Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors

In cardiac muscle, release of activator calcium from the sarcoplasmic reticulum occurs by calcium- induced calcium release through ryanodine receptors (RyRs), which are clustered in a dense, regular, two-dimensional lattice array at the diad junction. We simulated numerically the stochastic dynamics of RyRs and L-type sarcolemmal calcium channels interacting via calcium nano-domains in the junctional cleft. Four putative RyR gating schemes based on single-channel measurements in lipid bilayers all failed to give stable excitation-contraction coupling, due either to insufficiently strong inactivation to terminate locally regenerative calcium-induced calcium release or insufficient cooperativity to discriminate against RyR activation by background calcium. If the ryanodine receptor was represented, instead, by a phenomenological four-state gating scheme, with channel opening resulting from simultaneous binding of two Ca2+ ions, and either calcium-dependent or activation-linked inactivation, the simulations gave a good semiquantitative accounting for the macroscopic features of excitation-contraction coupling. It was possible to restore stability to a model based on a bilayer-derived gating scheme, by introducing allosteric interactions between nearest-neighbor RyRs so as to stabilize the inactivated state and produce cooperativity among calcium binding sites on different RyRs. Such allosteric coupling between RyRs may be a function of the foot process and lattice array, explaining their conservation during evolution.     

Torque and switching in the bacterial flagellar motor. An electrostatic model.

A model is presented for the rotary motor that drives bacterial flagella, using the electrochemical gradient of protons across the cytoplasmic membrane. The model unifies several concepts present in previous models. Torque is generated by proton-conducting particles around the perimeter of the rotor at the base of the flagellum. Protons in channels formed by these particles interact electrostatically with tilted lines of charges on the rotor, providing "loose coupling" between proton flux and rotation of the flagellum. Computer simulations of the model correctly predict the experimentally observed dynamic properties of the motor. Unlike previous models, the motor presented here may rotate either way for a given direction of the protonmotive force. The direction of rotation only depends on the level of occupancy of the proton channels. This suggests a novel and simple mechanism for the switching between clockwise and counterclockwise rotation that is the basis of bacterial chemotaxis.     

Myxococcus xanthus Gliding Motors Are Elastically Coupled to the Substrate as Predicted by the Focal Adhesion Model of Gliding Motility

Myxococcus xanthus is a model organism for studying bacterial social behaviors due to its ability to form complex multi-cellular structures. Knowledge of M. xanthus surface gliding motility and the mechanisms that coordinated it are critically important to our understanding of collective cell behaviors. Although the mechanism of gliding motility is still under investigation, recent experiments suggest that there are two possible mechanisms underlying force production for cell motility: the focal adhesion mechanism and the helical rotor mechanism, which differ in the biophysics of the cell–substrate interactions. Whereas the focal adhesion model predicts an elastic coupling, the helical rotor model predicts a viscous coupling. Using a combination of computational modeling, imaging, and force microscopy, we find evidence for elastic coupling in support of the focal adhesion model. Using a biophysical model of the M. xanthus cell, we investigated how the mechanical interactions between cells are affected by interactions with the substrate. Comparison of modeling results with experimental data for cell-cell collision events pointed to a strong, elastic attachment between the cell and substrate. These results are robust to variations in the mechanical and geometrical parameters of the model. We then directly measured the motor-substrate coupling by monitoring the motion of optically trapped beads and find that motor velocity decreases exponentially with opposing load. At high loads, motor velocity approaches zero velocity asymptotically and motors remain bound to beads indicating a strong, elastic attachment.     

Second-chance signal transduction explains cooperative flagellar switching

The reversal of flagellar motion (switching) results from the interaction between a switch complex of the flagellar rotor and a torque-generating stationary unit, or stator (motor unit). To explain the steeply cooperative ligand-induced switching, present models propose allosteric interactions between subunits of the rotor, but do not address the possibility of a reaction that stimulates a bidirectional motor unit to reverse direction of torque. During flagellar motion, the binding of a ligand-bound switch complex at the dwell site could excite a motor unit. The probability that another switch complex of the rotor, moving according to steady-state rotation, will reach the same dwell site before that motor unit returns to ground state will be determined by the independent decay rate of the excited-state motor unit. Here, we derive an analytical expression for the energy coupling between a switch complex and a motor unit of the stator complex of a flagellum, and demonstrate that this model accounts for the cooperative switching response without the need for allosteric interactions. The analytical result can be reproduced by simulation when (1) the motion of the rotor delivers a subsequent ligand-bound switch to the excited motor unit, thereby providing the excited motor unit with a second chance to remain excited, and (2) the outputs from multiple independent motor units are constrained to a single all-or-none event. In this proposed model, a motor unit and switch complex represent the components of a mathematically defined signal transduction mechanism in which energy coupling is driven by steady-state and is regulated by stochastic ligand binding. Mathematical derivation of the model shows the analytical function to be a general form of the Hill equation (Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40: iv-vii).     

Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

A statistical mechanical model for voltage-gated ion channels in cell membranes is proposed using the transfer matrix method. Equilibrium behavior of the system is studied. Representing the distribution of channels over the cellular membrane on a one-dimensional array with each channel having two states (open and closed) and incorporating channel–channel cooperative interactions, we calculate the fraction of channels in the open state at equilibrium. Experimental data obtained from batrachotoxin-modified sodium channels in the squid giant axon, using the cut-open axon technique, is best fit by the model when there is no interaction between the channels.     

Dynamic interreceptor coupling: a novel working mechanism of two-dimensional ryanodine receptor array

Ryanodine receptors (RyRs) usually form two-dimensional regular array in sarcoplasmic reticulum membranes in muscle cells. The inter-RyRs coupling may be essential for the maintenance of quiescent Ca2+ release in resting state, as well as for the coordinated activation and rapid termination of RyR-mediated Ca2+ release during excitation-contraction coupling. In our previous work, we have reported that the inter-RyRs interaction is modulated by RyR channel's functional state, which inspired us to propose a novel working mechanism of RyR array: "dynamic inter-RyR coupling". In this work, we built a simple model based on cellular automata and the Monte-Carlo method to quantitatively investigate the roles of intermolecular coupling and its modulation in regulating the signaling capabilities of RyR array. Our simulation results showed that with a suitable inter-RyR coupling strength, the combination of rest stability and high response efficiency, namely optimal signal/noise ratio, of Ca2+ signaling could be achieved. Moreover, we also found the continued coupling between open RyRs would delay the system termination rate. The coacquisition of robust termination of array opening relied on the proper decrease of coupling strength between activated RyRs. Obviously, such temporally asymmetric coupling would simultaneously endow the system with physiologically relevant resting stability and fast termination.     

Novel nucleotide-binding sites in ATP-sensitive potassium channels formed at gating interfaces

The coupling of cell metabolism to membrane electrical activity is a vital process that regulates insulin secretion, cardiac and neuronal excitability and the responses of cells to ischemia. ATP-sensitive potassium channels (K(ATP); Kir6.x) are a major part of this metabolic-electrical coupling system and translate metabolic signals such as the ATP:ADP ratio to changes in the open or closed state (gate) of the channel. The localization of the nucleotide-binding site (NBS) on Kir6.x channels and how nucleotide binding gates these K(ATP) channels remain unclear. Here, we use fluorescent nucleotide binding to purified Kir6.x proteins to define the peptide segments forming the NBS on Kir6.x channels and show that unique N- and C-terminal interactions from adjacent subunits are required for high-affinity nucleotide binding. The short N- and C-terminal segments comprising the novel intermolecular NBS are next to helices that likely move with channel opening/closing, suggesting a lock-and-key model for ligand gating.     

Interactions between dihydropyridine receptors and ryanodine receptors in striated muscle

Excitation-contraction coupling in both skeletal and cardiac muscle depends on structural and functional interactions between the voltage-sensing dihydropyridine receptor L-type Ca²⁺ channels in the surface/transverse tubular membrane and ryanodine receptor Ca²⁺ release channels in the sarcoplasmic reticulum membrane. The channels are targeted to either side of a narrow junctional gap that separates the external and internal membrane systems and are arranged so that bi-directional structural and functional coupling can occur between the proteins. There is strong evidence for a physical interaction between the two types of channel protein in skeletal muscle. This evidence is derived from studies of excitation–contraction coupling in intact myocytes and from experiments in isolated systems where fragments of the dihydropyridine receptor can bind to the ryanodine receptors in sarcoplasmic reticulum vesicles or in lipid bilayers and alter channel activity. Although micro-regions that participate in the functional interactions have been identified in each protein, the role of these regions and the molecular nature of the protein–protein interaction remain unknown. The trigger for Ca²⁺ release through ryanodine receptors in cardiac muscle is a Ca²⁺ influx through the L-type Ca²⁺ channel. The Ca²⁺ entering through the surface membrane Ca²⁺ channels flows directly onto underlying ryanodine receptors and activates the channels. This was thought to be a relatively simple system compared with that in skeletal muscle. However, complexities are emerging and evidence has now been obtained for a bi-directional physical coupling between the proteins in cardiac as well as skeletal muscle. The molecular nature of this coupling remains to be elucidated.     

