Analysis of the kinetics of Ca2+ signals in Ehrlich ascites tumor cells upon the inhibition of the mitochondrial Na+/Ca2+ exchanger

Signals of cytosolic Ca2+ (Ca2+c) and mitochondrial Ca2+ (Ca2+m) evoked by the activation of purinoreceptors of Ehrlich ascites tumor cells at different extents of inhibition of the mitochondrial Na+/Ca2+ exchanger by tetraphenylphosphonium (TPP+) were investigated. [Ca2+c] was measured by Fura-2 fluorescence, and [Ca2+m] changes were inferred from NAD(P)H fluorescence. The addition of ATP to the cell suspension induced a NAD(P)H response, which replicated Ca2+c signal with some retardation of the peak and a slower decay. In the presence of increasing TPP+ concentrations, NAD(P)H responses evidenced that the rate of [Ca2+m] decay strongly decreases, while the phase of initial rise does not change. The maximal TPP+ dose did not affect [Ca2+c] and NAD(P)H fluorescence in the resting state, as well as ATP-induced [Ca2+c] responses. These data are described in a mathematical model, which accounts for Ca2+ transport through the membranes of endoplasmic reticulum and mitochondria, as well as through the plasma membrane. The model indicates a low rate of the mitochondrial cycle of Ca2+ uptake/efflux at rest and a strong activation of the uptake with increasing [Ca2+c] to which a Hill coefficient of no less than 4 corresponds. Furthermore, the rise of the uptake rate changes in a short time to a decline, and the peak of the rate is markedly ahead of the peak of [Ca2+c].     

Spontaneous electrical and calcium oscillations in unstimulated pituitary gonadotrophs.

Single pituitary cells often fire spontaneous action potentials (APs), which are believed to underlie spiking fluctuations in cytosolic calcium concentration ([Ca2+]i). To address how these basal [Ca2+]i fluctuations depend on changes in plasma membrane voltage (V), simultaneous measurements of V and [Ca2+]i were performed in rat pituitary gonadotrophs. The data show that each [Ca2+]i spike is produced by the Ca2+ entry during a single AP. Using these and previously obtained patch-clamp data, we develop a quantitative mathematical model of this plasma membrane oscillator and the accompanying spatiotemporal [Ca2+]i oscillations. The model demonstrates that AP-induced [Ca2+]i spiking is prominent only in a thin shell layer neighboring the cell surface. This localized [Ca2+]i spike transiently activates the Ca2(+)- dependent K+ current resulting in a sharp afterhyperpolarization following each voltage spike. In accord with experimental observations, the model shows that the frequency and amplitude of the voltage spikes are highly sensitive to current injection and to the blocking of the Ca(2+)-sensitive current. Computations also predict that leaving the membrane channels intact, the firing rate can be modified by changing the Ca2+ handling parameters: the Ca2+ diffusion rate, the Ca2+ buffering capacity, and the plasma membrane Ca2+ pump rate. Finally, the model suggests reasons that spontaneous APs were seen in some gonadotrophs but not in others. This model provides a basis for further exploring how plasma membrane electrical activity is involved in the control of cytosolic calcium level in unstimulated as well as agonist-stimulated gonadotrophs.     

Sensitivity of CaM kinase II to the frequency of Ca2+ oscillations: a simple model

The rules that govern the activation and autophosphorylation of the multifunctional Ca2+-calmodulin kinase II (CaMKII) by Ca2+ and calmodulin (CaM) are thought to underlie its ability to decode Ca2+ oscillations and to control multiple cellular functions. We propose a simple biophysical model for the activation of CaMKII by Ca2+ and calmodulin. The model describes the transition of the subunits of the kinase between their different possible states (inactive, bound to Ca2+-CaM, phosphorylated at Thr(286), trapped and autonomous). All transitions are described by classical kinetic equations except for the autophosphorylation step, which is modeled in an empirical manner. The model quantitatively reproduces the experimentally demonstrated frequency sensitivity of CaMKII [Science 279 (1998) 227]. We further use the model to investigate the role of several characterized features of the kinase--as well as some that are not easily attainable by experiments--in its frequency-dependent responses. In cellular microdomains, CaMKII is expected to sense very brief Ca2+ spikes; our simulations under such conditions reveal that the enzyme response is tuned to optimal frequencies. This prediction is then confirmed by experimental data. This novel and simple model should help in understanding the rules that govern CaMKII regulation, as well as those involved in decoding intracellular Ca2+ signals.     

