Stochastic Gating Research Articles

Stochastically Gating Ion Channels Enable Patterned Spike Firing through Activity-Dependent Modulation of Spike Probability

The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.

Stochastic Dynamics of Release Unit in a Cardiac Cell in Electron-Conformational Model

To further understand the role of stochastic dynamics of ryanodine receptor (RyR) channels on spark generating process we studied the stochastic RyR's cluster gating in calcium release unit (RU) in cardiomyocytes under steady-state conditions. We apply a simple biophysically-reasonable electron-conformational (EC) model [Moskvin ea, PBMB, 2006] for the RyR channel. Single RyR channels are characterized by fast electronic and slow classical conformational degrees of freedom. The RyR gating implies calcium induced electronic transitions between two branches of a conformational potential, a conformational Langevin dynamics, thermoactivated transitions and quantum tunneling. The sarcoplasmic (SR) load is incorporated into the model through the effective conformational strain.We examined different model dependencies of the electronic transition probability on the calcium ion concentration and effective temperature in dyadic space to reproduce all the features observed in lipid bilayer experiments. The 11 × 11 RyR cluster was build into a simple RU dynamic unit. Model simulations performed in frames of a diabatic approximation with a conformational inter-RyR coupling have revealed different gating regimes with a single RyR channel openings generating a Ca2+ synapse (quark) and a cooperative cluster mode, due to a step-by-step opening of a fraction of coupled RyR channels. We have found and analyzed the spark generating openings of groups of channels, providing for a sufficient release. The SR overload was shown to lead to the autooscillation regime with nearly periodical openings-closings of RyR-channels.The RU functioning was examined under different rates of SR load and different strength of the inter-RyR coupling. The EC model was shown to provide an adequate description of the cardiomyocite RU dynamics with valid prediction abilities.Supported by RFBR Grants 05-04-48352, 07-04-96126.

Single molecule kinetics under stochastic gating

In this note, we generally calculate the statistical blinking properties of single molecule based on the generating function approach developed recently. Specifically, we investigate the statistical variables of single molecule blinking kinetics under the stochastic gating.

Stochastic Gating and Drug–Ribosome Interactions

Gentamicin is a potent antibiotic that is used in combination therapy for inhalation anthrax disease. The drug is also often used in therapy for methicillin-resistant Staphylococcus aureus. Gentamicin works by flipping a conformational switch on the ribosome, disrupting the reading head (i.e., 16S ribosomal decoding bases 1492–1493) used for decoding messenger RNA. We use explicit solvent all-atom molecular simulation to study the thermodynamics of the ribosomal decoding site and its interaction with gentamicin. The replica exchange molecular dynamics simulations used an aggregate sampling of 15 μs when summed over all replicas, allowing us to explicitly calculate the free-energy landscape, including a rigorous treatment of enthalpic and entropic effects. Here, we show that the decoding bases flip on a timescale faster than that of gentamicin binding, supporting a stochastic gating mechanism for antibiotic binding, rather than an induced-fit model where the bases only flip in the presence of a ligand. The study also allows us to explore the nonspecific binding landscape near the binding site and reveals that, rather than a two-state bound/unbound scenario, drug dissociation entails shuttling between many metastable local minima in the free-energy landscape. Special care is dedicated to validation of the obtained results, both by direct comparison to experiment and by estimation of simulation convergence.

Calcium release site ultrastructure and the dynamics of puffs and sparks

When Markov chain models of intracellular Ca(2+)-regulated Ca(2+) channels are coupled via a mathematical representation of a Ca(2+) microdomain, simulated Ca(2+) release sites may exhibit the phenomenon of 'stochastic Ca(2+) excitability' reminiscent of Ca(2+) puffs and sparks. Interestingly, some single-channel models that include Ca(2+) inactivation are not particularly sensitive to channel density, so long as the requirement for inter-channel communication is satisfied, while other single-channel models that do not include Ca(2+) inactivation open and close synchronously only when the channel density is in a prescribed range. This observation led us to hypothesize that single-channel models with Ca(2+) inactivation would be less sensitive to the details of release site ultrastructure than models that lack a slow Ca(2+) inactivation process. To determine if this was the case, we simulated Ca(2+) release sites composed of instantaneously coupled Ca(2+)-regulated Ca(2+) channels whose random spatial locations were chosen from a uniform distribution on a disc of specified radius and compared the resulting release site dynamics to simulations with channels arranged on hexagonal lattices. Analysis of puff/spark statistics confirmed our hypothesis that puffs and sparks are less sensitive to the spatial organization of release sites when the single-channel model includes a slow inactivation process. We also investigated the validity of several different mean-field reductions that do not explicitly account for the details of release site ultrastructure. The most successful approximation maintains a distinction between each channel's substantial influence on its own stochastic gating and the collective contribution of elevated [Ca(2+)] from neighbouring channels.

