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 $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ 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 Zn$_{0.9}$Fe$_{0.1}$O 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$^{3+}$ ionic state with mixture of a small amount of Fe$^{2+}$ and that Fe$^{3+}$ ions are dominant in the surface region of the nano-particles. It is shown that the room temperature ferromagnetism in the Zn$_{0.9}$Fe$_{0.1}$O nano-particles is primarily originated from the antiferromagnetic coupling between unequal amounts of Fe$^{3+}$ ions occupying two sets of nonequivalent positions in the region of the XMCD probing depth of $\sim$ 2-3 nm.Comment: Single column, 12 pages, 8 figures, 1 tabl