Noise reduction for enzymatic reactions: A case study for stochastic product clearance

A basic (though rather general) enzymatic reaction scheme is investigated here, with a substrate that transforms into a product by means of the catalytic action of an enzyme. The aim is of quantifying the effects of feedback in noise propagation. Noise sources are twofold: one affects the enzyme production, assuming to happen according to finite bursts of molecules; the other concerns the product clearance, with the classical linear elimination rate affected by a Bernoulli random variable that can switch `on' or `off' the clearance. Two distinct feedback control schemes on enzyme production are considered here: one from the final product of the pathway activity, the other from the enzyme accumulation (negative autoregulation). Metabolic noise is defined in terms of the square of the coefficient of variation of the product, and computations are carried out by means of moment equations. Results show that, according to the type of the feedback parameter chosen to tune the feedback action, one of the two feedback schemes is preferable to the other with respect to noise reduction.

[1]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[2]  J. Hespanha,et al.  Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems , 2005 .

[3]  U. Alon,et al.  Just-in-time transcription program in metabolic pathways , 2004, Nature Genetics.

[4]  Abhyudai Singh,et al.  Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits , 2015, IEEE Transactions on Biomedical Circuits and Systems.

[5]  Domitilla Del Vecchio,et al.  Modularity, context-dependence, and insulation in engineered biological circuits , 2015 .

[6]  Lee A. Segel,et al.  On the validity of the steady state assumption of enzyme kinetics , 1988 .

[7]  Domitilla Del Vecchio,et al.  Synthetic Biology: A Systems Engineering Perspective , 2008 .

[8]  Eduardo Sontag,et al.  Exact Moment Dynamics for Feedforward Nonlinear Chemical Reaction Networks , 2015, IEEE Life Sciences Letters.

[9]  G. W. Hatfield,et al.  Autoregulation: a role for a biosynthetic enzyme in the control of gene expression. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Jay D. Keasling,et al.  Engineering Static and Dynamic Control of Synthetic Pathways , 2010, Cell.

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

[12]  João Pedro Hespanha,et al.  Approximate Moment Dynamics for Chemically Reacting Systems , 2011, IEEE Transactions on Automatic Control.

[13]  G. Stephanopoulos,et al.  Metabolic Engineering: Principles And Methodologies , 1998 .

[14]  J. Hespanha,et al.  Optimal feedback strength for noise suppression in autoregulatory gene networks. , 2009, Biophysical journal.

[15]  E. Cox,et al.  Real-Time Kinetics of Gene Activity in Individual Bacteria , 2005, Cell.

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

[17]  Alberto Maria Bersani,et al.  Deterministic and stochastic models of enzymatic networks - applications to pharmaceutical research , 2008, Comput. Math. Appl..

[18]  Eduardo Sontag,et al.  Modular cell biology: retroactivity and insulation , 2008, Molecular systems biology.

[19]  Pasquale Palumbo,et al.  Impact of negative feedback in metabolic noise propagation. , 2016, IET systems biology.

[20]  Pasquale Palumbo,et al.  Metabolic noise reduction for enzymatic reactions: The role of a negative feedback , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).