arXiv subjects

Mohit Kumar Jolly

Publications and source records attributed to Mohit Kumar Jolly.

16 recordsLinked to original sources

arXiv2026

A Single Equation Explains Go-or-Grow Dynamics in Cyclic Hypoxia

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes linear diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether these two coupled phenotype-specific equations can be reduced to a single mixed-phenotype equation under cyclic hypoxia. We establish a connection between the minimal go-or-grow model with distinct phenotypic populations and a reduced model describing a single-cell population with oxygen-dependent diffusion and proliferation in the fast-phenotypic-switching regime. This theoretical reduction is validated through numerical simulations.

math.AP↗

arXiv2025

Unifying Theories in High-Dimensional Biology: Approaches, Challenges and Opportunities

Across biological subdisciplines, the last decade has seen an explosion of high-dimensional datasets, including datasets for cells, species, immune systems, neurons and behaviour. At the ICTS workshop 'Unifying Theories in High-Dimensional Biophysics' we discussed whether this high dimensionality poses a challenge or opportunity for describing, understanding and predicting biological systems theoretically. We discussed methods, models and frameworks that can help with addressing empirical observations based on these high-dimensional datasets. We summarize the challenges and opportunities that emerged in discussions according to individual participants below.

physics.bio-ph↗

arXiv2025

Fractal Geometry and Fractional Calculus for Integrative Morphological Mapping of Breast Cancer Complexity

Breast cancer exhibits intricate morphological and dynamical heterogeneity across cellular, tissue, and tumor scales, posing challenges to conventional modeling approaches that fail to capture its nonlinear, self-similar, or self-affine, and memory-dependent behavior. Despite increasing applications of fractal geometry and fractional calculus in cancer modeling, their methodological integration and biological interpretation remain insufficiently consolidated. This review aims to synthesize these frameworks within an integrative morphological perspective to elucidate their collective potential for quantitative characterization of breast cancer complexity. Fractal geometry-based analyses quantify spatial and temporal irregularities along with spatiotemporal morphodynamics, while fractional calculus introduces non-local and memory-dependent formulations describing tumor growth. Together, these frameworks establish a mathematical link between fractal structure and fractional dynamics. Nevertheless, their application remains hindered by inconsistent methodologies and a lack of reproducible standards. This review consolidates existing evidence, delineates methodological interrelations between fractal geometry and fractional calculus, and outlines reproducibility requirements, including standardized preprocessing, parameter reporting, and benchmark datasets. Collectively, the findings emphasize that reproducible and biologically interpretable integration of these two approaches is fundamental to achieving clinically relevant modeling of breast cancer morphology and dynamics.

q-bio.QM↗

arXiv2025

Balancing the cellular budget: lessons in metabolism from microbes to cancer

Cancer cells are often seen to prefer glycolytic metabolism over oxidative phosphorylation even in the presence of oxygen-a phenomenon termed the Warburg effect. Despite significant strides in the decades since its discovery, a clear basis is yet to be established for the Warburg effect and why cancer cells show such a preference for aerobic glycolysis. In this review, we draw on what is known about similar metabolic shifts both in normal mammalian physiology and overflow metabolism in microbes to shed new light on whether aerobic glycolysis in cancer represents some form of optimisation of cellular metabolism. From microbes to cancer, we find that metabolic shifts favouring glycolysis are sometimes driven by the need for faster growth, but the growth rate is by no means a universal goal of optimal metabolism. Instead, optimisation goals at the cellular level are often multi-faceted and any given metabolic state must be considered in the context of both its energetic costs and benefits over a range of environmental contexts. For this purpose, we identify the conceptual framework of resource allocation as a potential testbed for the investigation of the cost-benefit balance of cellular metabolic strategies. Such a framework is also readily integrated with dynamical systems modelling, making it a promising avenue for new answers to the age-old question of why cells, from cancers to microbes, choose the metabolic strategies they do.

q-bio.SC↗

arXiv2025

GRiNS: A Python Library for Simulating Gene Regulatory Network Dynamics

The emergent dynamics of complex gene regulatory networks govern various cellular processes. However, understanding these dynamics is challenging due to the difficulty of parameterizing the computational models for these networks, especially as the network size increases. Here, we introduce a simulation library, Gene Regulatory Interaction Network Simulator (GRiNS), to address these challenges. GRiNS integrates popular parameter-agnostic simulation frameworks, RACIPE and Boolean Ising formalism, into a single Python library capable of leveraging GPU acceleration for efficient and scalable simulations. GRiNS extends the ordinary differential equations (ODE) based RACIPE framework with a more modular design, allowing users to choose parameters, initial conditions, and time-series outputs for greater customisability and accuracy in simulations. For large networks, where ODE-based simulation formalisms do not scale well, GRiNS implements Boolean Ising formalism, providing a simplified, coarse-grained alternative, significantly reducing the computational cost while capturing key dynamical behaviours of large regulatory networks. The documentation and installation instructions for GRiNS can be found at https://moltenecdysone09.github.io/GRiNS/.

