A deterministic mathematical model for bidirectional excluded flow with Langmuir kinetics

Abstract

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological “particles” move along some kind of “tracks”. The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Inverted translational control of eukaryotic gene expression by ribosome collisions

“…In the simple abortive termination (SAT) model, stalled ribosomes are subject to kinetic competition between abortive termination and normal elongation (Fig 3A). This SAT model has been considered in recent modeling studies [35, 48, 49]. Because recent experiments found a role for ribosome collisions in quality control [26, 36, 37], we then considered two possible effects of ribosome collisions on abortive termination.…”

Inverted translational control of eukaryotic gene expression by ribosome collisions

“…Thus the extent of ribosome interference inferred in these earlier studies using the traf c jam model might not accurately represent the in vivo frequency of ribosome collisions. Modeling studies that consider abortive termination assume that ribosomes randomly drop-off during elongation 43,44 , or that abortive termination due to ribosome collisions is negligible 63 . Our work instead reveals that abortive termination occurs in response to ribosome collisions caused by elongation stalls, and that this process is highly regulated by cells using dedicated quality control factors.…”

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

“…Of course, implementing this with a very large r (or q) means very high effective transition rates, but our results suggest that even for r not much larger than one the increase in the flow is non-negligible. Another interesting topic for further research is generalizing the EFRBM to include the possibility of attachment/detachment of particles from intermediate sites in the lattice (see [45] for some related ideas).…”