P/Q-type V S C C s . Therefore, we sought to determine whether a similar coupling between V S C C s and stores would facilitate C I C R action. In Fig . 20 we located the C a 2 + stores at varying distances from V S C C s . When the stores were within 50 nm of the C a 2 + channels we observed a robust store-dependent intracellular C a 2 + increase. Whereas, moving the C a 2 + stores 2 um from C a 2 + channels resulted in a large reduction in the elevation of C a 2 + concentration. 71 L-type Cytoplasmic Ca transient P/Q-type 2 pm 500 n M 250 ms Nuclear Ca transient 50 nm J\J m i l Figure 20 Critical role of spatial coupling between V S C C s and C a z + stores. To examine the role of spatial coupling between V S C C s and C a 2 + stores on intracellular C a 2 + dynamics, cytoplasmic and nuclear C a 2 + transients were obtained with C a 2 + stores placed 50 nm and 2 p m away from the plasma membrane respectively. Left panel shows intracellular C a 2 + transients with L-type V S C C s on the soma. Right panel shows simulation results with P/Q-type V S C C s on the soma. 72 Chapter 4 Discussion 4.1 Significance of this study This compartmental cell model, built with N E U R O N , contains 4 compartments, including one soma, one axon and two dendrites. It includes 12 kinds of ion channels that were found in hippocampal C A 1 neurons experimentally, and reproduces many electrophysiological properties of hippocampal C A 1 neurons. B y adjusting the amount of persistent sodium current along dendrites, the model cell exhibits nonbursting or bursting behavior, which resembles properties of two types of hippocampal C A 1 neurons respectively (Jensen et al., 1996). B y including a complex array of active conductances in dendrites based on experimental data and other modeling studies, we reproduced another key feature of hippocampal C A 1 neurons, A P backpropagation. We were able to closely model most features of A P backpropagation in hippocampal C A 1 neurons, such as the amount of amplitude attenuation along dendrites (see F ig . 9) and the propagation time course (the delay between somatic A P and dendritic A P at 200 um from the soma is approximately 1.5 ms, similar to what was reported in Stuart et al. (1997). The literature suggests that hippocampal C A 1 neurons exhibit a complex firing behavior, such as A P frequency accommodation and A P spike adaptation. Many studies have been carried out to investigate the mechanisms underlying these behaviors in hippocampal C A 1 neurons. It has been suggested that four types of potassium currents (IM, B K , S K and SIAHP) are responsible for the induction of A P frequency accommodation (Azouz et al., 1997; Storm, 1990; Yoshida et a l , 1991), whereas the slow-inactivation of sodium current is responsible for A P spike adaptation (Fleidervish et al., 1996; Mickus et al., 1999). B y 73 including the above mechanisms, the model cell exhibits complex firing behavior similar to what was recorded from hippocampal neurons (see Fig. 10). Being able to reproduce several key features of hippocampal C A 1 neuron electrophysiology, we sought to examine the role of L-type V S C C s in differentiating synaptic activity that leads to gene expression from normal synaptic activity. In order to study the activation of V S C C s by stimuli that are relevant to synaptic plasticity, we have modeled high frequency presynaptic stimulation and its effect on postsynaptic membrane potential. The L-type V S C C model was based on experimental data from Mermelstein et al. (2000) in which experiments were conducted at room temperature. A Qjo equal to 2.5 was used to predict the behavior of L-type V S C C s at physiological temperature (Acerbo and Nobile, 1994). Simulation results suggest that a plateau waveform with steady-state depolarization to —30 m V is preferred by L-type V S C C s over repetitive APs . The integral of the C a 2 + current mediated by L-type V S C C s in response to repetitive APs ( g m a x ( N M D A , A M P A ) = 0.015 uS) is only 47% of that of plateau, although the repetitive A P firing pattern contains a larger number of A P s (see F ig . 14). This phenomenon is L-type V S C C specific, since with P/Q-type V S C C s on the soma instead of L-type V S C C s , the integral of C a 2 + current in response to above two waveforms is similar ( I r e p e t i t i v e A P S 2 / I p i a t e a u = 102% (see F ig . 