Modelling intracellular transport in crowded environments: effects of motor association to cargos.

In intracellular transports, motor proteins transport macromolecules as cargos to desired locations by moving on biopolymers such as microtubules. Recent experiments suggest that, while moving in crowded environments, cargos that can associate motor proteins during their translocation have larger run-length and association time compared to free motors. Here, we model the dynamics of a cargo that can associate at the most m free motors present on the microtubule track as obstacles to its motion.

Small RNA-driven feed-forward loop: fine-tuning of protein synthesis through sRNA-mediated crosstalk.

Often in bacterial regulatory networks, small non-coding RNAs (sRNA) interact with several mRNA species. The competition among mRNAs for binding to the common pool of sRNA might lead to crosstalk between the mRNAs. This is similar to the competing endogenous RNA effect that leads to complex gene regulation with stabilized gene expression in Eukaryotes.

Global Density Profile For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows.

The totally asymmetric simple exclusion process along with particle adsorption and evaporation kinetics is a model of boundary-induced nonequilibrium phase transition. In the continuum limit, the average particle density across the system is described by a singular differential equation involving multiple scales which lead to the formation of boundary layers (BL) or shocks. A renormalization group analysis is developed here by using the location and the width of the BL as the renormalization parameters.

Small RNA driven feed-forward loop: critical role of sRNA in noise filtering.

Gene regulatory networks are often partitioned into different types of recurring network motifs. A feed-forward loop (FFL) is a common motif in which an upstream regulator is a protein, typically a transcription factor, that regulates the expression of the target protein in two ways-first, directly by regulating the mRNA levels of the target protein and second, indirectly via an intermediate molecule that in turn regulates the target protein level. Investigations on two variants of FFL-purely transcriptional FFL (tFFL) and sRNA-mediated FFL (smFFL) reveal several advantages of using such motifs.

Asymmetric simple exclusion process with position-dependent hopping rates: Phase diagram from boundary-layer analysis.

In this paper, we study a one-dimensional totally asymmetric simple exclusion process with position-dependent hopping rates. Under open boundary conditions, this system exhibits boundary-induced phase transitions in the steady state. Similarly to totally asymmetric simple exclusion processes with uniform hopping, the phase diagram consists of low-density, high-density, and maximal-current phases.

Threshold response and bistability in gene regulation by small noncoding RNA.

In this paper, we study through mathematical modelling the combined effect of transcriptional and translational regulation by proteins and small noncoding RNAs (sRNA) in a genetic feedback motif that has an important role in the survival of E. coli under stress associated with oxygen and energy availability. We show that subtle changes in this motif can bring in drastically different effects on the gene expression.

Renormalization group analysis for an asymmetric simple exclusion process.

A perturbative renormalization group method is used to obtain steady-state density profiles of a totally asymmetric simple exclusion process with particle adsorption and evaporation. This method allows us to obtain a globally valid solution for the density profile without the asymptotic matching of bulk and boundary layer solutions. In addition, we show a nontrivial scaling of the boundary layer width with the system size close to specific phase boundaries.

Length-dependent dynamics of microtubules.

Certain regulatory proteins influence the polymerization dynamics of microtubules by inducing catastrophe with a rate that depends on the microtubule length. Using a discrete formulation, here we show that, for a catastrophe rate proportional to the microtubule length, the steady-state probability distributions of length decay much faster with length than an exponential decay as seen in the absence of these proteins.

Multishocks in driven diffusive processes: insights from fixed-point analysis of the boundary layers.

Boundary-induced phase transitions in a driven diffusive process can be studied through a phase-plane analysis of the boundary-layer equations. In this paper, we generalize this approach further to show how various shapes including multishocks and downward shocks in the bulk particle density profile can be understood by studying the dependence of the fixed points of the boundary-layer equation on an appropriate parameter. This is done for a particular driven interacting particle system as a prototypical example.

Fixed points and boundary layers in asymmetric simple exclusion processes.

In this paper, we show how a fixed-point-based boundary layer analysis can be used to understand phases and phase transitions in asymmetric simple exclusion processes (ASEPs) with open boundaries. In order to illustrate this method, we choose a two-species ASEP which has interesting phase transitions not seen in the one-species case. We also apply this method to the single-species problem where the analysis is simple but nevertheless quite insightful.

Model for the unidirectional motion of a dynein molecule.

Cytoplasmic dyneins transport cellular organelles by moving on a microtubule filament. It has been found recently that depending on the applied force and the concentration of the adenosine triphosphate molecules, dynein's step size varies. Based on these studies, we propose a simple model for dynein's unidirectional motion taking into account the variations in its step size.

Shocks in asymmetric simple exclusion processes of interacting particles.

In this paper, we study shocks and related transitions in asymmetric simple exclusion processes of particles with nearest-neighbor interactions. We consider two kinds of interparticle interactions. In one case, the particle-hole symmetry is broken due to the interaction.

Bulk and surface transitions in asymmetric simple exclusion process: impact on boundary layers.

In this paper, we study the boundary-induced phase transitions in a particle nonconserving asymmetric simple exclusion process with open boundaries. Using a boundary layer analysis on the mean field version of the model, we show that the key signatures of various bulk phase transitions are present in the boundary layers of the density profiles. In addition, we also find surface transitions in the low- and high-density phases.

Dynamic instability of microtubules: effect of catastrophe-suppressing drugs.

Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very rapidly; this phenomenon is known as a "catastrophe.