Calcium currents in bullfrog sympathetic neurons. II. Inactivation

Calcium currents in bullfrog sympathetic neurons inactivate slowly and partially during depolarizations lasting 0.5-1 s. There is also a slower (minutes) inactivation process with a broad voltage dependence. An irreversible loss of current (rundown) is prominent with low concentrations of intracellular Ca2+ buffers, with either Ca2+ or Ba2+ as the charge carrier. The extent and rate of the more rapid inactivation process are maximal near the voltage at which the peak inward current is generated, suggesting that inactivation might be Ca2+ dependent. However, inactivation occurs with either Ca2+ or Ba2+ as the charge carrier, is not prevented by strong buffering of intracellular Ca2+ with 10 mM BAPTA, and varies little as the peak current is changed 10-fold by changing the divalent ion concentration. That is, rapid inactivation is not explained by simple versions of voltage, Ca2+- or current-dependent inactivation models. A model in which ion binding within the channel allows a slower, rate-limiting inactivation process fits some but not all of the observed features of inactivation. A purely voltage-dependent three-state cyclic model fits the data if microscopic inactivation is favored by hyperpolarization.     

Store‐operated Ca2+ entry: Vesicle fusion or reversible trafficking and de novo conformational coupling?

Store-operated Ca2+ entry (SOCE), a mechanism regulated by the filling state of the intracellular Ca2+ stores, is a major pathway for Ca2+ influx. Hypotheses to explain the communication between the Ca2+ stores and plasma membrane (PM) have considered both the existence of small messenger molecules, such as a Ca2+-influx factor (CIF), and both stable and de novo conformational coupling between proteins in the Ca2+ store and PM. Alternatively, a secretion-like coupling model based on vesicle fusion and channel insertion in the PM has been proposed, which shares some properties with the de novo conformational coupling model, such as the role of the actin cytoskeleton and soluble N-ethylmaleimide (NEM)-sensitive-factor attachment proteins receptor (SNARE) proteins. Here we review recent progress made in the characterization of the de novo conformational coupling and the secretion-like coupling models for SOCE. We pay particular attention into the involvement of SNARE proteins and the actin cytoskeleton in both SOCE models. SNAREs are recognized as proteins involved in exocytosis, participating in vesicle transport, membrane docking, and fusion. As with secretion, a role for the cortical actin network in Ca2+ entry has been demonstrated in a number of cell types. In resting cells, the cytoskeleton may prevent the interaction between the Ca2+ stores and the PM, or preventing fusion of vesicles containing Ca2+ channels with the PM. These are processes in which SNARE proteins might play a crucial role upon cell activation by directing a precise interaction between the membrane of the transported organelle and the PM.     

Added ATP influences some responses of rat synaptosomes to glutamate.

ATP added externally to rat synaptosomes activated uptake of both Ca2+ and glutamate which was partially accounted for by the uptake phenomena of synaptic vesicles and mitochondria, as shown by using specific inhibitors of the latter. Increasing concentrations of glutamate stimulated Ca2+ entry linearly, as shown by using 45Ca or a Ca-specific electrode. The processes of glutamate and Ca2+ uptake shared some common features and their ATP-dependence may be correlated with an ouabain-insensitive synaptosomal ectonucleotidase activity measured by a 31P-NMR or a luminometric technique. The ATP hydrolysis catalysed by the synaptosomes was activated by both Ca2+ and glutamate. The present synaptosomal activities may represent a model for studying the modulatory effects of ATP on the glutamatergic neurotransmission.     

The nature and mechanism of activation of the hepatocyte receptor-activated Ca2+ inflow system.