15)). We also examined the properties of the L-type V S C C that contribute to differentiating different firing patterns. It was found that the relatively low activation membrane potential together with slow activation rate contribute to this property of L-type V S C C s . Since it has been suggested that nuclear C a 2 + elevation plays a critical role in triggering activity-dependent gene expression, we sought to determine whether L-type 74 mediated - nuclear C a 2 + transient also discriminates different firing patterns. Thus, a detailed intracellular C a 2 + dynamics model was placed in the soma. Various mechanisms, including C a 2 + buffering, C a 2 + diffusion, C a 2 + release and C a 2 + pumps, were placed in cytoplasmic and nuclear compartments respectively according to the literature (See Chapter 2). B y adjusting parameter values (such as the diffusion constant of C a 2 + in nucleus), we were able to reproduce most features of cytoplasmic and nuclear C a 2 + dynamics in response to a single A P , such as the latencies and decay time constants (see Table 3). After reproducing C a 2 + dynamics in response to a single A P , we predicted intracellular C a 2 + dynamics in response to different firing patterns. Consistent with experimental data, it was found that intracellular C a 2 + stores play an important role in nuclear C a 2 + elevation in response to either a single A P or tetanic synaptic stimulation. Most interestingly, simulated nuclear C a 2 + dynamics mediated by L-type V S C C s can differentiate different firing patterns (see Fig. 16). The results suggest that L-type V S C C s have specific kinetic properties, which together with their somatic distribution, makes them able to distinguish different types of synaptic stimuli in terms of nuclear C a 2 + transients. The simulation results described above support the model for signal transduction from the synapse to the nucleus illustrated in F ig . 1.1. Synaptic activity causes depolarization of dendrites which propagates to the soma, resulting in somatic membrane potential changes. At the soma, L-type V S C C s , acting as filters, prefer synaptic stimuli and conditions that result in a high depolarization plateau over other types of waveforms including repetitive APs , subthreshold EPSPs, or burst firing. C a 2 + influx through L-type V S C C s efficiently causes C a 2 + release from C a 2 + stores, resulting in enhanced nuclear 75 C a 2 + elevation. Firing patterns are differentiated in terms of the amount of C a / + influx and the resulting nuclear C a 2 + elevation. This may account for how normal synaptic activity is discriminated from activity that leads to gene expression. To understand how differences in nuclear C a 2 + transients may lead to specific programs of gene expression, it is necessary to understand: 1) encoding and decoding strategies that may be used by C a 2 + ; 2) the characteristics of the intracellular C a 2 + transient and C a 2 + - sensitive transcriptional factors. It is well known that abundant information is encoded in C a 2 + signals (Berridge, 1998). Studies suggest that information might be encoded by the amplitude, duration, frequency and spatial localization of intracellular C a 2 + transients (Bading et al., 1997; Bito et al., 1997; Dolmetsch et al., 1998; Finkbeiner and Greenberg, 1998). Some transcription factors, such as c-Jun N-terminal kinase (JNK) , have been reported to be sensitive to the amplitude and duration of C a 2 + signals (Dolmetsch et al., 1997). With regard to frequency, Dolmetsch et al. (1998) reported that rapid oscillations activate N F - A T , Oc t /OAP and N F - k B , whereas infrequent oscillations activate only N F - k B . Moreover, direct in vitro experiments and computer simulation studies suggest that C a M K I I could act as a frequency decoder for intracellular C a 2 + signaling (De Koninck and Schulman, 1998; Hanson et al., 1994). Recent studies show that cytoplasmic and nuclear C a 2 + signals activate distinct mechanisms of transcriptional control (reviewed in Bading et al., 1997). The SRF-l inked pathway that is triggered by cytoplasmic C a 2 + elevation mediates SRE-dependent transcriptional activation in AfT20 cells and in primary hippocampal neurons, whereas nuclear C a 2 + elevation is required for CRE-dependent transcription. 76 Interestingly, activators of gene expression, such as N F - k B , N F - A T (Dolmetsch et al., 1998) and C a M K I I (De Koninck and Schulman, 1998), that have been reported to be sensitive to the intracellular C a 2 + oscillation frequency, have one common feature: their ability to be autonomous of C a 2 + after activation. H o w long they could remain active after intracellular C a 2 + concentration decreases determines the threshold frequency they decode. Activation of N F - k B , N F - A T , and Oc t /OAP is mediated by a Ca 2 +-dependent phosphatase called calcineurin. After dephosphorylation by calcineurin, active subunits dissociate from these transcription factors and migrate to the nucleus. Gene expression keeps on going as long as active subunits remain in the nucleus. N F - A T returns to the cytoplasm rapidly (~ one min) after rephosphorylation, whereas N F - k B returns much more slowly (>16 min after a single spike). So N F - A T needs higher frequency oscillation to be activated, whereas infrequent C a 2 + oscillation is enough to induce persistent activity of N F - k B (Dolmetsch et al., 1998). With regard to C a M K I I , once C a 2 + / C a M binds C a M K I I , the kinase not only phosphorylates its target substrates