Conformational changes of an ion-channel during gating and emerging electrophysiologic properties: Application of a computational approach to cardiac Kv7.1.

Ion channels are the "building blocks" of the excitation process in excitable tissues. Despite advances in determining their molecular structure, understanding the relationship between channel protein structure and electrical excitation remains a challenge. The Kv7.1 potassium channel is an important determinant of the cardiac action potential and its adaptation to rate changes. It is subject to beta adrenergic regulation, and many mutations in the channel protein are associated with the arrhythmic long QT syndrome. In this theoretical study, we use a novel computational approach to simulate the conformational changes that Kv7.1 undergoes during activation gating and compute the resulting electrophysiologic function in terms of single-channel and macroscopic currents. We generated all possible conformations of the S4-S5 linker that couples the S3-S4 complex (voltage sensor domain, VSD) to the pore, and all associated conformations of VSD and the pore (S6). Analysis of these conformations revealed that VSD-to-pore mechanical coupling during activation gating involves outward translation of the voltage sensor, accompanied by a translation away from the pore and clockwise twist. These motions cause pore opening by moving the S4-S5 linker upward and away from the pore, providing space for the S6 tails to move away from each other. Single channel records, computed from the simulated motion trajectories during gating, have stochastic properties similar to experimentally recorded traces. Macroscopic current through an ensemble of channels displays two key properties of Kv7.1: an initial delay of activation and fast inactivation. The simulations suggest a molecular mechanism for fast inactivation; a large twist of the VSD following its outward translation results in movement of the base of the S4-S5 linker toward the pore, eliminating open pore conformations to cause inactivation.

Physically-induced cytoskeleton remodeling of cells in three-dimensional culture.

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.

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.

Three-residue loop closure in proteins: a new kinematic method reveals a locus of connected loop conformations.

The closure of a three-residue loop was studied using a developed kinematic method. It was shown that there are infinite number of three-residue loops (a locus of conformations), which can connect two segments of a polypeptide. This adds to the current understanding of a finite number of conformations for three-residue loop-closure. In the developed method, some of the equations can be solved analytically to reduce the computation cost. Benefiting from the reduced computation time, we determined all the relative positions of two polypeptide segments that can be connected by a three-residue loop.

Quantification of fibre polymerization through Fourier space image analysis.

Quantification of changes in the total length of randomly oriented and possibly curved lines appearing in an image is a necessity in a wide variety of biological applications. Here, we present an automated approach based upon Fourier space analysis. Scaled, band-pass filtered power spectral densities of greyscale images are integrated to provide a quantitative measurement of the total length of lines of a particular range of thicknesses appearing in an image. A procedure is presented to correct for changes in image intensity. The method is most accurate for two-dimensional processes with fibres that do not occlude one another.

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.

A multiscale model linking ion-channel molecular dynamics and electrostatics to the cardiac action potential.

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 (I(Ks)) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the I(Ks) alpha-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 mutation-progressively 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.

Stretch-activated force shedding, force recovery, and cytoskeletal remodeling in contractile fibroblasts.

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.

Modeling subunit cooperativity in opening of tetrameric ion channels.

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.

Statistical properties of ion channel records. Part I: relationship to the macroscopic current.

Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), through G(t) = P(t) - H(t) * Q(t) where P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.

Statistical properties of ion channel records. Part II: estimation from the macroscopic current.

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.

A simplified approach to quasi-linear viscoelastic modeling.

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.

Incremental mechanics of collagen gels: new experiments and a new viscoelastic model.

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.