On contraction analysis for non-linear systems
Automatica (Journal of IFAC)
A Lyapunov function for tridiagonal competitive-cooperative systems
SIAM Journal on Mathematical Analysis
On the Steady-State Distribution in the Homogeneous Ribosome Flow Model
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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Gene translation is a central process in all living organisms. Developing a better understanding of this complex process may have ramifications to almost every biomedical discipline. Recently, Reuveni et al. proposed a new computational model of this process called the ribosome flow model (RFM). In this study, we show that the dynamical behavior of the RFM is relatively simple. There exists a unique equilibrium point e and every trajectory converges to e. Furthermore, convergence is monotone in the sense that the distance to e can never increase. This qualitative behavior is maintained for any feasible set of parameter values, suggesting that the RFM is highly robust. Our analysis is based on a contraction principle and the theory of monotone dynamical systems. These analysis tools may prove useful in studying other properties of the RFM as well as additional intracellular biological processes.