but also autophosphorylates its own auto-inhibitory domain. Autophosphorylation increases its C a M affinity from 45 n M to 60 p M , and thus prolongs the binding of C a M to over 3 s even when free C a 2 + is reduced to basal level. Moreover, autophosphorylation disrupts the function of the auto-inhibitory domain so that the kinase remains partially active (autonomous of C a 2 + ) even after C a 2 + / C a M dissociates and until the site is dephosphorylated (reviewed in Heist et al. 1998). Interestingly, these C a 2 + frequency-sensitive activators of gene expression are all localized in the cytoplasm (Dolmetsch et al., 1998; Heist et al., 1998; Meberg et al., 1996). Whereas, t i l l now, there is no report about the frequency sensitivity of C a M kinase 77 I V , which is predominantly localized in the nucleus (Nakamura et al., 1995; Jensen et al., 1991) and has been suggested to be the nuclear mediator of Ca 2 +-regulated transcription (Hardingham et al., 1999; Chawla et al., 1998). In contrast to activation of C a M K I I which only needs C a 2 + and C a M , regulation of C a M K I V involves several phosphorylation steps that require not only C a 2 + / C a M but also other activated C a M K kinase (reviewed in (Heist and Schulman, 1998)). C a 2 + / C a M directly activate C a M K kinase, which in turn phosphorylates and upregulates C a M K I V . C a 2 + / C a M must be bound to C a M K I V when it is phosphorylated by activated C a M K kinase. This requirement for the phosphorylation of C a M K I V may make activation steeply dependent on the concentration of C a 2 + / C a M , which may make C a M K I V more sensitive to duration and amplitude of nuclear C a 2 + elevation, instead of frequency. Experimental data and simulation results show that cytoplasmic C a 2 + and nuclear C a 2 + transients have different kinetics (see Table 3). The cytoplasmic C a 2 + transient has relatively fast kinetics (see Table 3), which makes it tend to oscillate in response to a repetitive stimulus. On the other hand, the nuclear C a 2 + transient has a much slower decay time constant (see Table 3) and would be a better integrator. Interestingly, consistent with the kinetics of the cytoplasmic C a 2 + transient, its downstream effectors, those cytoplasmic distributed Ca 2 +-sensitive activators of gene expression described above are reported to be sensitive to the frequency of C a 2 + oscillation. While consistent with the slow kinetics of the nuclear C a 2 + transient, properties of C a M K I V , which is localized in nucleus, make it more sensitive to the amplitude and duration instead of frequency. 78 4.2 Is the simple structure of our model enough to represent the complex properties of hippocampal CA1 neurons? Neurons have a very complex array of axonal and dendritic processes. In contrast, our cell model only contains 2 primary dendrites, one soma and one axon. Can such simple structure represent most features of a real neuron, especially when firing patterns induced by synaptic activity are concerned? Many recent studies have addressed this important question and suggest that compartmental models, first developed by Rai l in 1960s, provide a practical approach and a sound basis for representing dendritic function (Cook and Johnston, 1997; Cook and Johnston, 1999; Jaffe and Carnevale, 1999; Mainen and Sejnowski, 1996; Shepherd, 1999). The influence of a synaptic current on the soma could be represented by the transfer impedance, which reflects how a current applied at one location affects membrane potential at other locations. Simulation studies by (Jaffe and Carnevale, 1999) in 4 reconstructed C A 1 pyramidal cell models suggest that the transfer impedance decreases with distance from the soma but second- or higher order dendritic branches produce very little further decline. Their results suggest that a synaptic current that enters anywhere along a terminal branch w i l l produce almost the same PSP at the soma regardless of its exact location on that branch. So moving all synaptic inputs to the primary dendrites and using two cylinders instead of reconstructed dendritic processes to represent the complex dendritic structure of hippocampal C A 1 neurons should not have much effect on postsynaptic membrane potential at the soma. Moreover, studies by Mainen and Sejnowski (1996) and Pinsky and Rinzel (1994) show that the full range of regular spiking responses, adaptation, after-depolarization, and repetitive 79 bursting observed in recordings and in models of reconstructed pyramidal cells could be reproduced in a model with only two compartments. To simplify our model we have used very few synapses with strong synaptic conductances, in contrast to the situation in vivo where many relatively weak synapses are present. Therefore, a second major question is whether a few synapses with adjustable synaptic conductances on the apical dendrites can represent thousands of synapses distributed on dendritic processes? The passive