Robust adaptation and homeostasis by autocatalysis.

Robust homeostatic mechanisms are essential for the protection and adaptation of organisms in a changing and challenging environment. Integral feedback is a control-engineering concept that leads to robust, i.e., perturbation-independent, adaptation and homeostatic behavior in the controlled variable. Addressing two-component negative feedback loops of a controlled variable A and a controller molecule E, we have shown that integral control is closely related to the presence of zero-order fluxes in the removal of the manipulated variable E. Here we show that autocatalysis is an alternative mechanism to obtain integral control. Although the conservative and marginal stability of the Lotka-Volterra oscillator (LVO) with autocatalysis in both A and E is often considered as a major inadequacy, homeostasis in the average concentrations of both A and E ( and ) is observed. Thus, autocatalysis does not only represent a mere driving force, but may also have regulatory roles.

[1]  M. Savageau.  Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. , 1969, Journal of theoretical biology.

[2]  Jacek Kuznicki,et al.  Calcium ions in neuronal degeneration , 2008, IUBMB life.

[3]  John C. Polkinghorne,et al.  Ordinary differential equations using MATLAB , 1999 .

[4]  M. Muir.  Physical Chemistry , 1888, Nature.

[5]  Victoria Tapia,et al.  An oxidative stress‐mediated positive‐feedback iron uptake loop in neuronal cells , 2002, Journal of neurochemistry.

[6]  A. Goldbeter,et al.  Biochemical Oscillations And Cellular Rhythms: Contents , 1996 .

[7]  Brian Ingalls,et al.  Considerations for using integral feedback control to construct a perfectly adapting synthetic gene network. , 2010, Journal of theoretical biology.

[8]  A Goldbeter,et al.  A mechanism for exact sensory adaptation based on receptor modification. , 1986, Journal of Theoretical Biology.

[9]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[10]  A. J. Lotka.  Contribution to the Theory of Periodic Reactions , 1909 .

[11]  C. Ladd Prosser,et al.  Homeostasis. Origins of the concept , 1976, Medical History.

[12]  D. DeAngelis,et al.  Positive Feedback in Natural Systems , 1986 .

[13]  K. Sneppen,et al.  Simplified models of biological networks. , 2010, Annual review of biophysics.

[14]  J. T. Reason,et al.  Handbook of Life Stress, Cognition and Health , 1988 .

[15]  Achim Peters,et al.  Modeling the hypothalamus–pituitary–adrenal system: homeostasis by interacting positive and negative feedback , 2009, Journal of biological physics.

[16]  J. Tyson,et al.  Design principles of biochemical oscillators , 2008, Nature Reviews Molecular Cell Biology.

[17]  Qingwu Yang,et al.  Dynamic responses of protein homeostatic regulatory mechanisms to perturbations from steady state. , 2003, Journal of theoretical biology.

[18]  Peter Ruoff,et al.  Integrating fluctuating nitrate uptake and assimilation to robust homeostasis. , 2012, Plant, cell & environment.

[19]  Charles H. Feinstein,et al.  Socialism, Capitalism and Economic Growth: Essays Presented to Maurice Dobb. , 1968 .

[20]  J. Doyle,et al.  Robust perfect adaptation in bacterial chemotaxis through integral feedback control. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Nori Kurata,et al.  Positive Autoregulation of a KNOX Gene Is Essential for Shoot Apical Meristem Maintenance in Rice[W][OA] , 2011, Plant Cell.

[22]  A. Winfree.  The geometry of biological time , 1991 .

[23]  G. Zajicek,et al.  The Wisdom of the Body , 1934, Nature.

[24]  J. Higgins.  The Theory of Oscillating Reactions - Kinetics Symposium , 1967 .

[25]  杉江 昇,et al.  J.H. Milsum: Biological Control Systems Analysis, McGraw-Hill Book Co., New York, 1966, 466頁, 15×23cm, 7,000円. , 1967 .

[26]  N. Mehlmer,et al.  Plant organellar calcium signalling: an emerging field. , 2012, Journal of experimental botany.

[27]  W. Lim,et al.  Defining Network Topologies that Can Achieve Biochemical Adaptation , 2009, Cell.

[28]  A. J. Lotka.  Elements of Physical Biology. , 1925, Nature.

[29]  J H Koeslag,et al.  Integral rein control in physiology. , 1998, Journal of theoretical biology.

[30]  Melissa Glendening Craig,et al.  Glutamate-induced glutamate release: a proposed mechanism for calcium bursting in astrocytes. , 2005, Chaos.

[31]  G. Kraepelin,et al.  A. T. Winfree, The Geometry of Biological Time (Biomathematics, Vol.8). 530 S., 290 Abb. Berlin‐Heidelberg‐New‐York 1980. Springer‐Verlag. DM 59,50 , 1981 .

[32]  M. Khammash,et al.  Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective. , 2002, Journal of theoretical biology.

[33]  William H. Press,et al.  Numerical recipes , 1990 .

[34]  John Jechura.  An introduction to control systems , 1995 .

[35]  Peter Ruoff,et al.  Predicting perfect adaptation motifs in reaction kinetic networks. , 2008, The journal of physical chemistry. B.

[36]  P. Ruoff,et al.  The control of the controller: molecular mechanisms for robust perfect adaptation and temperature compensation. , 2009, Biophysical journal.

[37]  J. Rogers.  Chaos , 1876 .

[38]  Michael F. Crowley,et al.  Experimental and theoretical studies of a coupled chemical oscillator: phase death, multistability, and in-phase and out-of-phase entrainment , 1989 .

[39]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

[40]  Walter B. Cannon.  THE WISDOM OF THE BODY. REVISED AND ENLARGED EDITION , 1940 .

[41]  Alan C. Hindmarsh,et al.  Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations , 1993 .

[42]  Jacques Demongeot,et al.  Roles of positive and negative feedback in biological systems. , 2002, Comptes rendus biologies.

[43]  William H. Press,et al.  Numerical recipes : the art of scientific computing : FORTRAN version , 1989 .

[44]  John H. Milsum,et al.  Biological Control Systems Analysis , 1966 .

[45]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[46]  Jay Schulkin.  Rethinking Homeostasis: Allostatic Regulation in Physiology and Pathophysiology , 2002 .

[47]  V. S. Markin,et al.  Theory of excitable media , 1987 .

[48]  L. Dolan,et al.  Local Positive Feedback Regulation Determines Cell Shape in Root Hair Cells , 2008, Science.

[49]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[50]  Peter Ruoff,et al.  Temperature compensation through systems biology , 2007, The FEBS journal.

[51]  Irving R. Epstein,et al.  TURING STRUCTURES IN SIMPLE CHEMICAL REACTIONS , 1993 .

[52]  A. J. Lotka.  UNDAMPED OSCILLATIONS DERIVED FROM THE LAW OF MASS ACTION. , 1920 .

[53]  J. R. Pomerening,et al.  Uncovering mechanisms of bistability in biological systems. , 2008, Current opinion in biotechnology.

[54]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[55]  Thomas Höfer,et al.  Models of IP3 and Ca2+ oscillations: frequency encoding and identification of underlying feedbacks. , 2006, Biophysical journal.

[56]  A. J. Lotka,et al.  Elements of Physical Biology. , 1925, Nature.

[57]  Grégoire Nicolis,et al.  Self-Organization in nonequilibrium systems , 1977 .

[58]  M. Savageau.  Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology , 1976 .

[59]  Peter J. Wangersky,et al.  Lotka-Volterra Population Models , 1978 .

[60]  R. J. Field,et al.  Oscillations and Traveling Waves in Chemical Systems , 1985 .