| Full text | |
| Author(s): |
Gonzalez-Navarrete, Manuel
Total Authors: 1
|
| Document type: | Journal article |
| Source: | Mathematical Biosciences and Engineering; v. 13, n. 5, p. 981-998, OCT 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fernandez et. al {[}13], and are useful since take account to inherent variability of gene expression. We analyze a non symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, invented by Elowitz and Leibler {[}7]. We consider a mean-field dynamics for a type-dependent Ising model, and then study the empirical-magnetization vector representing concentration of molecules. We apply a convergence result from stochastic jump processes to deterministic trajectories and present a bifurcation analysis for the associated dynamical system. We show that non-symmetric module under study can exhibit very rich behaviours, including the empirical oscillations described by repressilator. (AU) | |
| FAPESP's process: | 15/02801-6 - Ising models with periodical external fields: phase diagrams and stochastic evolution |
| Grantee: | Manuel Alejandro González Navarrete |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |