arXiv subjects

Rajesh Karmakar

Publications and source records attributed to Rajesh Karmakar.

28 records · Page 2Linked to original sources

arXiv2019

Noise in gene expression may be a choice of cellular system

Gene expression and its regulation is a nonequilibrium stochastic process. Different molecules are involved in several biochemical steps in this process with low copies. It is observed that the stochasticity in biochemical processes is mainly due to the low copy number of the molecules present in the system. Several studies also show that the nonequilibrium biochemical processes require energy cost. But cellular system has developed itself through natural evolution by minimizing energy cost for optimum output. Here we study the role of stochasticity qualitatively in a network of two genes using stochastic simulation method and approximately measure the energy consumption for the gene expression process. We find that the noise in gene expression process reduces the energy cost of protein synthesis. Therefore, we argued that the stochasticity in gene expression may be a choice of cellular system for protein synthesis with minimum energy cost.

q-bio.MN↗

arXiv2015

Two different modes of oscillation in a gene transcription regulatory network with interlinked positive and negative feedback loops

We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of oscillation. In one mode (mode 1) frequency remains constant over a wide range amplitude and in other mode (mode 2) the amplitude of oscillation remains constant over a wide range of frequency. Our study reproduces both features of oscillations in a single gene regulatory network and show that the negative plus positive feedback loops in gene regulatory network offer additional advantage. We identified the key parameters/variables responsible for different modes of oscillation. The network is flexible in switching between different modes by choosing appropriately the required parameters/variables.

q-bio.MN↗

arXiv2010

Conversion of graded to binary response in an activator-repressor system

Appropriate regulation of gene expression is essential to ensure that protein synthesis occurs in a selective manner. The control of transcription is the most dominant type of regulation mediated by a complex of molecules such as transcription factors. In general, regulatory molecules are of two types: activator and repressor. Activators promote the initiation of transcription whereas repressors inhibit transcription. In many cases, they regulate the gene transcription on binding the promoter mutually exclusively and the observed gene expression response is either graded or binary. In experiments, the gene expression response is quantified by the amount of proteins produced on varying the concentration of an external inducer molecules in the cell. In this paper, we study a gene regulatory network where activators and repressors both bind the same promoter mutually exclusively. The network is modeled by assuming that the gene can be in three possible states: repressed, unregulated and active. An exact analytical expression for the steady-state probability distribution of protein levels is then derived. The exact result helps to explain the experimental observations that in the presence of activator molecules the response is graded at all inducer levels whereas in the presence of both activator and repressor molecules, the response is graded at low and high inducer levels and binary at an intermediate inducer level.

q-bio.MN↗

arXiv2007

Positive Feedback, Stochasticity and Genetic Competence

A single gene, regulating its own expression via a positive feedback loop, constitutes a common motif in gene regulatory networks and signalling cascades. Recent experiments on the development of competence in the bacterial population \emph{B. subtilis} show that the autoregulatory genetic module by itself can give rise to two types of cellular states. The states correspond to the low and high expression states of the master regulator ComK. The high expression state is attained when the ComK protein level exceeds a threshold value leading to a full activation of the autostimulatory loop. Stochasticity in gene expression drives the transitions between the two stable states. In this paper, we explain the appearance of bimodal protein distributions in \emph{B. subtilis} cell population in the framework of three possible scenarios. In two of the cases, bistability provides the basis for binary gene expression. In the third case, the system is monostable in a deterministic description and stochasticity in gene expression is solely responsible for the appearance of the two expression states.

q-bio.QM↗

arXiv2006

Stochastic model of transcription factor-regulated gene expression

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of Gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with a knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx3.1, are explained with the help of the stochastic model of TF-regulated gene expression.

