Time Delays in a Genetic Positive-Feedback Circuit

Many principles of feedback control can be found implemented in complex biological networks. Dealing with transcription networks, positive feedbacks have been shown to frequently occur, providing biological toggle switches eventually leading a cell to its correct fate according to the proper stimulation. This note investigates the effects of delays related to the positive feedback of a basic transcription network. Motivation stems from the fact that, in spite of its toy-model features, the chosen transcription network is exploited to model the Tat feedback circuit that drives the HIV infected cells fate from active viral replication to latency. The delay is modeled by means of a cascade of transformations required to activate the transcription factor deputed to control: similar expedients are known to be exploited in cellular activities to schedule different biological functions at different timings. Our investigation is carried out by means of the stochastic approach, shown to be unavoidable to catch the noise-induced bimodality fashion of the circuit: by properly tuning the stochastic delay parameters, the regulatory circuit loses bimodality, and the transcription factor probability distribution converges to a Poisson distribution.

[1]  E. Rosenberg,et al.  Expansion and Contraction of HIV-Specific CD4 T Cells with Short Bursts of Viremia, but Physical Loss of the Majority of These Cells with Sustained Viral Replication1 , 2005, The Journal of Immunology.

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

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

[4]  Nils Blüthgen,et al.  Noise Management by Molecular Networks , 2009, PLoS Comput. Biol..

[5]  D. J. Kiviet,et al.  Stochasticity of metabolism and growth at the single-cell level , 2014, Nature.

[6]  M. Savageau.  Comparison of classical and autogenous systems of regulation in inducible operons , 1974, Nature.

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

[8]  Leor S Weinberger,et al.  Stochastic gene expression as a molecular switch for viral latency. , 2009, Current opinion in microbiology.

[9]  Gabriella Mavelli,et al.  Block-tridiagonal state-space realization of Chemical Master Equations: A tool to compute explicit solutions , 2016, J. Comput. Appl. Math..

[10]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[11]  Eduardo D. Sontag,et al.  Molecular Systems Biology and Control , 2005, Eur. J. Control.

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

[13]  J. Ferrell,et al.  Tuning the Activation Threshold of a Kinase Network by Nested Feedback Loops , 2009, Science.

[14]  Costanzo Manes,et al.  Whi5 phosphorylation embedded in the G1/S network dynamically controls critical cell size and cell fate , 2016, Nature Communications.

[15]  J. Ferrell,et al.  A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision , 2003, Nature.

[16]  M. L. Simpson,et al.  Transient-mediated fate determination in a transcriptional circuit of HIV , 2007, Nature Genetics.

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

[18]  D. Hazuda,et al.  The Challenge of Finding a Cure for HIV Infection , 2009, Science.

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

[20]  Abhyudai Singh,et al.  Stochastic analysis of genetic feedback circuit controlling HIV cell-fate decision , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[21]  Leor S Weinberger,et al.  An HIV Feedback Resistor: Auto-Regulatory Circuit Deactivator and Noise Buffer , 2006, PLoS biology.

[22]  Jan Vijg,et al.  Increased cell-to-cell variation in gene expression in ageing mouse heart , 2006, Nature.

[23]  M. Khammash,et al.  Systematic Identification of Signal-Activated Stochastic Gene Regulation , 2013, Science.

[24]  Lilia Alberghina,et al.  Mathematical Modelling of DNA Replication Reveals a Trade-off between Coherence of Origin Activation and Robustness against Rereplication , 2010, PLoS Comput. Biol..

[25]  Jared E. Toettcher,et al.  Stochastic Gene Expression in a Lentiviral Positive-Feedback Loop: HIV-1 Tat Fluctuations Drive Phenotypic Diversity , 2005, Cell.

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

[27]  Johan Paulsson,et al.  Stochastic Switching of Cell Fate in Microbes. , 2015, Annual review of microbiology.