Continuum Molecular Simulation of Large Conformational Changes during Ion–Channel Gating

A modeling framework was developed to simulate large and gradual conformational changes within a macromolecule (protein) when its low amplitude high frequency vibrations are not concerned. Governing equations were derived as alternative to Langevin and Smoluchowski equations and used to simulate gating conformational changes of the Kv7.1 ion-channel over the time scale of its gating process (tens of milliseconds). The alternative equations predict the statistical properties of the motion trajectories with good accuracy and do not require the force field to be constant over the diffusion length, as assumed in Langevin equation. The open probability of the ion–channel was determined considering cooperativity of four subunits and solving their concerted transition to the open state analytically. The simulated open probabilities for a series of voltage clamp tests produced current traces that were similar to experimentally recorded currents

State-dependent electrostatic interactions of S4 arginines with E1 in S2 during Kv7.1 activation

The voltage-sensing domain of voltage-gated channels is comprised of four transmembrane helices (S1–S4), with conserved positively charged residues in S4 moving across the membrane in response to changes in transmembrane voltage. Although it has been shown that positive charges in S4 interact with negative countercharges in S2 and S3 to facilitate protein maturation, how these electrostatic interactions participate in channel gating remains unclear. We studied a mutation in Kv7.1 (also known as KCNQ1 or KvLQT1) channels associated with long QT syndrome (E1K in S2) and found that reversal of the charge at E1 eliminates macroscopic current without inhibiting protein trafficking to the membrane. Pairing E1R with individual charge reversal mutations of arginines in S4 (R1–R4) can restore current, demonstrating that R1–R4 interact with E1. After mutating E1 to cysteine, we probed E1C with charged methanethiosulfonate (MTS) reagents. MTS reagents could not modify E1C in the absence of KCNE1. With KCNE1, (2-sulfonatoethyl) MTS (MTSES)− could modify E1C, but [2-(trimethylammonium)ethyl] MTS (MTSET)+ could not, confirming the presence of a positively charged environment around E1C that allows approach by MTSES− but repels MTSET+. We could change the local electrostatic environment of E1C by making charge reversal and/or neutralization mutations of R1 and R4, such that MTSET+ modified these constructs depending on activation states of the voltage sensor. Our results confirm the interaction between E1 and the fourth arginine in S4 (R4) predicted from open-state crystal structures of Kv channels and reveal an E1–R1 interaction in the resting state. Thus, E1 engages in electrostatic interactions with arginines in S4 sequentially during the gating movement of S4. These electrostatic interactions contribute energetically to voltage-dependent gating and are important in setting the limits for S4 movement

Stretch-Induced Stress Fiber Remodeling and the Activations of JNK and ERK Depend on Mechanical Strain Rate, but Not FAK

BACKGROUND: Cells within tissues are subjected to mechanical forces caused by extracellular matrix deformation. Cells sense and dynamically respond to stretching of the matrix by reorienting their actin stress fibers and by activating intracellular signaling proteins, including focal adhesion kinase (FAK) and the mitogen-activated proteins kinases (MAPKs). Theoretical analyses predict that stress fibers can relax perturbations in tension depending on the rate of matrix strain. Thus, we hypothesized stress fiber organization and MAPK activities are altered to an extent dependent on stretch frequency. PRINCIPAL FINDINGS: Bovine aortic endothelial cells and human osteosarcoma cells expressing GFP-actin were cultured on elastic membranes and subjected to various patterns of stretch. Cyclic stretching resulted in strain rate-dependent increases in stress fiber alignment, cell retraction, and the phosphorylation of the MAPKs JNK, ERK and p38. Transient step changes in strain rate caused proportional transient changes in the levels of JNK and ERK phosphorylations without affecting stress fiber organization. Disrupting stress fiber contractile function with cytochalasin D or Y27632 decreased the levels of JNK and ERK phosphorylation. Previous studies indicate that FAK is required for stretch-induced cell alignment and MAPK activations. However, cyclic uniaxial stretching induced stress fiber alignment and the phosphorylation of JNK, ERK and p38 to comparable levels in FAK-null and FAK-expressing mouse embryonic fibroblasts. CONCLUSIONS: These results indicate that cyclic stretch-induced stress fiber alignment, cell retraction, and MAPK activations occur as a consequence of perturbations in fiber strain. These findings thus shed new light into the roles of stress fiber relaxation and reorganization in maintenance of tensional homeostasis in a dynamic mechanical environment

The Viscoelastic Properties of Passive Eye Muscle in Primates. I: Static Forces and Step Responses

The viscoelastic properties of passive eye muscles are prime determinants of the deficits observed following eye muscle paralysis, the root cause of several types of strabismus. Our limited knowledge about such properties is hindering the ability of eye plant models to assist in formulating a patient's diagnosis and prognosis. To investigate these properties we conducted an extensive in vivo study of the mechanics of passive eye muscles in deeply anesthetized and paralyzed monkeys. We describe here the static length-tension relationship and the transient forces elicited by small step-like elongations. We found that the static force increases nonlinearly with length, as previously shown. As expected, an elongation step induces a fast rise in force, followed by a prolonged decay. The time course of the decay is however considerably more complex than previously thought, indicating the presence of several relaxation processes, with time constants ranging from 1 ms to at least 40 s. The mechanical properties of passive eye muscles are thus similar to those of many other biological passive tissues. Eye plant models, which for lack of data had to rely on (erroneous) assumptions, will have to be updated to incorporate these properties

The Viscoelastic Properties of Passive Eye Muscle in Primates. II: Testing the Quasi-Linear Theory

We have extensively investigated the mechanical properties of passive eye muscles, in vivo, in anesthetized and paralyzed monkeys. The complexity inherent in rheological measurements makes it desirable to present the results in terms of a mathematical model. Because Fung's quasi-linear viscoelastic (QLV) model has been particularly successful in capturing the viscoelastic properties of passive biological tissues, here we analyze this dataset within the framework of Fung's theory

Modeling the Afferent Dynamics of the Baroreflex Control System

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods