arXiv subjects

Rahul V. Kulkarni

Publications and source records attributed to Rahul V. Kulkarni.

23 records · Page 2Linked to original sources

arXiv2011

Intrinsic noise in stochastic models of gene expression with molecular memory and bursting

Regulation of intrinsic noise in gene expression is essential for many cellular functions. Correspondingly, there is considerable interest in understanding how different molecular mechanisms of gene expression impact variations in protein levels across a population of cells. In this work, we analyze a stochastic model of bursty gene expression which considers general waiting-time distributions governing arrival and decay of proteins. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. The derived results extend previous work by including the effects of arbitrary probability distributions representing the effects of molecular memory and bursting. The analytical expressions obtained provide insight into the role of transcriptional, post-transcriptional and post-translational mechanisms in controlling the noise in gene expression.

q-bio.MN↗

arXiv2010

Applications of Little's Law to stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of mRNA fluctuations ('Poisson' and 'Telegraph' processes) have been proposed in stochastic models of gene expression. Both Poisson and Telegraph scenario models explain experimental observations of noise in protein levels in terms of 'bursts' of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little's Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.

physics.bio-ph↗

arXiv2010

Post-transcriptional regulation of noise in protein distributions during gene expression

The intrinsic stochasticity of gene expression can lead to large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in particular, there is considerable interest in understanding the role of post-transcriptional regulation. To address this issue, we propose and analyze a stochastic model for post-transcriptional regulation of gene expression. The analytical solution of the model provides insight into the effects of different mechanisms of post-transcriptional regulation on the noise in protein distributions. The results obtained also demonstrate how different sources of intrinsic noise in gene expression can be discriminated based on observations of regulated protein distributions.

q-bio.MN↗

arXiv2004

Pattern formation within Escherichia coli: diffusion, membrane attachment, and self-interaction of MinD molecules

In E. coli, accurate cell division depends upon the oscillation of Min proteins from pole to pole. We provide a model for the polar localization of MinD based only on diffusion, a delay for nucleotide exchange, and different rates of attachment to the bare membrane and the occupied membrane. We derive analytically the probability density, and correspondingly the length scale, for MinD attachment zones. Our simple analytical model illustrates the processes giving rise to the observed localization of cellular MinD zones.

q-bio.SC↗

arXiv2003

Simulations of Oligomeric Intermediates in Prion Diseases

We extend our previous stochastic cellular automata based model for areal aggregation of prion proteins on neuronal surfaces. The new anisotropic model allow us to simulate both strong beta-sheet and weaker attachment bonds between proteins. Constraining binding directions allows us to generate aggregate structures with the hexagonal lattice symmetry found in recently observed in vitro experiments. We argue that these constraints on rules may correspond to underlying steric constraints on the aggregation process. We find that monomer dominated growth of the areal aggregate is too slow to account for some observed doubling time-to-incubation time ratios inferred from data, and so consider aggregation dominated by relatively stable but non-infectious oligomeric intermediates. We compare a kinetic theory analysis of oligomeric aggregation to spatially explicit simulations of the process. We find that with suitable rules for misfolding of oligomers, possibly due to water exclusion by the surrounding aggregate, the resulting oligomeric aggregation model maps onto our previous monomer aggregation model. Therefore it can produce some of the same attractive features for the description of prion incubation time data. We propose experiments to test the oligomeric aggregation model.

physics.bio-ph↗