Optimization of Structure and Metabolism
in Cellular Automata
A. CRISTEA
Abstract
Within a general theory of open systems isolated cells can be considered as
automata with superordinate control levels, being affected by the environment
as well as by interactions of the components. The equations of motion determine
the changes of position, shape, reactivity and activity. An overall criterion for
optimization of structure and metabolism fixes the mean trajectories, thus inducing
the logical control level to make the decisions optimal. The numerical value of
the maximum can be taken as an expression for biological quality, which in the
course of natural evolution increases autocatalytically.
Structure and Function of Automata
Cellular automata are open non-homogeneous systems revealing diverse
and variable structures. Interactions of the structures with signals partly
admit these to flow through the system according to certain drifts, and
partly allow free interactions of the components. A combined application
of methods derived from statistical mechanics as well as from cybernetics seems to be most appropriate to the description of biological
automata.
In the complete set of parameters, i.e. dimensions of the phase space
(5), the equations of motion form a dynamical system, referring (a) to
geometric characteristics, (b) to reactivities, i.e. symmetrical interactions
inducing shifts in the phase space, and (c) to activities, i.e. asymmetrical
interactions changing the signals following a prescribed program. The
structure can be represented by nodes and edges of a graph, described by
concentrations and flows, respectively, of signals. In this scheme the
outputs depend on the inputs. The structure is furthermore disposed of two
levels, one superior, exerting processing activity on the signals, which are
generated in the second, inferior one by accepting information from the
environment. The amount and efficiency of information and control can
be visualized by the distance existing between optimal and mean trajectory.
In a stochastic evolution the open system can be considered as a linear
Markovian process [1, 3]; by applying a generalized WIENER-FEYNMAN
procedure [4, 6], irreversible non-stationarities as a connection of the
in Cellular Automata
A. CRISTEA
Abstract
Within a general theory of open systems isolated cells can be considered as
automata with superordinate control levels, being affected by the environment
as well as by interactions of the components. The equations of motion determine
the changes of position, shape, reactivity and activity. An overall criterion for
optimization of structure and metabolism fixes the mean trajectories, thus inducing
the logical control level to make the decisions optimal. The numerical value of
the maximum can be taken as an expression for biological quality, which in the
course of natural evolution increases autocatalytically.
Structure and Function of Automata
Cellular automata are open non-homogeneous systems revealing diverse
and variable structures. Interactions of the structures with signals partly
admit these to flow through the system according to certain drifts, and
partly allow free interactions of the components. A combined application
of methods derived from statistical mechanics as well as from cybernetics seems to be most appropriate to the description of biological
automata.
In the complete set of parameters, i.e. dimensions of the phase space
(5), the equations of motion form a dynamical system, referring (a) to
geometric characteristics, (b) to reactivities, i.e. symmetrical interactions
inducing shifts in the phase space, and (c) to activities, i.e. asymmetrical
interactions changing the signals following a prescribed program. The
structure can be represented by nodes and edges of a graph, described by
concentrations and flows, respectively, of signals. In this scheme the
outputs depend on the inputs. The structure is furthermore disposed of two
levels, one superior, exerting processing activity on the signals, which are
generated in the second, inferior one by accepting information from the
environment. The amount and efficiency of information and control can
be visualized by the distance existing between optimal and mean trajectory.
In a stochastic evolution the open system can be considered as a linear
Markovian process [1, 3]; by applying a generalized WIENER-FEYNMAN
procedure [4, 6], irreversible non-stationarities as a connection of the