Tetanus toxin channel in phosphatidylserine planar bilayers: conductance states and pH dependence

Tetanus toxin (TeTx) forms ionic channel in phosphatidylserine bilayers. TeTx channels exhibit different modes of channel bursting activity, from a closed state to well defined open states of different amplitudes. At positive applied voltages, TeTx channels flicker continuously between a closed state and the various distinct open states. Furthermore, fast transitions into subconductance states are discernible within the bursts of channel activity. Elementary conductance steps submultiple of the open states were not identified in single channel records owing to rapid transitions between different states. However, statistical analysis shows that conductances cluster with amplitudes multiple of an elementary value: e.g. 25–30 pS at neutral pH. Single channel current amplitudes decrease with the pH of the bulk electrolyte solution. Conductance decrements can be accounted for by the relative decrease of permeant cation concentration at the membrane-water interface, by a relative enrichment of protons that block the channel or by the stabilization of a conformational state of the channel protein. Offprint requests to: F. Gambale     

Integrated allosteric model of voltage gating of HCN channels

Hyperpolarization-activated (pacemaker) channels are dually gated by negative voltage and intracellular cAMP. Kinetics of native cardiac f-channels are not compatible with HH gating, and require closed/open multistate models. We verified that members of the HCN channel family (mHCN1, hHCN2, hHCN4) also have properties not complying with HH gating, such as sigmoidal activation and deactivation, activation deviating from fixed power of an exponential, removal of activation "delay" by preconditioning hyperpolarization. Previous work on native channels has indicated that the shifting action of cAMP on the open probability (Po) curve can be accounted for by an allosteric model, whereby cAMP binds more favorably to open than closed channels. We therefore asked whether not only cAMP-dependent, but also voltage-dependent gating of hyperpolarization-activated channels could be explained by an allosteric model. We hypothesized that HCN channels are tetramers and that each subunit comprises a voltage sensor moving between "reluctant" and "willing" states, whereas voltage sensors are independently gated by voltage, channel closed/open transitions occur allosterically. These hypotheses led to a multistate scheme comprising five open and five closed channel states. We estimated model rate constants by fitting first activation delay curves and single exponential time constant curves, and then individual activation/deactivation traces. By simply using different sets of rate constants, the model accounts for qualitative and quantitative aspects of voltage gating of all three HCN isoforms investigated, and allows an interpretation of the different kinetic properties of different isoforms. For example, faster kinetics of HCN1 relative to HCN2/HCN4 are attributable to higher HCN1 voltage sensors' rates and looser voltage-independent interactions between subunits in closed/open transitions. It also accounts for experimental evidence that reduction of sensors' positive charge leads to negative voltage shifts of Po curve, with little change of curve slope. HCN voltage gating thus involves two processes: voltage sensor gating and allosteric opening/closing.     

Periodic forcing of a single ion channel: dynamic aspects of the open-closed switching

An unconventional approach to studying ion channel kinetics is exploited. Here we describe the effects of a periodically varying membrane potential on the open-closed transitions of single K⁺ channels. The use of cycle histograms allows one to measure the transition probabilities as functions of the stimulus phase. The results show that such probabilities vary with the stimulation frequency and with the stimulus history, thus highlighting a dynamic aspect in the switching of this ion channel. Received: 9 May 1997 / Revised version: 5 January 1998 / Accepted: 12 January 1998     

Inactivation of BK channels mediated by the NH(2) terminus of the beta3b auxiliary subunit involves a two-step mechanism: possible separation of binding and blockade

A family of auxiliary beta subunits coassemble with Slo alpha subunit to form Ca(2)+-regulated, voltage-activated BK-type K(+) channels. The beta subunits play an important role in regulating the functional properties of the resulting channel protein, including apparent Ca(2)+ dependence and inactivation. The beta3b auxiliary subunit, when coexpressed with the Slo alpha subunit, results in a particularly rapid ( approximately 1 ms), but incomplete inactivation, mediated by the cytosolic NH(2) terminus of the beta3b subunit (Xia et al. 2000). Here, we evaluate whether a simple block of the open channel by the NH(2)-terminal domain accounts for the inactivation mechanism. Analysis of the onset of block, recovery from block, time-dependent changes in the shape of instantaneous current-voltage curves, and properties of deactivation tails suggest that a simple, one step blocking reaction is insufficient to explain the observed currents. Rather, blockade can be largely accounted for by a two-step blocking mechanism (C(n) <---> O(n) <---> O(*)(n) <---> I(n)) in which preblocked open states (O*(n)) precede blocked states (I(n)). The transitions between O* and I are exceedingly rapid accounting for an almost instantaneous block or unblock of open channels observed with changes in potential. However, the macroscopic current relaxations are determined primarily by slower transitions between O and O*. We propose that the O to O* transition corresponds to binding of the NH(2)-terminal inactivation domain to a receptor site. Blockade of current subsequently reflects either additional movement of the NH(2)-terminal domain into a position that hinders ion permeation or a gating transition to a closed state induced by binding of the NH(2) terminus.     

