Calcium regulation of single ryanodine receptor channel gating analyzed using HMM/MCMC statistical methods

Microscopic mechanism of PIEZO1 activation by pressure-induced membrane stretch

Mechanosensitive PIEZO1 ion channels open in response to membrane stretch. Yet, the underlying microscopic mechanism of this activation remains unknown. To probe this mechanism, we used cell-attached pressure-clamp recordings to measure single channel currents at different steady-state negative pipette pressures, spanning the full range of the channel's pressure sensitivity. Pressure-dependent activation occurs through a sharp reduction of the mean shut duration and through a moderate increase of the mean open duration. Across all tested pressures, the distribution of open and shut dwell times best follows sums of two and three exponential components, respectively. As the magnitude of the pressure stimulus increases, the time constants of most of these exponential components gradually change, in opposite directions for open and shut dwell times, and to a similar extent. In addition, while the relative amplitudes of fast and slow components remain unchanged for open intervals, they fully reverse for shut intervals, further reducing the mean shut duration. Using two-dimensional dwell time analysis, Markov-chain modeling, and simulations, we identified a minimal five-states model which recapitulates essential characteristics of single channel data, including microscopic reversibility, correlations between adjacent open and shut intervals, and asymmetric modulation of dwell times by pressure. This study identifies a microscopic mechanism for the activation of PIEZO1 channels by pressure-induced membrane stretch and deepens our fundamental understanding of mechanotransduction by a vertebrate member of the PIEZO channel family.

Recent progress in the structural study of ion channels as insecticide targets

Ion channels, many expressed in insect neural and muscular systems, have drawn huge attention as primary targets of insecticides. With the recent technical breakthroughs in structural biology, especially in cryo-electron microscopy (cryo-EM), many new high-resolution structures of ion channel targets, apo or in complex with insecticides, have been solved, shedding light on the molecular mechanism of action of the insecticides and resistance mutations. These structures also provide accurate templates for structure-based insecticide screening and rational design. This review summarizes the recent progress in the structural studies of 5 ion channel families: the ryanodine receptor (RyR), the nicotinic acetylcholine receptor (nAChR), the voltage-gated sodium channel (VGSC), the transient receptor potential (TRP) channel, and the ligand-gated chloride channel (LGCC). We address the selectivity of the channel-targeting insecticides by examining the conservation of key coordinating residues revealed by the structures. The possible resistance mechanisms are proposed based on the locations of the identified resistance mutations on the 3D structures of the target channels and their impacts on the binding of insecticides. Finally, we discuss how to develop "green" insecticides with a novel mode of action based on these high-resolution structures to overcome the resistance.

Conformational motions and ligand-binding underlying gating and regulation in IP3R channel

Inositol-1,4,5-trisphosphate receptors (IP3Rs) are activated by IP3 and Ca2+ and their gating is regulated by various intracellular messengers that finely tune the channel activity. Here, using single particle cryo-EM analysis we determined 3D structures of the nanodisc-reconstituted IP3R1 channel in two ligand-bound states. These structures provide unprecedented details governing binding of IP3, Ca2+ and ATP, revealing conformational changes that couple ligand-binding to channel opening. Using a deep-learning approach and 3D variability analysis we extracted molecular motions of the key protein domains from cryo-EM density data. We find that IP3 binding relies upon intrinsic flexibility of the ARM2 domain in the tetrameric channel. Our results highlight a key role of dynamic side chains in regulating gating behavior of IP3R channels. This work represents a stepping-stone to developing mechanistic understanding of conformational pathways underlying ligand-binding, activation and regulation of the channel.

Modeling calcium dynamics in neurons with endoplasmic reticulum: existence, uniqueness and an implicit-explicit finite element scheme

Like many other biological processes, calcium dynamics in neurons containing an endoplasmic reticulum is governed by diffusion-reaction equations on interface-separated domains. Interface conditions are typically described by systems of ordinary differential equations that provide fluxes across the interfaces. Using the calcium model as an example of this class of ODE-flux boundary interface problems, we prove the existence, uniqueness and boundedness of the solution by applying comparison theorem, fundamental solution of the parabolic operator and a strategy used in Picard's existence theorem. Then we propose and analyze an efficient implicit-explicit finite element scheme which is implicit for the parabolic operator and explicit for the nonlinear terms. We show that the stability does not depend on the spatial mesh size. Also the optimal convergence rate in H ¹ norm is obtained. Numerical experiments illustrate the theoretical results.

