Interaction of a Digital System with a Continuous One in the Cell
37
Acknowledgment
Through kindness of the late Professor J INBO the analogue computer of the
Meiji University was used for this study. In the computer work the author
was assisted by Dr. OGAWA and other members of the University. I wish to express
to them my sincere gratitude for their cooperation.
References
1. GOODWIN, B.C.: Temporal organization in cells. New York: Academic Press
1963.
2. HEINMETS, F.: Analysis of normal and abnormal cell growth. New York:
Plenum Press 1966.
3. SUGITA, M.: J. Theor. Biol. 1, 415 (1961).
4. - J. Theor. Biol. 4, 179 (1963).
5. - J. Theor. Biol. 13, 330 (1966a).
6. - Helgolander wiss. Meeresunters. 14, 78 (1966 b).
7. YeAS, M., M. SUGITA and A. BENSAM: J. Theor. Biol. 9,444 (1965).
KAeSER:
Disctlssion
I would like to ask Dr. SUGITA whether he uses the switch in his models for
ease of representation or whether he wants to make a point that there are in
fact discontinuities in the system.
SUGITA:
You want to know whether switching is only a computational convenience
or whether it has some physical meaning for the model. In the analogy between
the flux of chemical processes and the electrical current, I am considering the
existence or non-existence of an enzyme as a correspondence to "make" or
"break" of switches. Even though the quantity of an enzyme may vary
continuously, only a step function approximation may lead to its complete
efficiency. Thus, (E) = ag + bg, that is, when g = 1, (E) = a; when g = 0,
(g = 1), (E) = b. The binary quantity g may be the state of an operator gene;
when this one is repressed (g = 0), the enzyme formation becomes b, i.e.
very small.
KAesER:
In terms of observables we always find a small amount of enzyme. We have
very little evidence that there is a zero; one situation in the organism.
GRIFFITH:
In relation to Dr. KAesER's remark, I should like to point out that it is possible
to have a simple cellular regulatory mechanism which admits of two stable states
of activity, with an enzyme present in the one and absent in the other. Take the
equations
•
352
M = - - - - M
1 + 25 2
.
5=M-5
representing a cooperative inductive effect of a protein 5 on the formation of its
messenger M. These equations have stable stationary solutions 5 = M = 0
and 5 = M = 1 and an unstable solution 5 = M = 1/ 2 .
SUGITA:
I thank you for your valuable suggestions which are useful to support our
own idea (or intuition) that in kinetics two possible states should be taken into
consideration.
37
Acknowledgment
Through kindness of the late Professor J INBO the analogue computer of the
Meiji University was used for this study. In the computer work the author
was assisted by Dr. OGAWA and other members of the University. I wish to express
to them my sincere gratitude for their cooperation.
References
1. GOODWIN, B.C.: Temporal organization in cells. New York: Academic Press
1963.
2. HEINMETS, F.: Analysis of normal and abnormal cell growth. New York:
Plenum Press 1966.
3. SUGITA, M.: J. Theor. Biol. 1, 415 (1961).
4. - J. Theor. Biol. 4, 179 (1963).
5. - J. Theor. Biol. 13, 330 (1966a).
6. - Helgolander wiss. Meeresunters. 14, 78 (1966 b).
7. YeAS, M., M. SUGITA and A. BENSAM: J. Theor. Biol. 9,444 (1965).
KAeSER:
Disctlssion
I would like to ask Dr. SUGITA whether he uses the switch in his models for
ease of representation or whether he wants to make a point that there are in
fact discontinuities in the system.
SUGITA:
You want to know whether switching is only a computational convenience
or whether it has some physical meaning for the model. In the analogy between
the flux of chemical processes and the electrical current, I am considering the
existence or non-existence of an enzyme as a correspondence to "make" or
"break" of switches. Even though the quantity of an enzyme may vary
continuously, only a step function approximation may lead to its complete
efficiency. Thus, (E) = ag + bg, that is, when g = 1, (E) = a; when g = 0,
(g = 1), (E) = b. The binary quantity g may be the state of an operator gene;
when this one is repressed (g = 0), the enzyme formation becomes b, i.e.
very small.
KAesER:
In terms of observables we always find a small amount of enzyme. We have
very little evidence that there is a zero; one situation in the organism.
GRIFFITH:
In relation to Dr. KAesER's remark, I should like to point out that it is possible
to have a simple cellular regulatory mechanism which admits of two stable states
of activity, with an enzyme present in the one and absent in the other. Take the
equations
•
352
M = - - - - M
1 + 25 2
.
5=M-5
representing a cooperative inductive effect of a protein 5 on the formation of its
messenger M. These equations have stable stationary solutions 5 = M = 0
and 5 = M = 1 and an unstable solution 5 = M = 1/ 2 .
SUGITA:
I thank you for your valuable suggestions which are useful to support our
own idea (or intuition) that in kinetics two possible states should be taken into
consideration.