arXiv subjects

Biplab Bose

Publications and source records attributed to Biplab Bose.

4 recordsLinked to original sources

arXiv2025

Switching Transition in a Resource Exchange Model on Graphs

In this work, we investigate a simple nonequilibrium system with many interconnected, open subsystems, each exchanging a globally conserved resource with an external reserve. The system is represented by a random graph, where nodes represent the subsystems connected through edges. At each time step, a randomly selected node gains a token (i.e, a resource) from the reserve with probability (1-p) or loses a token to the reserve with probability p. When a node loses a token, its neighbors also lose a token each. This asymmetric token exchange breaks the detailed balance. We investigate the steady state behavior of our model for different types of random graphs: graphs without edges, regular graphs, Erd\H{o}s-R\'enyi, and Barab\'asi-Albert graphs. In all cases, the system exhibits a sharp, switch-like transition between a token-saturated state and an empty state. When the control parameter p is below a critical threshold, almost all tokens accumulate on the graph. Furthermore, in a non-regular graph, most tokens accumulate or condense on nodes of minimum degree. A slight increase in p beyond the threshold drains almost all the tokens from the graph. This switching transition results from the interplay between drift and the conservation of tokens. However, the position of the critical threshold and the behavior at the transition zone depend on graph topology.

nlin.AO↗

arXiv2024

Pitchfork Bifurcation In A Coupled Cell System

Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation and are responsible for the emergence of diverse cell types. Mathematical investigations of such problems usually focus on bifurcation in a molecular network in individual cells. However, in a multicellular organism, cells interact, and intercellular interactions affect individual cell dynamics. Therefore, the bifurcation in an ensemble of cells could differ from that for a single cell. This work considers a ring of identical cells. When independent, each cell exhibits supercritical pitchfork bifurcation. Using analytical and numerical tools, we investigate the bifurcation in this ensemble when cells interact through positive and negative coupling. We show that within a specific parameter zone, an ensemble of positively coupled cells behaves like a single cell with supercritical pitchfork bifurcation. In this regime, all cells are synchronized and have the same steady state. However, this unique behaviour is lost when cells interact through negative coupling. Apart from the synchronized (or homogenous) states, cell-cell coupling leads to certain heterogeneous steady states with unique patterns. We also investigate the distribution of such heterogeneous states under positive and negative coupling.

math.DS↗

arXiv2024

Modal Analysis of Cellular Dynamics in the Morphospace in Epithelial-Mesenchymal Transition

During epithelial-mesenchymal transition (EMT), epithelial cells change their morphology, disperse, and gain mesenchymal-like characteristics. Usually, cells are categorized into discrete cell types or states based on gene expression and other cellular features. Subsequently, EMT is investigated as a dynamical process where cells jump from one discrete state to another. In the current work, we moved away from this idea of discrete state transition and investigated EMT dynamics in a continuous phenotypic space. We used morphology to define the phenotype of a cell. We used the data from quantitative image analysis of MDA-MB-468 cells undergoing EGF-induced EMT. We defined the morphological state space or 'morphospace' using the morphological features extracted through image analysis. During EMT, as the morphology changed, the distribution of cells in the morphospace also changed. However, this morphospace had a very high dimension. We reduced it to a 2-dimensional "reduced morphospace" and investigated the temporal change in the spatial distribution of cells in this reduced space. We used proper orthogonal decomposition to find dominant dynamical features of this spatio-temporal data. The modal analysis detected key features of EMT in this experimental system - reversible transition, distinct paths of phenotypic transition during induction and reversal of EMT, and enhanced diversity of cells during reversal of EMT. We also provide some intuitive physical meaning of the spatial modes and connect them to the key molecular event during EMT.

q-bio.CB↗

arXiv2023

Collective Alignment of Cells in Planar Cell Polarity: Insights from a Spin Model

In metazoans, cells collectively polarize and align along the tissue plane. This phenomenon is called Planar cell polarity (PCP). Polarization means asymmetric segregation of molecules and sub-cellular structures within a cell. In PCP, cells collectively align in a particular direction along the tissue plane through identical polarization. PCP in the Drosophila wing requires local cell-cell interactions in the presence of some global cue. We used a lattice-based equilibrium model and investigated the collective alignment of cells through local interactions and a global cue. This system undergoes a percolation transition and belongs to the universality class of 2D random percolation. We show that the local interaction should be beyond a threshold to trigger system-level coordinated polarization of cells. Under this condition, even a weak global cue can align all cells in the correct direction. With strong local interactions, this system is robust against local aberrations in global signaling, and collective alignment of cells is achieved even with a transient global signal.

nlin.AO↗