Ryanodine receptor as insecticide target

Ryanodine receptor (RyR) is one of the primary targets of commercial insecticides. The diamide insecticide family, including flubendiamide, chlorantraniliprole, cyantraniliprole, etc, targets insect RyRs and can be used to control a wide range of destructive agricultural pests. The diamide insecticides are highly selective against lepidopteran and coleopteran pests with relatively low toxicity for non-target species, such as mammals, fishes, and beneficial insects. However, recently mutations identified on insect RyRs have emerged and caused resistance in several major agricultural pests throughout different continents. This review paper summarizes the recent findings on structure and function of insect RyRs as insecticide target. Specifically, we examine the structures of RyRs from target and non-target species, which reveals the molecular basis for insecticide action and selectivity. We also examine the structural and functional changes of RyR caused by the resistance mutations. Finally, we examine the progress in RyR structure-based insecticide design, and discuss how this might help the development of new generation of green insecticides.

Ryanodine Receptor Open Times Are Determined in the Closed State

The ryanodine receptor (RyR) ion channel releases Ca²⁺ from intracellular stores by conducting Ca²⁺ but also by recruiting neighboring RyRs to open, as RyRs are activated by micromolar levels of cytosolic Ca²⁺. Using long single-RyR recordings of the cardiac isoform (RyR2), we conclude that Ca²⁺ binding to the cytosolic face of RyR while the channel is closed determines the distribution of open times. This mechanism explains previous findings that RyR is not activated by its own fluxed Ca²⁺. Our measurements also bolster previous findings that luminal [Ca²⁺] can affect both the cytosolic activation and inactivation sites and that RyR has different gating modes for the same ionic conditions.

Structure-function relationships of peptides forming the calcin family of ryanodine receptor ligands

Calcins are a novel family of scorpion peptides that bind with high affinity to ryanodine receptors (RyRs) and increase their activity by inducing subconductance states. Here, we provide a comprehensive analysis of the structure-function relationships of the eight calcins known to date, based on their primary sequence, three-dimensional modeling, and functional effects on skeletal RyRs (RyR1). Primary sequence alignment and evolutionary analysis show high similarity among all calcins (≥78.8% identity). Other common characteristics include an inhibitor cysteine knot (ICK) motif stabilized by three pairs of disulfide bridges and a dipole moment (DM) formed by positively charged residues clustering on one side of the molecule and neutral and negatively charged residues segregating on the opposite side. [(3)H]Ryanodine binding assays, used as an index of the open probability of RyRs, reveal that all eight calcins activate RyR1 dose-dependently with Kd values spanning approximately three orders of magnitude and in the following rank order: opicalcin1 > opicalcin2 > vejocalcin > hemicalcin > imperacalcin > hadrucalcin > maurocalcin >> urocalcin. All calcins significantly augment the bell-shaped [Ca(2+)]-[(3)H]ryanodine binding curve with variable effects on the affinity constants for Ca(2+) activation and inactivation. In single channel recordings, calcins induce the appearance of a subconductance state in RyR1 that has a unique fractional value (∼20% to ∼60% of the full conductance state) but bears no relationship to binding affinity, DM, or capacity to stimulate Ca(2+) release. Except for urocalcin, all calcins at 100 nM concentration stimulate Ca(2+) release and deplete Ca(2+) load from skeletal sarcoplasmic reticulum. The natural variation within the calcin family of peptides offers a diversified set of high-affinity ligands with the capacity to modulate RyRs with high dynamic range and potency.