Modeling local and global intracellular calcium responses mediated by diffusely distributed inositol 1,4,5-trisphosphate receptors

Considerable insight into intracellular Ca 2 + responses has been obtained through the development of whole cell models that are based on molecular mechanisms, e.g., single channel kinetics of the inositol 1,4,5-trisphosphate ( IP 3 ) receptor Ca 2 + channel. However, a limitation of most whole cell models to date is the assumption that IP 3 receptor Ca 2 + channels ( IP 3 R s) are globally coupled by a “continuously stirred” bulk cytosolic [ Ca 2 + ], when in fact open IP 3 R s experience elevated “domain” Ca 2 + concentrations. Here we present a 2 N + 2 -compartment whole cell model of local and global Ca 2 + responses mediated by N = 100 , 000 diffusely distributed IP 3 R s, each represented by a four-state Markov chain. Two of these compartments correspond to bulk cytosolic and luminal Ca 2 + concentrations, and the remaining 2 N compartments represent time-dependent cytosolic and luminal Ca 2 + domains associated with each IP 3 R . Using this Monte Carlo model as a starting point, we present an alternative formulation that solves a system of advection–reaction equations for the probability density of cytosolic and luminal domain [ Ca 2 + ] jointly distributed with IP 3 R state. When these equations are coupled to ordinary differential equations for the bulk cytosolic and luminal [ Ca 2 + ], a realistic but minimal model of whole cell Ca 2 + dynamics is produced that accounts for the influence of local Ca 2 + signaling on channel gating and global Ca 2 + responses. The probability density approach is benchmarked and validated by comparison to Monte Carlo simulations, and the two methods are shown to agree when the number of Ca 2 + channels is large (i.e., physiologically realistic). Using the probability density approach, we show that the time scale of Ca 2 + domain formation and collapse (both cytosolic and luminal) may influence global Ca 2 + oscillations, and we derive two reduced models of global Ca 2 + dynamics that account for the influence of local Ca 2 + signaling on global Ca 2 + dynamics when there is a separation of time scales between the stochastic gating of IP 3 R s and the dynamics of domain Ca 2 + .

Mechanisms of Intrinsic Beating Variability in Cardiac Cell Cultures and Model Pacemaker Networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

The dynamics of luminal depletion and the stochastic gating of [formula omitted]-activated [formula omitted] channels and release sites

Single channel models of intracellular calcium ( Ca 2 + ) channels such as the 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca 2 + -dependent transitions are mediated by constant background cytosolic [ Ca 2 + ] . This assumption neglects the fact that Ca 2 + released by open channels may influence subsequent gating through the processes of Ca 2 + -activation or inactivation. Similarly, the influence of the dynamics of luminal depletion on the stochastic gating of intracellular Ca 2 + channels is often neglected, in spite of the fact that the sarco/endoplasmic reticulum [ Ca 2 + ] near the luminal face of intracellular Ca 2 + channels influences the driving force for Ca 2 + , the rate of Ca 2 + release, and the magnitude and time course of the consequent increase in cytosolic domain [ Ca 2 + ] . Here we analyze how the steady-state open probability of several minimal Ca 2 + -regulated Ca 2 + channel models depends on the conductance of the channel and the time constants for the relaxation of elevated cytosolic [ Ca 2 + ] and depleted luminal [ Ca 2 + ] to the bulk [ Ca 2 + ] of both compartments. Our approach includes Monte Carlo simulation as well as numerical solution of a system of advection-reaction equations for the multivariate probability density of elevated cytosolic [ Ca 2 + ] and depleted luminal [ Ca 2 + ] conditioned on each state of the stochastically gating channel. Both methods are subsequently used to study the role of luminal depletion in the dynamics of Ca 2 + puff/spark termination in release sites composed of Ca 2 + channels that are activated, but not inactivated, by cytosolic Ca 2 + . The probability density approach shows that such minimal Ca 2 + release site models may exhibit puff/spark-like dynamics in either of two distinct parameter regimes. In one case, puffs/spark termination is due to the process of stochastic attrition and facilitated by rapid Ca 2 + domain collapse [cf. DeRemigio, H., Smith, G., 2005. The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 38, 73–86]. In the second case, puff/spark termination is promoted by the local depletion of luminal Ca 2 + .

