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. Here, we study an sRNA-driven feed-forward loop (sFFL) where the top-tier regulator, an sRNA, translationally activates the target protein (TP) as well as a transcriptional activator of the TP through binding to the respective mRNAs. We show that the sRNA-mediated crosstalk between the two mRNA species enables the sFFL to function in three different regimes depending on the synthesis rate of the transcriptional activator mRNA. Of these three regimes, there exists a sensitive regime where the TP level shows interesting features depending on the precise mechanism of target translation. In the case of translation entirely from sRNA-mRNA bound complexes, the TP level becomes maximum around the sensitive regime. Through stochastic analysis and simulations, we show that relative fluctuations in the TP level is minimized here. For translation both from mRNA and sRNA-mRNA bound complexes, the target expression shows a threshold response across the sensitive regime.

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. It not only allows us to cure the large distance divergences in the perturbative solution for the BL but also generates, from the BL solution, an analytical form for the global density profile. The predicted scaling form is checked against numerical solutions for finite systems.

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. Here, we study a distinct sRNA-driven FFL (sFFL) that was discovered recently in Salmonella enterica: the distinction being the upstream regulator here is not a protein but an sRNA that translationally activates the target protein expression directly; and also indirectly via regulation of the transcriptional activator of the target protein. This variant, i.e. sFFL has not been subjected to rigorous analysis. We, therefore, set out to understand two aspects. First is a quantitative comparison of the regulatory response of sFFL with tFFL and smFFL using a differential equation framework. Since the process of gene expression is inherently stochastic, the second objective is to find how noise in gene expression affects the functionality of the sFFL. We find that unlike for tFFL and smFFL, the response of sFFL is stronger and faster: the change in target protein concentration is rapid and depends critically on the initial concentration of sRNA. Further, our analysis based on generating function approach and stochastic simulations leads to a non-trivial prediction that an optimal noise filtration can be attained depending on the synthesis rate of the upstream sRNA and the degradation rate of the intermediate transcriptional activator. A comparison with a simpler process involving only translational activation by sRNA indicates that the design of sFFL is crucial for optimal noise filtration. These observations prompt us to conclude that sFFL has distinct advantages where the master regulator, sRNA, plays a critical role not only in driving a rapid and strong response, but also a reliable response that depends critically on its concentration.

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. In various phases, the shape of the average particle density profile across the lattice including its boundary-layer parts changes significantly. Using the tools of boundary-layer analysis, we obtain explicit solutions for the density profile in different phases. A detailed analysis of these solutions under different boundary conditions helps us obtain the equations for various phase boundaries. Next, we show how the shape of the entire density profile including the location of the boundary layers can be predicted from the fixed points of the differential equation describing the boundary layers. We discuss this in detail through several examples of density profiles in various phases. The maximal-current phase appears to be an especially interesting phase where the boundary layer flows to a bifurcation point on the fixed-point diagram.

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. In particular, we show that a threshold response in the gene expression changes to a bistable response as the regulation on sRNA synthesis or degradation is altered. These results are obtained under deterministic conditions. Next, we study how the gene expression is altered by additive and multiplicative noise which might arise due to probabilistic occurrences of different biochemical events. Using the Fokker-Planck formulation, we obtain steady-state probability distributions for sRNA concentration for the network motifs displaying bistability. The probability distributions are found to be bimodal with two peaks at low and high concentrations of sRNAs. We further study the variations in the probability distributions under different values of noise strength and correlations. The results presented here might be of interest for designing synthetic network for artificial control.

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.

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. The present analysis shows the special role of a specific bifurcation of the fixed points in giving rise to different kinds of shocks.

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.

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. We study how the average velocity and the relative dispersion in the displacement vary with the applied load. The model is amenable to further extensions by inclusion of details associated with the structure and the processivity of the molecule.

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. In the other case, particles have an effective repulsion due to which the particle current density drops down near one-half filling. These interacting particles move on a one-dimensional lattice which is open at both the ends with injection of particles at one end and withdrawal of particles at the other. In addition to this, there are possibilities of attachments or detachments of particles to or from the lattice with certain rates. The hydrodynamic equation that involves the exact particle current density of the particle conserving system and additional terms taking care of the attachment-detachment kinetics is studied using the techniques of boundary layer analysis.

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. The surface transition in the low-density phase provides a complete description of the nonequilibrium critical point found in this system.

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." However, often a shrinking microtubule is "rescued" and starts polymerizing again. Here we develop a model for the polymerization-depolymerization dynamics of microtubules in the presence of catastrophe-suppressing drugs. Solving the dynamical equations in the steady state, we derive exact analytical expressions for the length distributions of the microtubules tipped with drug-bound tubulin subunits as well as those of the microtubules, in the growing and shrinking phases, tipped with drug-free pure tubulin subunits. We also examine the stability of the steady-state solutions.