q-bio.QM↗

arXiv2004

Graded and Binary Responses in Stochastic Gene Expression

Recently, several theoretical and experimental studies have been undertaken to probe the effect of stochasticity on gene expression (GE). In experiments, the GE response to an inducing signal in a cell, measured by the amount of mRNAs/proteins synthesized, is found to be either graded or binary. The latter type of response gives rise to a bimodal distribution in protein levels in an ensemble of cells. One possible origin of binary response is cellular bistability achieved through positive feedback or autoregulation. In this paper, we study a simple, stochastic model of GE and show that the origin of binary response lies exclusively in stochasticity. The transitions between the active and inactive states of the gene are random in nature. Graded and binary responses occur in the model depending on the relative stability of the activated and deactivated gene states with respect to that of mRNAs/proteins.The theoretical results on binary response provide a good description of the ``all-or-none'' phenomenon observed in an eukaryotic system.

q-bio.OT↗

arXiv2004

Noise Characteristics of Feed Forward Loops

A prominent feature of gene transcription regulatory networks is the presence in large numbers of motifs, i.e, patterns of interconnection, in the networks. One such motif is the feed forward loop (FFL) consisting of three genes X, Y and Z. The protein product of x of X controls the synthesis of protein product y of Y. Proteins x and y jointly regulate the synthesis of z proteins from the gene Z. The FFLs, depending on the nature of the regulating interactions, can be of eight different types which can again be classified into two categories: coherent and incoherent. In this paper, we study the noise characteristics of FFLs using the Langevin formalism and the Monte Carlo simulation technique based on the Gillespie algorithm. We calculate the variances around the mean protein levels in the steady states of the FFLs and find that, in the case of coherent FFLs, the most abundant FFL, namely, the Type-1 coherent FFL, is the least noisy. This is however not so in the case of incoherent FFLs. The results suggest possible relationships between noise, functionality and abundance.

q-bio.MN↗

arXiv2003

Mathematical models of haploinsufficiency

We study simple mathematical models of gene expression to explore the possible origins of haploinsufficiency (HI). In a diploid organism, each gene exists in two copies and when one of these is mutated, the amount of proteins synthesized is reduced and may fall below a threshold level for the onset of some desired activity. This can give rise to HI, a manifestation of which is in the form of a disease. We consider both deterministic and stochastic models of gene expression and suggest possible scenarios for the occurrence of HI in the two cases. In the stochastic case, random fluctuations around the mean protein level give rise to a finite probability that the protein level falls below a threshold. Increased gene copy number and faster gene expression kinetics reduce the variance around the mean protein level. The difference between slow and fast gene expression kinetics, as regards response to a signaling gradient, is further pointed out. The majority of results reported in the paper are derived analytically.

q-bio.OT↗

arXiv2003

Simple Models of Plant Learning and Memory

Plants are capable of intelligent responses to complex environmental signals. Learning and memory play fundamental roles in such responses. Two simple models of plant memory are proposed based on the calcium-signalling system. The memory states correspond to steady state distributions of calcium ions.

cond-mat↗

arXiv2003

Stochastic Simulation of Gene Expression in a Single Cell

In this paper, we consider two stochastic models of gene expression in prokaryotic cells. In the first model, sixteen biochemical reactions involved in transcription, translation and transcriptional regulation in the presence of inducer molecules are considered. The time evolution of the number of biomolecules of a particular type is determined using the stochastic simulation method based on the Gillespie Algorithm. The results obtained show that if the number of inducer molecules, N(I), is greater than or equal to the number of regulatory molecules, N(R), the average protein level is high in the steady state (state 2). The magnitude of the level is the same as long as N{I) greater than or equal to N(R). When N(I) is very very less than N(R), the average protein level is low, practically zero (state 1). As N(I) increases, the protein level continues to remain low. When N(I)becomes close to N(R), protein levels in the steady state are intermediate between high and low.In the presence of autocatalysis, a cell mostly exists in either state 1 or state 2 giving rise to a bimodal distribution in the protein levels in an ensemble of cells. This corresponds to the "all or none'' phenomenon observed in experiments. In the second model, the inducer molecules are not considered explicitly. An exhaustive simulation over the parameter space of the model shows that there are three major patterns of gene expression, Type A, Type B and Type C. The effect of varying the cellular parameters on the patterns, in particular, the transition from one type of pattern to another, is studied. Type A and Type B patterns have been observed in experiments. Simple mathematical models of transcriptional regulation predict Type C pattern of gene expression in certain parameter regimes.

cond-mat↗