On chain models for contact electrification.

An exact analytical model of charge dynamics for a chain of atoms with asymmetric hopping terms is presented. Analytic and numeric results are shown to give rise to similar dynamics in both the absence and presence of electron interactions. The chain model is further extended to the case of two atoms per cell (a perfect alloy system). This extension is further applied to contact electrification between two different atomic chains and the effect of increasing the magnitude of the contact transfer matrix element is studied.

Mechanical contribution to muscle thin filament activation.

Vertebrate striated muscle thin filaments are thought to be thermodynamically activated in response to an increase in Ca2+ concentration. We tested this hypothesis by measuring time intervals for gliding runs and pauses of individual skeletal muscle thin filaments in cycling myosin motility assays. A classic thermodynamic mechanism predicts that if chemical potential is constant, transitions between runs and pauses of gliding thin filaments will occur at constant rate as given by a Poisson distribution. In this scenario, rate is given by the odds of a pause, and hence, run times between pauses fit an exponential distribution that slopes negatively for all observable run times. However, we determined that relative density of observed run times fits an exponential only at low Ca2+ levels that activate filament gliding. Further titration with Ca2+, or adding excess regulatory proteins tropomyosin and troponin, shifted the relative density of short run times to fit the positive slope of a gamma distribution, which derives from waiting times between Poisson events. Events that arise during a run and prevent the chance of ending a run for a random interval of time account for the observed run time distributions, suggesting that the events originate with cycling myosin. We propose that regulatory proteins of the thin filament require the mechanical force of cycling myosin to achieve the transition state for activation. During activation, combinations of cycling myosin that contribute insufficient activation energy delay deactivation.

Modeling Ca2+-Bound Troponin in Excitation Contraction Coupling.

To explain disparate decay rates of cytosolic Ca2+ and structural changes in the thin filaments during a twitch, we model the time course of Ca2+-bound troponin (Tn) resulting from the free Ca2+ transient of fast skeletal muscle. In fibers stretched beyond overlap, the decay of Ca2+ as measured by a change in fluo-3 fluorescence is significantly slower than the intensity decay of the meridional 1/38.5 nm-1 reflection of Tn; this is not simply explained by considering only the Ca2+ binding properties of Tn alone (Matsuo et al., 2010). We apply a comprehensive model that includes the known Ca2+ binding properties of Tn in the context of the thin filament with and without cycling crossbridges. Calculations based on the model predict that the transient of Ca2+-bound Tn correlates with either the fluo-3 time course in muscle with overlapping thin and thick filaments or the intensity of the meridional 1/38.5 nm-1 reflection in overstretched muscle. Hence, cycling crossbridges delay the dissociation of Ca2+ from Tn. Correlation with the fluo-3 fluorescence change is not causal given that the transient of Ca2+-bound Tn depends on sarcomere length, whereas the fluo-3 fluorescence change does not. Transient positions of tropomyosin calculated from the time course of Ca2+-bound Tn are in reasonable agreement with the transient of measured perturbations of the Tn repeat in overlap and non-overlap muscle preparations.

Enhanced troponin I binding explains the functional changes produced by the hypertrophic cardiomyopathy mutation A8V of cardiac troponin C.

Higher affinity for TnI explains how troponin C (TnC) carrying a causative hypertrophic cardiomyopathy mutation, TnC(A8V), sensitizes muscle cells to Ca(2+). Muscle fibers reconstituted with TnC(A8V) require ∼2.3-fold less [Ca(2+)] to achieve 50% maximum-tension compared to fibers reconstituted with wild-type TnC (TnC(WT)). Binding measurements rule out a significant change in N-terminus Ca(2+)-affinity of isolated TnC(A8V), and TnC(A8V) binds the switch-peptide of troponin-I (TnI(sp)) ∼1.6-fold more strongly than TnC(WT); thus we model the TnC-TnI(sp) interaction as competing with the TnI-actin interaction. Tension data are well-fit by a model constrained to conditions in which the affinity of TnC(A8V) for TnI(sp) is 1.5-1.7-fold higher than that of TnC(WT) at all [Ca(2+)]. Mean ATPase rates of reconstituted cardiac myofibrils is greater for TnC(A8V) than TnC(WT) at all [Ca(2+)], with statistically significant differences in the means at higher [Ca(2+)]. To probe TnC-TnI interaction in low Ca(2+), displacement of bis-ANS from TnI was monitored as a function of TnC. Whereas Ca(2+)-TnC(WT) displaces significantly more bis-ANS than Mg(2+)-TnC(WT), Ca(2+)-TnC(A8V) displaces probe equivalently to Mg(2+)-TnC(A8V) and Ca(2+)-TnC(WT), consistent with stronger Ca(2+)-independent TnC(A8V)-TnI(sp). A Matlab program for computing theoretical activation is reported. Our work suggests that contractility is constantly above normal in hearts made hypertrophic by TnC(A8V).

