Stochastic Gating Research Articles

Diffusive transport in the presence of stochastically gated absorption.

We analyze a population of Brownian particles moving in a spatially uniform environment with stochastically gated absorption. The state of the environment at time t is represented by a discrete stochastic variable k(t)∈{0,1} such that the rate of absorption is γ[1-k(t)], with γ a positive constant. The variable k(t) evolves according to a two-state Markov chain. We focus on how stochastic gating affects the attenuation of particle absorption with distance from a localized source in a one-dimensional domain. In the static case (no gating), the steady-state attenuation is given by an exponential with length constant sqrt[D/γ], where D is the diffusivity. We show that gating leads to slower, nonexponential attenuation. We also explore statistical correlations between particles due to the fact that they all diffuse in the same switching environment. Such correlations can be determined in terms of moments of the solution to a corresponding stochastic Fokker-Planck equation.

Inverse stochastic resonance in networks of spiking neurons.

Inverse Stochastic Resonance (ISR) is a phenomenon in which the average spiking rate of a neuron exhibits a minimum with respect to noise. ISR has been studied in individual neurons, but here, we investigate ISR in scale-free networks, where the average spiking rate is calculated over the neuronal population. We use Hodgkin-Huxley model neurons with channel noise (i.e., stochastic gating variable dynamics), and the network connectivity is implemented via electrical or chemical connections (i.e., gap junctions or excitatory/inhibitory synapses). We find that the emergence of ISR depends on the interplay between each neuron’s intrinsic dynamical structure, channel noise, and network inputs, where the latter in turn depend on network structure parameters. We observe that with weak gap junction or excitatory synaptic coupling, network heterogeneity and sparseness tend to favor the emergence of ISR. With inhibitory coupling, ISR is quite robust. We also identify dynamical mechanisms that underlie various features of this ISR behavior. Our results suggest possible ways of experimentally observing ISR in actual neuronal systems.

Calcium waves in a grid of clustered channels with synchronous IP3 binding and unbinding.

Calcium signals in cells occur at multiple spatial scales and variable temporal duration. However, a physical explanation for transitions between long-lasting global oscillations and localized short-term elevations (puffs) of cytoplasmic Ca2+ is still lacking. Here we introduce a phenomenological, coarse-grained model for the calcium variable, which is represented by ordinary differential equations. Due to its small number of parameters, and its simplicity, this model allows us to numerically study the interplay of multi-scale calcium concentrations with stochastic ion channel gating dynamics even in larger systems. We apply this model to a single cluster of inositol trisphosphate (IP 3) receptor channels and find further evidence for the results presented in earlier work: a single cluster may be capable of producing different calcium release types, where long-lasting events are accompanied by unbinding of IP 3 from the receptor (Rückl et al., PLoS Comput. Biol. 11, e1003965 (2015)). Finally, we show the practicability of the model in a grid of 64 clusters which is computationally intractable with previous high-resolution models. Here long-lasting events can lead to synchronized oscillations and waves, while short events stay localized. The frequency of calcium releases as well as their coherence can thereby be regulated by the amplitude of IP 3 stimulation. Finally the model allows for a new explanation of oscillating [IP 3], which is not based on metabolic production and degradation of IP 3.

Modeling Na+-Ca2 + exchange in the heart: Allosteric activation, spatial localization, sparks and excitation-contraction coupling