Emergence of ion channel modal gating from independent subunit kinetics

Many ion channels exhibit a slow stochastic switching between distinct modes of gating activity. This feature of channel behavior has pronounced implications for the dynamics of ionic currents and the signaling pathways that they regulate. A canonical example is the inositol 1,4,5-trisphosphate receptor (IP3R) channel, whose regulation of intracellular Ca(2+) concentration is essential for numerous cellular processes. However, the underlying biophysical mechanisms that give rise to modal gating in this and most other channels remain unknown. Although ion channels are composed of protein subunits, previous mathematical models of modal gating are coarse grained at the level of whole-channel states, limiting further dialogue between theory and experiment. Here we propose an origin for modal gating, by modeling the kinetics of ligand binding and conformational change in the IP3R at the subunit level. We find good agreement with experimental data over a wide range of ligand concentrations, accounting for equilibrium channel properties, transient responses to changing ligand conditions, and modal gating statistics. We show how this can be understood within a simple analytical framework and confirm our results with stochastic simulations. The model assumes that channel subunits are independent, demonstrating that cooperative binding or concerted conformational changes are not required for modal gating. Moreover, the model embodies a generally applicable principle: If a timescale separation exists in the kinetics of individual subunits, then modal gating can arise as an emergent property of channel behavior.

Markov chain Monte Carlo based analysis of post-translationally modified VDAC gating kinetics

The voltage-dependent anion channel (VDAC) is the main conduit for permeation of solutes (including nucleotides and metabolites) of up to 5 kDa across the mitochondrial outer membrane (MOM). Recent studies suggest that VDAC activity is regulated via post-translational modifications (PTMs). Yet the nature and effect of these modifications is not understood. Herein, single channel currents of wild-type, nitrosated, and phosphorylated VDAC are analyzed using a generalized continuous-time Markov chain Monte Carlo (MCMC) method. This developed method describes three distinct conducting states (open, half-open, and closed) of VDAC activity. Lipid bilayer experiments are also performed to record single VDAC activity under un-phosphorylated and phosphorylated conditions, and are analyzed using the developed stochastic search method. Experimental data show significant alteration in VDAC gating kinetics and conductance as a result of PTMs. The effect of PTMs on VDAC kinetics is captured in the parameters associated with the identified Markov model. Stationary distributions of the Markov model suggest that nitrosation of VDAC not only decreased its conductance but also significantly locked VDAC in a closed state. On the other hand, stationary distributions of the model associated with un-phosphorylated and phosphorylated VDAC suggest a reversal in channel conformation from relatively closed state to an open state. Model analyses of the nitrosated data suggest that faster reaction of nitric oxide with Cys-127 thiol group might be responsible for the biphasic effect of nitric oxide on basal VDAC conductance.

Statistical analysis of modal gating in ion channels

Ion channels regulate the concentrations of ions within cells. By stochastically opening and closing its pore, they enable or prevent ions from crossing the cell membrane. However, rather than opening with a constant probability, many ion channels switch between several different levels of activity even if the experimental conditions are unchanged. This phenomenon is known as modal gating: instead of directly adapting its activity, the channel seems to mix sojourns in active and inactive modes in order to exhibit intermediate open probabilities. Evidence is accumulating that modal gating rather than modulation of opening and closing at a faster time scale is the primary regulatory mechanism of ion channels. However, currently, no method is available for reliably calculating sojourns in different modes. In order to address this challenge, we develop a statistical framework for segmenting single-channel datasets into segments that are characteristic for particular modes. The algorithm finds the number of mode changes, detects their locations and infers the open probabilities of the modes. We apply our approach to data from the inositol-trisphosphate receptor. Based upon these results, we propose that mode changes originate from alternative conformational states of the channel protein that determine a certain level of channel activity.

Eudistomin D and penaresin derivatives as modulators of ryanodine receptor channels and sarcoplasmic reticulum Ca2+ ATPase in striated muscle

Eudistomin D (EuD) and penaresin (Pen) derivatives are bioactive alkaloids from marine sponges found to induce Ca(2+) release from striated muscle sarcoplasmic reticulum (SR). Although these alkaloids are believed to affect ryanodine receptor (RyR) gating in a "caffeine-like" manner, no single-channel study confirmed this assumption. Here, EuD and MBED (9-methyl-7-bromoeudistomin D) were contrasted against caffeine on their ability to modulate the SR Ca(2+) loading/leak from cardiac and skeletal muscle SR microsomes as well as the function of RyRs in planar bilayers. The effects of these alkaloids on [(3)H]ryanodine binding and SR Ca(2+) ATPase (SERCA) activity were also tested. MBED (1-5 μM) fully mimicked maximal activating effects of caffeine (20 mM) on SR Ca(2+) leak. At the single-channel level, MBED mimicked the agonistic action of caffeine on cardiac RyR gating (i.e., stabilized long openings characteristic of "high-open-probability" mode). EuD was a partial agonist at the maximal doses tested. The tested Pen derivatives displayed mild to no agonism on RyRs, SR Ca(2+) leak, or [(3)H]ryanodine binding studies. Unlike caffeine, EuD and some Pen derivatives significantly inhibited SERCA at concentrations required to modulate RyRs. Instead, MBED's affinity for RyRs (EC50 ∼ 0.5 μM) was much larger than for SERCA (IC50 > 285 μM). In conclusion, MBED is a potent RyR agonist and, potentially, a better choice than caffeine for microsomal and cell studies due to its reported lack of effects on adenosine receptors and phosphodiesterases. As a high-affinity caffeine-like probe, MBED could also help identify the caffeine-binding site in RyRs.

