Indrani Bose

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. It is these cells which adapt to nutrient depletion in the stationary phase via the stringent response. We find evidence of hysteresis in the expression of rel in response to changing concentrations of PPK1. Hysteresis promotes robustness in the maintenance of the induced state. 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 and suggest strategies for tackling tuberculosis like targeting transitions from the low to the high rel expression state.

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 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 shown to be true for all parameter values when the FFLs operate above their thresholds of activation/repression. In the case of incoherent FFLs, no such general conclusion can be shown. The results suggest possible relationships between noise, functionality and abundance.

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 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 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.

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.

Phenotypic heterogeneity in mycobacterial stringent response

BackgroundA 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.ResultsIn the present study, we characterise 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.ConclusionsThe 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.

Quantum discord in the ground and thermal states of spin clusters

Quantum discord (QD) 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 QD in the ground and thermal states of the clusters. The variations of the QD as a function of an anisotropy parameter, magnetic field and temperature are investigated. We obtain a number of interesting results such as a finite value of the QD 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 QD at first-order quantum phase transition points. A remarkable feature that is observed is that the QD completely vanishes only in the asymptotic limit of temperature T → ∞. We further study the dynamics of the QD 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 → ∞. 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.

Macroscopic entanglement jumps in model spin systems

In this paper, we consider some frustrated spin models for which the ground states are known exactly. The concurrence, a measure of the amount of entanglement can be calculated exactly for entangled spin pairs. Quantum phase transitions involving macroscopic magnetization changes at critical values of the magnetic field are accompanied by macroscopic jumps in the T=0 entanglement. A specific example is given in which magnetization plateaus give rise to a plateau structure in the amount of entanglement associated with nearest-neighbor bonds. We further show that macroscopic entanglement changes can occur in quantum phase transitions brought about by the tuning of exchange interaction strengths.

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.

Simple Models of Plant Learning and Memory

Plants are capable of intelligent responses to complex environmental signals. Learning and memory play fundamental roles in such responses. Two simple models of plant memory are proposed based on the calcium-signalling system. The memory states correspond to steady state distributions of calcium ions.

Thermal entanglement properties of small spin clusters

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. We consider a spin tetramer, with spins of magnitude