The cardiac sodium (Na+)/calcium (Ca2+) exchanger (NCX1) is an electrogenic membrane transporter that regulates Ca2+ homeostasis in cardiomyocytes, serving mainly to extrude Ca2+ during diastole. The direction of Ca2+ transport reverses at membrane potentials near that of the action potential plateau, generating an influx of Ca2+ into the cell. Therefore, there has been great interest in the possible roles of NCX1 in cardiac Ca2+-induced Ca2+ release (CICR). Interest has been reinvigorated by a recent super-resolution optical imaging study suggesting that ~18% of NCX1 co-localize with ryanodine receptor (RyR2) clusters, and ~30% of additional NCX1 are localized to within ~120nm of the nearest RyR2. NCX1 may therefore occupy a privileged position in which to modulate CICR. To examine this question, we have developed a mechanistic biophysically-detailed model of NCX1 that describes both NCX1 transport kinetics and Ca2+-dependent allosteric regulation. This NCX1 model was incorporated into a previously developed super-resolution model of the Ca2+ spark as well as a computational model of the cardiac ventricular myocyte that includes a detailed description of CICR with stochastic gating of L-type Ca2+ channels and RyR2s, and that accounts for local Ca2+ gradients near the dyad via inclusion of a peri-dyadic (PD) compartment. Both models predict that increasing the fraction of NCX1 in the dyad and PD decreases spark frequency, fidelity, and diastolic Ca2+ levels. Spark amplitude and duration are less sensitive to NCX1 spatial redistribution. On the other hand, NCX1 plays an important role in promoting Ca2+ entry into the dyad, and hence contributing to the trigger for RyR2 release at depolarized membrane potentials and in the presence of elevated local Na+ concentration. Whole-cell simulation of NCX1 tail currents are consistent with the finding that a relatively high fraction of NCX1 (~45%) resides in the dyadic and PD spaces, with a dyad-to-PD ratio of roughly 1:2. Allosteric Ca2+ activation of NCX1 helps to “functionally localize” exchanger activity to the dyad and PD by reducing exchanger activity in the cytosol thereby protecting the cell from excessive loss of Ca2+ during diastole.

Interplay of Membrane and Calcium Oscillators in Cardiac Pacemaker Cells

Recently it has been shown [Maltsev, Lakatta, Am J Physiol Heart Circ Physiol, 2009] that a stable calcium oscillatory dynamics in cardiac pacemaker cells is developed due to a synergetic effect of the coupling of the classic sarcolemmal voltage oscillator (“membrane” clock) and the intracellular calcium oscillator, or “Ca2+-clock”, whose functioning is governed by the ryanodine (RyR) channel gating. At variance with the Maltsev-Lakatta approach we developed an integrative model of coupled cellular oscillators using a simple electron-conformational theory [Moskvin et al., PBMB, 2006] to describe the stochastic RyR gating in a Ca2+ release unit (RU). The RU includes a junctional compartment of the sarcoplasmic reticulum (SR) network, a cluster of coupled RyR-channels, and adjacent sarcolemmal subspace (SS). The RU activity implies an intracellular Ca2+ cycling between the compartments. Computer simulations demonstrate that despite a stochastic Ca2+ dynamics the coupling of the cellular oscillators can provide a stable action potential generation in the cardiac pacemaker cells, however, with clear signatures of “micro-arrhythmia”, that is the fluctuations of the frequency and amplitude of the Ca2+ release. We studied in detail the effect of “funny” current and of the RyRs’ sensitivity to the [CaSR] and [CaSS] on the behavior of the calcium release system. A parametric analysis shows that depending on the model parameters either the membrane or Ca2+-clock actually plays the leading role providing the astonishing stability of the auto-oscillatory regime. At the same time, the inter-RyR coupling is shown to strongly influence the stability up to manifestation of the puzzling sudden break of Ca2+ oscillations. Supported by the Russian Science Foundation, project 14-35-00005.

Modeling the Role of NCX in the Regulation of Cardiomyocyte Microdomain Ca2+ Dynamics

The sodium (Na+)/calcium (Ca2+) exchanger (NCX) is an electrogenic membrane transporter that mainly serves as a Ca2+ removal mechanism during relaxation and maintains Ca2+ homeostasis in cardiomyocytes. The direction of transport reverses at membrane potentials near action the potential plateau, generating an influx of Ca2+ into the cell. Therefore, there has been great interest in the role NCX plays in cardiac Ca2+-induced Ca2+-release (CICR), with some controversial findings questioning whether NCX has any role at all. A recent super-resolution optical imaging study suggested that ∼17% of NCX co-localize within the domain occupied by ryanodine receptor (RyR) clusters and ∼30% of NCX are within 100nm of the dyad boundary. Therefore, NCX may play a critical role in modulating Ca2+ spark activity and CICR as a result of its spatial distribution in the T-tubule. Here we examine the potential role of NCX using computational modeling. We have developed a novel mechanistic and biophysically-detailed model of NCX that describes both NCX transport kinetics and dynamics of Ca2+-dependent allosteric regulation. We incorporated this new NCX model into a previously developed super-resolution Ca2+ spark model to examine effects of local NCX spatial distribution on properties of Ca2+ sparks. Dyadic NCX reduces spark frequency but has minimal effects on spark amplitude and half-width. Furthermore, we incorporate NCX into a previously developed computational model of the cardiac ventricular myocyte that includes a detailed description of CICR simulated with stochastic gating of L-Type Ca2+ channels and RyRs in the dyad and accounts for local Ca2+ gradients via inclusion of peri-dyadic compartments. We use this model to investigate the role of NCX and its localization on whole-cell Ca2+ dynamics, the Ca2+ levels in the junctional sarcoplasmic reticulum, and APs.