Progress in elucidation of the properties of the hepatocyte receptor-activated Ca2+ inflow system (RACIS) has been hampered by difficulties in measuring rates of Ca2+ inflow to hepatocytes. These difficulties have led, for example, to different conclusions about the relationship between the extracellular Ca2+ concentration and the movement of Ca2+ through the RACIS. The hepatocyte RACIS admits Mn2+ and a number of other divalent cations as well as Ca2+. Many of these cations also inhibit the movement of Ca2+ through this system. While the RACIS is inhibited by high concentrations of verapamil and by some other Ca2+ antagonists, it is relatively insensitive to inhibition by organic compounds which inhibit other Ca2+ channels and Ca2+ transporters. There is circumstantial evidence which suggests that the hepatocyte RACIS is an exchange system, possibly one which catalyses Ca(2+)-H+ exchange or the co-transport of Ca2+ and OH-. Other circumstantial evidence suggests that the RACIS is a channel, with some similarities to voltage-operated Ca2+ channels in excitable cells. However, experiments using the patch-clamp technique have not yet detected agonist-stimulated Ca2+ movement across the hepatocyte plasma membrane. The molecular components of the RACIS probably differ from those which facilitate the large inflow of Ca2+ to hepatocytes which occurs in the absence of an agonist. The mechanism by which agonists activate the RACIS has not been elucidated.(ABSTRACT TRUNCATED AT 250 WORDS)     

Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release.

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.     

Inactivation of HIT cell Ca2+ current by a simulated burst of Ca2+ action potentials.

A novel voltage-clamp protocol was developed to test whether slow inactivation of Ca2+ current occurs during bursting in insulin-secreting cells. Single insulin-secreting HIT cells were patch-clamped and their Ca2+ currents were isolated pharmacologically. A computed beta-cell burst was used as a voltage-clamp command and the net Ca2+ current elicited was determined as a cadmium difference current. Ca2+ current rapidly activated during the computed plateau and spike depolarizations and then slowly decayed. Integration of this Ca2+ current yielded an estimate of total Ca influx. To further analyze Ca2+ current inactivation during a burst, repetitive test pulses to + 10 mV were added to the voltage command. Current elicited by these pulses was constant during the interburst, but then slowly and reversibly decreased during the depolarizing plateau. This inactivation was reduced by replacing external Ca2+ with Ba2+ as a charge carrier, and in some cells inactivation was slower in Ba2+. Experimental results were compared with the predictions of the Keizer-Smolen mathematical model of bursting, after subjecting model equations to identical voltage commands. In this model, bursting is driven by the slow, voltage-dependent inactivation of Ca current during the plateau active phase. The K-S model could account for the slope of the slow decay of spike-elicited Ca current, the waveform of individual Ca current spikes, and the suppression of test pulse-elicited Ca current during a burst command. However, the extent and rate of fast inactivation were underestimated by the model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Progress and problems in understanding the involvement of calcium in heart function

In this article we have briefly reviewed the role of Ca2+ in the excitation contraction coupling in the myocardium and have indicated that cardiac contraction and relaxation are initiated upon raising and lowering the intracellular concentration of free Ca2+, respectively. Different mechanisms for the entry of Ca2+ through sarcolemma as well as release of Ca2+ from sarcoplasmic reticulum and possibly mitochondria have been outlined for initiating cardiac contraction. Relaxation of the cardiac muscle appears to be intimately dependent upon efflux of Ca2+ through sarcolemma as well as sequestration of Ca2+ by the intracellular storage sites, particularly sarcoplasmic reticulum and possibly mitochondria. The actions of some pharmacological and pathophysiological interventions have been explained on the basis of changes in subcellular Ca2+ movements in myocardium. Quinidine, which produced an initial positive inotropic action on rat heart was also found to increase sarcolemmal Ca2+-ATPase activity without any changes in the Na+-K+ ATPase. Other antiarrhythmic agents, procainamide and lidocaine, also increased sarcolemmal Ca2+-ATPase activity without affecting the Na+-K+ ATPase. On the other hand, both Ca2+-ATPase and Na+-K+ ATPase activities were increased in heart sarcolemma obtained from cardiomyopathic hamsters. In this model the increased Ca2+-ATPase activity may promote the occurrence of intracellular Ca2+ overload in the cardiac cell whereas the increased Na+-K+ ATPase activity may increase Ca2+ efflux through Na+-Ca2+ exchange systems as an adaptive mechanism. It has been suggested that some caution should be exercised while interpreting the data from in vitro experiments in terms of functional changes in the myocardium. Furthermore, it has been proposed that the pathophysiology and pharmacology of Ca2+ movements at different membrane sites be understood fully in normal and diseased myocardium in order to improve the therapy of heart disease.     

