8 research outputs found
Connecting protein and mRNA burst distributions for stochastic models of gene expression
The intrinsic stochasticity of gene expression can lead to large variability
in protein levels for genetically identical cells. Such variability in protein
levels can arise from infrequent synthesis of mRNAs which in turn give rise to
bursts of protein expression. Protein expression occurring in bursts has indeed
been observed experimentally and recent studies have also found evidence for
transcriptional bursting, i.e. production of mRNAs in bursts. Given that there
are distinct experimental techniques for quantifying the noise at different
stages of gene expression, it is of interest to derive analytical results
connecting experimental observations at different levels. In this work, we
consider stochastic models of gene expression for which mRNA and protein
production occurs in independent bursts. For such models, we derive analytical
expressions connecting protein and mRNA burst distributions which show how the
functional form of the mRNA burst distribution can be inferred from the protein
burst distribution. Additionally, if gene expression is repressed such that
observed protein bursts arise only from single mRNAs, we show how observations
of protein burst distributions (repressed and unrepressed) can be used to
completely determine the mRNA burst distribution. Assuming independent
contributions from individual bursts, we derive analytical expressions
connecting means and variances for burst and steady-state protein
distributions. Finally, we validate our general analytical results by
considering a specific reaction scheme involving regulation of protein bursts
by small RNAs. For a range of parameters, we derive analytical expressions for
regulated protein distributions that are validated using stochastic
simulations. The analytical results obtained in this work can thus serve as
useful inputs for a broad range of studies focusing on stochasticity in gene
expression
Quantifying mRNA synthesis and decay rates using small RNAs
Regulation of mRNA decay is a critical component of global cellular
adaptation to changing environments. The corresponding changes in mRNA
lifetimes can be coordinated with changes in mRNA transcription rates to
fine-tune gene expression. Current approaches for measuring mRNA lifetimes can
give rise to secondary effects due to transcription inhibition and require
separate experiments to estimate changes in mRNA transcription rates. Here, we
propose an approach for simultaneous determination of changes in mRNA
transcription rate and lifetime using regulatory small RNAs to control mRNA
decay. We analyze a stochastic model for coupled degradation of mRNAs and sRNAs
and derive exact results connecting RNA lifetimes and transcription rates to
mean abundances. The results obtained show how steady-state measurements of RNA
levels can be used to analyze factors and processes regulating changes in mRNA
transcription and decay
Rare Events Statistics in Reaction--Diffusion Systems
We develop an efficient method to calculate probabilities of large deviations
from the typical behavior (rare events) in reaction--diffusion systems. The
method is based on a semiclassical treatment of underlying "quantum"
Hamiltonian, encoding the system's evolution. To this end we formulate
corresponding canonical dynamical system and investigate its phase portrait.
The method is presented for a number of pedagogical examples.Comment: 12 pages, 6 figure
Towards Classification of Phase Transitions in Reaction--Diffusion Models
Equilibrium phase transitions are associated with rearrangements of minima of
a (Lagrangian) potential. Treatment of non-equilibrium systems requires
doubling of degrees of freedom, which may be often interpreted as a transition
from the ``coordinate'' to the ``phase'' space representation. As a result, one
has to deal with the Hamiltonian formulation of the field theory instead of the
Lagrangian one. We suggest a classification scheme of phase transitions in
reaction-diffusion models based on the topology of the phase portraits of
corresponding Hamiltonians. In models with an absorbing state such a topology
is fully determined by intersecting curves of zero ``energy''. We identify four
families of topologically distinct classes of phase portraits stable upon RG
transformations.Comment: 14 pages, 9 figure
Aging processes in reversible reaction-diffusion systems
Reversible reaction-diffusion systems display anomalous dynamics
characterized by a power-law relaxation toward stationarity. In this paper we
study in the aging regime the nonequilibrium dynamical properties of some model
systems with reversible reactions. Starting from the exact Langevin equations
describing these models, we derive expressions for two-time correlation and
autoresponse functions and obtain a simple aging behavior for these quantities.
The autoresponse function is thereby found to depend on the specific nature of
the chosen perturbation of the system.Comment: 12 pages, accepted for publication in Phys. Rev.
Determinants of drug-target interactions at the single cell level.
The physiochemical determinants of drug-target interactions in the microenvironment of the cell are complex and generally not defined by simple diffusion and intrinsic chemical reactivity. Non-specific interactions of drugs and macromolecules in cells are rarely considered formally in assessing pharmacodynamics. Here, we demonstrate that non-specific interactions lead to very slow incorporation kinetics of DNA binding drugs. We observe a rate of drug incorporation in cell nuclei three orders of magnitude slower than in vitro due to anomalous drug diffusion within cells. This slow diffusion, however, has an advantageous consequence: it leads to virtually irreversible binding of the drug to specific DNA targets in cells. We show that non-specific interactions drive slow drug diffusion manifesting as slow reaction front propagation. We study the effect of non-specific interactions in different cellular compartments by permeabilization of plasma and nuclear membranes in order to pinpoint differential compartment effects on variability in intracellular drug kinetics. These results provide the basis for a comprehensive model of the determinants of intracellular diffusion of small-molecule drugs, their target-seeking trajectories, and the consequences of these processes on the apparent kinetics of drug-target interactions