Ryanodine receptor sensitivity governs the stability and synchrony of local calcium release during cardiac excitation-contraction coupling

Calcium-induced calcium release is the principal mechanism that triggers the cell-wide [Ca2+]i transient that activates muscle contraction during cardiac excitation-contraction coupling (ECC). Here, we characterize this process in mouse cardiac myocytes with a novel mathematical action potential (AP) model that incorporates realistic stochastic gating of voltage-dependent L-type calcium (Ca2+) channels (LCCs) and sarcoplasmic reticulum (SR) Ca2+ release channels (the ryanodine receptors, RyR2s). Depolarization of the sarcolemma during an AP stochastically activates the LCCs elevating subspace [Ca2+] within each of the cell's 20,000 independent calcium release units (CRUs) to trigger local RyR2 opening and initiate Ca2+ sparks, the fundamental unit of triggered Ca2+ release. Synchronization of Ca2+ sparks during systole depends on the nearly uniform cellular activation of LCCs and the likelihood of local LCC openings triggering local Ca2+ sparks (ECC fidelity). The detailed design and true SR Ca2+ pump/leak balance displayed by our model permits investigation of ECC fidelity and Ca2+ spark fidelity, the balance between visible (Ca2+ spark) and invisible (Ca2+ quark/sub-spark) SR Ca2+ release events. Excess SR Ca2+ leak is examined as a disease mechanism in the context of “catecholaminergic polymorphic ventricular tachycardia (CPVT)”, a Ca2+-dependent arrhythmia. We find that that RyR2s (and therefore Ca2+ sparks) are relatively insensitive to LCC openings across a wide range of membrane potentials; and that key differences exist between Ca2+ sparks evoked during quiescence, diastole, and systole. The enhanced RyR2 [Ca2+]i sensitivity during CPVT leads to increased Ca2+ spark fidelity resulting in asynchronous systolic Ca2+ spark activity. It also produces increased diastolic SR Ca2+ leak with some prolonged Ca2+ sparks that at times become “metastable” and fail to efficiently terminate. There is a huge margin of safety for stable Ca2+ handling within the cell and this novel mechanistic model provides insight into the molecular signaling characteristics that help maintain overall Ca2+ stability even under the conditions of high SR Ca2+ leak during CPVT. Finally, this model should provide tools for investigators to examine normal and pathological Ca2+ signaling characteristics in the heart.

Particle-Based Multiscale Modeling of Calcium Puff Dynamics

Intracellular calcium is regulated in part by the release of Ca$^{2+}$ ions from the endoplasmic reticulum via inositol-4,5-triphosphate receptor (IP$_3$R) channels (among other possibilities such as RyR and L-type calcium channels). The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells, as observed in {\it Xenopus} oocytes, neurons, and other cell types. Local fluctuations in the number of calcium ions play a crucial role in the onset of these features. Previous modeling studies of calcium puff dynamics stemming from IP$_3$R channels have predominantly focused on stochastic channel models coupled to deterministic diffusion of ions, thereby neglecting local fluctuations of the ion number. Tracking of individual ions is computationally difficult due to the scale separation in the Ca$^{2+}$ concentration when channels are in the open or closed states. In this paper, a spatial multiscale model for investigating of the dynamics of puffs is presented. It couples Brownian motion (diffusion) of ions with a stochastic channel gating model. The model is used to analyze calcium puff statistics. Concentration time traces as well as channel state information are studied. We identify the regime in which puffs can be found and develop a mean-field theory to extract the boundary of this regime. Puffs are only possible when the time scale of channel inhibition is sufficiently large. Implications for the understanding of puff generation and termination are discussed.