Small conductance potassium channels cause an activity-dependent spike frequency adaptation and make the transfer function of neurons logarithmic

We made a computational model of a single neuron to study the effect of the small conductance (SK) Ca2+-dependent K+ channel on spike frequency adaptation. The model neuron comprised a Na+ conductance, a Ca2+ conductance, and two Ca2+-independent K+ conductances, as well as a small and a large (BK) Ca2+-activated K+ conductance, a Ca2+ pump, and mechanisms for Ca2+ buffering and diffusion. Sustained current injection that simulated synaptic input resulted in a train of action potentials (APs) which in the absence of the SK conductance showed very little adaptation with time. The transfer function of the neuron was nearly linear, i.e., both asymptotic spike rate as well as the intracellular free Ca2+ concentration ([Ca2+]i) were approximately linear functions of the input current. Adding an SK conductance with a steep nonlinear dependence on [Ca2+]i (. Pflügers Arch. 422:223-232; K?hler, Hirschberg, Bond, Kinzie, Marrion, Maylie, and Adelman. 1996. Science. 273:1709-1714) caused a marked time-dependent spike frequency adaptation and changed the transfer function of the neuron from linear to logarithmic. Moreover, the input range the neuron responded to with regular spiking increased by a factor of 2.2. These results can be explained by a shunt of the cell resistance caused by the activation of the SK conductance. It might turn out that the logarithmic relationships between the stimuli of some modalities (e.g., sound or light) and the perception of the stimulus intensity (Fechner's law) have a cellular basis in the involvement of SK conductances in the processing of these stimuli.     

A model of intracellular Ca2+ oscillations based on the activity of the intermediate-conductance Ca2+-activated K+ channels

Intracellular Ca2+ oscillations are observed in a large number of non-excitable cells. While most appear to reflect an intermittent Ca2+ release from intracellular stores, in some instances intracellular Ca2+ oscillations strongly depend on Ca2+ influx, and are coupled to oscillations of the membrane potential, suggesting that a plasma membrane-based mechanism may be involved. We have developed a theoretical model for the latter type of intracellular Ca2+ oscillations based on the Ca2+-dependent modulation of the intermediate-conductance, Ca2+-activated K+ (IKCa) channel. The functioning of this model relies on the Ca2+-dependent activation, and the much slower Ca2+-dependent rundown of this channel. We have shown that Ca2+-dependent activation of the IKCa channels, the consequent membrane hyperpolarization and the resulting increase in Ca2+ influx may confer the positive feedback mechanism required for the ascending phase of the oscillation. The much slower Ca2+-dependent rundown process will conversely halt this positive loop, and establish the descending phase of the intracellular Ca2+ oscillation. We found that this simple model gives rise to intracellular Ca2+ oscillations when using physiologically reasonable parameters, suggesting that IKCa channels could participate in the generation of intracellular Ca2+ oscillations.     

