Transport on a Lattice with Dynamical Defects

Many transport processes in nature take place on substrates, often considered as unidimensional lanes. These unidimensional substrates are typically non-static: affected by a fluctuating environment, they can undergo conformational changes. This is particularly true in biological cells, where the state of the substrate is often coupled to the active motion of macromolecular complexes, such as motor proteins on microtubules or ribosomes on mRNAs, causing new interesting phenomena. Inspired by biological processes such as protein synthesis by ribosomes and motor protein transport, we introduce the concept of localized dynamical sites coupled to a driven lattice gas dynamics. We investigate the phenomenology of transport in the presence of dynamical defects and find a novel regime characterized by an intermittent current and subject to severe finite-size effects. Our results demonstrate the impact of the regulatory role of the dynamical defects in transport, not only in biology but also in more general contexts

Mixed population of competing TASEPs with a shared reservoir of particles

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.Comment: 12 pages, 8 figure

Multiple phase transitions in a system of exclusion processes with limited reservoirs of particles and fuel carriers

The TASEP is a paradigmatic model from non-equilibrium statistical physics, which describes particles hopping along a lattice of discrete sites. The TASEP is applicable to a broad range of different transport systems, but does not consider the fact that in many such systems the availability of resources required for the transport is limited. In this paper we extend the TASEP to include the effect of a limited number of two different fundamental transport resources: the hopping particles, and the "fuel carriers", which provide the energy required to drive the system away from equilibrium. As as consequence, the system's dynamics are substantially affected: a "limited resources" regime emerges, where the current is limited by the rate of refuelling, and the usual coexistence line between low and high particle density opens into a broad region on the phase plane. Due to the combination of a limited amount of both resources, multiple phase transitions are possible when increasing the exit rate beta for a fixed entry rate alpha. This is a new feature that can only be obtained by the inclusion of both kinds of limited resources. We also show that the fluctuations in particle density in the LD and HD phases are unaffected by fluctuations in the number of loaded fuel carriers, except by the fact that when these fuel resources become limited, the particle hopping rate is severely reduced

The Dynamics of Supply and Demand in mRNA Translation

We study the elongation stage of mRNA translation in eukaryotes and find that, in contrast to the assumptions of previous models, both the supply and the demand for tRNA resources are important for determining elongation rates. We find that increasing the initiation rate of translation can lead to the depletion of some species of aa-tRNA, which in turn can lead to slow codons and queueing. Particularly striking “competition” effects are observed in simulations of multiple species of mRNA which are reliant on the same pool of tRNA resources. These simulations are based on a recent model of elongation which we use to study the translation of mRNA sequences from the Saccharomyces cerevisiae genome. This model includes the dynamics of the use and recharging of amino acid tRNA complexes, and we show via Monte Carlo simulation that this has a dramatic effect on the protein production behaviour of the system

Effects of dialysis technique on the acute hypotension: a model-based study

The patient's tendency to develop acute hemodialysis-induced hypotension can be influenced by the choice of hemodialysis technique (dialysate composition, filter, convection/diffusion ratio, etc.). We examined the hypothesis that the dialysis technique affects the pressure behavior during the sessions complicated by hypotension by altering the short-term compensatory reflexes to hemodialysis-induced hypovolemia. Hypotension-prone subjects were studied both during sessions of conventional bicarbonate dialysis (BD) and during sessions of acetate-free biofiltration (AFB) complicated by hypotension (8 BD vs 8 AFB). (a) During BD hypotension occurred, on average, about 70 min earlier than in AFB treatments (hypotension time: 120 \ub1 66 min in BD vs 193 \ub1 26 min in AFB, p < 0.01), and (b) patients exhibited a major susceptibility to blood volume reduction (blood volume reduction at hypotension time: 127.17 \ub1 3.26% in BD vs 1210.88 \ub1 2.46% in AFB, p < 0.05). A mathematical model was used to analyze the efficacy of reflex compensatory mechanisms during hemodialysis sessions. Data analysis using the model indicated that during BD sessions all the compensatory mechanisms were almost inoperative, whereas during the AFB sessions residual compensatory reflexes were active. Model simulation demonstrated that hypotension occurred later in AFB because the residual compensatory capacity in AFB was able to maintain arterial pressure for higher blood volume reductions