Interaction of a Digital (Genetic) System
with a Continuous (Enzymatic) One in the Cell
M. SUGITA
With 2 Figures
Abstract
According to certain assumptions concerning the interaction of a digital with
a continuous system in the cell-represented by the coupling of an analog computer with a relay circuit-mathematical models for mitosis and DNA replication
are proposed.
Introduction
In several papers [5, 6] we discussed the problem of an applicability of
continuous mathematics to cell metabolism, especially arising in the interaction of a continuous system with the so called molecular automaton [4].
Interactions of this kind can be observed e.g. in embryonic development,
in cytodifferentiation and in mitosis. We attempt to simulate such an
interacting system by applying a hybrid computing device and by taking
as an example a mathematical model of cell division.
Interaction of Continuous and Digital System
A DNA molecule carries genetic (i.e. base sequence of A, T, C, G) as
well as temporal information (active or inactive, i.e. readable or not). The
mRNA formation may correspond to reading and this digital information
may be envisaged as a control tape. The so-called repression or induction
may be considered as a feedback from the continuous to the digital system,
including DNA. The total system constitutes a molecular automaton,
whose internal states can be represented by a set of binary quantities,
&,g2'" .
Let us represent the kinetics of the continuous system by a set of
simultaneous first order differential equations
dXlk
~- = Alk - Blk
(1)
dt
3 3. Symp. Quant. BioI.
with a Continuous (Enzymatic) One in the Cell
M. SUGITA
With 2 Figures
Abstract
According to certain assumptions concerning the interaction of a digital with
a continuous system in the cell-represented by the coupling of an analog computer with a relay circuit-mathematical models for mitosis and DNA replication
are proposed.
Introduction
In several papers [5, 6] we discussed the problem of an applicability of
continuous mathematics to cell metabolism, especially arising in the interaction of a continuous system with the so called molecular automaton [4].
Interactions of this kind can be observed e.g. in embryonic development,
in cytodifferentiation and in mitosis. We attempt to simulate such an
interacting system by applying a hybrid computing device and by taking
as an example a mathematical model of cell division.
Interaction of Continuous and Digital System
A DNA molecule carries genetic (i.e. base sequence of A, T, C, G) as
well as temporal information (active or inactive, i.e. readable or not). The
mRNA formation may correspond to reading and this digital information
may be envisaged as a control tape. The so-called repression or induction
may be considered as a feedback from the continuous to the digital system,
including DNA. The total system constitutes a molecular automaton,
whose internal states can be represented by a set of binary quantities,
&,g2'" .
Let us represent the kinetics of the continuous system by a set of
simultaneous first order differential equations
dXlk
~- = Alk - Blk
(1)
dt
3 3. Symp. Quant. BioI.