The variety of cytosolic calcium responses and possible roles of PLC and PKC

A model of ligand-induced intracellular calcium (Ca2+) responses incorporating phospholipase C (PLC) and protein kinase C (PKC) is developed for the purpose of understanding the mechanisms underlying the observed temporal patterns of intracellular calcium (Ca(i)2+) under sustained agonist stimulation. Some studies have suggested that inhibition of ligand receptors and PLC by PKC could generate sinusoidal Ca2+ oscillations, while PKC-independent Ca2+-induced Ca2+ release (CICR) via IP(3)-gated Ca2+ channels on the endoplasmic reticulum (ER) is believed to be responsible for baseline spiking. However, some evidence also indicates that baseline spiking can be observed under high-PKC activity, or under low-PKC activity with low agonist stimulus, as well. Insight into the basis of these observations regarding the role of PKC in Ca(i)2+ response patterns can be gained by developing and analyzing a mathematical model of Ca(i)2+ responses. We do this herein and find that (1) interaction of CICR and the sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump is enough to generate both types of Ca(i)2+ oscillations, (2) there exist four possible Ca(i)2+ response patterns under sustained agonist stimulus: a sub-threshold response (SR), baseline spiking, sinusoidal oscillations (SO) and transient with plateau, and (3) the IP(3) concentration, which is controlled by the strength of the interaction between PKC and PLC, can be used to predict the Ca(i)2+ response patterns. From this analysis we conclude that the different patterns of Ca(i)2+ oscillations can be understood as a generic consequence of the interactions between CICR via the IP(3)-gated Ca(2+) channels in response to changes in the level of IP(3), and re-uptake into the ER/SR via the SERCA pump. PKC, in conjunction with PLC, can act as a switch between different Ca(i)2+ response patterns by modulating the cytosolic IP(3) level, which determines the Ca(i)2+ patterns.     

Kinetic model of spermine effect on the Mg2+, ATP-dependent transport of Ca ions in the smooth muscle mitochondria

In experiments, carried out with the use of a radioactive label (45Ca2+) on suspension of rat uterus myocytes treated with digitonin solution (0.1 mg/ml), influence of spermine on the Mg2+, ATP-dependent Ca2+ transport in the mitochondria was investigated. Ca2+ accumulation in the mitochondria was tested as such which was blocked by ruthenium red (10 microM) and was not sensitive to thapsigargin (100 nM). It was shown, that dependence of initial speed of Ca ions accumulation in the mitochondria on spermine concentration (0.1-10 mm) is described by a bell-shaped curve. Spermine concentration being increased in the range of 0.1-1 mM the stimulation of Ca2+ accumulation was observed, at the further increase in polyamine concentration up to 10 mM the suppression of this process took place. On the basis of the analysis of the authors' experimental results and the literature data the model of complex spermine action on Ca2+ accumulation in mitochondria was proposed and analyzed. The existence of two spermine binding sites on mitochondrial membrane--S1 and S2 occupation of which is connected to activation and inhibition of Ca(2+)-unipoter, accordingly, was taken into account. The kinetic analysis of the model which has been made in an equilibrium mode, allowed to calculate some important quantitative parameters describing spermine influence on Ca ions accumulation in mitochondria. It is supposed, that the proposed model can be useful in the further research of polyamine influence on transmembrane exchange of Ca ions in mitochondria.     

Regulation of store-operated calcium entry during cell division

Store-operate Ca2+ channels gate Ca2+ entry into the cytoplasm in response to the depletion of Ca2+ from endoplasmic reticulum Ca2+ stores. The major molecular components of store-operated Ca2+ entry are STIM (stromal-interacting molecule) 1 (and in some instances STIM2) that serves as the endoplasmic reticulum Ca2+ sensor, and Orai (Orai1, Orai2 and Orai3) which function as pore-forming subunits of the store-operated channel. It has been known for some time that store-operated Ca2+ entry is shut down during cell division. Recent work has revealed complex mechanisms regulating the functions and locations of both STIM1 and Orai1 in dividing cells.     

Inhibition of erythrocyte Ca2+-ATPase by activated oxygen through thiol- and lipid-dependent mechanisms

We have studied erythrocyte Ca2+-ATPase as a model target for elucidating effects of activated oxygen on the erythrocyte membrane. Either intracellular or extracellular generation of activated oxygen causes parallel decrements in Ca2+-ATPase activity and cytoplasmic GSH, oxidation of membrane protein thiols, and lipid peroxidation. Subsequent incubation with either dithiothreitol or glucose allows only partial recovery of Ca2+-ATPase, indicating both reversible and irreversible components which are modeled herein using diamide and t-butyl hydroperoxide. The reversible component reflects thiol oxidation, and its recovery depends upon GSH restoration. The irreversible component is largely due to lipid peroxidation, which appears to act through mechanisms involving neither malondialdehyde nor secondary thiol oxidation. However, some portion of the irreversible component could also reflect oxidation of thiols which are inaccessible for reduction by GSH, since we demonstrate existence of different classes of thiols relevant to Ca2+-ATPase activity. Activated oxygen has an exaggerated effect on Ca2+-ATPase of GSH-depleted cells. Sickle erythrocytes treated with dithiothreitol show a heterogeneous response of Ca2+-ATPase activity. These findings are potentially relevant to oxidant-induced hemolysis. They also may be pertinent to oxidative alteration of functional or structural membrane components in general, since many components share with Ca2+-ATPase both free thiols and close proximity to unsaturated lipid.     

