ENTROPIC CONTRIBUTIONS TO MORTALITY 



AND AGING* 



George A. Sacher 



Division of Biolo^^ical and Medical Research, 

 Argonne National Laboratory, Lemont, Illinois 



Abstract — All dynamic physiologic processes are attended by fluctuations. The magnitude of 

 these fluctuations is determined by the inherent regulatory capacity of the specific process 

 and by the magnitude of random disturbances arising both in the environment and within the 

 organism. A system with these characteristics has, in a given environment, a determinate 

 probability of failure per unit time. As a consequence of the ubiquitous random component 

 in physiologic performance, a population of individuals that are indistinguishable by any 

 combination of physiologic measurements will nevertheless manifest time-survival and dosage- 

 survival curves with finite dispersions. This is illustrated by means of a one-dimensional 

 model system subjected to a stationary Gaussian random noise disturbance. In real biological 

 populations, there is a component of variance between individuals. This can be taken into 

 account by a straightforward generalization of the basic equations for homogeneous popula- 

 tions. 



In this approach, aging is interpreted as a secular change in the values of the parameters 

 of the regulatory mechanisms. These secular changes are ultimately due to irreversible 

 changes in permanent or self-reproducing macromolecules. The rate of such irreversible 

 change is in turn dependent in part on the magnitude of local fluctuations away from 

 ideal steady state conditions for biochemical syntheses. There are thus two aspects to the 

 stability of organisms — the probability of mortality per unit time and the rate of increase 

 of this probability with time (age). Both are intimately dependent on the fluctuation 

 characteristics of physiologic performances. 



I. INTRODUCTION 



This paper discusses mortality and aging insofar as they depend on certain 

 statistical characteristics of organisms and populations. These characteristics, 

 which may be subsumed under the closely related concepts of fluctuation, 

 entropy, and information, have their origin in the dynamic nature of physiologic 

 processes. Much of the current methodology for the analysis of survival 

 curves is founded on the theory that the observed distributions of survival 

 are due to the existence of a distribution of sensitivities in the populations 

 tested. The present discussion is intended to emphasize the statistical nature 

 of the mortality process within the individual, or in populations of indistinguish- 

 able individuals. Only those aspects of behavior are considered that have to 

 do with the establishment and preservation of the steady state of physiologic 

 function, and that can be described by a set of fixed relations among a finite, 

 and in fact quite small, number of physiologic processes. Implicit in this 

 approach is the conception of physiologic process as functional unit rather 

 than as ultimate enzymatic reaction-step. 



* Work performed under the auspices of the U.S. Atomic Energy Commission. 



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