Cooperative Phenomena in Biology by George Karreman

By George Karreman

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Contracting muscles and conducting *The work was supported in part by NIH grants 1-R01-CA16301-01, 2-R01-GM1142211A1, and ONR Contract NONR-4371(00). John A. Hartford Foundation provided much of the basic facilities. I thank Miss Margaret Ochsenfeld and Mrs. Janice Malseed for much help. 39 40 Cooperative Phenomena in Biology nerves, for example, involve shifts of the protoplasm between these states. Both the resting and active states are separated by more-readily surmountable energy barriers than those separating the various living states from the death state.

Log y-^— = n log p 0 2 + nlogK (5). p 0 2 is the partial pressure of oxygen in the gas phase, y is the mole fraction of oxygen bound to hemoglobin. 1 — y is the mole fraction of sites not binding oxygen, n, an empirical constant called the Hill coefficient, has been recognized as an index of the "sigmoidity" of the oxygen binding curve; the larger the value of n, the greater the steepness of the S-shaped oxygen uptake curve. The tangent of the isotherm depicted by equation (4) at the locus where [Pilad e a i u a l s [Pjlad (Ling, 1964) is described by the following equation: log r-r- = n log 7—r- + n log K°° J^i [Pj: ad [Pjle (6).

S^ at the time (t+At) can then arise in one of the two following ways: either la) the variables Sj ,s 2 ,... ,s M already had the values s'j ,s 2 ,... ,s{^ at the time t and lb) did not change in the interval At, or 2a) one of the variables of a state, such as si5 had the value -sj, whereas all the other variables of state Sj (j=£i) had the value sj at the time t and 2b) Sj changed from the value —sj to the value sj in the interval At neglecting two or more changes in s' values in the interval At.

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