Voltage noise influences action potential duration in cardiac myocytes

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current–voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current–voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.

SingleIhChannels in Pyramidal Neuron Dendrites: Properties, Distribution, and Impact on Action Potential Output

The hyperpolarization-activated cation current (Ih) plays an important role in regulating neuronal excitability, yet its native single-channel properties in the brain are essentially unknown. Here we use variance-mean analysis to study the properties of single Ih channels in the apical dendrites of cortical layer 5 pyramidal neurons in vitro. In these neurons, we find that Ih channels have an average unitary conductance of 680 +/- 30 fS (n = 18). Spectral analysis of simulated and native Ih channels showed that there is little or no channel flicker below 5 kHz. In contrast to the uniformly distributed single-channel conductance, Ih channel number increases exponentially with distance, reaching densities as high as approximately 550 channels/microm2 at distal dendritic sites. These high channel densities generate significant membrane voltage noise. By incorporating a stochastic model of Ih single-channel gating into a morphologically realistic model of a layer 5 neuron, we show that this channel noise is higher in distal dendritic compartments and increased threefold with a 10-fold increased single-channel conductance (6.8 pS) but constant Ih current density. In addition, we demonstrate that voltage fluctuations attributable to stochastic Ih channel gating impact on action potential output, with greater spike-timing precision in models with the experimentally determined single-channel conductance. These data suggest that, in the face of high current densities, the small single-channel conductance of Ih is critical for maintaining the fidelity of action potential output.

Constitutively active L-type Ca 2+ channels

Ca(2+) influx through L-type Ca(2+) channels (LTCCs) influences numerous physiological processes ranging from contraction in muscle and memory in neurons to gene expression in many cell types. However, the spatiotemporal organization of functional LTCCs has been nearly impossible to investigate because of methodological limitations. Here, we examined LTCC function with high temporal and spatial resolution using evanescent field fluorescence microscopy. Surprisingly, we found that LTCCs operated in functionally organized clusters, not necessarily as individual proteins. Furthermore, LTCC function in these clusters does not appear to be controlled by simple stochastic gating but instead by a PKC-dependent switch mechanism. This work suggests that resting intracellular free calcium concentration in arterial myocytes is predominantly controlled by this process in combination with rare voltage-dependent openings of individual LTCCs. We propose that Ca(2+) influx via persistent LTCCs may be an important mechanism regulating steady-state local and global Ca(2+) signals.

The effect of residual [formula omitted] on the stochastic gating of [formula omitted]-regulated [formula omitted] channel models

Single-channel models of intracellular Ca 2 + channels such as the inositol 1,4,5-trisphosphate receptor and ryanodine receptor often assume that Ca 2 + -dependent transitions are mediated by a constant background [ Ca 2 + ] as opposed to a dynamic [ Ca 2 + ] representing the formation and collapse of a localized Ca 2 + domain. This assumption neglects the fact that Ca 2 + released by open intracellular Ca 2 + channels may influence subsequent gating through the processes of Ca 2 + -activation or -inactivation. We study the effect of such “residual Ca 2 + ” from previous channel opening on the stochastic gating of minimal and realistic single-channel models coupled to a restricted cytoplasmic compartment. Using Monte Carlo simulation as well as analytical and numerical solution of a system of advection–reaction equations for the probability density of the domain [ Ca 2 + ] conditioned on the state of the channel, we determine how the steady-state open probability ( p open ) of single-channel models of Ca 2 + -regulated Ca 2 + channels depends on the time constant for Ca 2 + domain formation and collapse. As expected, p open for a minimal model including Ca 2 + activation increases as the domain time constant becomes large compared to the open and closed dwell times of the channel, that is, on average the channel is activated by residual Ca 2 + from previous openings. Interestingly, p open for a channel model that is inactivated by Ca 2 + also increases as a function of the domain time constant when the maximum domain [ Ca 2 + ] is fixed, because slow formation of the Ca 2 + domain attenuates Ca 2 + -mediated inactivation. Conversely, when the source amplitude of the channel is fixed, increasing the domain time constant leads to elevated domain [ Ca 2 + ] and decreased open probability. Consistent with these observations, a realistic De Young–Keizer-like IP 3 R model responds to residual Ca 2 + with a steady-state open probability that is a monotonic function of the domain time constant, though minimal models that include both Ca 2 + -activation and -inactivation show more complex behavior. We show how the probability density approach described here can be generalized for arbitrarily complex channel models and for any value of the domain time constant. In addition, we present a comparatively simple numerical procedure for estimating p open for models of Ca 2 + -regulated Ca 2 + channels in the limit of a very fast or very slow Ca 2 + domain. When the ordinary differential equation for the [ Ca 2 + ] in a restricted cytoplasmic compartment is replaced by a partial differential equation for the buffered diffusion of intracellular Ca 2 + in a homogeneous isotropic cytosol, we find the dependence of p open on the buffer time constant is qualitatively similar to the above-mentioned results.

