Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2203.15888

Cusp Bifurcation in Metastatic Breast Cancer Cells

Brenda Delamonica·Gabor Balazsi·Michael Shub
View original source ↗Read source document ↗Export metadata ↓

Abstract

Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We have found that concepts in bifurcation theory may be applied to model metastatic cell behavior. Our results show how a specific phenomenon called a cusp bifurcation describes metastatic cell state transitions, separating two qualitatively different transition modalities. Moreover, we show how the cusp bifurcation models other genetic networks, and we relate the dynamics after the bifurcation to observed phenomena in commitment to enter the cell cycle.

Explore related subjects

q-bio.CBmath.DS

Keep this discovery

BibTeXRIS

Brenda Delamonica, Gabor Balazsi, Michael Shub. 2022-03-29. Cusp Bifurcation in Metastatic Breast Cancer Cells. https://arxiv.org/abs/2203.15888

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Modeling Tissue Detachment and Rupture Using an Extended Vertex Model with T2-inverse Transitions

The vertex model is widely used to describe the mechanics of epithelial tissues, but its conventional formulation assumes that all cells remain tightly packed and always share edges with their neighbors, making it difficult to represent local detachment or gap formation. Here, we propose a minimal extension of the vertex model that enables cell detachment by introducing a new topological transformation, T2-inverse, which acts as the inverse of the classical T2 transition. When the imbalance of forces acting on a vertex, quantified by a tension metric $T$, exceeds a threshold, the T2-inverse splits the vertex into multiple vertices and creates a closed polygon that is incorporated as a pseudo-cell. This operation allows the model to represent the emergence and propagation of local detachment events. Using this framework, we simulate the stretching of a cell sheet and show that force-induced local detachments can accumulate to produce macroscopic tissue rupture. These results demonstrate that the proposed model extends the capability of the vertex model to describe tissue-level breakdown processes, including detachment and tearing, and provides a foundation for studying a broader class of epithelial mechanical phenomena.

q-bio.CB↗
arXiv2026

3D hybrid cellular Potts model with a discrete deformable fiber network: modeling cell contraction and extracellular matrix remodeling

The extracellular matrix (ECM) is a fibrous and dynamic network that plays a critical role in development, homeostasis, and disease. Cells both respond to and remodel the ECM, engaging in a mechanical reciprocity that shapes tissues. To study these interactions, computational models have been developed that simulate either ECM mechanics or cell behavior. The Cellular Potts Model (CPM) is a flexible cell-based framework that has been extended to many biological processes, including coupling to a discrete deformable fiber network. So far, however, this extension has only been applied in two dimensions, even though a three-dimensional setting is biologically more relevant. Here, we present a 3D hybrid framework that couples the CPM with a discrete and deformable representation of the ECM. This model enables explicit simulation of cell-induced ECM remodeling, including fiber reorientation and matrix densification. By incorporating contractile forces through static adhesion points, the model captures how ECM elasticity and fiber stiffness influences cell shape. The simulations show that ECM stiffness, controlled by fiber crosslinking, resists contraction and reaches equilibrium, while crosslink density modulates fiber alignment and local matrix accumulation. This framework provides a versatile platform for studying cell-ECM mechanics and supports future studies of multicellular behavior in realistic 3D environments.

q-bio.CB↗
arXiv2026

Coarse-Graining Agent-Based Models of Bacterial Infections

Agent-based models (ABMs) provide a natural framework for representing cell-level rules and spatial heterogeneity in bacterial infections, but their computational cost limits their use for macroscopic tissue-scale simulations and broad parameter exploration. We derive a deterministic coarse-grained description for a class of bacterial-infection ABMs in which immune cells and extracellular bacteria diffuse, immune cells ingest nearby bacteria, and intracellular bacterial loads evolve through prescribed birth and clearance processes. The first coarse-grained model is a semidiscrete reaction--diffusion system that retains a discrete internal state for each immune-cell bacterial load while representing cell and bacterial populations by continuum concentration fields. The key technical step is the derivation of state-dependent effective ingestion rates from the microscopic ABM parameters: these rates are obtained by solving an auxiliary diffusion problem around a single bacterium and computing the flux of immune cells into the interaction region. We then take a continuum limit in the internal state variable, yielding a state-structured reaction--diffusion system in which intracellular dynamics appear as advection and diffusion in state space. Numerical comparisons with ensemble-averaged ABM simulations show close agreement in biologically motivated parameter regimes. The resulting framework preserves the rule-based structure of the ABM while producing PDE models that are substantially more tractable for large-scale simulation and parameter studies.

q-bio.CB↗