Regulation of Sodium and Calcium Channels by Signaling Complexes

Membrane depolarization and intracellular calcium transients generated by activation of voltage-gated sodium and calcium channels are local signals, which initiate physiological processes such as action potential conduction, synaptic transmission, and excitation-contraction coupling. Targeting of effector proteins and regulatory proteins to ion channels is an important mechanism to ensure speed, specificity, and precise regulation of signaling events in response to local stimuli. In this article, we review recent experimental results showing that sodium and calcium channels form local signaling complexes, in which effector proteins, anchoring proteins, and regulatory proteins interact directly with ion channels. The intracellular domains of these channels serve as signaling platforms, mediating their participation in intracellular signaling processes. These protein-protein interactions are important for efficient synaptic transmission and for regulation of ion channels by neurotransmitters and intracellular second messengers. These localized signaling complexes are essential for normal function and regulation of electrical excitability, synaptic transmission, and excitation-contraction coupling.     

Regulation of sodium and calcium channels by signaling complexes

Membrane depolarization and intracellular calcium transients generated by activation of voltage-gated sodium and calcium channels are local signals, which initiate physiological processes such as action potential conduction, synaptic transmission, and excitation-contraction coupling. Targeting of effector proteins and regulatory proteins to ion channels is an important mechanism to ensure speed, specificity, and precise regulation of signaling events in response to local stimuli. In this article, we review recent experimental results showing that sodium and calcium channels form local signaling complexes, in which effector proteins, anchoring proteins, and regulatory proteins interact directly with ion channels. The intracellular domains of these channels serve as signaling platforms, mediating their participation in intracellular signaling processes. These protein-protein interactions are important for efficient synaptic transmission and for regulation of ion channels by neurotransmitters and intracellular second messengers. These localized signaling complexes are essential for normal function and regulation of electrical excitability, synaptic transmission, and excitation-contraction coupling.     

Transportsomes and channelsomes: are they functional units for physiological responses?

Channels and transporters play essential biological roles primarily through the transportation of ions and small molecules that are required to maintain cellular activities across the biomembrane. Secondary to transportation, channels and transporters also integrate and coordinate biological functions at different levels, ranging from the subcellular (nm) to multicellular (μm) scales. This is underpinned by efficient functional coupling within molecular assemblies of channels, transporters, proteins, small molecules, and lipids. Molecular interactions create local microenvironments that, in some cases, uniquely modify the functional properties of the channels and transporters. These molecular assemblies built around a transporter or channel (“transportsomes” and “channelsomes”) can be considered as physiological functional units. In this special issue, we provide an overview of recent progress in our understanding of protein-protein and molecular interactions in transportsomes and channelsomes, which occur through both direct molecular contacts and more distal functional coupling, and examine the validity of these “somes”.     

Geomagnetic cyclotron resonance in living cells

Although considerable experimental evidence now exists to indicate that low-frequency magnetic fileds influence living cells, the mode of coupling remains a mystery. We propose a radical new model for electromagnetic interactions with cells, one resulting from a cyclotron resonance mechanism attached to ions moving through transmembrane channels. It is shown that the cyclotron resonance condition on such ions readily leads to a predicted ELF-coupling at geomagnetic levels. This model quantitatively explains the results reported by Blackman et al. (1984), identifying the focus of magnetic interaction in these experiments as K⁺ charge carriers. The cyclotron resonance concept is consistent with recent indications showing that many membrane channels have helical configurations. This model is quite testable, can probably be applied to other circulating charge components within the cell and, most important, leads to the feasibility of direct resonant electromagnetic energy transfer to selected compartments of the cell.     

A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes

Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost.     

Synchronization of coupled biological oscillators under spatially heterogeneous environmental forcing

Spatially heterogeneous intensities of environmental signals are common in nature, being caused, e.g., by rugged or curved surfaces leading to varying angles of incidence and intensities. In this work, we perform numerical studies of one-dimensional arrays of coupled phase oscillators driven by a periodic signal with spatially heterogeneous amplitude, considering both random and gradual amplitude distributions of the driving. We compare the effects of global and next-neighbor interactions, respectively, on the mutual and forced synchronization in the array. Weak global coupling leads to full mutual synchronization for all studied driving configurations. The degree of external synchronization follows a majority rule, depending on the number of externally entrained oscillators in the uncoupled case. The effects of next-neighbor coupling depend on the spatial distribution of the driving amplitude. For random distributions, local interactions show the same qualitative effects as global coupling. In contrast, for gradual distributions and large driving heterogeneities, next-neighbor coupling is detrimental to both mutual and external synchronization. We discuss these observations with respect to fundamental aspects of heterogeneity and variability of dynamical systems, as well as the intercellular synchronization of circadian oscillators.     

