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• Rate constant of muscle force redevelopment reflects coopera...

  Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics Biophysical Journal, Volume 72, Issue 1, 1 January 1997, Pages 254-262 K. Campbell Abstract The rate of muscle force redevelopment after release-restretch protocols has previously been interpreted using a simple two-state cross-bridge cycling model with rate constants for transitions between non-force-bearing and force-bearing states, f, and between force-bearing and non-force-bearing states, g. Changes in the rate constant of force redevelopment, as with varying levels of Ca2+ activation, have traditionally been attributed to Ca(2+)-dependent f. The current work adds to this original model a state of unactivated, noncycling cross-bridges. The resulting differential equation for activated, force-bearing cross-bridges, Ncf, was Ncf = -[g+f(K/(K + 1))] Ncf+f(K/(K + 1))NT, where K is an equilibrium constant defining the distribution between cycling and noncycling cross-bridges and NT is the total number of cross-bridges. Cooperativity by which force-bearing cross-bridges participate in their own activation was introduced by making K depend on Ncf. Model results demonstrated that such cooperativity, which tends to enhance force generation at low levels of Ca2+ activation, has a counter-intuitive effect of slowing force redevelopment. These dynamic effects of cooperativity are most pronounced at low Ca2+ activation. As Ca2+ activation increases, the cooperative effects become less important to the dynamics of force redevelopment and, at the highest levels of Ca2+ activation, the dynamics of force redevelopment reflect factors other than cooperative mechanisms. These results expand on earlier interpretations of Ca2+ dependence of force redevelopment; rather than Ca(2+)-dependent f, Ca(2+)-dependent force redevelopment arises from changing expressions of cooperativity between force-bearing cross-bridges and activation. Abstract | PDF (898 kb)

• Effects of cardiac thin filament Ca2+: statistical mechanica...

  Effects of cardiac thin filament Ca2+: statistical mechanical analysis of a troponin C site II mutant Biophysical Journal, Volume 70, Issue 3, 1 March 1996, Pages 1447-1455 Q. Huynh, C.A. Butters, J.M. Leiden and L.S. Tobacman Abstract Cardiac thin filaments contain many troponin C (TnC) molecules, each with one regulatory Ca2+ binding site. A statistical mechanical model for the effects of these sites is presented and investigated. The ternary troponin complex was reconstituted with either TnC or the TnC mutant CBMII, in which the regulatory site in cardiac TnC (site II) is inactivated. Regardless of whether Ca2+ was present, CBMII-troponin was inhibitory in a thin filament-myosin subfragment 1 MgATPase assay. The competitive binding of [3H]troponin and [14C]CBMII-troponin to actin.tropomyosin was measured. In the presence of Mg2+ and low free Ca2+ they had equal affinities for the thin filament. When Ca274+ was added, however, troponin's affinity for the thin filament was 2.2-fold larger for the mutant than for the wild type troponin. This quantitatively describes the effect of regulatory site Ca2+ on troponin's affinity for actin.tropomyosin; the decrease in troponin-thin filament binding energy is small. Application of the theoretical model to the competitive binding data indicated that troponin molecules bind to interdependent rather than independent sites on the thin filament. Ca2+ binding to the regulatory site of TnC has a long-range rather than a merely local effect. However, these indirect TnC-TnC interactions are weak, indicating that the cooperativity of muscle activation by Ca2+ requires other sources of cooperativity. Abstract | PDF (1066 kb)

• Ising Model of Cardiac Thin Filament Activation with Nearest...

  Ising Model of Cardiac Thin Filament Activation with Nearest-Neighbor Cooperative Interactions Biophysical Journal, Volume 84, Issue 2, 1 February 2003, Pages 897-909 John Jeremy Rice, Gustavo Stolovitzky, Yuhai Tu and Pieter P. de Tombe Abstract We have developed a model of cardiac thin filament activation using an Ising model approach from equilibrium statistical physics. This model explicitly represents nearest-neighbor interactions between 26 troponin/tropomyosin units along a one-dimensional array that represents the cardiac thin filament. With transition rates chosen to match experimental data, the results show that the resulting force-pCa () relations are similar to Hill functions with asymmetries, as seen in experimental data. Specifically, Hill plots showing (log(F/(1-F)) vs. log [Ca]) reveal a steeper slope below the half activation point () compared with above. Parameter variation studies show interplay of parameters that affect the apparent cooperativity and asymmetry in the relations. The model also predicts that Ca binding is uncooperative for low [Ca], becomes steeper near , and becomes uncooperative again at higher [Ca]. The steepness near mirrors the steep as a result of thermodynamic considerations. The model also predicts that the correlation between troponin/tropomyosin units along the one-dimensional array quickly decays at high and low [Ca], but near , high correlation occurs across the whole array. This work provides a simple model that can account for the steepness and shape of relations that other models fail to reproduce. Abstract | Full Text | PDF (269 kb)

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Abstract

To study the initial kinetics of Ins(1,4,5)P3-induced [Ca2+]i elevations with a high time resolution and to avoid the problem of cell-to-cell heterogeneity, we have used the combined patch-clamp/microfluorimetry technique. The mathematical description of the microperfusion of Ins(1,4,5)P3 and the subsequent Ca2+ release consists of a monoexponential decay (cytosolic Ins(1,4,5)P3 concentration) and a Hill equation (Ins(1,4,5)P3 dose-response curve). Two additional Hill equations and an integration were necessary to include a putative dependence of Ins(1,4,5)P3-induced Ca2+ release on [Ca2+]i. Best-fitting analysis assuming [Ca2+]i-independent Ca2+ release yielded Hill coefficients between 4 and 12. The high cooperativity was also observed with the poorly metabolizable analog Ins(2,4,5)P3 and was independent of extracellular [Ca2+]. Best-fitting analysis including a positive [Ca2+]i feedback suggested a cooperativity on the level of Ins(1,4,5)P3-induced channel opening (n = 2) and an enhancement of Ins(1,4,5)P3-induced Ca2+ release by [Ca2+]i. In summary, the onset kinetics of Ins(1,4,5)P3-induced [Ca2+]i elevations in single HL-60 granulocytes showed a very high cooperativity, presumably because of a cooperativity on the level of channel opening and a positive Ca2+ feedback, but not because of Ca2+ influx or Ins(1,4,5)P3 metabolism. This high cooperativity, acting in concert with negative feedback mechanisms, might play an important role in the fine-tuning of the cellular Ca2+ signal.