A LOCAL-OSCILLATOR THEORY OF SHUTTLE STREAMING IN PHYSARUM-POLYCEPHALUM .2. PHASE-CONTROL BY CYTOPLASMIC CALCIUM

Shuttle streaming in an isolated strand of Physarum plasmodium requires the isometric tensions at each end to oscillate with a constant phase difference, preferably 180 degrees. The stability of in-phase (IP)- and anti-phase (AP)-locked states of an oscillating strand is studied in terms of two diffusion-coupled oscillators, whose frequencies are determined by their total calcium levels. Anti-phase locking is generated by oscillatory frequency modulations, which occur when the difference in total calcium levels oscillates through zero. The anti-phase-lacked state is generated when diffusive coupling is small, the initial difference in free calcium levels exceeds a minimum value, and the initial difference in total calcium levels is small. It is shown that these conditions are maintained. The stabilities of phase-locked states can be exchanged following an imposed transfer of free calcium between the ends. The AP --> IP transition occurs for ail sufficiently large transfers, whereas IP --> AP conversion occurs only in a narrow range of amount transferred when the oscillator receiving calcium is near minimum value for its free calcium level. The in-phase-locked state is always stable when diffusive coupling is large: this occurs for small volumes of cytoplasm and creates the required internal phase coherence. The relationship of these results to recent experiments on Physarum is discussed.