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.

Ion-channel function is determined by its gating movement. Yet, molecular dynamics and electrophysiological simulations were never combined to link molecular structure to function. We performed multiscale molecular dynamics and continuum electrostatics calculations to simulate a cardiac K ؉ channel (IKs) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the IKs ␣-subunit KCNQ1, based on the recent Kv1.2 structure, is used to calculate electrostatic energies during gating. Simulations are compared with experiments where varying degrees of positive charge-added via point mutationprogressively reduce current. Whole-cell simulations show that mutations cause action potential and ECG QT interval prolongation, consistent with clinical phenotypes. This framework allows integration of multiscale observations to study the molecular basis of excitation and its alteration by disease.cardiac arrhythmias ͉ long QT syndrome T he current carried by ion channels during the action potential (AP) in excitable tissues is determined by dynamic changes of the ion channel conformation during gating. Recently determined crystal structures of ion channel proteins (e.g., ref. 1) provide a structural basis for computer simulations of the ion-channel protein molecular dynamics (MD) during conformational changes. In parallel, recently acquired experimental data on ion-channel electrophysiological function have provided the basis for detailed Markov models of channel electrical function during gating (2, 3). These models can be used to link cellular consequences of genetic mutations in cardiac ion channels that alter channel kinetics to cardiac arrhythmias [see ref.4 for review]. Although consistent in reproducing the kinetics of channel opening and closing, the molecular conformations represented by the states of these Markov models are not identified.In this article, we develop a multiscale computational approach that combines molecular dynamics simulations and PoissonBoltzmann continuum electrostatic calculations with electrophysiological modeling for establishing structure-function relationships between ion channel movement during gating, its function as a carrier of transmembrane ionic current, and its role in the wholecell AP. Detailed understanding of these relationships is necessary for the development of effective genetic/molecular therapies and specific drug treatment of disease states that involve abnormal electrical function of excitable tissues. We present an example of a cardiac ion channel, the slow delayed rectifier I Ks , which participates in AP repolarization and its rate dependence (4). We consider mutations to its alpha subunit, KCNQ1, that lead to reduction of I Ks current and prolongation of the AP. The clinical phenotype associated with such mutations is the Long-QT syndrome type 1, LQT1; it presents as QT interval prolongation on the ECG and predisposes patients to cardiac arrhythmia and sudden death. Results and DiscussionSeveral charged residues that participate i...

Paired incremental uniaxial step (i.e., relaxation) and ramp tests were conducted simultaneously on four (nominally) identical samples of type I collagen gel, over a direct strain range 0 < epsilon < 0.2. The paired step and ramp responses could not both be predicted by a simple viscoelastic constitutive relation (either linear or Fung-type), but could be predicted reasonably accurately by a general nonlinear viscoelastic relation with a strain-dependent relaxation spectrum, of the form sigma(t) = f(t)-infinity g(t-tau,epsilon)[d(epsilon)(tau)/d(tau)]d(tau). Based on a four-term exponential-series approximation, we measured the stiffness moduli and time constants of the relaxation function, g(t,epsilon), for the four gel samples that we tested, and found that the time constants were independent of strain but the moduli increased strongly with strain. Further, we found that the time constants did not vary across the four gels, but the moduli varied by a factor of about 2 across the gels. Some additional tests show features of the response of collagen gels to cycles of application and removal of loading.

The fitting of quasi-linear viscoelastic (QLV) constitutive models to material data often involves somewhat cumbersome numerical convolution. A new approach to treating quasi-linearity in 1-D is described and applied to characterize the behavior of reconstituted collagen. This approach is based on a new principle for including nonlinearity and requires considerably less computation than other comparable models for both model calibration and response prediction, especially for smoothly applied stretching. Additionally, the approach allows relaxation to adapt with the strain history. The modeling approach is demonstrated through tests on pure reconstituted collagen. Sequences of "ramp-and-hold" stretching tests were applied to rectangular collagen specimens. The relaxation force data from the "hold" was used to calibrate a new "adaptive QLV model" and several models from literature, and the force data from the "ramp" was used to check the accuracy of model predictions. Additionally, the ability of the models to predict the force response on a reloading of the specimen was assessed. The "adaptive QLV model" based on this new approach predicts collagen behavior comparably to or better than existing models, with much less computation.

Characterizing how cells in three-dimensional (3D) environments or natural tissues respond to biophysical stimuli is a longstanding challenge in biology and tissue engineering. We demonstrate a strategy to monitor morphological and mechanical responses of contractile fibroblasts in a 3D environment. Cells responded to stretch through specific, cell-wide mechanisms involving staged retraction and reinforcement. Retraction responses occurred for all orientations of stress fibers and cellular protrusions relative to the stretch direction, while reinforcement responses, including extension of cellular processes and stress fiber formation, occurred predominantly in the stretch direction. A previously unreported role of F-actin clumps was observed, with clumps possibly acting as F-actin reservoirs for retraction and reinforcement responses during stretch. Responses were consistent with a model of cellular sensitivity to local physical cues. These findings suggest mechanisms for global actin cytoskeleton remodeling in non-muscle cells and provide insight into cellular responses important in pathologies such as fibrosis and hypertension.

The stress fiber network within contractile fibroblasts structurally reinforces and provides tension, or "tone", to tissues such as those found in healing wounds. Stress fibers have previously been observed to polymerize in response to mechanical forces. We observed that, when stretched sufficiently, contractile fibroblasts diminished the mechanical tractions they exert on their environment through depolymerization of actin filaments then restored tissue tension and rebuilt actin stress fibers through staged Ca ++ -dependent processes. These staged Ca ++ -modulated contractions consisted of a rapid phase that ended less than a minute after stretching, a plateau of inactivity, and a final gradual phase that required several minutes to complete. Active contractile forces during recovery scaled with the degree of rebuilding of the actin cytoskeleton. This complementary action demonstrates a programmed regulatory mechanism that protects cells from excessive stretch through choreographed active mechanical and biochemical healing responses.

Most potassium channels are tetramers of four homologous polypeptides (subunits). During channel gating, each subunit undergoes several conformational changes independent of the state of other subunits before reaching a permissive state, from which the channel can open. However, transition from the permissive states to the open state involves a concerted movement of all subunits. This cooperative transition must be included in Markov models of channel gating. Previously, it was implemented by considering all possible combinations of four subunit states in a much larger expanded model of channel states (e.g., 27,405 channel states versus 64 subunit states), which complicates modeling and is computationally intense, especially when accurate modeling requires a large number of subunit states. To overcome these complexities and retain the tetrameric molecular structure, a modeling approach was developed to incorporate the cooperative transition directly from the subunit models. In this approach, the open state is separated from the subunit models and represented by the net flux between the open state and the permissive states. Dynamic variations of the probability of state residencies computed using this direct approach and the expanded model were identical. Implementation of the direct approach is simple and its computational time is orders-of-magnitude shorter than the equivalent expanded model.

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.