ON THE RELATION BETWEEN TOXICITY, RESISTANCE, AND TIME OF SURVIVAL, AND ON RELATED PHENOMENA

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Abstract
The fundamental equation is t=[long dash]a ln (h [long dash] r)+K, where t = time, h = toxicity, r = resistance and a and K are constants. Test of the theory is here restricted to the action of various agents on unicellular organisms. Calculations are based on exps. described in the literature. There are 4 independent variables; time, toxicity, resistance and temp. 2 may be kept constant while the other 2 are allowed to vary. If temperature and toxicity remain constant, a normal frequency distribution curve is obtained by plotting % of organisms killed against resistance, although the corresponding mortality-time curve is asymmetrical. When temp. and resistance remain constant and toxicity and time of survival are varied, toxicity can be taken as proportional to concentration of noxious agent for narrow ranges of conc. It is necessary, however, to assume a relation between toxicity and conc. for wide ranges of conc. For unicellular organisms, toxicity is taken as proportional to adsorbed amount of agent (calculated by Langmuir''s equation) . When temp. and time are constant, mortality-resistance curves are symmetrical distribution curves. The corresponding mortality-concentration curves are symmetrical only if toxicity is a linear function of conc. Variation of temp. and time affect mainly the constant a, the reciprocal of which is similar in character to the velocity constant of a chemical reaction. In all cases examined agreement of calculated with experimental results was satisfactory. The relation between time and conc., time and toxicity, and time and distribution of resistance are demonstrated in arbitrary units. It is suggested that applicability of the theory need not be restricted to unicellular organisms, but may be extended to various biological phenomena in which a feature common to all is the occurrence of a time factor and a threshold value.

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