Stochastic and deterministic simulations of a delayed genetic oscillation model: Investigating the validity of reductions |
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| Authors: | Samuel Bottani Basil Grammaticos |
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| Affiliation: | 1. Laboratoire Matières et Systèmes Complexes, Université Paris 7 Diderot, CNRS UMR 705710 rue A. Domon et L. Duquet, 75205 Paris Cedex 13, France;2. CNRS UMR 8165, Universités Paris 7 Diderot, Paris 11, Lab. IMNC, bât. 440, 91406 Orsay Cedex, France;1. Ecole National Superieure, 46 rue d''Ulm, 75230 Paris, France;2. Hopital de la Salpetriere, 47 bd. de l''Hopital, 75651 Paris Cedex 13, France;3. CNRS&Universite 7-Denis Diderot, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13, France;1. Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin 300071, PR China;2. Laboratory of Clinic, People''s Hospital of Gaomi City, Gaomi, Shandong 261000, PR China;3. Tianjin Key Laboratory of Biosensing and Molecular Recognition, Tianjin 300071, PR China;4. State Key Laboratory of Medicinal Chemical Biology, Tianjin 300071, PR China;5. Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin 300071, PR China;1. The Associated Laboratory for Green Chemistry (LAQV) of the Network of Chemistry and Technology (REQUIMTE) - the Portuguese Research Centre for Sustainable Chemistry, Department of Chemical Sciences, Faculty of Pharmacy, University of Porto, 4050-313, Porto, Portugal;2. Research Centre in Chemistry (CIQ-UP), DGAOT, Faculty of Sciences, University of Porto, 4169-007, Porto, Portugal;1. College of Life Sciences, Northwest University, Xi''an, 710069, China;2. The Seventh Affiliated Hospital, Sun Yat-sen University, Shenzhen, 518107, China |
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| Abstract: | ![]()
Quasi-stationary approximations are commonly used in order to simplify and reduce the number of equations of genetic circuit models. Protein/protein and protein/DNA binding reactions are considered to occur on much shorter time scale than protein production and degradation processes and often tacitly assumed at a quasi-equilibrium. Taking a biologically inspired, typical, small, abstract, negative feedback, genetic circuit model as study case, we investigate in this paper how different quasi-stationary approximations change the system behaviour both in deterministic and stochastic frameworks. We investigate the consistence between the deterministic and stochastic behaviours of our time-delayed negative feedback genetic circuit model with different implementations of quasi-stationary approximations. Quantitative and qualitative differences are observed among the various reduction schemes and with the underlying microscopic model, for biologically reasonable ranges and combinations of the microscopic model kinetic rates. The different reductions do not behave in the same way: correlations and amplitudes of the stochastic oscillations are not equally captured and the population behaviour is not always in consistence with the deterministic curves. |
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