The Interplay between Feedback and Buffering in Cellular Homeostasis.

Buffering, the use of reservoirs of molecules to maintain concentrations of key molecular species, and negative feedback are the primary known mechanisms for robust homeostatic regulation. To our knowledge, however, the fundamental principles behind their combined effect have not been elucidated. Here, we study the interplay between buffering and negative feedback in the context of cellular homeostasis. We show that negative feedback counteracts slow-changing disturbances, whereas buffering counteracts fast-changing disturbances. Furthermore, feedback and buffering have limitations that create trade-offs for regulation: instability in the case of feedback and molecular noise in the case of buffering. However, because buffering stabilizes feedback and feedback attenuates noise from slower-acting buffering, their combined effect on homeostasis can be synergistic. These effects can be explained within a traditional control theory framework and are consistent with experimental observations of both ATP homeostasis and pH regulation in vivo. These principles are critical for studying robustness and homeostasis in biology and biotechnology.

[1]  Douglas P. Looze,et al.  A Sensitivity Tradeoff for Plants with Time Delay , 1985, 1985 American Control Conference.

[2]  Jordan Ang,et al.  Physical constraints on biological integral control design for homeostasis and sensory adaptation. , 2013, Biophysical journal.

[3]  Jorge Goncalves,et al.  Control theory and systems biology , 2009 .

[4]  G. Vinnicombe,et al.  Fundamental limits on the suppression of molecular fluctuations , 2010, Nature.

[5]  B. Sharma Kinetic Characterisation of Phosphofructokinase Purified from Setaria cervi: A Bovine Filarial Parasite , 2011, Enzyme research.

[6]  M. Khammash,et al.  Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. , 2016, Cell systems.

[7]  Fuzhong Zhang,et al.  Negative feedback regulation of fatty acid production based on a malonyl-CoA sensor-actuator. , 2015, ACS synthetic biology.

[8]  J. Lowenstein,et al.  The purine nucleotide cycle. 3. Oscillations in metabolite concentrations during the operation of the cycle in muscle extracts. , 1973, The Journal of biological chemistry.

[9]  Hiroaki Kitano,et al.  Biological robustness , 2008, Nature Reviews Genetics.

[10]  J. Forchhammer,et al.  Growth rate of polypeptide chains as a function of the cell growth rate in a mutant of Escherichia coli 15. , 1971, Journal of molecular biology.

[11]  Norman S. Nise,et al.  Control Systems Engineering , 1991 .

[12]  M. Kushmerick,et al.  Mammalian skeletal muscle fibers distinguished by contents of phosphocreatine, ATP, and Pi. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

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

[14]  Ramon Grima,et al.  Linear-noise approximation and the chemical master equation agree up to second-order moments for a class of chemical systems. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  D. W. Pettigrew,et al.  Rabbit muscle phosphofructokinase. A model for regulatory kinetic behavior. , 1979, The Journal of biological chemistry.

[16]  Abhyudai Singh,et al.  Nonspecific transcription factor binding can reduce noise in the expression of downstream proteins , 2015, Physical biology.

[17]  S. Skogestad,et al.  Buffer Tank Design for Acceptable Control Performance , 2003 .

[18]  L. Segel,et al.  Extending the quasi-steady state approximation by changing variables. , 1996, Bulletin of mathematical biology.

[19]  J. Elf,et al.  Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. , 2003, Genome research.

[20]  K. Tornheim,et al.  Modulation by citrate of glycolytic oscillations in skeletal muscle extracts. , 1991, The Journal of biological chemistry.

[21]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[22]  A. T. Reid On Stochastic Processes in Biology , 1953 .

[23]  J. Weiss,et al.  Glycolytic Oscillations in Isolated Rabbit Ventricular Myocytes* , 2008, Journal of Biological Chemistry.

[24]  J. Keasling,et al.  Effect of Polyphosphate Metabolism on the Escherichia coli Phosphate‐Starvation Response , 1999, Biotechnology progress.

[25]  A. Kornberg Inorganic polyphosphate: a molecule of many functions. , 2003, Annual review of biochemistry.

[26]  J. Collins,et al.  A brief history of synthetic biology , 2014, Nature Reviews Microbiology.

[27]  D. Mashek,et al.  Regulation of Glucose Metabolism - A Perspective From Cell Bioprocessing. , 2016, Trends in biotechnology.