q-bio.QM↗

arXiv2023

An integrative phenotype-structured partial differential equation model for the population dynamics of epithelial-mesenchymal transition

Phenotypic heterogeneity along the epithelial-mesenchymal (E-M) axis contributes to cancer metastasis and drug resistance. Recent experimental efforts have collated detailed time-course data on the emergence and dynamics of E-M heterogeneity in a cell population. However, it remains unclear how different possible processes interplay in shaping the dynamics of E-M heterogeneity: a) intracellular regulatory interaction among biomolecules, b) cell division and death, and c) stochastic cell-state transition (biochemical reaction noise and asymmetric cell division). Here, we propose a Cell Population Balance (Partial Differential Equation (PDE)) based model that captures the dynamics of cell population density along the E-M phenotypic axis due to abovementioned multi-scale cellular processes. We demonstrate how population distribution resulting from intracellular regulatory networks driving cell-state transition gets impacted by stochastic fluctuations in E-M regulatory biomolecules, differences in growth rates among cell subpopulations, and initial population distribution. Further, we reveal that a linear dependence of the cell growth rate on the population heterogeneity is sufficient to recapitulate the faster in vivo growth of orthotopic injected heterogeneous E-M subclones reported before experimentally. Overall, our model contributes to the combined understanding of intracellular and cell-population levels dynamics in the emergence of E-M heterogeneity in a cell population.

math.AP↗

arXiv2023

Theoretical and computational tools to model multistable gene regulatory networks

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

q-bio.MN↗

arXiv2023

Link updating strategies influence consensus decisions as a function of the direction of communication

Consensus decision-making in social groups strongly depends on communication links that determine to whom individuals send, and from whom they receive, information. Here, we ask how consensus decisions are affected by strategic updating of links and how this effect varies with the direction of communication. We quantified the co-evolution of link and opinion dynamics in a large population with binary opinions using mean-field numerical simulations of two voter-like models of opinion dynamics: an Incoming model (where individuals choose who to receive opinions from) and an Outgoing model (where individuals choose who to send opinions to). We show that individuals can bias group-level outcomes in their favor by breaking disagreeing links while receiving opinions (Incoming Model) and retaining disagreeing links while sending opinions (Outgoing Model). Importantly, these biases can help the population avoid stalemates and achieve consensus. However, the role of disagreement avoidance is diluted in the presence of strong preferences - highly stubborn individuals can shape decisions to favor their preferences, giving rise to non-consensus outcomes. We conclude that collectively changing communication structures can bias consensus decisions, as a function of the strength of preferences and the direction of communication.

physics.soc-ph↗

arXiv2020

Towards decoding the coupled decision-making of metabolism and epithelial-mesenchymal transition in cancer

Cancer cells have the plasticity to adjust their metabolic phenotypes for survival and metastasis. During metastasis, a developmental program known as the epithelial-mesenchymal transition (EMT) plays a critical role. There is extensive cross-talk between metabolism and EMT, but how this leads to coordinated physiological changes is still uncertain. The elusive connection between metabolism and EMT compromises the efficacy of metabolic therapies targeting metastasis. In this review, we aim for clarifying causation between metabolism and EMT based on recent experimental studies and propose integrated theoretical-experimental efforts to better understand the coupled decision-making of metabolism and EMT.

q-bio.CB↗

arXiv2020

Understanding the principles of pattern formation driven by Notch signaling by integrating experiments and theoretical models

Notch signaling is an evolutionary conserved cell-cell communication pathway. Besides regulating cell-fate decisions at an individual cell level, Notch signaling coordinates the emergent spatiotemporal patterning in a tissue through ligand-receptor interactions among transmembrane molecules of neighboring cells, as seen in embryonic development, angiogenesis, or wound healing. Due to its ubiquitous nature, Notch signaling is also implicated in several aspects of cancer progression, including tumor angiogenesis, stemness of cancer cells and cellular invasion. Here, we review experimental and computational models to help understand the operating principles of cell patterning driven by Notch signaling. First, we discuss the basic mechanisms of spatial patterning via canonical lateral inhibition and lateral induction mechanisms, including examples from angiogenesis, inner ear development and cancer metastasis. Next, we analyze additional layers of complexity in the Notch pathway such as the effects of varying cell sizes and shapes, ligand-receptor binding within the same cell, variable binding affinity of different ligand/receptor subtypes, and filopodia. Finally, we discuss some recent evidence of mechanosensitivity in the Notch pathway in driving collective epithelial cell migration and cardiovascular morphogenesis.

