Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node.

Single pacemaker heart cells discharge irregularly. Data on fluctuations in interbeat interval of single pacemaker cells isolated from the rabbit sinoatrial node are presented. The coefficient of variation of the interbeat interval is quite small, approximately 2%, even though the coefficient of variation of diastolic depolarization rate is approximately 15%. It has been hypothesized that random fluctuations in interbeat interval arise from the stochastic behavior of the membrane ionic channels. To test this hypothesis, we constructed a single channel model of a single pacemaker cell isolated from the rabbit sinoatrial node, i.e., a model into which the stochastic open-close kinetics of the individual membrane ionic channels are incorporated. Single channel conductances as well as single channel open and closed lifetimes are based on experimental data from whole cell and single channel experiments that have been published in the past decade. Fluctuations in action potential parameters of the model cell are compared with those observed experimentally. It is concluded that fluctuations in interbeat interval of single sinoatrial node pacemaker cells indeed are due to the stochastic open-close kinetics of the membrane ionic channels.     

Stochastic amplification of calcium-activated potassium currents in Ca<Superscript>2+</Superscript> microdomains

Small conductance (SK) calcium-activated potassium channels are found in many tissues throughout the body and open in response to elevations in intracellular calcium. In hippocampal neurons, SK channels are spatially co-localized with L-Type calcium channels. Due to the restriction of calcium transients into microdomains, only a limited number of L-Type Ca²⁺ channels can activate SK and, thus, stochastic gating becomes relevant. Using a stochastic model with calcium microdomains, we predict that intracellular Ca²⁺ fluctuations resulting from Ca²⁺ channel gating can increase SK2 subthreshold activity by 1–2 orders of magnitude. This effectively reduces the value of the Hill coefficient. To explain the underlying mechanism, we show how short, high-amplitude calcium pulses associated with stochastic gating of calcium channels are much more effective at activating SK2 channels than the steady calcium signal produced by a deterministic simulation. This stochastic amplification results from two factors: first, a supralinear rise in the SK2 channel’s steady-state activation curve at low calcium levels and, second, a momentary reduction in the channel’s time constant during the calcium pulse, causing the channel to approach its steady-state activation value much faster than it decays. Stochastic amplification can potentially explain subthreshold SK2 activation in unified models of both sub- and suprathreshold regimes. Furthermore, we expect it to be a general phenomenon relevant to many proteins that are activated nonlinearly by stochastic ligand release.     

Cooperative gating between single HCN pacemaker channels

HCN pacemaker channels (I(f), I(q), or I(h)) play a fundamental role in the physiology of many excitable cell types, including cardiac myocytes and central neurons. While cloned HCN channels have been studied extensively in macroscopic patch clamp experiments, their extremely small conductance has precluded single channel analysis to date. Nevertheless, there remain fundamental questions about HCN gating that can be resolved only at the single channel level. Here we present the first detailed single channel study of cloned mammalian HCN2. Excised patch clamp recordings revealed discrete hyperpolarization-activated, cAMP-sensitive channel openings with amplitudes of 150-230 fA in the activation voltage range. The average conductance of these openings was approximately 1.5 pS at -120 mV in symmetrical 160 mM K(+). Some traces with multiple channels showed unusual gating behavior, characterized by a variable long delay after a voltage step followed by runs of openings. Noise analysis on macroscopic currents revealed fluctuations whose magnitudes were systematically larger than predicted from the actual single channel current size, consistent with cooperativity between single HCN channels.     

Determinants of Beat-to-Beat Variability of Repolarization Duration in the Canine Ventricular Myocyte: A Computational Analysis

Beat-to-beat variability of repolarization duration (BVR) is an intrinsic characteristic of cardiac function and a better marker of proarrhythmia than repolarization prolongation alone. The ionic mechanisms underlying baseline BVR in physiological conditions, its rate dependence, and the factors contributing to increased BVR in pathologies remain incompletely understood. Here, we employed computer modeling to provide novel insights into the subcellular mechanisms of BVR under physiological conditions and during simulated drug-induced repolarization prolongation, mimicking long-QT syndromes type 1, 2, and 3. We developed stochastic implementations of 13 major ionic currents and fluxes in a model of canine ventricular-myocyte electrophysiology. Combined stochastic gating of these components resulted in short- and long-term variability, consistent with experimental data from isolated canine ventricular myocytes. The model indicated that the magnitude of stochastic fluctuations is rate dependent due to the rate dependence of action-potential (AP) duration (APD). This process (the “active” component) and the intrinsic nonlinear relationship between membrane current and APD (“intrinsic component”) contribute to the rate dependence of BVR. We identified a major role in physiological BVR for stochastic gating of the persistent Na⁺ current (I_Na) and rapidly activating delayed-rectifier K⁺ current (I_Kr). Inhibition of I_Kr or augmentation of I_Na significantly increased BVR, whereas subsequent β-adrenergic receptor stimulation reduced it, similar to experimental findings in isolated myocytes. In contrast, β-adrenergic stimulation increased BVR in simulated long-QT syndrome type 1. In addition to stochastic channel gating, AP morphology, APD, and beat-to-beat variations in Ca²⁺ were found to modulate single-cell BVR. Cell-to-cell coupling decreased BVR and this was more pronounced when a model cell with increased BVR was coupled to a model cell with normal BVR. In conclusion, our results provide new insights into the ionic mechanisms underlying BVR and suggest that BVR reflects multiple potentially proarrhythmic parameters, including increased ion-channel stochasticity, prolonged APD, and abnormal Ca²⁺ handling.     