[28]  H. Rosenberg,et al.  The determination and distribution of phosphocreatine in animal tissues. , 1952, The Biochemical journal.

[29]  E. Hofmann,et al.  Some kinetic and molecular properties of yeast phosphofructokinase , 1968, FEBS letters.

[30]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[31]  Mathieu Cloutier,et al.  The control systems structures of energy metabolism , 2010, Journal of The Royal Society Interface.

[32]  Alberto Maria Bersani,et al.  Quasi steady-state approximations in complex intracellular signal transduction networks – a word of caution , 2008 .

[33]  P. Walker,et al.  A comparison of the properties of the phosphofructokinases of the fat body and flight muscle of the adult male desert locust. , 1969, The Biochemical journal.

[34]  Jozef Nahalka,et al.  Polyphosphate - an ancient energy source and active metabolic regulator , 2011, Microbial cell factories.

[35]  Konstantinos Michalodimitrakis,et al.  Noise in transcription negative feedback loops: simulation and experimental analysis , 2006, Molecular systems biology.

[36]  P. W. Hochachka,et al.  Activation of muscle glycolysis: A role for creatine phosphate in phosphofructokinase regulation , 1974, FEBS letters.

[37]  Jose B. Cruz,et al.  Feedback systems , 1971 .

[38]  Arthur Kornberg,et al.  Inorganic polyphosphate: essential for growth and survival. , 2009, Annual review of biochemistry.

[39]  D. Looze,et al.  A sensitivity tradeoff for plants with time delay , 1987 .

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

[41]  E. Newsholme,et al.  The contents of adenine nucleotides, phosphagens and some glycolytic intermediates in resting muscles from vertebrates and invertebrates. , 1975, The Biochemical journal.

[42]  R. G. Kemp,et al.  The mechanism of ATP inhibition of wild type and mutant phosphofructo-1-kinase from Escherichia coli. , 1992, The Journal of biological chemistry.

[43]  Edda Klipp,et al.  Systems Biology , 1994 .

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

[45]  James P. Keener,et al.  Mathematical physiology , 1998 .

[46]  H. Othmer,et al.  Oscillatory cAMP signaling in the development of Dic-tyostelium discoideum , 1998 .

[47]  H. Kitano Towards a theory of biological robustness , 2007, Molecular systems biology.

[48]  Antonis Papachristodoulou,et al.  Simplified mechanistic models of gene regulation for analysis and design , 2015, Journal of The Royal Society Interface.

[49]  W. Cannon The Wisdom of the Body , 1932 .

[50]  U. Alon An introduction to systems biology : design principles of biological circuits , 2019 .

[51]  M. Rooman,et al.  Stochastic noise reduction upon complexification: positively correlated birth-death type systems. , 2014, Journal of theoretical biology.

[52]  David Moxey,et al.  Glycolytic Oscillations and Limits on Robust Efficiency , 2011 .

[53]  Yuhai Tu,et al.  Perfect and near-perfect adaptation in a model of bacterial chemotaxis. , 2002, Biophysical journal.

[54]  Deepak Mishra,et al.  A load driver device for engineering modularity in biological networks , 2014, Nature Biotechnology.

[55]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[56]  J. Raser,et al.  Noise in Gene Expression: Origins, Consequences, and Control , 2005, Science.

[57]  R. G. Kemp Rabbit liver phosphofructokinase. Comparison of some properties with those of muscle phosphofructokinase. , 1971, The Journal of biological chemistry.

[58]  A. Sols,et al.  Modulation of muscle phosphofructokinase at physiological concentration of enzyme. , 1985, The Journal of biological chemistry.

[59]  J. Keasling,et al.  Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids , 2012, Nature Biotechnology.

[60]  A. Oudenaarden,et al.  A Systems-Level Analysis of Perfect Adaptation in Yeast Osmoregulation , 2009, Cell.

[61]  L. Sherwood Human Physiology : From Cells to Systems , 1989 .

[62]  Diego A Oyarzún,et al.  Noise propagation in synthetic gene circuits for metabolic control. , 2015, ACS synthetic biology.

[63]  P. Sugden,et al.  The effects of ammonium, inorganic phosphate and potassium ions on the activity of phosphofructokinases from muscle and nervous tissues of vertebrates and invertebrates. , 1975, The Biochemical journal.

[64]  M. McCormick,et al.  Interaction among Skeletal Muscle Metabolic Energy Systems during Intense Exercise , 2010, Journal of nutrition and metabolism.

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