Stochastically gated diffusion-limited reactions for a small target in a bounded domain.

We calculate the reaction rate for stochastically gated ligands diffusing in a two-dimensional and a three-dimensional bounded domain with a single small target. Each ligand independently switches between an open and a closed state according to a two-state Markov process; a reaction between ligand and target can only occur when the former is an open state. In the large-time limit the reaction-rate is an exponentially decaying function of time, whose rate of decay is given by the principal eigenvalue of the Laplacian. We calculate the principal eigenvalue using matched asymptotics and determine the leading-order reduction in the reaction rate due to stochastic gating. We also develop a probabilistic interpretation of the reaction rate in terms of the first-passage time density to the target.

A temperature rise reduces trial-to-trial variability of locust auditory neuron responses.

The neurophysiology of ectothermic animals, such as insects, is affected by environmental temperature, as their body temperature fluctuates with ambient conditions. Changes in temperature alter properties of neurons and, consequently, have an impact on the processing of information. Nevertheless, nervous system function is often maintained over a broad temperature range, exhibiting a surprising robustness to variations in temperature. A special problem arises for acoustically communicating insects, as in these animals mate recognition and mate localization typically rely on the decoding of fast amplitude modulations in calling and courtship songs. In the auditory periphery, however, temporal resolution is constrained by intrinsic neuronal noise. Such noise predominantly arises from the stochasticity of ion channel gating and potentially impairs the processing of sensory signals. On the basis of intracellular recordings of locust auditory neurons, we show that intrinsic neuronal variability on the level of spikes is reduced with increasing temperature. We use a detailed mathematical model including stochastic ion channel gating to shed light on the underlying biophysical mechanisms in auditory receptor neurons: because of a redistribution of channel-induced current noise toward higher frequencies and specifics of the temperature dependence of the membrane impedance, membrane potential noise is indeed reduced at higher temperatures. This finding holds under generic conditions and physiologically plausible assumptions on the temperature dependence of the channels' kinetics and peak conductances. We demonstrate that the identified mechanism also can explain the experimentally observed reduction of spike timing variability at higher temperatures.

Electron-Conformational Transformations in Nanoscopic RyR2 Channels Govern both the Heart's Contraction and Beating

We argue that the gating of the ryanodine receptor (RyR) channels, key molecular determinants in the Ca2+ homeostasis, recognized as important novel therapeutic targets, is determined by electron-conformational transformations described by a simple electron-conformational model (ECM).The model differs from conventional markovian models in several points, in particular, these are the RyR energy, inter-RyR coupling, conformational dynamics and unconventional quantum effects.The model describes the RyR gating under varying cis and trans [Ca2+] with the same set of the parameters.We present an overview of computer modeling of the stochastic RyR2 gating in cardiomyocytes and sinoatrial node cells (SANC). The model does explain main features of the in vitro single RyR dynamics including modal gating and adaptation phenomena, effect of the cis[Ca2+] and cis[Mg2+], the temperature effects. Cooperative dynamics of the RyR clusters in Ca release units (CRU) and the Ca2+ spark features have been studied in a series of model simulations for 11x11 square RyR lattice incorporated into the cell calcium dynamics. The model does explain and describe the spontaneous oscillatory regime of the CRU both in SANCs (so-called Ca2+ clock) and in cardiomyocytes under Ca2+ sarcoplasmic reticulum overload. Puzzlingly, the intracellular clock obeys the Bowditch behavior without any membrane clock assistance. Given strong enough RyR-RyR coupling we observed novel effect of sudden inhibition of the oscillations with emergence of stable subclusters (2x2, 2x4,…) of opened channels and a steady-state Ca2+ leakage. The CRU oscillatory regime is restored by external membrane stimuli, so only working synergistically two types of clocks ensure robust and flexible pacemaker function. Despite the ECM is intentionally simplistic, it offers novel insight into the actual physical mechanisms involved in the gating behavior of the RyR channels with a sound framework for future studies.

