arXiv subjects

Indrani Bose

Publications and source records attributed to Indrani Bose.

At least 37 records · Page 2Linked to original sources

arXiv2012

Routes to Binary Gene Expression

Systems biology approaches combining theoretical modeling with experiments have been singularly successful in uncovering novel features of cellular phenomena. One such feature is that of binary gene expression in which the expression level is either low or high, i.e., digital in nature. This gives rise to two distinct subpopulations in a population of genetically identical cells. The fraction of cells in the high expression state is raised as the strength of the inducing signal is increased indicating that the response is not graded. In this review, we discuss the possible origins of binary gene expression with emphasis on three principal mechanisms: purely stochastic, positive feedback-based and emergent bistability. In the latter case, two stable expression states are obtained due to an autoregulatory positive feedback loop in protein synthesis along with cell growth retardation by the proteins synthesized. The theoretical foundations of the observed phenomena are described in each case.

q-bio.SC↗

arXiv2012

Emergent Bistability : Effects of Additive and Multiplicative Noise

Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been proposed which involves only positive feedback and no cooperativity in the regulation. An additional positive feedback loop is effectively generated due to the inhibition of cellular growth by the synthesized proteins. The mechanism, demonstrated for a synthetic circuit, may be prevalent in natural systems also as some recent experimental results appear to suggest. In this paper, we study the effects of additive and multiplicative noise on the dynamics governing emergent bistability. The calculational scheme employed is based on the Langevin and Fokker-Planck formalisms. The steady state probability distributions of protein levels and the mean first passage times are computed for different noise strengths and system parameters. In the region of bistability, the bimodal probability distribution is shown to be a linear combination of a lognormal and a Gaussian distribution. The variances of the individual distributions and the relative weights of the distributions are further calculated for varying noise strengths and system parameters. The experimental relevance of the model results is also pointed out.

q-bio.QM↗

arXiv2012

Transverse Ising Model: Markovian evolution of classical and quantum correlations under decoherence

The transverse Ising Model (TIM) in one dimension is the simplest model which exhibits a quantum phase transition (QPT). Quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity are known to provide signatures of QPTs. The issue is less well explored when the quantum system is subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. In this paper we study the dynamics of the mutual information $I(ρ_{AB})$, the classical correlations $C(ρ_{AB})$ and the quantum correlations $Q(ρ_{AB})$, as measured by the QD, in a two-qubit state the density matrix of which is the reduced density matrix obtained from the ground state of the TIM in 1d. The time evolution brought about by system-environment interactions is assumed to be Markovian in nature and the quantum channels considered are amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum channel is shown to be distinguished by a specific type of dynamics. In the case of the phase-flip channel, there is a finite time interval in which the quantum correlations are larger in magnitude than the classical correlations. For this channel as well as the bit-phase-flip channel, appropriate quantities associated with the dynamics of the correlations can be derived which signal the occurrence of a QPT.

quant-ph↗

arXiv2011

Quantum Discord in the Ground and Thermal States of Spin Clusters

Quantum discord is a general measure of bipartite quantum correlations with a potential role in quantum information processing tasks. Spin clusters serve as ideal candidates for the implementation of some of the associated protocols. In this paper, we consider a symmetric spin trimer and a tetramer, which describe a number of known molecular magnets, and compute the quantum discord in the ground and thermal states of the clusters. The variations of the quantum discord as a function of anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the quantum discord in the trimer ground state for which the pairwise entanglement is known to be zero, differences in the nature of some of the variations in the ferromagnetic and antiferromagnetic cases and discontinuous jumps in the magnitude of the quantum discord at first order quantum phase transition points. A remarkable feature that is observed is that the quantum discord completely vanishes only in the asymptotic limit of temperature $T\rightarrow\infty$. We further study the dynamics of the quantum discord and the pairwise entanglement at T=0 under the effect of a dephasing channel describing the interaction of the reduced spin cluster state with independent local environments. The QD is found to vanish asymptotically as $t\rightarrow\infty$. In the case of the spin trimer, the pairwise entanglement has a zero value at all times and reaches a zero value in a finite time in the case of the tetramer.

