Abstract
Down regulation of mRNA translation is an important problem in various bio-medical domains ranging from developing effective medicines for tumors and for viral diseases to developing attenuated virus strains that can be used for vaccination. Here, we study the problem of down regulation of mRNA translation using a mathematical model called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as a chain of n sites. The flow of ribosomes between consecutive sites is regulated by n + 1 transition rates. Given a set of feasible transition rates, that models the outcome of all possible mutations, we consider the problem of maximally down regulating protein production by altering the rates within this set of feasible rates. Under certain conditions on the feasible set, we show that an optimal solution can be determined efficiently. We also rigorously analyze two special cases of the down regulation optimization problem. Our results suggest that one must focus on the position along the mRNA molecule where the transition rate has the strongest effect on the protein production rate. However, this rate is not necessarily the slowest transition rate along the mRNA molecule. We discuss some of the biological implications of these results.
Highlights
Down regulation of mRNA translation is an important problem in various bio-medical domains ranging from developing effective medicines for tumors and for viral diseases to developing attenuated virus strains that can be used for vaccination
Our results suggest that one must focus on the position along the mRNA molecule where the transition rate has the strongest effect on the protein production rate
We consider down regulation of specific genes via targeting specific codons/regions in these genes. This leads to the problem of finding the codon regions that have the most effect on the steady-state production rate. We pose this problem of optimal down regulation of mRNA translation as a general optimization problem (Problem 1 above) for a mathematical model for ribosome flow, the ribosome flow model (RFM)
Summary
Yoram Zarai[1], Michael Margaliot1,2 & Tamir Tuller[2,3] received: 10 May 2016 accepted: 19 December 2016. We study the problem of down regulation of mRNA translation using a mathematical model called the ribosome flow model (RFM). A standard model for translation is the totally asymmetric simple exclusion process (TASEP)[25,26] In this model, particles hop unidirectionaly along an ordered lattice of N sites. The ribosome flow model (RFM)[29] is a nonlinear, continuous-time compartmental model for the unidirectional flow of “material” along a chain of n consecutive compartments (or sites) It can be derived via a mean-field approximation of TASEP27,30. The RFM approximates the equations describing the stochastic evolution of the site occupancy probabilities in TASEP by ignoring high-order correlations This provides a good approximation except perhaps at specific parameter values where TASEP undergoes a sharp change (phase transition). To the best of our knowledge, this is the first time that such a problem is analyzed in a dynamical model of mRNA translation
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