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).

Effect of Ca2+ binding properties of troponin C on rate of skeletal muscle force redevelopment.

To investigate effects of altering troponin (Tn)C Ca(2+) binding properties on rate of skeletal muscle contraction, we generated three mutant TnCs with increased or decreased Ca(2+) sensitivities. Ca(2+) binding properties of the regulatory domain of TnC within the Tn complex were characterized by following the fluorescence of an IAANS probe attached onto the endogenous Cys(99) residue of TnC. Compared with IAANS-labeled wild-type Tn complex, V43QTnC, T70DTnC, and I60QTnC exhibited ∼1.9-fold higher, ∼5.0-fold lower, and ∼52-fold lower Ca(2+) sensitivity, respectively, and ∼3.6-fold slower, ∼5.7-fold faster, and ∼21-fold faster Ca(2+) dissociation rate (k(off)), respectively. On the basis of K(d) and k(off), these results suggest that the Ca(2+) association rate to the Tn complex decreased ∼2-fold for I60QTnC and V43QTnC. Constructs were reconstituted into single-skinned rabbit psoas fibers to assess Ca(2+) dependence of force development and rate of force redevelopment (k(tr)) at 15°C, resulting in sensitization of both force and k(tr) to Ca(2+) for V43QTnC, whereas T70DTnC and I60QTnC desensitized force and k(tr) to Ca(2+), I60QTnC causing a greater desensitization. In addition, T70DTnC and I60QTnC depressed both maximal force (F(max)) and maximal k(tr). Although V43QTnC and I60QTnC had drastically different effects on Ca(2+) binding properties of TnC, they both exhibited decreases in cooperativity of force production and elevated k(tr) at force levels <30%F(max) vs. wild-type TnC. However, at matched force levels >30%F(max) k(tr) was similar for all TnC constructs. These results suggest that the TnC mutants primarily affected k(tr) through modulating the level of thin filament activation and not by altering intrinsic cross-bridge cycling properties. To corroborate this, NEM-S1, a non-force-generating cross-bridge analog that activates the thin filament, fully recovered maximal k(tr) for I60QTnC at low Ca(2+) concentration. Thus TnC mutants with altered Ca(2+) binding properties can control the rate of contraction by modulating thin filament activation without directly affecting intrinsic cross-bridge cycling rates.

Striated muscle regulation of isometric tension by multiple equilibria.

Cooperative activation of striated muscle by calcium is based on the movement of tropomyosin described by the steric blocking theory of muscle contraction. Presently, the Hill model stands alone in reproducing both myosin binding data and a sigmoidal-shaped curve characteristic of calcium activation (Hill TL (1983) Two elementary models for the regulation of skeletal muscle contraction by calcium. Biophys J 44: 383-396.). However, the free myosin is assumed to be fixed by the muscle lattice and the cooperative mechanism is based on calcium-dependent interactions between nearest neighbor tropomyosin subunits, which has yet to be validated. As a result, no comprehensive model has been shown capable of fitting actual tension data from striated muscle. We show how variable free myosin is a selective advantage for activating the muscle and describe a mechanism by which a conformational change in tropomyosin propagates free myosin given constant total myosin. This mechanism requires actin, tropomyosin, and filamentous myosin but is independent of troponin. Hence, it will work equally well with striated, smooth and non-muscle contractile systems. Results of simulations with and without data are consistent with a strand of tropomyosin composed of approximately 20 subunits being moved by the concerted action of 3-5 myosin heads, which compares favorably with the predicted length of tropomyosin in the overlap region of thick and thin filaments. We demonstrate that our model fits both equilibrium myosin binding data and steady-state calcium-dependent tension data and show how both the steepness of the response and the sensitivity to calcium can be regulated by the actin-troponin interaction. The model simulates non-cooperative calcium binding both in the presence and absence of strong binding myosin as has been observed. Thus, a comprehensive model based on three well-described interactions with actin, namely, actin-troponin, actin-tropomyosin, and actin-myosin can explain the cooperative calcium activation of striated muscle.