三氟氯氰菊酯对棉铃虫神经细胞钠及钙通道作用机理研究

用膜片钳技术对比分析了棉铃虫三氟氯氰菊脂抗性品系（R）及其同源对照品系（S）幼虫了体培养中枢神经细胞Na^2 通道的门控特性及杀虫剂对R和S神经细胞Na^ 、Ca^ 通道门控过程的影响。结果表明,S神经细胞Na^ 通道电流（S－INa）在－50－40mV激活,－20mV左右达峰值,R神经细胞Na^2 通道电流（R－INa）在－40mV左右激活,－10－0mV达峰值,即R－INa激活电压与峰值电压均向正电位方向移动约10mV,提示二者Na^ 通道控特性不同,R神经细胞Na^ 通道功能发生了变异。三氟氯氰菊酯作用后,S－INgn R-ISs的I－V曲线均向负电位方向移动的10mV,S－INa在20min后基本消失,而R－INa被阻断需时约90min,延长近5倍,其幅值有减小再增大的现象。对Ca^2 通道分析表明,杀虫剂作用后,R及S神经细胞Ca^2 通道电流的I－V曲线均向负电位移动10－20mV,提示三氟氯氰菊酯对Ca^2 通道的门控过程也有影响。与R－INa幅值起伏变化相联系,可推知杀虫剂对神经细胞的毒性作用中,Na^2 、Ca^2 通道均受影响。     

Gating current noise produced by Brownian models of a voltage sensor

The activation of voltage-dependent ion channels is associated with the movement of gating charges, which give rise to gating currents. Although gating currents from a single channel are too small to be detected, analysis of the fluctuations of macroscopic gating currents from a population of channels allows a good guess of their magnitude. The analysis of experimental gating current fluctuations, when interpreted in terms of a rate model of channel activation and assuming sufficiently high bandwidth, is in accordance with the presence of a main step along the activation pathway carrying a charge of 2.3–2.4 e₀. To give a physical interpretation to these results and to relate them to the known atomic structure of the voltage sensor domain, we used a Brownian model of voltage-dependent gating based on atomic detail structure, that follows the laws of electrodynamics. The model predicts gating currents and gating current fluctuations essentially similar to those experimentally observed. The detailed study of the model output, also performed by making several simplifications aimed at understanding the basic dependencies of the gating current fluctuations, suggests that in real channels the voltage sensor moves along a sequence of intermediate states separated by relatively low (<5 kT) energy barriers. As a consequence, crossings of successive gating charges through the gating pore become very frequent, and the corresponding current shots are often seen to overlap because of the relatively high filtering. Notably, this limited bandwidth effect is at the origin of the relatively high single-step charge experimentally detected.     

Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. We present a Kronecker-structured representation for calcium release site models and perform benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. In particular, multi-level methods provide excellent convergence with modest additional memory requirements for the Kronecker representation of calcium release site models. When an exact solution is not feasible, iterative approximate methods based on the power method may be used, with performance similar to Monte Carlo estimates. This suggests approximate methods with multi-level iterative engines as a promising avenue of future research for large-scale calcium release site models.     

ATP-sensitive potassium channels exhibit variance in the number of open channels below the limit predicted for identical and independent gating

In small cells containing small numbers of ion channels, noise due to stochastic channel opening and closing can introduce a substantial level of variability into the cell's membrane potential. Negatively cooperative interactions that couple a channel's gating conformational change to the conformation of its neighbor(s) provide a potential mechanism for mitigating this variability, but such interactions have not previously been directly observed. Here we show that heterologously expressed ATP-sensitive potassium channels generate noise (i.e., variance in the number of open channels) below the level possible for identical and independent channels. Kinetic analysis with single-molecule resolution supports the interpretation that interchannel negative cooperativity (specifically, the presence of an open channel making a closed channel less likely to open) contributes to the decrease in noise. Functional coupling between channels may be important in modulating stochastic fluctuations in cellular signaling pathways.     