Role of gap junction channel in the development of beat-to-beat action potential repolarization variability and arrhythmias.

The short-term beat-to-beat variability of cardiac action potential duration (SBVR) occurs as a random alteration of the ventricular repolarization duration. SBVR has been suggested to be more predictive of the development of lethal arrhythmias than the action potential prolongation or QT prolongation of ECG alone. The mechanism underlying SBVR is not completely understood but it is known that SBVR depends on stochastic ion channel gating, intracellular calcium handling and intercellular coupling. Coupling of single cardiomyocytes significantly decreases the beat-to-beat changes in action potential duration (APD) due to the electrotonic current flow between neighboring cells. The magnitude of this electrotonic current depends on the intercellular gap junction resistance. Reduced gap junction resistance causes greater electrotonic current flow between cells, and reduces SBVR. Myocardial ischaemia (MI) is known to affect gap junction channel protein expression and function. MI increases gap junction resistance that leads to slow conduction, APD and refractory period dispersion, and an increase in SBVR. Ultimately, development of reentry arrhythmias and fibrillation are associated post-MI. Antiarrhythmic drugs have proarrhythmic side effects requiring alternative approaches. A novel idea is to target gap junction channels. Specifically, the use of gap junction channel enhancers and inhibitors may help to reveal the precise role of gap junctions in the development of arrhythmias. Since cell-to-cell coupling is represented in SBVR, this parameter can be used to monitor the degree of coupling of myocardium.

Modeling the influence of short term depression in vesicle release and stochastic calcium channel gating on auditory nerve spontaneous firing statistics.

We propose several modifications to an existing computational model of stochastic vesicle release in inner hair cell ribbon synapses, with the aim of producing simulated auditory nerve fiber spiking data that more closely matches empirical data. Specifically, we studied the inter-spike-interval (ISI) distribution, and long and short term ISI correlations in spontaneous spiking in post-synaptic auditory nerve fibers. We introduced short term plasticity to the pre-synaptic release probability, in a manner analogous to standard stochastic models of cortical short term synaptic depression. This modification resulted in a similar distribution of vesicle release intervals to that estimated from empirical data. We also introduced a biophysical stochastic model of calcium channel opening and closing, but showed that this model is insufficient for generating a match with empirically observed spike correlations. However, by combining a phenomenological model of channel noise and our short term depression model, we generated short and long term correlations in auditory nerve spontaneous activity that qualitatively match empirical data.

The Ryanodine Receptor Patchwork: Knitting Calcium Spark Dynamics

The Ryanodine Receptor Patchwork: Knitting Calcium Spark Dynamics

Modeling interneuron-specific (IS) interneurons in hippocampus

The hippocampus and cortex have a large diversity in inhibitory interneuron types. These local interneurons exert inhibitory control over neuronal populations in the hippocampus [1]. Although much is known about how hippocampal inhibitory interneurons exert control over pyramidal cells and synchronize local network activity, less is known about how the activity of these interneurons are controlled themselves. Moreover, the existence of interneuron-specific (IS) interneurons is known and information about how these IS interneurons exert their influence is accumulating [2]. In particular, interneuron-specific 3 (IS3) cells are being characterized and they have been shown to primarily synapse onto other interneuron dendrites with the ability to control their firing patterns. Morphological and synaptic aspects are being examined, but what type, how much and where voltage-gated channels are present on IS3 has not been determined. As other hippocampal interneuron types are known to have high densities of voltage-gated channels on their dendrites [3,4], it seems likely that this could be the case for IS3 cells also. Determining and understanding particular characteristics of particular cell types is a highly challenging endeavour using purely experimental means. Thus, we have begun development of IS3 computational cell models to help address this challenge. Using the NEURON software environment [5], we have reconstructed IS3 cell morphologies and built multi-compartment models from them in which appropriate passive properties were obtained. Further, we were able to match several characteristics of representative IS3 cell firings (spike amplitude, spike threshold, rheobase) using four somatically located voltage-gated channel types (sodium current (INa), slow delayed rectifier potassium current (IKdrs), fast delayed rectifier potassium current (IKdrf) and A-type potassium current (IKa). Preliminary data from IS3 cells indicate that they express intrinsic, subthreshold activities similar to other hippocampal interneuron types [6], and previous models captured this aspect with the incorporation of additive white noise to represent stochastic gating characteristics [7]. Similarly here, to capture these aspects, we somatically injected white noise current into our models and found that output similar to experimental data was observed. Given the present correspondence with data, our models already make predictions about channel types and balances found in IS3 cells. Thus our present multi-compartment IS3 models represent a solid basis for determining and understanding the biophysical contributions for IS3 cell firings and their ability to control inhibitory cells and functionally contribute to the generation of hippocampal oscillations.