Bayesian approaches for mechanistic ion channel modeling

We consider the Bayesian analysis of mechanistic models describing the dynamic behavior of ligand-gated ion channels. The opening of the transmembrane pore in an ion channel is brought about by conformational changes in the protein, which results in a flow of ions through the pore. Remarkably, given the diameter of the pore, the flow of ions from a small number of channels or indeed from a single ion channel molecule can be recorded experimentally. This produces a large time-series of high-resolution experimental data, which can be used to investigate the gating process of these channels. We give a brief overview of the achievements and limitations of alternative maximum-likelihood approaches to this type of modeling, before investigating the statistical issues associated with analyzing stochastic model reaction mechanisms from a Bayesian perspective. Finally, we compare a number of Markov chain Monte Carlo algorithms that may be used to tackle this challenging inference problem.

A mechanistic description of gating of the human cardiac ryanodine receptor in a regulated minimal environment

Cardiac muscle contraction, triggered by the action potential, is mediated by the release of Ca²⁺ from the sarcoplasmic reticulum through ryanodine receptor (RyR)2 channels. In situ, RyR2 gating is modulated by numerous physiological and pharmacological agents, and altered RyR2 function underlies the occurrence of arrhythmias in both inherited and acquired diseases. To understand fully the mechanisms underpinning the regulation of RyR2 in the normal heart and how these systems are altered in pathological conditions, we must first gain a detailed knowledge of the fundamental processes of RyR2 gating. In this investigation, we provide key novel mechanistic insights into the physical reality of RyR2 gating revealed by new experimental and analytical approaches. We have examined in detail the single-channel gating kinetics of the purified human RyR2 when activated by cytosolic Ca²⁺ in a stringently regulated environment where the modulatory influence of factors external to the channel were minimized. The resulting gating schemes are based on an accurate description of single-channel kinetics using hidden Markov model analysis and reveal several novel aspects of RyR2 gating behavior: (a) constitutive gating is observed as unliganded opening events; (b) binding of Ca²⁺ to the channel stabilizes it in different open states; (c) RyR2 exists in two preopening closed conformations in equilibrium, one of which binds Ca²⁺ more readily than the other; (d) the gating of RyR2 when bound to Ca²⁺ can be described by a kinetic scheme incorporating bursts; and (e) analysis of flicker closing events within bursts reveals gating activity that is not influenced by ligand binding. The gating schemes generated in this investigation provide a framework for future studies in which the mechanisms of action of key physiological regulatory factors, disease-linked mutations, and potential therapeutic compounds can be described precisely.

Coupled gating of skeletal muscle ryanodine receptors is modulated by Ca2+, Mg2+, and ATP