Fractal dimension in health and heart failure.

BACKGROUND: Non-linear analysis of heart rate variability (HRV) can give additional information about autonomic control of the heart rate. This study applied the fractal dimension (FD) in a congestive heart failure (CHF) population. METHODS: FD and HRV were evaluated in a healthy population (n=21) and an end-stage heart failure population (n=21) using 1-h segments during the day and night from Holter recordings. RESULTS: CHF patients presented a loss of circadian variation in both FD and conventional time- and frequency-domain HRV indices. FD was higher in the CHF population both during the day and night. In the CHF population the correlation between FD and high-frequency power of HRV was lost. CONCLUSION: Day-night variations of heart rate fluctuations are lost in heart failure. Changes in FD reflecting physiological and pathophysiological changes were observed.     

Functional interaction of syntaxin and SNAP-25 with voltage-sensitive L- and N-type Ca2+ channels.

We have used an electrophysiological assay to investigate the functional interaction of syntaxin 1A and SNAP-25 with the class C, L-type, and the class B, N-type, voltage-sensitive calcium channels. Co-expression of syntaxin 1A with the pore-forming subunits of the L- and N-type channels in Xenopus oocytes generates a dramatic inhibition of inward currents (>60%) and modifies the rate of inactivation (tau) and steady-state voltage dependence of inactivation. Syntaxin 1-267, which lacks the transmembrane region (TMR), and syntaxin 2 do not modify channel properties, suggesting that the syntaxin 1A interaction site resides predominantly in the TMR. Co-expression of SNAP-25 significantly modifies the gating properties of L- and N-type channels and displays modest inhibition of current amplitude. Syntaxin 1A and SNAP-25 combined restore the syntaxin-inhibited N-type inward current but not the reduced rate of inactivation. Hence, a distinct interaction of a putative syntaxin 1A-SNAP-25 complex with the channel is apparent, consistent with the formation of a synaptosomal SNAP receptors (SNAREs) complex. The in vivo functional reconstitution: (i) establishes the proximity of the SNAREs to calcium channels; (ii) provides new insight into a potential regulatory role for the two SNAREs in controlling calcium influx through N- and L-type channels; and (iii) may suggest a pivotal role for calcium channels in the secretion process.     

Computing transient gating charge movement of voltage-dependent ion channels

The opening of voltage-gated sodium, potassium, and calcium ion channels has a steep relationship with voltage. In response to changes in the transmembrane voltage, structural movements of an ion channel that precede channel opening generate a capacitative gating current. The net gating charge displacement due to membrane depolarization is an index of the voltage sensitivity of the ion channel activation process. Understanding the molecular basis of voltage-dependent gating of ion channels requires the measurement and computation of the gating charge, Q. We derive a simple and accurate semianalytic approach to computing the voltage dependence of transient gating charge movement (Q–V relationship) of discrete Markov state models of ion channels using matrix methods. This approach allows rapid computation of Q–V curves for finite and infinite length step depolarizations and is consistent with experimentally measured transient gating charge. This computational approach was applied to Shaker potassium channel gating, including the impact of inactivating particles on potassium channel gating currents.     

A single lysine in the N-terminal region of store-operated channels is critical for STIM1-mediated gating

Store-operated Ca(2+) entry is controlled by the interaction of stromal interaction molecules (STIMs) acting as endoplasmic reticulum ER Ca(2+) sensors with calcium release-activated calcium (CRAC) channels (CRACM1/2/3 or Orai1/2/3) in the plasma membrane. Here, we report structural requirements of STIM1-mediated activation of CRACM1 and CRACM3 using truncations, point mutations, and CRACM1/CRACM3 chimeras. In accordance with previous studies, truncating the N-terminal region of CRACM1 or CRACM3 revealed a 20-amino acid stretch close to the plasma membrane important for channel gating. Exchanging the N-terminal region of CRACM3 with that of CRACM1 (CRACM3-N(M1)) results in accelerated kinetics and enhanced current amplitudes. Conversely, transplanting the N-terminal region of CRACM3 into CRACM1 (CRACM1-N(M3)) leads to severely reduced store-operated currents. Highly conserved amino acids (K85 in CRACM1 and K60 in CRACM3) in the N-terminal region close to the first transmembrane domain are crucial for STIM1-dependent gating of CRAC channels. Single-point mutations of this residue (K85E and K60E) eliminate store-operated currents induced by inositol 1,4,5-trisphosphate and reduce store-independent gating by 2-aminoethoxydiphenyl borate. However, short fragments of these mutant channels are still able to communicate with the CRAC-activating domain of STIM1. Collectively, these findings identify a single amino acid in the N terminus of CRAC channels as a critical element for store-operated gating of CRAC channels.     