The Role of Stochastic and Modal Gating of Cardiac L-Type Ca 2+ Channels on Early After-Depolarizations

Certain signaling events that promote L-type Ca 2+ channel (LCC) phosphorylation, such as β-adrenergic stimulation or an increased expression of Ca 2+/calmodulin-dependent protein kinase II, promote mode 2 gating of LCCs. Experimental data suggest the hypothesis that these events increase the likelihood of early after-depolarizations (EADs). We test this hypothesis using an ionic model of the canine ventricular myocyte incorporating stochastic gating of LCCs and ryanodine-sensitive calcium release channels. The model is extended to describe myocyte responses to the β-adrenergic agonist isoproterenol. Results demonstrate that in the presence of isoproterenol the random opening of a small number of LCCs gating in mode 2 during the plateau phase of the action potential (AP) can trigger EADs. EADs occur randomly, where the likelihood of these events increases as a function of the fraction of LCCs gating in mode 2. Fluctuations of the L-type Ca 2+ current during the AP plateau lead to variability in AP duration. Consequently, prolonged APs are occasionally observed and exhibit an increased likelihood of EAD formation. These results suggest a novel stochastic mechanism, whereby phosphorylation-induced changes in LCC gating properties contribute to EAD generation.

Stochastic Nonlinear Dynamics: How Many Ion Channels are in a Single Neuron?

We apply our stochastic cell model to simulate the noisy shape of single neuronal action potentials on the basis of the nonlinear oscillatory Brusselator model. By comparison with the experimental action potentials as measured by Laurent and co-workers in the olfactory system of the locust, we conclude that at least ∼14 000 ion channels in a local neuron (LN) and ∼70 000 ion channels in a project neueron (PN) are responsible for the stochastic appearance of the measured action potentials. Instead of treating the stochastic gating of ionic channels as a multistate Markov process, we use a computer simulation that performs a direct count of all events of each individual reaction step on the basis of their Poisson distributions. Our stochastic analysis is independent of the particular architecture of the neuronal network.

Theoretical analysis of the influence of stochastic gating on the transient effect in fluorescence quenching by electron transfer

For electron transfer (ET) reactions in liquid media, it is not uncommon to find that the stereoselectivity, mutual orientations, conformational fluctuations, spin multiplicity restrictions of the reacting system may kinetically limit its reactivity. We assume that the system in question can stochastically interconvert between reactive (open gate) and nonreactive (closed gate) states at rates competitive with diffusion-influenced ET, and refer to this kind of reaction as stochastically gated diffusion-influenced ET reactions. We utilize the Zhou and Szabo model of stochastically gated diffusion-influenced reactions in order to study the effect of such stochastic fluctuations of reactivity on the transient kinetics of fluorescence quenching in through-solvent photoinduced ET reaction. Different types of transient kinetics, fluorophore gated vis-a-vis quencher gated, are demonstrated in terms of survival probability of the fluorophore, which shows that the analysis of experimental results ignoring such phenomena can be dramatically in error. Approximate analytical solutions of the theory based on projection operator formalism are presented. The exact numerical results including the role of liquid structure and the hydrodynamic hindrance of fluorophore-quencher diffusion rates are found to compare extremely well with the results obtained from a molecular dynamics simulation of the same reaction system. The simulations are based on the rate equations obtained from the first principle. Illustrative calculations and comparisons are presented to demonstrate the competitive interplay between the reaction sink strength, diffusion, and gating rates on the reaction kinetics. A simple method, based on the distribution of ET distance and quantum yield of ET of gateless reactions, is proposed to help delineate the features of such competitive interplay on the asymmetry of the reaction kinetics.