Termination of calcium puffs and coupled closings of inositol trisphosphate receptor channels

Calcium puffs are localized Ca2+ signals mediated by Ca2+ release from the endoplasmic reticulum (ER) through clusters of inositol trisphosphate receptor (IP3R) channels. The recruitment of IP3R channels during puffs depends on Ca2+-induced Ca2+ release, a regenerative process that must be terminated to maintain control of cell signaling and prevent Ca2+ cytotoxicity. Here, we studied puff termination using total internal reflection microscopy to resolve the gating of individual IP3R channels during puffs in intact SH-SY5Y neuroblastoma cells. We find that the kinetics of IP3R channel closing differ from that expected for independent, stochastic gating, in that multiple channels tend to remain open together longer than predicted from their individual open lifetimes and then close in near-synchrony. This behavior cannot readily be explained by previously proposed termination mechanisms, including Ca2+-inhibition of IP3Rs and local depletion of Ca2+ in the ER lumen. Instead, we postulate that the gating of closely adjacent IP3Rs is coupled, possibly via allosteric interactions, suggesting an important mechanism to ensure robust puff termination in addition to Ca2+-inactivation.

Hierarchical clustering of ryanodine receptors enables emergence of a calcium clock in sinoatrial node cells.

The sinoatrial node, whose cells (sinoatrial node cells [SANCs]) generate rhythmic action potentials, is the primary pacemaker of the heart. During diastole, calcium released from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) interacts with membrane currents to control the rate of the heartbeat. This "calcium clock" takes the form of stochastic, partially periodic, localized calcium release (LCR) events that propagate, wave-like, for limited distances. The detailed mechanisms controlling the calcium clock are not understood. We constructed a computational model of SANCs, including three-dimensional diffusion and buffering of calcium in the cytosol and SR; explicit, stochastic gating of individual RyRs and L-type calcium channels; and a full complement of voltage- and calcium-dependent membrane currents. We did not include an anatomical submembrane space or inactivation of RyRs, the two heuristic components that have been used in prior models but are not observed experimentally. When RyRs were distributed in discrete clusters separated by >1 µm, only isolated sparks were produced in this model and LCR events did not form. However, immunofluorescent staining of SANCs for RyR revealed the presence of bridging RyR groups between large clusters, forming an irregular network. Incorporation of this architecture into the model led to the generation of propagating LCR events. Partial periodicity emerged from the interaction of LCR events, as observed experimentally. This calcium clock becomes entrained with membrane currents to accelerate the beating rate, which therefore was controlled by the activity of the SERCA pump, RyR sensitivity, and L-type current amplitude, all of which are targets of β-adrenergic-mediated phosphorylation. Unexpectedly, simulations revealed the existence of a pathological mode at high RyR sensitivity to calcium, in which the calcium clock loses synchronization with the membrane, resulting in a paradoxical decrease in beating rate in response to β-adrenergic stimulation. The model indicates that the hierarchical clustering of surface RyRs in SANCs may be a crucial adaptive mechanism. Pathological desynchronization of the clocks may explain sinus node dysfunction in heart failure and RyR mutations.

Stochastic Gating and Molecular Transport in Carbon Nanotube Ion Channels

Living systems control transport of ions or small molecules across biological membranes using ion channels that form highly efficient and selective pores in lipid bilayers. Although bottom-up synthesis and top-down fabrication could produce pores of comparable size, an unresolved challenge remains to build nanopore scaffolds that fully replicate transport properties of membrane channels. We will show that pores in lipid membranes formed by ultra-short carbon nanotubes (CNTs) have transport properties that come remarkably close to that goal. These carbon nanotube channels can transport water, protons, small ions, and DNA and their ion-rejection properties can be controlled by the charge at the pore mouth. Interestingly, these pores also display the stochastic gating behavior common for biological ion channels. We attribute this effect to a spontaneous reversible ionic penetration-exclusion transition, suggesting that it represents a general feature of nanofluidic transport in sub-2-nm pores. Overall, transmembrane CNT ion channels represent a robust and versatile biomimetic scaffold for studying fundamentals of transport in biological channels, artificial cell design, and stochastic sensing.