Monotonic and non-monotonic single channel open time distributions with two sequential open states

Some conditions under which kinetic schemes including two sequential open states of identical conductance will display a non-monotonic (i.e. with a deficit of short open times and a maximum at t>0) distribution of single channel open times are described theoretically. Neither a closed cyclic scheme nor exclusively irreversible transitions between states are required for non-monotonic distributions. A required condition for the schemes considered here is that all openings are to a state from which closing is not possible. It is the presence of a precursor process to channel closing that produces the non-monotonic distribution. Following each channel opening some time is required for a transition into the second open state from which all closings proceed. Simple schemes of this sort cannot provide the basis of any experimental reports of non-monotonic distributions.     

Dynamic interaction of S5 and S6 during voltage-controlled gating in a potassium channel

A gain-of-function mutation in the Caenorhabditis elegans exp-2 K(+)-channel gene is caused by a cysteine-to-tyrosine change (C480Y) in the sixth transmembrane segment of the channel (Davis, M.W., R. Fleischhauer, J.A. Dent, R.H. Joho, and L. Avery. 1999. Science. 286:2501-2504). In contrast to wild-type EXP-2 channels, homotetrameric C480Y mutant channels are open even at -160 mV, explaining the lethality of the homozygous mutant. We modeled the structure of EXP-2 on the 3-D scaffold of the K(+) channel KcsA. In the C480Y mutant, tyrosine 480 protrudes from S6 to near S5, suggesting that the bulky side chain may provide steric hindrance to the rotation of S6 that has been proposed to accompany the open-closed state transitions (Perozo, E., D.M. Cortes, and L.G. Cuello. 1999. Science. 285:73-78). We tested the hypothesis that only small side chains at position 480 allow the channel to close, but that bulky side chains trap the channel in the open state. Mutants with small side chain substitutions (Gly and Ser) behave like wild type; in contrast, bulky side chain substitutions (Trp, Phe, Leu, Ile, Val, and His) generate channels that conduct K(+) ions at potentials as negative as -120 mV. The side chain at position 480 in S6 in the pore model is close to and may interact with a conserved glycine (G421) in S5. Replacement of G421 with bulky side chains also leads to channels that are trapped in an active state, suggesting that S5 and S6 interact with each other during voltage-dependent open-closed state transitions, and that bulky side chains prevent the dynamic changes necessary for permanent channel closing. Single-channel recordings show that mutant channels open frequently at negative membrane potentials indicating that they fail to reach long-lasting, i.e., stable, closed states. Our data support a "two-gate model" with a pore gate responsible for the brief, voltage-independent openings and a separately located, voltage-activated gate (Liu, Y., and R.H. Joho. 1998. Pflügers Arch. 435:654-661).     

Calculations of quantum tunnelling between closed and open states of sodium channels

Transitions between states of ion channels have previously been considered in terms of classical statistical mechanics. However, transitions in many systems, including some organic molecules, are known to occur by quantum mechanical tunnelling. In this report, we have calculated the time for sodium channel activation by tunnelling, starting from a mechanistic model based on the structural models of Catterall and Guy. In doing this, we have calculated the Coulomb interactions between the S4 -helix and negative residues on nearest-neighbor helices and have included longer range interactions in terms of an effective background interaction. Periodic pairing of charges between the S4 and adjacent helices in the model causes the resting and depolarized states of the channel to correspond to local minima in the S4 potential energy curve. Harmonic potentials closely fit the energy curves around each of the two minima and the energy barrier between them is closely modelled by a parabola. These approximations allow a semiclassical calculation of the S4 helix's tunnelling rate to be made. At 37°C, for an interhelix axial spacing of 10 Å, tunnelling times in the range of 1 s to a few ms were computed for a single S4 segment, depending of the equilibrium temperature of the cell membrane.     