quant-ph↗

arXiv2011

Phenotypic Heterogeneity in Mycobacterial Stringent Response

A common survival strategy of microorganisms subjected to stress involves the generation of phenotypic heterogeneity in the isogenic microbial population enabling a subset of the population to survive under stress. In a recent study, a mycobacterial population of M. smegmatis was shown to develop phenotypic heterogeneity under nutrient depletion. The observed heterogeneity is in the form of a bimodal distribution of the expression levels of the Green Fluorescent Protein (GFP) as reporter with the gfp fused to the promoter of the rel gene. The stringent response pathway is initiated in the subpopulation with high rel activity.In the present study, we characterize quantitatively the single cell promoter activity of the three key genes, namely, mprA, sigE and rel, in the stringent response pathway with gfp as the reporter. The origin of bimodality in the GFP distribution lies in two stable expression states, i.e., bistability. We develop a theoretical model to study the dynamics of the stringent response pathway. The model incorporates a recently proposed mechanism of bistability based on positive feedback and cell growth retardation due to protein synthesis. Based on flow cytometry data, we establish that the distribution of GFP levels in the mycobacterial population at any point of time is a linear superposition of two invariant distributions, one Gaussian and the other lognormal, with only the coefficients in the linear combination depending on time. This allows us to use a binning algorithm and determine the time variation of the mean protein level, the fraction of cells in a subpopulation and also the coefficient of variation, a measure of gene expression noise.The results of the theoretical model along with a comprehensive analysis of the flow cytometry data provide definitive evidence for the coexistence of two subpopulations with overlapping protein distributions.

q-bio.SC↗

arXiv2010

Motion of Bound Domain Walls in a Spin Ladder

The elementary excitation spectrum of the spin-$\frac{1}{2}$ antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension $d>1$, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin-$\frac{1}{2}$ AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.

cond-mat.str-el↗

arXiv2010

Transient Pulse Formation in Jasmonate Signaling Pathway

The jasmonate (JA) signaling pathway in plants is activated as defense response to a number of stresses like attacks by pests or pathogens and wounding by animals. Some recent experiments provide significant new knowledge on the molecular detail and connectivity of the pathway. The pathway has two major components in the form of feedback loops, one negative and the other positive. We construct a minimal mathematical model, incorporating the feedback loops, to study the dynamics of the JA signaling pathway. The model exhibits transient gene expression activity in the form of JA pulses in agreement with experimental observations. The dependence of the pulse amplitude, duration and peak time on the key parameters of the model is determined computationally. The deterministic and stochastic aspects of the pathway dynamics are investigated using both the full mathematical model as well as a reduced version of it. We also compare the mechanism of pulse formation with the known mechanisms of pulse generation in some bacterial and viral systems.

q-bio.SC↗

arXiv2009

Entanglement in a molecular three-qubit system

We study the entanglement properties of a molecular three-qubit system described by the Heisenberg spin Hamiltonian with anisotropic exchange interactions and including an external magnetic field. The system exhibits first order quantum phase transitions by tuning two parameters, $x$ and $y$, of the Hamiltonian to specific values. The three-qubit chain is open ended so that there are two types of pairwise entanglement : nearest-neighbour (n.n.) and next-nearest-neighbour (n.n.n.). We calculate the ground and thermal state concurrences, quantifying pairwise entanglement, as a function of the parameters $x$, $y$ and the temperature $T$. The entanglement threshold and gap temperatures are also determined as a function of the anisotropy parameter $x$. The results obtained are of relevance in understanding the entanglement features of the recently engineered molecular $Cr_{7}Ni$-$Cu^{2+}$-$Cr_{7}Ni$ complex which serves as a three-qubit system at sufficiently low temperatures.

quant-ph↗

arXiv2009

Functional characteristics of a double positive feedback loop coupled with autorepression

