A deterministic model for one-dimensional excluded flow with local interactions

Modeling mRNA Translation With Ribosome Abortions

We derive a deterministic mathematical model for the flow of ribosomes along a mRNA called the ribosome flow model with extended objects and abortions (RFMEOA). This model incorporates important cellular features such as every ribosome covers several codons and they may detach from various regions along the track due to more realistic biological situations including phenomena of ribosome-ribosome collisions. We prove that the ribosome density profile along the mRNA in the RFMEOA and in particular, the protein production rate converge to a unique steady-state. Simulations of the RFMEOA demonstrate a surprising result that an increase in the initiation rate may sometimes lead to a decrease in the production rate. We believe that this model could be helpful to provide insight into the effects of premature termination on the protein expression and be useful for understanding and re-engineering the translation process.

A theoretical framework to analyse the flow of particles in a dynamical system with stochastic transition rates and site capacities

We study the stochasticity in a dynamical model: ribosome flow model with different site sizes that models the unidirectional movement of particles controlled by transition rates along a lattice having different site sizes. Our work models the parameters as random variables with known distributions and investigates the steady-state flow rate under this notion by using tools from the random matrix theory. Some closed-form theoretical results are derived for the steady-state flow rate under some restrictive assumptions such as random variables being independent and identically distributed. Furthermore, for arbitrary but bounded stochastic transition rates, stochastic site capacities, or both, we establish bounds for the steady-state flow rate. Our analysis can be generalized and applied to study the flow of particles in numerous transport systems in the stochastic environment.

Modeling transport of extended interacting objects with drop-off phenomenon

We study a deterministic framework for important cellular transport phenomena involving a large number of interacting molecules called the excluded flow of extended interacting objects with drop-off effect (EFEIOD). This model incorporates many realistic features of biological transport process including the length of biological “particles” and the fact that they can detach along the biological ‘tracks’. The flow between the consecutive sites is unidirectional and is described by a “soft” simple exclusion principle and by repelling or attracting forces between neighboring particles. We show that the model admits a unique steady-state. Furthermore, if the parameters are periodic with common period T, then the steady-state profile converge to a unique periodic solution of period T. Simulations of the EFEIOD demonstrate several non-trivial effects of the interactions on the system steady-state profile. For example, detachment rates may help in increasing the steady-state flow by alleviating traffic jams that can exist due to several reasons like bottleneck rate or interactive forces between the particles. We also analyze the special case of our model, when there are no forces exerted by neighboring particles, and called it as the ribosome flow model of extended objects with drop-off effect (RFMEOD), and study the sensitivity of its steady-state to variations in the parameters.

Variability in mRNA translation: a random matrix theory approach

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.