Dynamics of Calcium Sparks and SR Calcium Leak During Excitation-Contraction Coupling in Mouse Heart Cells

Stable calcium-induced calcium release (CICR) is critical for maintaining normal cell contraction during cardiac excitation-contraction (EC) coupling in heart cells. The fundamental element of CICR in heart is the calcium (Ca2+) spark which arises from the regenerative release of Ca2+ from a cluster of ryanodine receptors (RyR2) in the junctional sarcoplasmic reticulum membrane. We have shown how stochastic gating of RyR2s could produce an SR Ca2+ leak capable of balancing SR Ca2+-ATPase (SERCA2a) activity under quiescent conditions (Williams et al. BJ 2011). This investigation suggested the surprising finding that a single, or even multiple, RyR2 openings could fail probabilistically to trigger a Ca2+ spark. To further investigate this effect, we expanded upon that formulation to create a detailed, local control model of EC coupling in mouse heart. A number of features were added or modified, including the addition of a novel seven-state Markov chain model of the sarcolemmal L-type Ca2+ channel (LCC). This model features dynamic action-potential (AP) generation, robust Ca2+ spark initiation and termination, realistic [Ca2+]i transients, and true SR Ca2+ pump/leak balance. The model suggests that numerous LCC openings are often required to trigger a single Ca2+ spark. This is consistent with our prior work where multiple RyR2 openings were needed to trigger a spontaneous Ca2+ spark during quiescent conditions. We also investigated how RyR2 mutations associated with catecholaminergic polymorphic ventricular tachycardia (CPVT) influence the dynamics of Ca2+ sparks, “invisible” non-spark Ca2+ leak, [Ca2+]i transients, and SR Ca2+ content. We observe that CPVT mutations can lead to unstable Ca2+ spark dynamics, altering SR Ca2+ content and promoting [Ca2+]i signaling instability. Our new model provides significant insights into the dynamics of local control of CICR under physiological and pathological conditions.

The molecular mechanism of ion-dependent gating in secondary transporters.

LeuT-like fold Na-dependent secondary active transporters form a large family of integral membrane proteins that transport various substrates against their concentration gradient across lipid membranes, using the free energy stored in the downhill concentration gradient of sodium ions. These transporters play an active role in synaptic transmission, the delivery of key nutrients, and the maintenance of osmotic pressure inside the cell. It is generally believed that binding of an ion and/or a substrate drives the conformational dynamics of the transporter. However, the exact mechanism for converting ion binding into useful work has yet to be established. Using a multi-dimensional path sampling (string-method) followed by all-atom free energy simulations, we established the principal thermodynamic and kinetic components governing the ion-dependent conformational dynamics of a LeuT-like fold transporter, the sodium/benzyl-hydantoin symporter Mhp1, for an entire conformational cycle. We found that inward-facing and outward-facing states of Mhp1 display nearly the same free energies with an ion absent from the Na2 site conserved across the LeuT-like fold transporters. The barrier separating an apo-state from inward-facing or outward-facing states of the transporter is very low, suggesting stochastic gating in the absence of ion/substrate bound. In contrast, the binding of a Na2 ion shifts the free energy stabilizing the outward-facing state and promoting substrate binding. Our results indicate that ion binding to the Na2 site may also play a key role in the intracellular thin gate dynamics modulation by altering its interactions with the transmembrane helix 5 (TM5). The Potential of Mean Force (PMF) computations for a substrate entrance displays two energy minima that correspond to the locations of the main binding site S1 and proposed allosteric S2 binding site. However, it was found that substrate's binds to the site S1 ∼5 kcal/mol more favorable than that to the site S2 for all studied bound combinations of ions and a substrate.