We study the functional characteristics of a two-gene motif consisting of a double positive feedback loop and an autoregulatory negative feedback loop. The motif appears in the gene regulatory network controlling the functional activity of pancreatic $β$-cells. The model exhibits bistability and hysteresis in appropriate parameter regions. The two stable steady states correspond to low (OFF state) and high (ON state) protein levels respectively. Using a deterministic approach, we show that the region of bistability increases in extent when the copy number of one of the genes is reduced from two to one. The negative feedback loop has the effect of reducing the size of the bistable region. Loss of a gene copy, brought about by mutations, hampers the normal functioning of the $β$-cells giving rise to the genetic disorder, maturity-onset diabetes of the young (MODY). The diabetic phenotype makes its appearance when a sizable fraction of the $β$-cells is in the OFF state. Using stochastic simulation techniques, we show that, on reduction of the gene copy number, there is a transition from the monostable ON to the ON state in the bistable region of the parameter space. Fluctuations in the protein levels, arising due to the stochastic nature of gene expression, can give rise to transitions between the ON and OFF states. We show that as the strength of autorepression increases, the ON$\to$OFF state transitions become less probable whereas the reverse transitions are more probable. The implications of the results in the context of the occurrence of MODY are pointed out..

q-bio.MN↗

arXiv2008

Spin-1/2 Heisenberg ladder: variation of entanglement and fidelity measures close to quantum critical points

We consider a two-chain, spin-1/2 antiferromagnetic Heisenberg spin ladder in an external magnetic field H. The spin ladder is known to undergo second order quantum phase transitions (QPTs) at two critical values, Hc1 and Hc2, of the magnetic field. There are now known examples of strongly coupled (rung exchange interaction much stronger than nearest-neighbour intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures like one-site von Neumann entropy, two-site von Neumann entropy and concurrence develop special features close to the quantum critical points. As suggested by an earlier theorem, the first derivatives of the measures with respect to magnetic field are expected to diverge as H tends to Hc1 and Hc2. Based on numerical diagonalization data and a mapping of the strongly-coupled ladder Hamiltonian onto the XXZ chain Hamiltonian, for which several analytical results are known, we find that the derivatives of the entanglement measures diverge as H tends to Hc2 but remain finite as H tend to Hc1. The reason for this discrepancy is analysed. We further calculate two recently proposed quantum information theoretic measures, the reduced fidelity and reduced fidelity susceptibility, and show that these measures provide appropriate signatures of the QPTs occuring at the critical points H=Hc1 and H=Hc2.

quant-ph↗

arXiv2008

Entanglement and fidelity signatures of quantum phase transitions in spin liquid models

We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values u=0 and infinity. We study the variation of entanglement and fidelity measures in the ground states as a function of u and specially look for signatures of quantum phase transitions at u=0 and infinity. The two different entanglement measures used are S(i) (the single-site von Neumann entropy) and S(i, j) (the two-body entanglement). At the quantum critical point (QCP) u=infinity, the entanglement measure E (=S(i) ,S(i, j)) vanishes but remains nonzero at the other QCP u=0. The first and second derivatives of E with respect to the parameter u and the entanglement length associated with S(i, j) are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity F and a quantity ln(D) related to the second derivative of F and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.

quant-ph↗

arXiv2008

Positive feedback and noise activate the stringent response regulator Rel in mycobacteria

Phenotypic heterogeneity in an isogenic, microbial population enables a subset of the population to persist under stress. In mycobacteria, stresses like nutrient and oxygen deprivation activate the stress response pathway involving the two-component system MprAB and the sigma factor, SigE. SigE in turn activates the expression of the stringent response regulator, rel. The enzyme polyphosphate kinase 1 (PPK1) regulates this pathway by synthesizing polyphosphate required for the activation of MprB. The precise manner in which only a subpopulation of bacterial cells develops persistence, remains unknown. Rel is required for mycobacterial persistence. Here we show that the distribution of rel expression levels in a growing population of mycobacteria is bimodal with two distinct peaks corresponding to low (L) and high (H) expression states, and further establish that a positive feedback loop involving the mprAB operon along with stochastic gene expression are responsible for the phenotypic heterogeneity. Combining single cell analysis by flow cytometry with theoretical modeling, we observe that during growth, noise-driven transitions take a subpopulation of cells from the L to the H state within a "window of opportunity" in time preceding the stationary phase. We find evidence of hysteresis in the expression of rel in response to changing concentrations of PPK1. Our results provide, for the first time, evidence that bistability and stochastic gene expression could be important for the development of "heterogeneity with an advantage" in mycobacteria.