Channels in Mitochondrial Membranes: Knowns,Unknowns, and Prospects for the Future

Abstract

Rapid diffusion of hydrophilic molecules across the outer membrane of mitochondria has been related to the presence of a protein of 29 to 37 kDa, called voltage-dependent anion channel (VDAC), able to generate large aqueous pores when integrated in planar lipid bilayers. Functional properties of VDAC from different origins appear highly conserved in artificial membranes: at low transmembrane potentials, the channel is in a highly conducting state, but a raise of the potential (both positive and negative) reduces drastically the current and changes the ionic selectivity from slightly anionic to cationic. It has thus been suggested that VDAC is not a mere molecular sieve but that it may control mitochondrial physiology by restricting the access of metabolites of different valence in response to voltage and/or by interacting with a soluble protein of the intermembrane space. The latest application of the patch clamp and tip-dip techniques, however, has indicated both a different electric behavior of the outer membrane and that other proteins may play a role in the permeation of molecules. Biochemical studies, use of site-directed mutants, and electron microscopy of two-dimensional crystal arrays of VDAC have contributed to propose a monomelic β barrel as the structural model of the channel. An important insight into the physiology of the inner membrane of mammalian mitochondria has come from the direct observation of the membrane with the patch clamp. A slightly anionic., voltage-dependent conductance of 107 pS and one of 9.7 pS, K⁺-selective and ATP-sensitive, are the best characterized at the single channel level. Under certain conditions, however, the inner membrane can also show unselective nS peak transitions, possibly arising from a cooperative assembly of multiple substates.     

Interactions of the channel forming peptide alamethicin with artificial and natural membranes

Alamethicin and related α-aminoisobutyric acid peptides form transmembrane channels across lipid bilayers. This article briefly reviews studies on the effect of alamethicin on lipid phase transitions in lipid bilayers and on mitochondrial oxidative phosphorylation. Fluorescence polarization studies, employing 1,6-diphenyl-1,3,5-hexatriene as a probe, suggest that alamethicin fluidizes lipid bilayers below the phase transition t-emperature, but has little effect above the gel-liquid crystal transition point. Alamethicin is shown to function as an uncoupler of oxidative phosphorylation in rat liver mitochondria. The influence of alamethicin on mitochondrial respiration is modulated by the phosphate ion concentration in the medium. Classical uncoupling activity is evident at low phosphate levels while inhibitory effects set in at higher phosphate concentrations. Time-dependent changes in respiration rates following peptide addition are rationalized in terms of alamethicin interactions with mitochondrial membrane components.     

Blockade of a mitochondrial cationic channel by an addressing peptide: An electrophysiological study

Summary A voltage-dependent cationic channel of large conductance is observed in phospholipid bilayers formed at the tip of microelectrodes from proteoliposomes derived from mitochondrial membranes. This channel was blocked by a 13-residue peptide with the sequence of the amino terminal extremity of the nuclear-coded subunit IV of cytochromec oxidase. The blockade was reversible, voltage- and dose-dependent. The peptide did not affect the activity of aTorpedo chloride channel observed under the same conditions. From experiments with phospholipid monolayers, it is unlikely that the peptide inserts into bilayers under the experimental conditions used. The blockade was observed from both sides of the membrane, being characterized by more frequent transitions to the lower conductance states, and a maximum effect was observed around 0 mV. Channels, the gating mechanism of which had been eliminated by exposure to trypsin, were also blocked by the peptide. For trypsinized channels, the duration of the closure decreased and the blockade saturated at potentials below –30 mV. These observations are consistent with a translocation of the peptide through the channel. Dynorphin B, which has the same length and charge as the peptide, had some blocking activity. Introduction of negative charges in the peptide by succinylation suppressed the activity.     