Theory of the diffusion-influenced substrate binding rate to a buried and gated active site

The effects of stochastic gating on the diffusion-influenced substrate binding rate to a buried active site are studied. An approximation introduced by Samson and Deutch [J. Chem. Phys. 68, 285 (1978)] is shown to be equivalent to making the constant-flux approximation on the entrance to the active site. The constant-flux approximation is then extended to the case where the entrance to the active site is stochastically gated because of conformational fluctuations of the enzyme. The stochastically gated rate constant, ksg, is found to be given by the relation 1/ksg=1/k+wo/wc(wo+wc)ĥ(wo+wc), where k is the rate constant in the absence of gating, ĥ(s) is the Laplace transform of the total flux across the entrance after the substrate is started from an equilibrium distribution outside the entrance, and wo and wc are the transition rates between the open and closed gating states. This relation reduces to an approximate relation derived earlier for a more restrictive situation, where the reactivity within the active site is gated. The leading term in the expansion of sĥ(s) for large s is DA〈exp(−βU)〉(s/D)1/2/2, where D is the diffusion coefficient of the substrate, A is the total area of the entrance, and 〈exp(−βU)〉 is the average Boltzmann factor on the entrance. The time scale of conformational fluctuations, ∼ a few picoseconds, is much shorter than the time scale of diffusion, so this leading term is useful for estimating (wo+wc)ĥ(wo+wc). A further consequence of the disparity in time scales is that the value of (wo+wc)ĥ(wo+wc) is much larger than k. As a result the decrease of the rate constant due to gating is relatively small (unless the entrance to the active site is closed nearly all the time). This suggests that a buried and gated active site may play the important role of controlling enzyme specificity without sacrificing efficiency.

Stochastic gating influence on the kinetics of diffusion-limited reactions

We study how the kinetics of diffusion-influenced reactions is modified when the reactivity of species fluctuates in time (stochastically gated) with emphasis on the many-particle aspect of the problem. Because of the fact that the dynamics of ligand binding to proteins originally motivated the problem, it is considered in that context. Recently, Zhou and Szabo [J. Phys. Chem. 100, 2597 (1996)] have demonstrated many-particle effects in the problem and found that the kinetics of reaction between a gated protein with a large number of ligands significantly differs from that between a protein and gated ligands. With our approach, the difference between the kinetics of ligand-gated and protein-gated reactions appears formally the same as the difference between the target and trapping problems despite the origin of the corresponding effects and their manifestations are distinctly different. A simple approximate method to treat the many-particle effects is proposed. The theory is applied to a particular two-state gating model. Explicit analytical expressions for the protein survival probability are obtained. We show that (1) for ligand-gated reactions, gating is effectively accounted for by the appropriate reduction of the species reactivity and (2) for protein-gated reactions, the survival probability changes its time behavior from exponential (fast gating) to nonexponential (slow gating). The role of intensity and asymmetry of the gate motion is discussed.

Smoluchowski-type theory of stochastically gated diffusion-influenced reactions

The Smoluchowski–Collins–Kimball theory of irreversible diffusion-influenced reactions with one of the reactants in excess is generalized to the case of stochastic gating when one of the reactants can be in one of M states. Distinct states are characterized by various efficiencies of the reaction of contacting partners. General expressions are derived for the rate constant and for the survival probability of the reactant which is in deficiency. We present these quantities in terms of the solution of the isolated pair problem. The difference between the cases when gating is due to the reactant, which is in excess, and one, which is in deficiency, is explicitly demonstrated. General relationships between the rate constants and the survival probabilities in the two cases are established. We show that in the former case the reaction goes faster compared to the latter one. To make the problem treatable analytically in the case when gating is due to the reactant which is in deficiency, a partial mean-field approximation is introduced. General theory is applied to a particular case of the two-state gating model. Explicit analytical solutions for the time-dependent rate constant and the survival probability are obtained in one dimension. They illustrate the general theory as well as show how the kinetics depends on the jump rate between the two states of the gate in both cases when gating is due to the reactant, which is in excess, and one, which is in deficiency.

Stochastic gating in diffusion-influenced ligand binding to proteins: Gated protein versus gated ligands.

The kinetics of the irreversible diffusion-influenced binding of a mobile ligand to a stationary protein is studied, when the ligand concentration is larger than that of proteins and the efficiency of binding is stochastically gated due to conformational fluctuations of one of the species. A general case of M conformational (gate) states is considered with the goal to better understand the difference between the cases of gated ligand and gated protein discovered for the two gate state model [Zhou and Szabo, J. Phys. Chem. 100, 2597 (1996)]. It is shown that in the former case the binding goes faster than in the latter one. \textcopyright{} 1996 The American Physical Society.

Molecular motion under stochastic gating

We investigate molecular passage through a geometrical barrier. We assume that the barrier is a stochastic gate so that the passage rate depends on its fluctuating nature and on the molecular size. We calculate the dependence of the passage rate Keff on relaxation rate of the gate radius and therefore on the solvent viscosity η. Two cases are solved: an open-or-closed gate and an harmonic gate. The latter is shown to lead to the experimentally observed fractional power law dependence of Keff on η.