q-bio.MN↗

arXiv2007

The p53-MDM2 network: from oscillations to apoptosis

The p53 protein is well-known for its tumour suppressor function. The p53-MDM2 negative feedback loop constitutes the core module of a network of regulatory interactions activated under cellular stress. In normal cells, the level of p53 proteins is kept low by MDM2, i.e. MDM2 negatively regulates the activity of p53. In the case of DNA damage,the p53-mediated pathways are activated leading to cell cycle arrest and repair of the DNA. If repair is not possible due to excessive damage, the p53-mediated apoptotic pathway is activated bringing about cell death. In this paper, we give an overview of our studies on the p53-MDM2 module and the associated pathways from a systems biology perspective. We discuss a number of key predictions, related to some specific aspects of cell cycle arrest and cell death, which could be tested in experiments.

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↗

arXiv2007

Quantum Critical Point and Entanglement in a Matrix Product Ground State

In this paper, we study the entanglement properties of a spin-1 model the exact ground state of which is given by a Matrix Product state. The model exhibits a critical point transition at a parameter value a=0. The longitudinal and transverse correlation lengths are known to diverge as a tends to zero. We use three different entanglement measures S(i) (the one-site von Neumann entropy), S(i,j) (the two-body entanglement) and G(2,n) (the generalized global entanglement) to determine the entanglement content of the MP ground state as the parameter a is varied. The entanglement length, associated with S(i,j), is found to diverge in the vicinity of the quantum critical point a=0. The first derivative of the entanglement measure E (=S(i), S(i,j)) w.r.t. the parameter a also diverges. The first derivative of G(2,n) w.r.t. a does not diverge as a tends to zero but attains a maximum value at a=0. At the QCP itself all the three entanglement measures become zero. We further show that multipartite correlations are involved in the QPT at a=0.

cond-mat.str-el↗

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↗

arXiv2006

Entangled spin clusters: some special features

In this paper, we study three specific aspects of entanglement in small spin clusters. We first study the effect of inhomogeneous exchange coupling strength on the entanglement properties of the S=1/2 antiferromagnetic linear chain tetramer compound NaCuAsO_{4}. The entanglement gap temperature, T_{E}, is found to have a non-monotonic dependence on the value of $α$, the exchange coupling inhomogeneity parameter. We next determine the variation of T_{E} as a function of S for a spin dimer, a trimer and a tetrahedron. The temperature T_{E} is found to increase as a function of S, but the scaled entanglement gap temperature t_{E} goes to zero as S becomes large. Lastly, we study a spin-1 dimer compound to illustrate the quantum complementarity relation. We show that in the experimentally realizable parameter region, magnetization and entanglement plateaus appear simultaneously at low temperatures as a function of the magnetic field. Also, the sharp increase in one quantity as a function of the magnetic field is accompanied by a sharp decrease in the other so that the quantum complementarity relation is not violated.

quant-ph↗

arXiv2005

Gene Copy Number and Cell Cycle Arrest

The cell cycle is an orderly sequence of events which ultimately lead to the division of a single cell into two daughter cells. In the case of DNA damage by radiation or chemicals, the damage checkpoints in the $G_{1}$ and $G_{2}$ phases of the cell cycle are activated. This results in an arrest of the cell cycle so that the DNA damage can be repaired. Once this is done, the cell continues with its usual cycle of activity. We study a mathematical model of the DNA damage checkpoint in the $G_{2}$ phase which arrests the transition from the $G_{2}$ to the $M$ (mitotic) phase of the cell cycle. The tumor suppressor protein p53 plays a key role in activating the pathways leading to cell cycle arrest in mammalian systems. If the DNA damage is severe, the p53 proteins activate other pathways which bring about apoptosis, i.e., programmed cell death. Loss of the p53 gene results in the proliferation of cells containing damaged DNA, i.e., in the growth of tumors which may ultimately become cancerous. There is some recent experimental evidence which suggests that the mutation of a single copy of the p53 gene (in the normal cell each gene has two identical copies) is sufficient to trigger the formation of tumors. We study the effect of reducing the gene copy number of the p53 and two other genes on cell cycle arrest and obtain results consistent with experimental observations.

q-bio.MN↗