2,362 research outputs found
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.Comment: 17 pages, 11 figures. Accepted for publication in Physical Biolog
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
Extended states in 1D lattices: application to quasiperiodic copper-mean chain
The question of the conditions under which 1D systems support extended
electronic eigenstates is addressed in a very general context. Using real space
renormalisation group arguments we discuss the precise criteria for determining
the entire spertrum of extended eigenstates and the corresponding
eigenfunctions in disordered as well as quasiperiodic systems. For purposes of
illustration we calculate a few selected eigenvalues and the corresponding
extended eigenfunctions for the quasiperiodic copper-mean chain. So far, for
the infinite copper-mean chain, only a single energy has been numerically shown
to support an extended eigenstate [ You et al. (1991)] : we show analytically
that there is in fact an infinite number of extended eigenstates in this
lattice which form fragmented minibands.Comment: 10 pages + 2 figures available on request; LaTeX version 2.0
Phase Transition in the Number Partitioning Problem
Number partitioning is an NP-complete problem of combinatorial optimization.
A statistical mechanics analysis reveals the existence of a phase transition
that separates the easy from the hard to solve instances and that reflects the
pseudo-polynomiality of number partitioning. The phase diagram and the value of
the typical ground state energy are calculated.Comment: minor changes (references, typos and discussion of results
Particle-hole symmetry in a sandpile model
In a sandpile model addition of a hole is defined as the removal of a grain
from the sandpile. We show that hole avalanches can be defined very similar to
particle avalanches. A combined particle-hole sandpile model is then defined
where particle avalanches are created with probability and hole avalanches
are created with the probability . It is observed that the system is
critical with respect to either particle or hole avalanches for all values of
except at the symmetric point of . However at the
fluctuating mass density is having non-trivial correlations characterized by
type of power spectrum.Comment: Four pages, our figure
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.Comment: 17 page
Electronic structure and magnetism of the diluted magnetic semiconductor Fe-doped ZnO nano-particles
We have studied the electronic structure of ZnFeO
nano-particles, which have been reported to show ferromagnetism at room
temperature, by x-ray photoemission spectroscopy (XPS), resonant photoemission
spectroscopy (RPES), x-ray absorption spectroscopy (XAS) and x-ray magnetic
circular dichroism (XMCD). From the experimental and cluster-model calculation
results, we find that Fe atoms are predominantly in the Fe ionic state
with mixture of a small amount of Fe and that Fe ions are
dominant in the surface region of the nano-particles. It is shown that the room
temperature ferromagnetism in the ZnFeO nano-particles is
primarily originated from the antiferromagnetic coupling between unequal
amounts of Fe ions occupying two sets of nonequivalent positions in the
region of the XMCD probing depth of 2-3 nm.Comment: Single column, 12 pages, 8 figures, 1 tabl
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