electrotonic structure of dendrites makes synaptic inputs from distal dendritic locations suffer considerable attenuation on the way to the soma (Mainen and Sejnowski, 1996). Or in other words, with only passive dendrites, the effect of a synaptic input on the soma depends on its dendritic location. Hence, besides synapse strength, with passive dendrites, synapse location is an important component of the synaptic signal. Experimental evidence established that the dendrites of central neurons contain a complex array of voltage-gated channels (Hoffman et al., 1997; Johnston et al., 1999). Experimental and modeling studies suggest that sodium current boosts the amplitude of distal synaptic EPSPs measured at the soma (Lipowsky et al., 1996; Stuart and Sakmann, 1995). Furthermore, studies by (Cook and Johnston, 1997; Cook and Johnston, 1999) suggest that the active property of dendrites minimizes the location-dependent variability of the synaptic inputs. Thus, a few synapses on the main branch of apical dendrites should still be able to reproduce most features of synaptic activity. 80 4.3 Shortcomings of the intracellular Ca 2 + model Although the current intracellular C a 2 + model reproduces important kinetic properties of cytoplasmic and nuclear C a 2 + dynamics in response to single A P , there are some shortcomings that could be compensated in the future. One-dimensional model without longitudinal diffusion Because of the limitation of the current N E U R O N version, the intracellular C a 2 + model is a one-dimensional cylindrical model without longitudinal diffusion of C a 2 + from one compartment to another. Without longitudinal diffusion, it is not possible to examine the contribution of dendritic P/Q-type V S C C s to the nuclear C a 2 + transient since the endogenous P/Q-type V S C C s are distributed on dendrites and axonal terminals instead of soma. Although N E U R O N has tools to deal with longitudinal diffusion, they are currently not stable and could not reflect the real situation (personal communication with Dr. Carnevale). Moreover, because of time limitation and what we are most interested in is L-type V S C C s which are distributed on the neuronal soma, longitudinal diffusion was not implemented. IP3 receptors It has been suggested that intracellular C a 2 + stores play an important role in intracellular C a 2 + dynamics (Berridge, 1998; Garaschuk et al., 1997). There are two types of Ca 2 +-sensitive C a 2 + channels, IP3RS and RyRs, distributed on C a 2 + stores in many kinds of brain neurons including hippocampal C A 1 neurons (Verkhratsky and Petersen, 1998). As has been discussed in Chapter 1 and Chapter 2, for simplicity, only RyRs were taken into consideration in the intracellular C a 2 + dynamics model. IP3RS are sensitive to 81 both IP3 and C a 2 + (Bezprozvanny et al., 1991). To include I P 3 R S , the dynamic change of IP3 within cytoplasm after synaptic stimulation has to be considered, which makes the story even more complicated since we would also need to model the characteristics and distribution of metabotropic receptors that are coupled to phospholipase C activity. Currently, considerably less is known about the kinetic behavior of metabotropic receptors and their localization as compared with ionotropic receptors. Since IP3RS are sensitive to C a 2 + and similar to RyRs they also exhibit the C I C R phenomenon, it is reasonable to combine IP3RS into RyRs, by assuming that the intracellular IP 3 level does not change dramatically following neuronal electrical activity. Exogenous C a 2 + buffer (fluo-3) In the C a 2 + imaging experiments, C a 2 + indicator fluo-3 was loaded into the cell. The low capacity, affinity and mobility of the endogenous C a 2 + buffer makes it possible for relatively small amounts of exogenous C a 2 + buffers, such as fluo-3, to exert a significant influence on the characteristics of the C a 2 + concentration signal (Neher and Augustine, 1992). In our model, exogenous C a 2 + buffer was not included. Including C a 2 + indicator could give us a better understanding of experimental data and the effect of C a 2 + indicator on intracellular C a 2 + dynamics. The following method could be used to add C a 2 + indicator fluo-3 into the model in the future. To model the effect of C a 2 + indicator Fluo-3, the following assumptions were made, a) Since the on-binding rate of fluo-3 (1000 /mM-ms) is more than 1000 times faster than other processes, we can assume that it is always in equilibrium at each time step, b) We assume that the diffusion constant for free fluo-3 and Ca-bound fluo-3 are the 82 same, so the total amount of fluo-3 remain constant in each shell. So the Ca 2 + -bound fluo-3 concentration at each shell can be calculated by the following equilibrium equation: Cafluo - Totalfluo - fluo = Totalfluol(\ H — ) KdCa K j = 800 n M is the dissociation constant of fluo-3 to C a 2 + (Minta et al., 1989). 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