Coupled gating (synchronous openings and closures) of groups of skeletal muscle ryanodine receptors (RyR1), which mimics RyR1-mediated Ca(2+) release underlying Ca(2+) sparks, was first described by Marx et al. (Marx SO, Ondrias K, Marks AR. Science 281: 818-821, 1998). The nature of the RyR1-RyR1 interactions for coupled gating still needs to be characterized. Consequently, we defined planar lipid bilayer conditions where ∼25% of multichannel reconstitutions contain mixtures of coupled and independently gating RyR1. In ∼10% of the cases, all RyRs (2-10 channels; most frequently 3-4) gated in coupled fashion, allowing for quantification. Our results indicated that coupling required cytosolic solutions containing ATP/Mg(2+) and high (50 mM) luminal Ca(2+) (Ca(lum)) or Sr(2+) solutions. Bursts of coupled activity (events) started and ended abruptly, with all channels activating/deactivating within ∼300 μs. Coupled RyR1 were heterogeneous, where highly active RyR1 ("drivers") seemed open during the entire coupled event (P(o) = 1), while other RyR1s ("followers") displayed abundant flickering and smaller amplitude. Drivers mean open time increased with cytosolic Ca(2+) (Ca(cyt)) or caffeine, whereas followers flicker frequency was Ca(cyt) independent and more sensitive to inhibition by cytosolic Mg(2+). Coupled events were insensitive to varying lumen-to-cytosol Ca(2+) fluxes from ∼1 to 8 pA, which does not corroborate coupling of neighboring RyR1 by local Ca(2+)-induced Ca(2+) release. However, coupling requires specific Ca(lum) sites, as it was lost when Ca(lum) was replaced by luminal Ba(2+) or Mg(2+). In summary, coupled events reveal complex interactions among heterogeneous RyR1, differentially modulated by cytosolic ATP/Mg(2+), Ca(cyt), and Ca(lum,) which under cell-like ionic conditions may parallel synchronous RyR1 gating during Ca(2+) sparks.

Modulation of cardiac ryanodine receptor channels by alkaline earth cations

Cardiac ryanodine receptor (RyR2) function is modulated by Ca(2+) and Mg(2+). To better characterize Ca(2+) and Mg(2+) binding sites involved in RyR2 regulation, the effects of cytosolic and luminal earth alkaline divalent cations (M(2+): Mg(2+), Ca(2+), Sr(2+), Ba(2+)) were studied on RyR2 from pig ventricle reconstituted in bilayers. RyR2 were activated by M(2+) binding to high affinity activating sites at the cytosolic channel surface, specific for Ca(2+) or Sr(2+). This activation was interfered by Mg(2+) and Ba(2+) acting at low affinity M(2+)-unspecific binding sites. When testing the effects of luminal M(2+) as current carriers, all M(2+) increased maximal RyR2 open probability (compared to Cs(+)), suggesting the existence of low affinity activating M(2+)-unspecific sites at the luminal surface. Responses to M(2+) vary from channel to channel (heterogeneity). However, with luminal Ba(2+)or Mg(2+), RyR2 were less sensitive to cytosolic Ca(2+) and caffeine-mediated activation, openings were shorter and voltage-dependence was more marked (compared to RyR2 with luminal Ca(2+)or Sr(2+)). Kinetics of RyR2 with mixtures of luminal Ba(2+)/Ca(2+) and additive action of luminal plus cytosolic Ba(2+) or Mg(2+) suggest luminal M(2+) differentially act on luminal sites rather than accessing cytosolic sites through the pore. This suggests the presence of additional luminal activating Ca(2+)/Sr(2+)-specific sites, which stabilize high P(o) mode (less voltage-dependent) and increase RyR2 sensitivity to cytosolic Ca(2+) activation. In summary, RyR2 luminal and cytosolic surfaces have at least two sets of M(2+) binding sites (specific for Ca(2+) and unspecific for Ca(2+)/Mg(2+)) that dynamically modulate channel activity and gating status, depending on SR voltage.

MCMC estimation of Markov models for ion channels

Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data. In this article, different approaches for the MCMC sampling of Markov models are combined. This method, new to our knowledge, detects overparameterizations and gives more accurate results than existing MCMC methods. It shows similar performance as QuB-MIL, which indicates that it also compares well with maximum likelihood estimators. Data collected from an inositol trisphosphate receptor is used to demonstrate how the best model for a given data set can be found in practice.

Luminal Ca(2+) content regulates intracellular Ca(2+) release in subepicardial myocytes of intact beating mouse hearts: effect of exogenous buffers