Cooperative nature of gating transitions in K+ channels as seen from dynamic importance sampling calculations

The growing dataset of K⁺ channel x‐ray structures provides an excellent opportunity to begin a detailed molecular understanding of voltage‐dependent gating. These structures, while differing in sequence, represent either a stable open or closed state. However, an understanding of the molecular details of gating will require models for the transitions and experimentally testable predictions for the gating transition. To explore these ideas, we apply dynamic importance sampling to a set of homology models for the molecular conformations of K⁺ channels for four different sets of sequences and eight different states. In our results, we highlight the importance of particular residues upstream from the Pro‐Val‐Pro (PVP) region to the gating transition. This supports growing evidence that the PVP region is important for influencing the flexibility of the S6 helix and thus the opening of the gating domain. The results further suggest how gating on the molecular level depends on intra‐subunit motions to influence the cooperative behavior of all four subunits of the K⁺ channel. We hypothesize that the gating process occurs in steps: first sidechain movement, then inter‐S5‐S6 subunit motions, and lastly the large‐scale domain rearrangements. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Gating of the bacterial sodium channel, NaChBac: voltage-dependent charge movement and gating currents

The bacterial sodium channel, NaChBac, from Bacillus halodurans provides an excellent model to study structure-function relationships of voltage-gated ion channels. It can be expressed in mammalian cells for functional studies as well as in bacterial cultures as starting material for protein purification for fine biochemical and biophysical studies. Macroscopic functional properties of NaChBac have been described previously (Ren, D., B. Navarro, H. Xu, L. Yue, Q. Shi, and D.E. Clapham. 2001. Science. 294:2372-2375). In this study, we report gating current properties of NaChBac expressed in COS-1 cells. Upon depolarization of the membrane, gating currents appeared as upward inflections preceding the ionic currents. Gating currents were detectable at -90 mV while holding at -150 mV. Charge-voltage (Q-V) curves showed sigmoidal dependence on voltage with gating charge saturating at -10 mV. Charge movement was shifted by -22 mV relative to the conductance-voltage curve, indicating the presence of more than one closed state. Consistent with this was the Cole-Moore shift of 533 micros observed for a change in preconditioning voltage from -160 to -80 mV. The total gating charge was estimated to be 16 elementary charges per channel. Charge immobilization caused by prolonged depolarization was also observed; Q-V curves were shifted by approximately -60 mV to hyperpolarized potentials when cells were held at 0 mV. The kinetic properties of NaChBac were simulated by simultaneous fit of sodium currents at various voltages to a sequential kinetic model. Gating current kinetics predicted from ionic current experiments resembled the experimental data, indicating that gating currents are coupled to activation of NaChBac and confirming the assertion that this channel undergoes several transitions between closed states before channel opening. The results indicate that NaChBac has several closed states with voltage-dependent transitions between them realized by translocation of gating charge that causes activation of the channel.     

Activation kinetics of single high-threshold calcium channels in the membrane of sensory neurons from mouse embryos

Summary Activation kinetics of single high-threshold inactivating (HTI orN-type) calcium channels of cultured dorsal root ganglion cells from mouse embryos was studied using a patchclamp method. Calcium channels displayed bursting activity. The open-time histogram was single exponential with an almost potential-independent mean open time _op. The closed-time histogram was multicomponent; at least three of the components were associated with the activation process. The fast exponential component with the potential-independent time constant _cl ^f included all intraburst gaps, while two slower ones with potential-dependent time constants _cl ^vs described shut times between bursts and between clusters of bursts. The burst length histogram was biexponential. The fast component with a relatively potential-independent time constant _bur ^f described short, isolated channel openings while the slow component characterized real bursts with a potential-dependent mean life time. The waiting-time histogram could be fitted by a difference of two exponentials with time constants being the same as _cl ^s and _cl ^vs . The data obtained were described in the frame of a 4-state sequential model of calcium channel activation, in which the first two stages are formally attributed to potential-dependent transmembrane transfer of two charged gating particles accompanying the channel transitions between three closed states, and the third one to fast conformational changes in channel protein leading to the opening of the channel. The rate constants for all transitions were defined. The validity of the proposed model for both low-threshold inactivating (LTI orT-type) and high-threshold noninactivating (HTN orL-type) calcium channels is discussed.     

Single-channel recordings of apical membrane chloride conductance in A6 epithelial cells

Summary The apical membrane of epithelial cells from the A6 cell line grown on impermeable substrata was studied using the patch-clamp technique. We defined the apical membrane as that membrane in contact with the growth medium. In about 50% of the patches, channels with single-unit conductances of 360±45 pS in symmetrical 105mm NaCl solutions, and characteristic voltage-dependent inactivation were observed. Using excised membrane patches and varying the ionic composition of the bathing medium, we determined that the channels were anion selective, with a permeability ratio for Cl^– over Na⁺ of about 91, calculated from the reversal potential using the constantfield equation. The channel was most active at membrane potentials between ±20 mV and inactivated, usually within a few seconds, at higher potentials of either polarity. Reactivation from this inactivation was slow, sometimes requiring minutes. In addition to its fully open state, the channel could also enter a flickering state, which appeared to involve rapid transitions to one or more submaximal conductance levels. The channel was inhibited by the disulfonic stilbene SITS in a manner characteristic of reversible open-channel blockers.     

