Abstract: The dynamic behavior of various types of cytochromes c in the redox reaction with iron hexacyanides was studied using a temperature-jump method in order to elucidate the molecular mechanism of the redox reaction of cytochromes with their oxidoreductants. Transmittance after the temperature jump changed through a single exponential decay for all cytochromes investigated. Under a constant concentration of anion, the redox reaction of various types of cytochrome c with iron hexacyanides was analyzed according to the scheme: Ki=kt/k-i (i=1,2,3) where C(III) and C(II) are ferric and ferrous cytochromes, respectively, Fe(III) and Fe(II) are ferri- and ferrocyanides, respectively, C(III) [middle dot] Fe(II) is the ferricytochrome-ferrocyanide complex and C(II) [middle dot] Fe(III) is the ferrocytochrome-ferricyanide complex. When step B is slower than the other two steps A and C, τ-1 can be represented approximately as where the bar over the variables denotes the equilibrium value. In a large excess of ferrocyanide against cytochrome, we can estimate k2, k-2, K1 and K3 independently. In the case of horse cytochrome c at 18[degree sign]C in 0.1 M phosphate buffer at pH 7 with 0.3 M KNO3, the estimated parameters are k2 = 100 +/- 50 s-1, k-2 = (3.5 +/- 1.0) [middle dot] 103 s-1, K1 = 15 +/- 7 M-1 and K3 = (8.5 +/- 1.5) [middle dot] 10-4 M. From the same experiments for seven cytochromes (cytochrome c from horse, tuna, Candida krusei, Saccharomyces oviformis, Rhodospirillum rubrum cytochrome c2, Spirulina platensis cytochrome c-554 and Thermus thermophilus cytochrome c-552), the following results can be deduced. (1) Each parameter defined in the scheme above (k2, k-2, K1, K3) diverged beyond the error range. Above all, k2 values of cytochromes c-554 and c-552 are as large as 1 [middle dot] 104 s-1 and much larger than those for the other cytochromes (to 50 approx. 700 S-1). (2) The variance of k2K1 and k-2/K3 are relatively less than the variances of individual parameters (k2, k-2, K1 and K3), which suggests that the values of k2K1 and k-2/K3 have been conserved during the course of evolution.

Abstract: (1) A conceptual model is developed in which spatial behaviour is density-dependent. The behaviour is classified as congregatory or migratory according to whether it results in movement towards or away from population concentrations. (2) Spatial behaviour is shown to result from both individual and population interactions. (3) The stability properties of the model are explored and it is shown how, under particular conditions, populations obeying the model have a population density regulating mechanism. (4) The similarity between the model and the potential energy curve of physics is noted, but it is emphasized that this is a behavioural not a physical model.