Ca(+)-induced Ca(2+) release tightly controls the function of ventricular cardiac myocytes under normal and pathological conditions. Two major factors contributing to the regulation of Ca(2+) release are the cytosolic free Ca(2+) concentration and sarcoplasmic reticulum (SR) Ca(2+) content. We hypothesized that the amount of Ca(2+) released from the SR during each heart beat strongly defines the refractoriness of Ca(2+) release. To test this hypothesis, EGTA AM, a high-affinity, slow-association rate Ca(2+) chelator, was used as a tool to modify luminal SR Ca(2+) content. An analysis of the cytosolic and luminal SR Ca(2+) dynamics recorded from the epicardial layer of intact mouse hearts indicated that the presence of EGTA reduced the diastolic SR free Ca(2+) concentration and fraction of SR Ca(2+) depletion during each beat. In addition, this maneuver shortened the refractory period and accelerated the restitution of Ca(2+) release. As a consequence of the accelerated restitution, the frequency dependence of Ca(2+) alternans was significantly shifted toward higher heart rates, suggesting a role of luminal SR Ca(2+) in the genesis of this highly arrhythmogenic phenomenon. Thus, intra-SR Ca(2+) dynamics set the refractoriness and frequency dependence of Ca(2+) transients in subepicardial ventricular myocytes.

Ryanodine receptor luminal Ca2+ regulation: swapping calsequestrin and channel isoforms

Sarcoplasmic reticulum (SR) Ca(2+) release in striated muscle is mediated by a multiprotein complex that includes the ryanodine receptor (RyR) Ca(2+) channel and the intra-SR Ca(2+) buffering protein calsequestrin (CSQ). Besides its buffering role, CSQ is thought to regulate RyR channel function. Here, CSQ-dependent luminal Ca(2+) regulation of skeletal (RyR1) and cardiac (RyR2) channels is explored. Skeletal (CSQ1) or cardiac (CSQ2) calsequestrin were systematically added to the luminal side of single RyR1 or RyR2 channels. The luminal Ca(2+) dependence of open probability (Po) over the physiologically relevant range (0.05-1 mM Ca(2+)) was defined for each of the four RyR/CSQ isoform pairings. We found that the luminal Ca(2+) sensitivity of single RyR2 channels was substantial when either CSQ isoform was present. In contrast, no significant luminal Ca(2+) sensitivity of single RyR1 channels was detected in the presence of either CSQ isoform. We conclude that CSQ-dependent luminal Ca(2+) regulation of single RyR2 channels lacks CSQ isoform specificity, and that CSQ-dependent luminal Ca(2+) regulation in skeletal muscle likely plays a relatively minor (if any) role in regulating the RyR1 channel activity, indicating that the chief role of CSQ1 in this tissue is as an intra-SR Ca(2+) buffer.

Inositol trisphosphate receptor and ion channel models based on single-channel data

The inositol trisphosphate receptor (IPR) plays an important role in controlling the dynamics of intracellular Ca(2+). Single-channel patch-clamp recordings are a typical way to study these receptors as well as other ion channels. Methods for analyzing and using this type of data have been developed to fit Markov models of the receptor. The usual method of parameter fitting is based on maximum-likelihood techniques. However, Bayesian inference and Markov chain Monte Carlo techniques are becoming more popular. We describe the application of the Bayesian methods to real experimental single-channel data in three ion channels: the ryanodine receptor, the K(+) channel, and the IPR. One of the main aims of all three studies was that of model selection with different approaches taken. We also discuss the modeling implications for single-channel data that display different levels of channel activity within one recording.

Mining, modeling, and evaluation of subnetworks from large biomolecular networks and its comparison study

In this paper, we present a novel method to mine, model, and evaluate a regulatory system executing cellular functions that can be represented as a biomolecular network. Our method consists of two steps. First, a novel scale-free network clustering approach is applied to such a biomolecular network to obtain various subnetworks. Second, computational models are generated for the subnetworks and simulated to predict their behavior in the cellular context. We discuss and evaluate some of the advanced computational modeling approaches, in particular, state-space modeling, probabilistic Boolean network modeling, and fuzzy logic modeling. The modeling and simulation results represent hypotheses that are tested against high-throughput biological datasets (microarrays and/or genetic screens) under normal and perturbation conditions. Experimental results on time-series gene expression data for the human cell cycle indicate that our approach is promising for subnetwork mining and simulation from large biomolecular networks.

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

In many cell types, the inositol trisphosphate receptor (IPR) is one of the important components that control intracellular calcium dynamics, and an understanding of this receptor (which is also a calcium channel) is necessary for an understanding of calcium oscillations and waves. Recent advances in experimental techniques now allow for the measurement of single-channel activity of the IPR in conditions similar to its native environment, and these data can be used to determine the rate constants in Markov models of the IPR. We illustrate a parameter estimation method based on Markov chain Monte Carlo, which can be used to fit directly to single-channel data, and determining, as an intrinsic part of the fit, the times at which the IPR is opening and closing. We show, using simulated data, the most complex Markov model that can be unambiguously determined from steady-state data and show that non-steady-state data is required to determine more complex models.

