Bacteria such as Escherichia coli move about in a series of runs and tumbles: while a run state (... more Bacteria such as Escherichia coli move about in a series of runs and tumbles: while a run state (straight motion) entails all the flagellar motors spinning in counterclockwise mode, a tumble is caused by a shift in the state of one or more motors to clockwise spinning mode. In the presence of an attractant gradient in the environment, runs in the favourable direction are extended, and this results in a net drift of the organism in the direction of the gradient. The underlying signal transduction mechanism produces directed motion through a bi-lobed response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration. The two lobes (positive and negative) of the response function are separated by a time interval of ∼ 1s, such that the bacterium effectively compares the concentration at two different positions in space and responds accordingly. We present here a novel path-integral method which allows us to address this problem in the most general way possible, including multi-step CW-CCW transitions, directional persistence and power-law waiting time distributions. The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, in a power series expansion in the attractant gradient. Explicit results in the lowest order in the expansion are presented for specific models, which, wherever applicable, agree with the known results. New results for gamma-distributed run interval distributions are also presented.
A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is s... more A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is studied here with the goal of elucidating the effects of intrinsic network noise in their conformational dynamics. The model was originally proposed to explain the robust and near-perfect adaptation of E. coli observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. In the model, a receptor is either active or inactive and can stochastically switch between the two states. The enzyme CheR methylates inactive receptors while CheB demethylates active receptors and the probability for a receptor to be active depends on its level of methylation and ligand occupation. In a simple version of the model with two methylation sites per receptor (M = 2), we show rigorously, under a quasi-steady state approximation, that the mean active fraction of receptors is an ultrasensitive function of [CheR]/[CheB] in the limit of saturating receptor concentration. Hence the model shows zeroorder ultrasensitivity (ZOU), similar to the classical two-state model of covalent modification studied by Goldbeter and Koshland (GK). We also find that in the limits of extremely small and extremely large ligand concentrations, the system reduces to two different two-state GK modules. A quantitative measure of the spontaneous fluctuations in activity is provided by the variance σ 2 a in the active fraction, which is estimated mathematically under linear noise approximation (LNA). It is found that σ 2 a peaks near the ZOU transition. The variance is a non-monotonic, but weak function of ligand concentration and a decreasing function of receptor concentration. Gillespie simulations are also performed in models with M = 2, 3 and 4. For M = 2, simulations show excellent agreement with analytical results obtained under LNA. Numerical results for M = 3 and M = 4 are qualitatively similar to our mathematical results in M = 2; while all the models show ZOU in mean activity, the variance is found to be smaller for larger M. The magnitude of receptor noise deduced from available experimental data is consistent with our predictions. A simple analysis of the downstream signaling pathway shows that this noise is large enough to affect the motility of the organism, and may have a beneficial effect on it. The response of mean receptor activity to small time-dependent changes in the external ligand concentration is computed within linear response theory, and found to have a bilobe form, in agreement with earlier experimental observations.
Biological systems are majorly dependent on their property of bistability in order to exhibit non... more Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to underlying bistability, may play significant role in phenomena like biofilm development, adaptation, cell motility etc. While nonlinear positive feedback regulation, like cooperative heterodimer formation are the usual reason behind bistability, similar dynamics can also occur as a consequence of host-circuit interaction. In this paper, we have investigated the pattern formation by a motif with non-cooperative positive feedback, that imposes a metabolic burden on its host due to its expression. In a cellular array set inside diffusible environment, we investigate spatio-temporal diffusion in one dimension as well as in two dimension in the context of various initial conditions respectively. Moreover, the number of cells exhibiting the same steady st...
Spatiotemporal pattern formation plays a key role in various biological phenomena including embry... more Spatiotemporal pattern formation plays a key role in various biological phenomena including embryogenesis and neural network formation. Though the reaction-diffusion systems enabling pattern formation have been studied phenomenonlogically, the biomolecular mechanisms behind these processes has not been modelled in detail. Here, we study the emergence of spatiotemporal patterns due to simple synthetic commonly observed two- and three-node gene regulatory network motifs coupled with their molecular diffusion in one- and two-dimensional space. We investigate the patterns formed due to the coupling of inherent multistable and oscillatory behavior of toggle switch (two mutually repressing nodes), toggle switch with double self-activation, toggle triad (three mutually repressing nodes) and repressilator (three nodes repressing the other sequentially in a cyclic manner) with the effect of spatial diffusion of these molecules. We probe various parameter regimes corresponding to different re...
Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in ... more Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor progression. Diverse cellular functions and behaviors, for instance, cell protrusions, active contractions, cell-cell adhesion, biochemical signaling, remodeling of tissue micro-environment, etc., play their own role concomitantly to have a single concerted consequence of multicellular migration. Thus unveiling the driving principles, both biochemical and biophysical, of the inherently complex process of collective cell migration is an insurmountable task. Mathematical and computational models, in tandem with experimental data, help in shedding some light on it. Here we review different factors influencing Collective Cell Migration and then focus on different mathematical and computational models - discrete, hybrid, and continuum - which helps in revealin...
Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and woun... more Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller sub-clusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics, and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and ...
Phenotypic decision-making is a process of determining important phenotypes in accordance with th... more Phenotypic decision-making is a process of determining important phenotypes in accordance with the available microenvironmental information. Although phenotypic decision at the level of a single cell has been precisely studied, but the knowledge is still imperceptible at the multicellular level. How cells sense their environment and adapt? How single cells change their phenotype in a multicellular complex environment (without knowing the interactions among the cells), is still a rheotorical question. To unravel the fragmental story of multicellular decision-making, Least microEnvironmental Uncertainty Principle (LEUP) was refined and applied in this context. To address this set of questions, we use variational principle to grasp the role of sensitivity, build a LEUP driven agent-based model on a lattice which solely hinges on microenvironmental information and investigate the parallels in a well-known biological system, viz., Notch-Delta-Jagged signaling pathway. The analyses of thi...
Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and woun... more Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller subclusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one-and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.
ABSTRACTCollections of cells exhibit coherent migration during morphogenesis, cancer metastasis, ... more ABSTRACTCollections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller sub-clusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics, and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell cont...
Signal propagation over long distances is a ubiquitous feature of multicellular communities. In b... more Signal propagation over long distances is a ubiquitous feature of multicellular communities. In biofilms of the bacterium Bacillus subtilis, we recently discovered that some, but not all, cells participate in the propagation of an electrical signal, and the ones that do are organized in a way that is statistically consistent with percolation theory. However, two key assumptions of percolation theory are violated in this system. First, we find here that the probability for a cell to signal is not independent from other cells but instead is correlated with its nearby neighbors. We develop a mechanistic model, in which correlated signaling emerges from cell division, phenotypic inheritance, and cell displacement, that reproduces the experimental results. Second, we observed previously that the fraction of signaling cells is not constant but instead varies from biofilm to biofilm. We use our model to understand why percolation theory remains a valid description of the system despite these two violations of its assumptions. We find that the first violation does not significantly affect the spatial statistics, which we rationalize using a renormalization argument. We find that the second violation widens the range of signaling fractions around the percolation threshold at which one observes the characteristic power-law statistics of cluster sizes, consistent with our previous experimental results. We validate our model using a mutant biofilm whose signaling probability decays along the propagation direction. Our results identify key statistical features of a correlated percolating system and demonstrate their functional utility for a multicellular community.
Journal of Physics A: Mathematical and Theoretical, 2019
Bacteria such as Escherichia coli move about in a series of runs and tumbles: while a run state (... more Bacteria such as Escherichia coli move about in a series of runs and tumbles: while a run state (straight motion) entails all the flagellar motors spinning in counterclockwise mode, a tumble is caused by a shift in the state of one or more motors to clockwise spinning mode. In the presence of an attractant gradient in the environment, runs in the favourable direction are extended, and this results in a net drift of the organism in the direction of the gradient. The underlying signal transduction mechanism produces directed motion through a bi-lobed response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration. The two lobes (positive and negative) of the response function are separated by a time interval of ∼ 1s, such that the bacterium effectively compares the concentration at two different positions in space and responds accordingly. We present here a novel path-integral method which allows us to address this problem in the most general way possible, including multi-step CW-CCW transitions, directional persistence and power-law waiting time distributions. The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, in a power series expansion in the attractant gradient. Explicit results in the lowest order in the expansion are presented for specific models, which, wherever applicable, agree with the known results. New results for gamma-distributed run interval distributions are also presented.
A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is s... more A stochastic version of the Barkai-Leibler model of chemotaxis receptors in Escherichia coli is studied here with the goal of elucidating the effects of intrinsic network noise in their conformational dynamics. The model was originally proposed to explain the robust and near-perfect adaptation of E. coli observed across a wide range of spatially uniform attractant/repellent (ligand) concentrations. In the model, a receptor is either active or inactive and can stochastically switch between the two states. The enzyme CheR methylates inactive receptors while CheB demethylates active receptors and the probability for a receptor to be active depends on its level of methylation and ligand occupation. In a simple version of the model with two methylation sites per receptor (M = 2), we show rigorously, under a quasi-steady state approximation, that the mean active fraction of receptors is an ultrasensitive function of [CheR]/[CheB] in the limit of saturating receptor concentration. Hence th...
Modern biology has decisively moved in a direction where we scrutinise systems holistically rathe... more Modern biology has decisively moved in a direction where we scrutinise systems holistically rather than looking at entities in different levels discretely or in isolation. Unlike previous reductionist approaches; in this new approach called Systems Biology, networks play a crucial role in arriving at and summing up the holistic picture and in understanding the emergent properties of the system. In this chapter, we give an overview of how network approaches are useful at various levels in biology. After a conceptual introduction to networks and various network metrics used to quantify networks; we discuss various concepts like network motifs and random networks. We then examine at length about how networks shed insight at virtually every layer of life like gene regulatory networks, networks involving proteins and metabolic networks. We end the chapter with a discussion of the application of networks to epidemiology.
HIGHLIGHTS • A push-pull enzyme-substrate system is ultrasensitive under enzyme saturation. • Det... more HIGHLIGHTS • A push-pull enzyme-substrate system is ultrasensitive under enzyme saturation. • Deterministic chemical rate equations are inadequate for small substrate populations. • We adopt a probabilistic approach, starting from master equation. • Fluctuations are estimated within the linear noise approximation. • Analytical results are supported by stochastic simulations.
Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of... more Temperature sensing is a ubiquitous cell behavior, but the fundamental limits to the precision of temperature sensing are poorly understood. Unlike in chemical concentration sensing, the precision of temperature sensing is not limited by extrinsic fluctuations in the temperature field itself. Instead, we find that precision is limited by the intrinsic copy number, turnover, and binding kinetics of temperature-sensitive proteins. Developing a model based on the canonical TlpA protein, we find that a cell can estimate temperature to within 2%. We compare this prediction with in vivo data on temperature sensing in bacteria.
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Papers by Ushasi Roy