q-bio.MN↗

arXiv2019

Mathematical Modeling of Plasticity and Heterogeneity in EMT

Epithelial-Mesenchymal Transition (EMT), and the corresponding reverse process, Mesenchymal-Epithelial Transition (MET), are dynamic and reversible cellular programs orchestrated by many changes at biochemical and morphological levels. A recent surge in identifying the molecular mechanisms underlying EMT/MET has led to the development of various mathematical models that have contributed to our improved understanding of dynamics at single-cell and population levels: a) multi-stability (how many phenotypes can cells attain en route EMT/MET?), b) reversibility/irreversibility (what time and/or concentration of an EMT inducer marks the 'tipping point' when cells induced to undergo EMT cannot revert?), c) symmetry in EMT/MET (do cells take the same path while reverting as they took during the induction of EMT?), and d) non-cell autonomous mechanisms (how does a cell undergoing EMT alter the tendency of its neighbors to undergo EMT?). These dynamical traits may facilitate a heterogeneous response within a cell population undergoing EMT/MET. Here, we present a few examples of designing different mathematical models that can contribute to decoding EMT/MET dynamics.

q-bio.MN↗

arXiv2019

Quantifying cancer epithelial-mesenchymal plasticity and its association with stemness and immune response

Cancer cells can acquire a spectrum of stable hybrid epithelial/mesenchymal (E/M) states during epithelial-mesenchymal transition (EMT). Cells in these hybrid E/M phenotypes often combine epithelial and mesenchymal features and tend to migrate collectively commonly as small clusters. Such collectively migrating cancer cells play a pivotal role in seeding metastases and their presence in cancer patients indicates an adverse prognostic factor. Moreover, cancer cells in hybrid E/M phenotypes tend to be more associated with stemness which endows them with tumor-initiation ability and therapy resistance. Most recently, cells undergoing EMT have been shown to promote immune suppression for better survival. A systematic understanding of the emergence of hybrid E/M phenotypes and the connection of EMT with stemness and immune suppression would contribute to more effective therapeutic strategies. In this review, we first discuss recent efforts combining theoretical and experimental approaches to elucidate mechanisms underlying EMT multi-stability (i.e. the existence of multiple stable phenotypes during EMT) and the properties of hybrid E/M phenotypes. Following we discuss non-cell-autonomous regulation of EMT by cell cooperation and extracellular matrix. Afterwards, we discuss various metrics that can be used to quantify EMT spectrum. We further describe possible mechanisms underlying the formation of clusters of circulating tumor cells. Last but not least, we summarize recent systems biology analysis of the role of EMT in the acquisition of stemness and immune suppression.

q-bio.CB↗

arXiv2018

Deciphering the dynamics of Epithelial-Mesenchymal Transition and Cancer Stem Cells in tumor progression

Purpose of review: The epithelial-Mesenchymal Transition (EMT) and the generation of Cancer Stem Cells (CSC) are two fundamental aspects contributing to tumor growth, acquisition of resistance to therapy, formation of metastases, and tumor relapse. Recent experimental data identifying the circuits regulating EMT and CSCs have driven the development of computational models capturing the dynamics of these circuits and consequently various aspects of tumor progression. Recent findings: We review the contribution made by these models in a) recapitulating experimentally observed behavior, b) making experimentally testable predictions, and c) driving emerging notions in the field, including the emphasis on the aggressive potential of hybrid epithelial/mesenchymal (E/M) phenotype(s). We discuss dynamical and statistical models at intracellular and population level relating to dynamics of EMT and CSCs, and those focusing on interconnections between these two processes. Summary: These models highlight the insights gained via mathematical modeling approaches, and emphasizes that the connections between hybrid E/M phenotype(s) and stemness can be explained by analyzing underlying regulatory circuits. Such experimentally curated models have the potential of serving as platforms for better therapeutic design strategies.

q-bio.MN↗

arXiv2017

Analysis of hierarchical organization in gene expression networks reveals underlying principles of collective tumor cell dissemination and metastatic aggressiveness of inflammatory breast cancer