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.     

Subthreshold Voltage Noise Due to Channel Fluctuations in Active Neuronal Membranes

Voltage-gated ion channels in neuronal membranes fluctuate randomly between different conformational states due to thermal agitation. Fluctuations between conducting and nonconducting states give rise to noisy membrane currents and subthreshold voltage fluctuations and may contribute to variability in spike timing. Here we study subthreshold voltage fluctuations due to active voltage-gated Na⁺ and K⁺ channels as predicted by two commonly used kinetic schemes: the Mainen et al. (1995) (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (1952) (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temperatures. We contrast the results from Monte Carlo simulations of the stochastic nonlinear kinetic schemes with analytical, closed-form expressions derived using passive and quasi-active linear approximations to the kinetic schemes. For all subthreshold voltage ranges, the quasi-active linearized approximation is accurate within 8% and may thus be used in large-scale simulations of realistic neuronal geometries.     

Charge displacements in a single potassium ion channel macromolecule during gating.

Single ion channel currents can only provide indirect information on channel molecular events (except for timing). In contrast, the electric displacement currents associated with channel gating, termed gating currents, can provide direct information regarding the channel molecule's conformational changes. However, thus far gating currents have been measured only from ensembles of numerous stochastically activated channels and therefore the information they provide is limited. This work presents, for the first time, measurements of gating currents from a single channel molecule. Averaging close to 8000 pre-open currents, aligned to the single channel opening time, enabled the detection of single channel gating currents with a resolution of 2 electron charges. The measured charge displacements show: 1) a slow component, approximately 2 fA above baseline level, assumed to represent stochastic conformational changes, and 2) transients, the most significant of which occur 1.1 and 0.3 ms before channel opening. The transients most likely represent apparent deterministic stages in the gating process. The largest transient current peak was 5.1 +/- 1.6 fA and the total equivalent charge transported across the membrane was 4.7 +/- 2.5 electron charges. This data is unique also in that it presents monitoring of the behavior of a single, well-defined macromolecule.     

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.     

Microscopic origin of gating current fluctuations in a potassium channel voltage sensor

Voltage-dependent ion channels open and close in response to changes in membrane electrical potential due to the motion of their voltage-sensing domains (VSDs). VSD charge displacements within the membrane electric field are observed in electrophysiology experiments as gating currents preceding ionic conduction. The elementary charge motions that give rise to the gating current cannot be observed directly, but appear as discrete current pulses that generate fluctuations in gating current measurements. Here we report direct observation of gating-charge displacements in an atomistic molecular dynamics simulation of the isolated VSD from the KvAP channel in a hydrated lipid bilayer on the timescale (10-μs) expected for elementary gating charge transitions. The results reveal that gating-charge displacements are associated with the water-catalyzed rearrangement of salt bridges between the S4 arginines and a set of conserved acidic side chains on the S1-S3 transmembrane segments in the hydrated interior of the VSD.     

FPL 64176 modification of Ca(V)1.2 L-type calcium channels: dissociation of effects on ionic current and gating current

FPL 64176 (FPL) is a nondihydropyridine compound that dramatically increases macroscopic inward current through L-type calcium channels and slows activation and deactivation. To understand the mechanism by which channel behavior is altered, we compared the effects of the drug on the kinetics and voltage dependence of ionic currents and gating currents. Currents from a homogeneous population of channels were obtained using cloned rabbit Ca(V)1.2 (alpha1C, cardiac L-type) channels stably expressed in baby hamster kidney cells together with beta1a and alpha2delta1 subunits. We found a striking dissociation between effects of FPL on ionic currents, which were modified strongly, and on gating currents, which were not detectably altered. Inward ionic currents were enhanced approximately 5-fold for a voltage step from -90 mV to +10 mV. Kinetics of activation and deactivation were slowed dramatically at most voltages. Curiously, however, at very hyperpolarized voltages (< -250 mV), deactivation was actually faster in FPL than in control. Gating currents were measured using a variety of inorganic ions to block ionic current and also without blockers, by recording gating current at the reversal potential for ionic current (+50 mV). Despite the slowed kinetics of ionic currents, FPL had no discernible effect on the fundamental movements of gating charge that drive channel gating. Instead, FPL somehow affects the coupling of charge movement to opening and closing of the pore. An intriguing possibility is that the drug causes an inactivated state to become conducting without otherwise affecting gating transitions.