Mode switching is the major mechanism of ligand regulation of InsP3 receptor calcium release channels

The inositol 1,4,5-trisphosphate (InsP₃) receptor (InsP₃R) plays a critical role in generation of complex Ca²⁺ signals in many cell types. In patch clamp recordings of isolated nuclei from insect Sf9 cells, InsP₃R channels were consistently detected with regulation by cytoplasmic InsP₃ and free Ca²⁺ concentrations ([Ca²⁺]_i) very similar to that observed for vertebrate InsP₃R. Long channel activity durations of the Sf9-InsP₃R have now enabled identification of a novel aspect of InsP₃R gating: modal gating. Using a novel algorithm to analyze channel modal gating kinetics, InsP₃R gating can be separated into three distinct modes: a low activity mode, a fast kinetic mode, and a burst mode with channel open probability (P_o) within each mode of 0.007 ± 0.002, 0.24 ± 0.03, and 0.85 ± 0.02, respectively. Channels reside in each mode for long periods (tens of opening and closing events), and transitions between modes can be discerned with high resolution (within two channel opening and closing events). Remarkably, regulation of channel gating by [Ca²⁺]_i and [InsP₃] does not substantially alter channel P_o within a mode. Instead, [Ca²⁺]_i and [InsP₃] affect overall channel P_o primarily by changing the relative probability of the channel being in each mode, especially the high and low P_o modes. This novel observation therefore reveals modal switching as the major mechanism of physiological regulation of InsP₃R channel activity, with implications for the kinetics of Ca²⁺ release events in cells.

Mining and state-space modeling and verification of sub-networks from large-scale biomolecular networks

Background

Biomolecular networks dynamically respond to stimuli and implement cellular function. Understanding these dynamic changes is the key challenge for cell biologists. As biomolecular networks grow in size and complexity, the model of a biomolecular network must become more rigorous to keep track of all the components and their interactions. In general this presents the need for computer simulation to manipulate and understand the biomolecular network model.

Results

In this paper, we present a novel method to model the regulatory system which executes a cellular function and can be represented as a biomolecular network. Our method consists of two steps. First, a novel scale-free network clustering approach is applied to the large-scale biomolecular network to obtain various sub-networks. Second, a state-space model is generated for the sub-networks and simulated to predict their behavior in the cellular context. The modeling results represent hypotheses that are tested against high-throughput data sets (microarrays and/or genetic screens) for both the natural system and perturbations. Notably, the dynamic modeling component of this method depends on the automated network structure generation of the first component and the sub-network clustering, which are both essential to make the solution tractable.

Conclusion

Experimental results on time series gene expression data for the human cell cycle indicate our approach is promising for sub-network mining and simulation from large-scale biomolecular network.

Calcium activation of ryanodine receptor channels--reconciling RyR gating models with tetrameric channel structure

Despite its importance and abundance of experimental data, the molecular mechanism of RyR2 activation by calcium is poorly understood. Recent experimental studies involving coexpression of wild-type (WT) RyR2 together with a RyR2 mutant deficient in calcium-dependent activation (Li, P., and S.R. Chen. 2001. J. Gen. Physiol. 118:33–44) revealed large variations of calcium sensitivity of the RyR tetramers with their monomer composition. Together with previous results on kinetics of Ca activation (Zahradníková, A., I. Zahradník, I. Györke, and S. Györke. 1999. J. Gen. Physiol. 114:787–798), these data represent benchmarks for construction and testing of RyR models that would reproduce RyR behavior and be structurally realistic as well. Here we present a theoretical study of the effects of RyR monomer substitution by a calcium-insensitive mutant on the calcium dependence of RyR activation. Three published models of tetrameric RyR channels were used either directly or after adaptation to provide allosteric regulation. Additionally, two alternative RyR models with Ca binding sites created jointly by the monomers were developed. The models were modified for description of channels composed of WT and mutant monomers. The parameters of the models were optimized to provide the best approximation of published experimental data. For reproducing the observed calcium dependence of RyR tetramers containing mutant monomers (a) single, independent Ca binding sites on each monomer were preferable to shared binding sites; (b) allosteric models were preferable to linear models; (c) in the WT channel, probability of opening to states containing a Ca²⁺-free monomer had to be extremely low; and (d) models with fully Ca-bound closed states, additional to those of an Monod-Wyman-Changeaux model, were preferable to models without such states. These results provide support for the concept that RyR activation is possible (albeit vanishingly small in WT channels) in the absence of Ca²⁺ binding. They also suggest further avenues toward understanding RyR gating.

