Driven transport on a flexible polymer with particle recycling: A model inspired by transcription and translation

Distributed fixed resources exchanging particles: Phases of an asymmetric exclusion process connected to two reservoirs

We propose and study a conceptual one-dimensional model to explore how the combined interplay between fixed resources with unlimited carrying capacity and particle exchanges between different parts of an extended system can affect the stationary densities in a current-carrying channel connecting different parts of the system. Our model is composed of a totally asymmetric simple exclusion process (TASEP) connecting two particle reservoirs without any internal dynamics, but which can directly exchange particles between each other, ensuring nonvanishing currents in the TASEP lane in the steady states. The total particle number in the system that defines the "resources" available, although held conserved by the model dynamics, can take any value giving unrestricted carrying capacity. We show how the resulting phase diagrams of the model are controlled by relevant parameters, together with the total available resources. These control parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous with localized domain walls, and can also control populations of the two reservoirs. In general, the phase diagrams are quite different from a TASEP with open boundaries. However, in the limit of a large amount of resources, the phase diagrams in the plane of the control parameters become topologically identical to that for an open TASEP along with delocalization of domain walls.

Availability versus carrying capacity: Phases of asymmetric exclusion processes competing for finite pools of resources

We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady-state currents and density profiles in the one-dimensional current-carrying lanes connecting the different parts of the system. To study this, we set up a minimal model consisting of two particle reservoirs of the same finite carrying capacity connected by two equally sized antiparallel totally asymmetric simple exclusion processes (TASEPs). We focus on the steady-state currents and particle density profiles in the two TASEP lanes. The ensuing phases and the phase diagrams, which can be remarkably complex, are parametrized by the model parameters defining particle exchange between the TASEP lanes and the reservoirs and the filling fraction of the particles that determine the total resources available. These parameters may be tuned to make the densities of the two TASEP lanes globally uniform or piece-wise continuous in the form of a combination of a single localized domain wall and a spatially constant density or a pair of delocalized domain walls. Our model reveals that the two reservoirs can be preferentially populated or depopulated in the steady states.

Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

We explore how the interplay of finite availability, carrying capacity of particles at different parts of a spatially extended system, and particle diffusion between them control the steady-state currents and density profiles in a one-dimensional current-carrying channel connecting the different parts of the system. To study this, we construct a minimal model consisting of two particle reservoirs of finite carrying capacities connected by a totally asymmetric simple exclusion process (TASEP). In addition to particle transport via TASEP between the reservoirs, the latter can also directly exchange particles via Langmuir kinetics-like processes, modeling particle diffusion between them that can maintain a steady current in the system. We calculate the steady-state density profiles and the associated particle currents in the TASEP lane. The resulting phases and the phase diagrams are quite different from an open TASEP, and are characterized by the model parameters defining particle exchanges between the TASEP and the reservoirs, direct particle exchanges between the reservoirs, and the filling fraction of the particles that determines the total resources available. These parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous, and can make the two reservoirs preferentially populated or depopulated.

Vectorial channeling as a mechanism for translational control by functional prions and condensates

Translation of messenger RNA (mRNA) is regulated through a diverse set of RNA-binding proteins. A significant fraction of RNA-binding proteins contains prion-like domains which form functional prions. This raises the question of how prions can play a role in translational control. Local control of translation in dendritic spines by prions has been invoked in the mechanism of synaptic plasticity and memory. We show how channeling through diffusion and processive translation cooperate in highly ordered mRNA/prion aggregates as well as in less ordered mRNA/protein condensates depending on their substructure. We show that the direction of translational control, whether it is repressive or activating, depends on the polarity of the mRNA distribution in mRNA/prion assemblies which determines whether vectorial channeling can enhance recycling of ribosomes. Our model also addresses the effect of changes of substrate concentration in assemblies that have been suggested previously to explain translational control by assemblies through the introduction of a potential of mean force biasing diffusion of ribosomes inside the assemblies. The results from the model are compared with the experimental data on translational control by two functional RNA-binding prions, CPEB involved in memory and Rim4 involved in gametogenesis.

Modelling the effect of ribosome mobility on the rate of protein synthesis

Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and that mRNA circularization enhances the efficiency of translation, see e.g. Lodish et al. (Molecular cell biology, 8th edn, W.H. Freeman and Company, San Francisco, 2016). In order to estimate the effect of cytoplasmic diffusion on the rate of translation, we consider a totally asymmetric simple exclusion process coupled to a finite diffusive reservoir, which we call the ribosome transport model with diffusion. In this model, we derive an analytical expression for the rate of protein synthesis as a function of the diffusion constant of ribosomes, which is corroborated with results from continuous-time Monte Carlo simulations. Using a wide range of biological relevant parameters, we conclude that diffusion is not a rate limiting factor in translation initiation because diffusion is fast enough in biological cells.

What determines eukaryotic translation elongation: recent molecular and quantitative analyses of protein synthesis

Protein synthesis from mRNA is an energy-intensive and tightly controlled cellular process. Translation elongation is a well-coordinated, multifactorial step in translation that undergoes dynamic regulation owing to cellular state and environmental determinants. Recent studies involving genome-wide approaches have uncovered some crucial aspects of translation elongation including the mRNA itself and the nascent polypeptide chain. Additionally, these studies have fuelled quantitative and mathematical modelling of translation elongation. In this review, we provide a comprehensive overview of the key determinants of translation elongation. We discuss consequences of ribosome stalling or collision, and how the cells regulate translation in case of such events. Next, we review theoretical approaches and widely used mathematical models that have become an essential ingredient to interpret complex molecular datasets and study translation dynamics quantitatively. Finally, we review recent advances in live-cell reporter and related analysis techniques, to monitor the translation dynamics of single cells and single-mRNA molecules in real time.

Current-density relation in the exclusion process with dynamic obstacles

We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of obstacles that dynamically bind and unbind from the lattice. The model is motivated by biological processes such as transcription in the presence of DNA-binding proteins. Similar models have been studied before using the mean-field approximation, but the exact relation between the particle current and density remains elusive. Here, we first show using extensive Monte Carlo simulations that the current-density relation in this model assumes a quasiparabolic form similar to that of the ordinary TASEP without obstacles. We then attempt to explain this relation using exact calculations in the limit of low and high density of particles. Our results suggest that the symmetric, quasiparabolic current-density relation arises through a nontrivial cancellation of higher-order terms, similarly as in the standard TASEP.