Stoichiometry of transjunctional voltage-gating polarity reversal by a negative charge substitution in the amino terminus of a connexin32 chimera

Gap junctions are intercellular channels formed by the serial, head to head arrangement of two hemichannels. Each hemichannel is an oligomer of six protein subunits, which in vertebrates are encoded by the connexin gene family. All intercellular channels formed by connexins are sensitive to the relative difference in the membrane potential between coupled cells, the transjunctional voltage (Vj), and gate by the separate action of their component hemichannels (Harris, A.L., D.C. Spray, and M.V. Bennett. 1981. J. Gen. Physiol. 77:95-117). We reported previously that the polarity of Vj dependence is opposite for hemichannels formed by two closely related connexins, Cx32 and Cx26, when they are paired to form intercellular channels (Verselis, V.K., C.S. Ginter, and T.A. Bargiello. 1994. Nature. 368:348-351). The opposite gating polarity is due to a difference in the charge of the second amino acid. Negative charge substitutions of the neutral asparagine residue present in wild-type Cx32 (Cx32N2E or Cx32N2D) reverse the gating polarity of Cx32 hemichannels from closure at negative Vj to closure at positive Vj. In this paper, we further examine the mechanism of polarity reversal by determining the gating polarity of a chimeric connexin, in which the first extracellular loop (E1) of Cx32 is replaced with that of Cx43 (Cx43E1). The resulting chimera, Cx32*Cx43E1, forms conductive hemichannels when expressed in single Xenopus oocytes and intercellular channels in pairs of oocytes (Pfahnl, A., X.W. Zhou, R. Werner, and G. Dahl. 1997. Pflügers Arch. 433:733-779). We demonstrate that the polarity of Vj dependence of Cx32*Cx43E1 hemichannels in intercellular pairings is the same as that of wild-type Cx32 hemichannels and is reversed by the N2E substitution. In records of single intercellular channels, Vj dependence is characterized by gating transitions between fully open and subconductance levels. Comparable transitions are observed in Cx32*Cx43E1 conductive hemichannels at negative membrane potentials and the polarity of these transitions is reversed by the N2E substitution. We conclude that the mechanism of Vj dependence of intercellular channels is conserved in conductive hemichannels and term the process Vj gating. Heteromeric conductive hemichannels comprised of Cx32*Cx43E1 and Cx32N2E*Cx43E1 subunits display bipolar Vj gating, closing to substates at both positive and negative membrane potentials. The number of bipolar hemichannels observed in cells expressing mixtures of the two connexin subunits coincides with the number of hemichannels that are expected to contain a single oppositely charged subunit. We conclude that the movement of the voltage sensor in a single connexin subunit is sufficient to initiate Vj gating. We further suggest that Vj gating results from conformational changes in individual connexin subunits rather than by a concerted change in the conformation of all six subunits.     

Allosteric regulation of pentameric ligand-gated ion channels: An emerging mechanistic perspective

Pentameric ligand-gated ion channels (pLGICs) play a central role in intercellular communications in the nervous system by converting the binding of a chemical messenger—a neurotransmitter—into an ion flux through the postsynaptic membrane. They are oligomeric assemblies that provide prototypical examples of allosterically regulated integral membrane proteins. Here, we present an overview of the most recent advances on the signal transduction mechanism based on the X-ray structures of both prokaryotic and invertebrate eukaryotic pLGICs and on atomistic Molecular Dynamics simulations. The present results suggest that ion gating involves a large structural reorganization of the molecule mediated by two distinct quaternary transitions, a global twisting and the blooming of the extracellular domain, which can be modulated by ligand binding at the topographically distinct orthosteric and allosteric sites. The emerging model of gating is consistent with a wealth of functional studies and will boost the development of novel pharmacological strategies.     

