A Model for Sustained Rhythmic Binary Logic
in Biochemical Systems
CH. WALTER l
With 2 Figures
Abstract
A model chemical system is discussed as a possible basis for sustained rhythmic
binary logic in biological systems. The model includes a "branch point" enzyme
and two metabolic pathways. One pathway is a typical negative feedback scheme
of the Yates-Pardee type; the other pathway involves a series of enzymes capable
of displaying sigmoid relationships between activity and substrate concentration.
Under the conditions described the concentration of one substance in the model
is either very low ("off") or, except for a short interval, very high ("on"). The
time of the "off" to "on" or "on" to "off" transition is small compared to the
total period of each cycle. The "on" -"off" cycle is sustained for at least 200 periods.
I. Introduction
Experimental results in biology often suggest the existence of rhythmic
events which seem to either occur or not occur. Since the fundamental
cause of all biological events stems from the constituent biochemical
reactions, it seems likely that the cause of sustained rhythms of such biological "on-off" switches must also result from chemical reactions.
For a chemical model to serve as the source of sustained rhythmic
events it is necessary for the model to be capable of sustained oscillation
and to exhibit binary or "on-off" character. However, in most concepts of
chemical reactions the process is considered to be essentially continuous.
Furthermore, it is well known that chemical oscillations around an equilibrium state are thermodynamically impossible. These facts have served as
the basis of criticism of suggestions that chemical systems can exhibit
sustained oscillations or serve as the source of binary logic.
There are several reasons why this criticism is not justified in the case
of chemical reactions in biological systems. First, experimental results
clearly illustrate the existence of both oscillatory events and binary logic in
biological systems. Second, the fact that chemical reactions are essentially
1 Public Health Service Career Development Awardee, National Institutes of
Health award number K3-GM-ll,237.
in Biochemical Systems
CH. WALTER l
With 2 Figures
Abstract
A model chemical system is discussed as a possible basis for sustained rhythmic
binary logic in biological systems. The model includes a "branch point" enzyme
and two metabolic pathways. One pathway is a typical negative feedback scheme
of the Yates-Pardee type; the other pathway involves a series of enzymes capable
of displaying sigmoid relationships between activity and substrate concentration.
Under the conditions described the concentration of one substance in the model
is either very low ("off") or, except for a short interval, very high ("on"). The
time of the "off" to "on" or "on" to "off" transition is small compared to the
total period of each cycle. The "on" -"off" cycle is sustained for at least 200 periods.
I. Introduction
Experimental results in biology often suggest the existence of rhythmic
events which seem to either occur or not occur. Since the fundamental
cause of all biological events stems from the constituent biochemical
reactions, it seems likely that the cause of sustained rhythms of such biological "on-off" switches must also result from chemical reactions.
For a chemical model to serve as the source of sustained rhythmic
events it is necessary for the model to be capable of sustained oscillation
and to exhibit binary or "on-off" character. However, in most concepts of
chemical reactions the process is considered to be essentially continuous.
Furthermore, it is well known that chemical oscillations around an equilibrium state are thermodynamically impossible. These facts have served as
the basis of criticism of suggestions that chemical systems can exhibit
sustained oscillations or serve as the source of binary logic.
There are several reasons why this criticism is not justified in the case
of chemical reactions in biological systems. First, experimental results
clearly illustrate the existence of both oscillatory events and binary logic in
biological systems. Second, the fact that chemical reactions are essentially
1 Public Health Service Career Development Awardee, National Institutes of
Health award number K3-GM-ll,237.