Analysis of macroscopic ionic currents mediated by GABArho1 receptors during lanthanide modulation predicts novel states controlling channel gating

Lanthanide-induced modulation of GABA(C) receptors expressed in Xenopus oocytes was studied. We obtained two-electrode voltage-clamp recordings of ionic currents mediated by recombinant homomeric GABArho(1) receptors and performed numerical simulations of kinetic models of the macroscopic ionic currents.GABA-evoked chloride currents were potentiated by La(3+), Lu(3+) and Gd(3+) in the micromolar range. Lanthanide effects were rapid, reversible and voltage independent. The degree of potentiation was reduced by increasing GABA concentration.Lu(3+) also induced receptor desensitization and decreased the deactivation rate of GABArho(1) currents. In the presence of 300 microM Lu(3+), dose-response curves for GABA-evoked currents showed a significant enhancement of the maximum amplitude and an increase of the apparent affinity. The rate of onset of TPMPA and picrotoxin antagonism of GABArho(1) receptors was modulated by Lu(3+). These results suggest that the potentiation of the anionic current was the result of a direct lanthanide-receptor interaction at a site capable of allosterically modulating channel properties. Based on kinetic schemes, which included a second open state and a nonconducting desensitized state that closely reproduced the experimental results, two nonexclusive probable models of GABArho(1) channels gating are proposed.

Phthalic acid diamides activate ryanodine-sensitive Ca2+ release channels in insects

Flubendiamide represents a novel chemical family of substituted phthalic acid diamides with potent insecticidal activity. So far, the molecular target and the mechanism of action were not known. Here we present for the first time evidence that phthalic acid diamides activate ryanodine-sensitive intracellular calcium release channels (ryanodine receptors, RyR) in insects. With Ca(2+) measurements, we showed that flubendiamide and related compounds induced ryanodine-sensitive cytosolic calcium transients that were independent of the extracellular calcium concentration in isolated neurons from the pest insect Heliothis virescens as well as in transfected CHO cells expressing the ryanodine receptor from Drosophila melanogaster. Binding studies on microsomal membranes from Heliothis flight muscles revealed that flubendiamide and related compounds interacted with a site distinct from the ryanodine binding site and disrupted the calcium regulation of ryanodine binding by an allosteric mechanism. This novel insecticide mode of action seems to be restricted to specific RyR subtypes because the phthalic acid diamides reported here had almost no effect on mammalian type 1 ryanodine receptors.

Using independent open-to-closed transitions to simplify aggregated Markov models of ion channel gating kinetics

Deducing plausible reaction schemes from single-channel current traces is time-consuming and difficult. The goal is to find the simplest scheme that fits the data, but there are many ways to connect even a small number of states (>2 million schemes with four open and four closed states). Many schemes make identical predictions. An exhaustive search over model space does not address the many equivalent schemes that will result. We have found a canonical form that can express all reaction schemes for binary channels. This form has the minimal number of rate constants for any rank (number of independent open-closed transitions), unlike other canonical forms such as the well established "uncoupled" scheme. Because all of the interconductance transitions in the new form are independent, we refer to it as the manifest interconductance rank (MIR) form. In the case of four open and four closed states, there are four MIR form schemes, corresponding to ranks 1-4. For many models proposed in the literature for specific ion channels, the equivalent MIR form has dramatically fewer links than the uncoupled form. By using the MIR form we prove that all rank 1 topologies with a given number of open and closed states make identical predictions in steady state, thus narrowing the search space for simple models. Moreover, we prove that fitting to canonical form preserves detailed balance. We also propose an efficient hierarchical algorithm for searching for the simplest possible model consistent with a given data set.