'Quantal' Ca2+ release and the control of Ca2+ entry by inositol phosphates--a possible mechanism

The release of Ca2+ from intracellular stores by sub-optimal doses of inositol trisphosphate has been shown to be dose-related ('quantal'), and a simple model is proposed here to account for this phenomenon. It is suggested that there is a regulatory Ca2(+)-binding site on, or associated with, the luminal domain of the InsP3 receptor, which allosterically controls Ca2+ efflux, and the affinity for Ca2+ of that site is modulated by InsP3 binding to the cytoplasmic domain of the receptor; a similar mechanism applied to the ryanodine receptor might also explain some aspects of Ca2(+)-induced Ca2+ release. The stimulated entry of Ca2+ into a cell which occurs upon activation of inositide-linked receptors has been variously and confusingly proposed to be regulated by InsP3, InsP4, and/or a 'capacitative' Ca2+ pool; the mechanism of InsP3 receptor action suggested here is shown to lead to a potential reconciliation of all these conflicting proposals.     

Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations

Calcium (Ca2+) oscillations play fundamental roles in various cell signaling processes and have been the subject of numerous modeling studies. Here we have implemented a general mathematical model to simulate the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. In addition, we have compared two different models of the inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) and their influences on intracellular Ca2+ oscillations. Store-operated Ca2+ entry following Ca2+ depletion of endoplasmic reticulum (ER) is an important component of Ca2+ signaling. We have developed a phenomenological model of store-operated Ca2+ entry via store-operated Ca2+ (SOC) channels, which are activated upon ER Ca2+ depletion. The depletion evokes a bi-phasic Ca2+ signal, which is also produced in our mathematical model. The IP3R is an important regulator of intracellular Ca2+ signals. This IP3 sensitive Ca2+ channel is also regulated by Ca2+. We apply two IP3R models, the Mak-McBride-Foskett model and the De Young and Keizer model, with significantly different channel characteristics. Our results show that the two separate IP3R models evoke intracellular Ca2+ oscillations with different frequencies and amplitudes. Store-operated Ca2+ entry affects the oscillatory behavior of these intracellular Ca2+ oscillations. The IP3 threshold is altered when store-operated Ca2+ entry is excluded from the model. Frequencies and amplitudes of intracellular Ca2+ oscillations are also altered without store-operated Ca2+ entry. Under certain conditions, when intracellular Ca2+ oscillations are absent, excluding store-operated Ca2+ entry induces an oscillatory response. These findings increase knowledge concerning store-operated Ca2+ entry and its impact on intracellular Ca2+ oscillations.     

A model for the Ca2+-induced conformational transition of troponin C. A trigger for muscle contraction

The initial contractile event in muscle is the binding of Ca2+ ions to troponin C of the troponin complex, leading to a series of conformational changes in the members of the thin and thick filaments. Knowledge of the crystal structure of turkey skeletal muscle troponin C has provided a structural basis for the modeling of the first stage of this process in atomic detail. This crystal structure probably represents the molecule in the relaxed state of muscle, with two of the maximum of 4 Ca2+ ions bound. The basis for the model presented here is that upon binding of the additional two Ca2+ ions, the regulatory domain of the molecule undergoes a conformational transition to become closely similar in structure to the domain which always binds Ca2+ or Mg2+ under physiological conditions. The root mean square discrepancy in atomic coordinates between the apo and the modeled Ca2+-bound states of the regulatory domain is 4.8 A, with some shifts as large as 10-15 A in the region near the linker between the two Ca2+ binding sites. It is demonstrated that this Ca2+-bound conformation of the regulatory domain conforms to accepted protein structure rules and that the change in conformation can be accomplished without encountering any barriers too high to be surmounted on the physiological time scale.     

A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes

Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.