Calcium and glial cell death

Calcium (Ca2+) homeostasis is crucial for development and survival of virtually all types of cells including glia of the central nervous system (CNS). Astrocytes, oligodendrocytes and microglia, the major glial cell types in the CNS, are endowed with a rather sophisticated array of Ca2+-permeable receptors and channels, as well as store-operated channels and pumps, all of which determine Ca2+ homeostasis. In addition, glial cells detect functional activity in neighbouring neurons and respond to it by means of Ca2+ signals that can modulate synaptic interactions. Like in neurons, Ca2+ overload resulting from dysregulation of channels and pumps can be deleterious to glia. In this review, we summarize recent advances in the understanding Ca2+ homeostasis in glial cells, the consequences of its alteration in cell demise as well as in neurological and psychiatric disorders that experience glial cell loss.     

High-extinction-ratio and low-insertion-loss Plasmonic Filter with Coherent Coupled Nano-cavity Array in a MIM Waveguide

In this paper, a novel plasmonic filter with very high extinction ratio and low insertion loss is proposed based on the coherent coupled nano-cavity array in a metal–insulator–metal (MIM) waveguide. The coherent coupling interactions among nano-cavities are investigated with an analytical model which is derived based on the temporal coupled-mode theory and transfer-matrix method. The destructive interference of the surface plasmon polaritons coupled from the nano-cavities at the resonant wavelength is achieved by suitably designing the period of the cavity array, which may be used for increasing the extinction ratio of the filter based on the nano-cavity array in the MIM waveguide. A plasmonic filter with an extinction ratio higher than 60 dB and an insertion loss less than 1.0 dB is obtained by applying the destructive interference in the design of a six-rectangular-cavity array in an Ag–air–Ag waveguide. And the correctness of the design for the filter is verified by the results obtained with the finite-difference time-domain simulation technique. This work may provide useful schemes and approaches for realization of various wavelength-sensitive devices in plasmonic integrated circuits.     

Ryanodine receptor arrays: not just a pretty pattern?

Ryanodine receptors (RyRs) are colossal membrane protein complexes that reside in the endoplasmic reticulum of skeletal and cardiac muscle myocytes and neurons, in addition to many non-excitable cells. They comprise high-conductance ion channels that mediate the massive release of Ca2+ ions from the endoplasmic reticulum into the cytoplasm. This is the trigger for contraction during each muscle excitation-contraction coupling cycle. Individual RyRs are believed to network with other RyRs indirectly, through diffusion of released Ca2+ ions, namely the Ca2+-induced Ca2+ release phenomenon. However, RyRs can intrinsically organize into a regular array resembling a distinctive checkerboard pattern, with each square-shaped receptor appearing to abut four neighbours at each corner. In this opinion article, we describe recent data showing structural interactions between RyR oligomers in reconstituted arrays, and we suggest that this provides strong evidence for direct inter-RyR communication through a novel, allosteric regulatory mechanism.     

Ryanodine受体间相互作用及其与钙释放功能的关系

在真核生物和原核生物的生物膜上都存在由同种受体蛋白相互连接在一起形成的紧密二维排列。最近的模型计算表明这种排列方式可能是一种新型信号转导机制的结构基础,相邻受体可通过功能上的耦联优化信号处理性能。Ryanodine受体（ryanodine receptor,RyR）／钙释放通道通常在肌肉的肌浆网膜上形成二维晶格排列,该蛋白成为研究受体二维排列及其生理功能的一个很好的模型。本文综述了近几年在RyR相互作用及其二维排列工作模式和生理功能研究方面的进展,着重介绍了我们实验室利用新方法对RyR相互作用及其调控进行的研究工作。我们研究中发现了RyR功能状态对其相互作用的调控,本文对据此提出的RyR二维排列的“动态耦联模型”及其可能的生理功能进行了详细讨论。     

Mapping Electromechanical Coupling Pathways in Voltage-Gated Ion Channels: Challenges and the Way Forward

Inter- and intra-molecular allosteric interactions underpin regulation of activity in a variety of biological macromolecules. In the voltage-gated ion channel superfamily, the conformational state of the voltage-sensing domain regulates the activity of the pore domain via such long-range allosteric interactions. Although the overall structure of these channels is conserved, allosteric interactions between voltage-sensor and pore varies quite dramatically between the members of this superfamily. Despite the progress in identifying key residues and structural interfaces involved in mediating electromechanical coupling, our understanding of the biophysical mechanisms remains limited. Emerging new structures of voltage-gated ion channels in various conformational states will provide a better three-dimensional view of the process but to conclusively establish a mechanism, we will also need to quantitate the energetic contribution of various structural elements to this process. Using rigorous unbiased metrics, we want to compare the efficiency of electromechanical coupling between various sub-families in order to gain a comprehensive understanding. Furthermore, quantitative understanding of the process will enable us to correctly parameterize computational approaches which will ultimately enable us to predict allosteric activation mechanisms from structures. In this review, we will outline the challenges and limitations of various experimental approaches to measure electromechanical coupling and highlight the best practices in the field.