The excitable fluid mosaic

The Fluid Mosaic Model by Singer & Nicolson proposes that biological membranes consist of a fluid lipid layer into which integral proteins are embedded. The lipid membrane acts as a two-dimensional liquid in which the proteins can diffuse and interact. Until today, this view seems very reasonable and is the predominant picture in the literature. However, there exist broad melting transitions in biomembranes some 10–20 degrees below physiological temperatures that reach up to body temperature. Since they are found below body temperature, Singer & Nicolson did not pay any further attention to the melting process. But this is a valid view only as long as nothing happens. The transition temperature can be influenced by membrane tension, pH, ionic strength and other variables. Therefore, it is not generally correct that the physiological temperature is above this transition. The control over the membrane state by changing the intensive variables renders the membrane as a whole excitable. One expects phase behavior and domain formation that leads to protein sorting and changes in membrane function. Thus, the lipids become an active ingredient of the biological membrane. The melting transition affects the elastic constants of the membrane. This allows for the generation of propagating pulses in nerves and the formation of ion-channel-like pores in the lipid membranes. Here we show that on top of the fluid mosaic concept there exists a wealth of excitable phenomena that go beyond the original picture of Singer & Nicolson.¹     

Rate of opening of a population of Na channels in frog skeletal muscle fibers

Linear Systems convolution analysis of muscle sodium currents was used to predict the opening rate of sodium channels as a function of time during voltage clamp pulses. If open sodium channel lifetimes are exponentially distributed, the channel opening rate corresponding to a sodium current obtained at any particular voltage, can be analytically obtained using a simple equation, given single channel information about the mean open-channel lifetime and current.Predictions of channel opening rate during voltage clamp pulses show that sodium channel inactivation arises coincident with a decline in channel opening rate.Sodium currents pharmacologically modified with Chloramine-T treatment so that they do not inactivate, show a predicted sustained channel opening rate.Large depolarizing voltage clamp pulses produce channel opening rate functions that resemble gating currents.The predicted channel opening rate functions are best described by kinetic models for Na channels which confer most of the charge movement to transitions between closed states.Comparisons of channel opening rate functions with gating currents suggests that there may be subtypes of Na channel with some contributing more charge movement per channel opening than others.Na channels open on average, only once during the transient period of Na activation and inactivation.After transiently opening during the activation period and then closing by entering the inactivated state, Na channels reopen if the voltage pulse is long enough and contribute to steady-state currents.The convolution model overestimates the opening rate of channels contributing to the steady-state currents that remain after the transient early Na current has subsided.     

Hydrophobic coupling of lipid bilayer energetics to channel function

The hydrophobic coupling between membrane-spanning proteins and the lipid bilayer core causes the bilayer thickness to vary locally as proteins and other "defects" are embedded in the bilayer. These bilayer deformations incur an energetic cost that, in principle, could couple membrane proteins to each other, causing them to associate in the plane of the membrane and thereby coupling them functionally. We demonstrate the existence of such bilayer-mediated coupling at the single-molecule level using single-barreled as well as double-barreled gramicidin channels in which two gramicidin subunits are covalently linked by a water-soluble, flexible linker. When a covalently attached pair of gramicidin subunits associates with a second attached pair to form a double-barreled channel, the lifetime of both channels in the assembly increases from hundreds of milliseconds to a hundred seconds--and the conductance of each channel in the side-by-side pair is almost 10% higher than the conductance of the corresponding single-barreled channels. The double-barreled channels are stabilized some 100,000-fold relative to their single-barreled counterparts. This stabilization arises from: first, the local increase in monomer concentration around a single-barreled channel formed by two covalently linked gramicidins, which increases the rate of double-barreled channel formation; and second, from the increased lifetime of the double-barreled channels. The latter result suggests that the two barrels of the construct associate laterally. The underlying cause for this lateral association most likely is the bilayer deformation energy associated with channel formation. More generally, the results suggest that the mechanical properties of the host bilayer may cause the kinetics of membrane protein conformational transitions to depend on the conformational states of the neighboring proteins.     

Stochastic Markovian modeling of electrophysiology of ion channels: reconstruction of standard deviations in macroscopic currents

Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We extend and study two different ion channel models: a simple model with only a single open and a closed state and a detailed model of the cardiac rapidly activating delayed rectifier potassium current. We demonstrate the efficacy of stochastic Galerkin methods for computing solutions to systems with random model parameters. Our studies illustrate the characteristic changes in distributions of state transitions and electrical currents through ion channels due to random rate coefficients. Furthermore, the studies indicate the applicability of the stochastic Galerkin technique for uncertainty and sensitivity analysis of bio-mathematical models.