Clusters of circulating tumor cells (CTCs), although rare, may account for more than 95% of metastases. Inflammatory breast cancer (IBC) is a highly aggressive subtype that chiefly metastasizes via CTC clusters. Theory suggests that physical systems with hierarchical organization tend to be more adaptable due to their ability to efficiently span the set of available states. We used the cophenetic correlation coefficient (CCC) to quantify the hierarchical organization in the expression of collective dissemination associated and IBC associated genes, and found that the CCC of both gene sets was higher in (a) epithelial cell lines as compared to mesenchymal cell lines and (b) IBC tumor samples as compared to non-IBC breast cancer samples. A higher CCC of both networks was also correlated with a higher rate of metastatic relapse in breast cancer patients. Gene set enrichment analysis could not provide similar insights, indicating that the CCC provides additional information regarding the organizational complexity of gene expression. These results suggest that retention of epithelial traits in disseminating tumor cells as IBC progresses promotes successful metastasis and the CCC may be a prognostic factor for IBC.

q-bio.MN↗

arXiv2017

Distinguishing Mechanisms Underlying EMT Tristability

Background: The Epithelial-Mesenchymal Transition (EMT) endows epithelial-looking cells with enhanced migratory ability during embryonic development and tissue repair. EMT can also be co-opted by cancer cells to acquire metastatic potential and drug-resistance. Recent research has argued that epithelial (E) cells can undergo either a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype that typically displays collective migration, or a complete EMT to adopt a mesenchymal (M) phenotype that shows individual migration. The core EMT regulatory network - miR-34/SNAIL/miR-200/ZEB1 - has been identified by various studies, but how this network regulates the transitions among the E, E/M, and M phenotypes remains controversial. Two major mathematical models - ternary chimera switch (TCS) and cascading bistable switches (CBS) - that both focus on the miR-34/SNAIL/miR-200/ZEB1 network, have been proposed to elucidate the EMT dynamics, but a detailed analysis of how well either or both of these two models can capture recent experimental observations about EMT dynamics remains to be done. Results: Here, via an integrated experimental and theoretical approach, we first show that both these two models can be used to understand the two-step transition of EMT - E-E/M-M, the different responses of SNAIL and ZEB1 to exogenous TGF-b and the irreversibility of complete EMT. Next, we present new experimental results that tend to discriminate between these two models. We show that ZEB1 is present at intermediate levels in the hybrid E/M H1975 cells, and that in HMLE cells, overexpression of SNAIL is not sufficient to initiate EMT in the absence of ZEB1 and FOXC2. Conclusions: These experimental results argue in favor of the TCS model proposing that miR-200/ZEB1 behaves as a three-way decision-making switch enabling transitions among the E, hybrid E/M and M phenotypes.

q-bio.CB↗

arXiv2015

Implications of the hybrid epithelial/mesenchymal phenotype in metastasis

Understanding cell-fate decisions during tumorigenesis and metastasis is a major challenge in modern cancer biology. One canonical cell-fate decision that cancer cells undergo is Epithelial-to-Mesenchymal Transition (EMT) and its reverse Mesenchymal-to-Epithelial Transition (MET). While transitioning between these two phenotypes - epithelial and mesenchymal - cells can also attain a hybrid epithelial/mesenchymal (i.e. partial or intermediate EMT) phenotype. Cells in this phenotype have mixed epithelial (e.g. adhesion) and mesenchymal (e.g. migration) properties, thereby allowing them to move collectively as clusters of Circulating Tumor Cells (CTCs). If these clusters enter the circulation, they can be more apoptosis-resistant and more capable of initiating metastatic lesions than cancer cells moving individually with wholly mesenchymal phenotypes, having undergo a complete EMT. Here, we review the operating principles of the core regulatory network for EMT/MET that acts as a three-way switch giving rise to three distinct phenotypes - epithelial, mesenchymal and hybrid epithelial/mesenchymal. We further characterize this hybrid E/M phenotype in terms of its capabilities in terms of collective cell migration, tumor-initiation, cell-cell communication, and drug resistance. We elucidate how the highly interconnected coupling between these modules coordinates cell-fate decisions among a population of cancer cells in the dynamic tumor, hence facilitating tumor-stoma interactions, formation of CTC clusters, and consequently cancer metastasis. Finally, we discuss the multiple advantages that the hybrid epithelial/mesenchymal phenotype have as compared to a complete EMT phenotype and argue that these collectively migrating cells are the primary 'bad actors' of metastasis.

q-bio.CB↗