Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automaton

Sugita, Motoyosi

doi:10.1016/0022-5193(63)90027-4

Cited by 94 publications

(15 citation statements)

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“…Several authors have proposed to approximate the Hill functions by piecewise-linear (PWL) functions [5,22,23,31,44,45]. This approximation is based on the switch-like character displayed by some genes whose expression is regulated by steep sigmoid curves.…”

Section: Ordinary Differential Equationsmentioning

confidence: 99%

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

153

103

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A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical models for the purposes of analysis and design. For example, to synthesize a gene regulatory network, the derivation of a mathematical model is important in order to carry out in silico investigations of the network dynamics and to investigate parameter variations and robustness issues. Different mathematical frameworks have been proposed to derive such models. In particular, the use of sets of nonlinear ordinary differential equations (ODEs) has been proposed to model the dynamics of the concentrations of mRNAs and proteins. These models are usually characterized by the presence of highly nonlinear Hill function terms. A typical simplification is to reduce the number of equations by means of a quasi-steady-state assumption on the mRNA concentrations. This yields a class of simplified ODE models. A radically different approach is to replace the Hill functions by piecewise-linear approximations [5]. A further modelling approach is the use of discretetime maps [7] where the evolution of the system is modelled in discrete, rather than continuous, time. The aim of this paper is to discuss and compare these different modelling approaches, using a representative gene regulatory network. We will show that different models often lead to conflicting conclusions concerning the existence and stability of equilibria and stable oscillatory behaviours. Moreover, we shall discuss, where possible, the viability of making certain modelling approximations (e.g. quasi-steady-state mRNA dynamics or piecewise-linear approximations of Hill functions) and their effects on the overall system dynamics.

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Section: Ordinary Differential Equationsmentioning

confidence: 99%

Comparing different ODE modelling approaches for gene regulatory networks

Polynikis

Hogan

Bernardo

2009

Journal of Theoretical Biology

153

103

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“…In view of the sigmoidal character of the interactions, it was tempting to assimilate them to Heaviside on-off functions (Class and Kauffman, 1972Kauffman, , 1973Sugita, 1963;Thomas, 1973). Consequently, the control network is assimilated to a switching network which is described by a boolean mapping.…”

Section: Introductionmentioning

confidence: 99%

Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach

Snoussi

1989

Dynamics and Stability of Systems

114

122

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We propose a discrete mapping to study the qualitative properties of the dynamics of biological or other complex networks, involving switchlike interactions between the various elements. The stable steady states and the limit cycles of the piecewise-linear equations which model such networks are derived from the dynamical behaviour of the proposed discrete mapping. Furthermore, this mapping takes into account not only the logical structure of the network but also the parameters used in the description.

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“…Step by step his way of thinking became cybernetics-like, where the feedback control systems played an important role in his theory [46]- [59] [81] [83]- [91]. One of them was cited in Steuart Kauffman's famous book, The Origins of Order [99].…”

Section: The Research History Of Motoyosi Sugitamentioning

confidence: 99%

Motoyosi Sugita—A “Widely Unknown” Japanese Thermodynamicist Who Explored the 4th Law of Thermodynamics for Creation of the Theory of Life

Iguchi¹

2016

OJBIPHY

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The purpose of this paper is to introduce to you, the Western people, nowadays a "widely unknown" Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine's theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin's maximum principle in the theory of optimal control, I would like to explain

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Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automaton

Cited by 94 publications

References 1 publication

Comparing different ODE modelling approaches for gene regulatory networks

Comparing different ODE modelling approaches for gene regulatory networks

Qualitative dynamics of piecewise-linear differential equations: a discrete mapping approach

Motoyosi Sugita—A “Widely Unknown” Japanese Thermodynamicist Who Explored the 4th Law of Thermodynamics for Creation of the Theory of Life

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