Locally and globally coupled oscillators in muscle.

At an intermediate activation level, striated muscle exhibits autonomous oscillations called SPOC, in which the basic contractile units, sarcomeres, oscillate in length, and various oscillatory patterns such as traveling waves and their disrupted forms appear in a myofibril. Here we show that these patterns are reproduced by mechanically connecting in series the unit model that explains characteristics of SPOC at the single-sarcomere level. We further reduce the connected model to phase equations, revealing that the combination of local and global couplings is crucial to the emergence of these patterns.

Noise-induced phase locking in coupled coherence-resonance oscillators.

We investigate the effects of additive noise on coupled excitable chemical oscillators, particularly focusing on how oscillatory coupled modes can be induced by noise. We find that phase locking in the weak coupling regime occurs through coherence resonance, although the resulting phase locking modes are apparently similar to those in coupled deterministic oscillators. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.

A theory on auto-oscillation and contraction in striated muscle.

It is widely accepted that muscle cells take either force-generating or relaxing state in an all-or-none fashion through the so-called excitation-contraction coupling. On the other hand, the membrane-less contractile apparatus takes the third state, i.e., the auto-oscillation (SPOC) state, at the activation level that is intermediate between full activation and relaxation. Here, to explain the dynamics of all three states of muscle, we construct a novel theoretical model based on the balance of forces not only parallel but also perpendicular to the long axis of myofibrils, taking into account the experimental fact that the spacing of myofilament lattice changes with sarcomere length and upon contraction. This theory presents a phase diagram composed of several states of the contractile apparatus and explains the dynamic behavior of SPOC, e.g., periodical changes in sarcomere length with the saw-tooth waveform. The appropriate selection of the constant of the molecular friction due to the cross-bridge formation can explain the difference in the SPOC periods observed under various activating conditions and in different muscle types, i.e., skeletal and cardiac. The theory also predicts the existence of a weak oscillation state at the boundary between SPOC and relaxation regions in the phase diagram. Thus, the present theory comprehensively explains the characteristics of auto-oscillation and contraction in the contractile system of striated muscle.

Actin oligomers at the initial stage of polymerization induced by increasing temperature at low ionic strength: Study with small-angle X-ray scattering.

Using small-angle X-ray scattering (SAXS), we have studied the initial stage (nucleation and oligomerization) of actin polymerization induced by raising temperature in a stepwise manner from 1°C to 30°C at low ionic strength (4.0 mg ml-1 actin in G-buffer). The SAXS experiments were started from the mono-disperse G-actin state, which was confirmed by comparing the scattering pattern in q- and real space with X-ray crystallographic data. We observed that the forward scattering intensity I(q → 0), used as an indicator for the extent of poly-merization, began to increase at ∼14°C for Mg-actin and ∼20°C for Ca-actin, and this critical temperature did not depend on the nucleotide species, i.e., ATP or ADP. At the temperatures higher than ∼20°C for Mg-actin and ∼25°C for Ca-actin, the coherent reflection peak, which is attributed to the helical structure of F-actin, appeared. The pair-distance distribution functions, p(r), corresponding to the frequency of vector lengths (r) within the molecule, were obtained by the indirect Fourier transformation (IFT) of the scattering curves, I(q). Next, the size distributions of oligomers at each temperature were analyzed by fitting the experimentally obtained p(r) with the theoretical p(r) for the helical and linear oligomers (2-13mers) calculated based on the X-ray crystallographic data. We found that p(r) at the initial stage of polymerization was well accounted for by the superposition of monomer, linear/helical dimers, and helical trimer, being independent of the type of divalent cations and nucleotides. These results suggest that the polymerization of actin in G-buffer induced by an increase in temperature proceeds via the elongation of the helical trimer, which supports, in a structurally resolved manner, a widely believed hypothesis that the polymerization nucleus is a helical trimer.