arXiv subjects

Samuel W. S. Johnson

Publications and source records attributed to Samuel W. S. Johnson.

6 recordsLinked to original sources

arXiv2026

Theory of adhesion-driven self-organisation in growing tissues

Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly different behaviours within a single mechanistic model for adhesion-mediated self-organisation in growing cell populations. Using a multiscale analysis, we show that the balance between cell-cell adhesion, self-diffusion, and proliferation controls the emergence of distinct collective dynamics. We find that for weak adhesion, tissues invade through stable monotone fronts. As adhesion increases, invasion slows, fronts become unstable, leading to aggregates and spatial patterns emerging behind the advancing edge. In two spatial dimensions, these instabilities generate fingering morphologies reminiscent of dysregulated invasion in cancer. Crucially, we show that density-dependent regulation of adhesion suppresses these instabilities and restores cohesive tissue expansion. Together, our results identify adhesion strength and its regulation as key determinants of whether tissues invade cohesively or fragment into patterns, and provide a unified framework for understanding collective migration, morphogenesis, and dysregulated growth.

q-bio.TO↗

arXiv2026

Cell-cell adhesion cannot sustain extended follower streams in a minimal non-local model of leader-follower migration

Cell-cell adhesion is widely hypothesised to maintain cohesion within the long streams of follower cells that trail leader subpopulations during collective migration, including in neural crest cell migration, angiogenesis, and cancer cell invasion. Mathematically, non-local advection-diffusion equations provide the canonical continuum framework within which to study such adhesive cell-cell interactions. Here, we study a minimal model of leader-follower migration within this framework, in which leaders migrate at constant velocity while followers are attracted to leaders and to one another over a finite spatial interaction range. Numerical simulations reveal that, although the model can maintain small cohorts of travelling follower cells, the size of these cohorts is limited by the adhesive interaction lengthscale, and is far below what is needed to reproduce the extended streams observed in vivo. This points to a structural limitation of the standard non-local adhesion formulation and highlights the need for the development of extended continuum models capable of sustaining long, coherent migratory streams through purely mass-conserving collective cell movement.

q-bio.CB↗

arXiv2026

Spatial correlations in SIS processes on random regular graphs

In network-based SIS models of infectious disease transmission, infection can only occur between directly connected individuals. This constraint naturally gives rise to spatial correlations between the states of neighboring nodes, as the infection status of connected individuals becomes interdependent. Although mean-field approximations and the standard pairwise model are commonly used to simplify disease forecasting on networks, they inadequately capture spatial correlations; mean-field frameworks assume that populations are well-mixed, while the pairwise model neglects correlations beyond nearest-neighbor connections, which leads to inaccurate predictions of infection numbers over time. As such, the development of approximations that account for higher order spatially correlated infections is of great interest, as they offer a compromise between accurate disease forecasting and analytic tractability. Here, we use existing corrections to mean-field theory on the regular lattice to construct a more general framework for equivalent corrections on random regular graph topologies. We derive and simulate a hierarchical system of ordinary differential equations for the time evolution of the spatial correlation function at various geodesic distances on random networks. Solving these equations allows us to predict the time-dependent global infection density, which agrees well with numerical simulations. Our results substantially improve on existing corrections to mean-field theory for infectious individuals in SIS processes and provide an in-depth characterization of how structural randomness in networks affects the dynamical trajectories of infectious diseases on networks.

cond-mat.stat-mech↗

arXiv2026

The spontaneous emergence of leaders and followers in a mathematical model of cranial neural crest cell migration

Many agent-based mathematical models of cranial neural crest cell (CNCC) migration impose a binary phenotypic partition of cells into either leaders or followers. In such models, the movement of leader cells at the front of collectives is guided by local chemoattractant gradients, while follower cells behind leaders move according to local cell-cell guidance cues. Although such model formulations have yielded many insights into the mechanisms underpinning CNCC migration, they rely on fixed phenotypic traits that are difficult to reconcile with evidence of phenotypic plasticity in vivo. A later agent-based model of CNCC migration aimed to address this limitation by allowing cells to adaptively combine chemotactic and cell-cell guidance cues during migration. In this model, cell behaviour adapts instantaneously in response to environmental cues, which precludes the identification of a persistent subset of cells as leader-like over biologically relevant timescales, as observed in vivo. Here, we build on previous leader-follower and adaptive phenotype models to develop a polarity-based agent-based model of CNCC migration, in which all cells evolve according to identical rules, interact via a pairwise interaction potential, and carry polarity vectors that evolve according to a dynamical system driven by time-averaged exposure to chemoattractant gradients. Numerical simulations of this model show that a leader-follower phenotypic partition emerges spontaneously from the underlying collective dynamics of the model. Furthermore, the model reproduces behaviour that is consistent with experimental observations of CNCC migration in the chick embryo. Thus, we provide an experimentally consistent, mechanistically-grounded mathematical model that captures the emergence of leader and follower cell phenotypes without their imposition a priori.

q-bio.CB↗

arXiv2025

An energy-based mathematical model of actin-driven protrusions in eukaryotic chemotaxis

In eukaryotic cell chemotaxis, cells extend and retract transient actin-driven protrusions at their membrane that facilitate both the detection of external chemical gradients and directional movement via the formation of focal adhesions with the extracellular matrix. Although extensive experimental work has detailed how cellular protrusions and morphology vary under different environmental conditions, the mechanistic principles linking protrusive activity to these factors remain poorly understood. Here, we model the extension of actin-based protrusions in chemotaxis as an optimisation problem, wherein cells balance the detection of chemical gradients with the energetic cost of protrusion formation. Our model, built on the assumption of energy minimisation, provides a framework that successfully reproduces experimentally observed patterns of protrusive activity across a range of biological systems and environmental conditions, suggesting that energetic efficiency may underpin the morphology and chemotactic behaviour of motile eukaryotic cells. Additionally, we leverage the model to generate novel predictions regarding cellular responses to other, experimentally untested environmental perturbations, providing testable hypotheses for future experimental work that may be used to validate and refine the model presented here.

q-bio.CB↗

arXiv2025

Optimal control in combination therapy for heterogeneous cell populations with drug synergies

Cell heterogeneity plays an important role in patient responses to drug treatments. In many cancers, it is associated with poor treatment outcomes. Many modern drug combination therapies aim to exploit cell heterogeneity, but determining how to optimise responses from heterogeneous cell populations while accounting for multi-drug synergies remains a challenge. In this work, we introduce and analyse a general optimal control framework that can be used to model the treatment response of multiple cell populations that are treated with multiple drugs that mutually interact. In this framework, we model the effect of multiple drugs on the cell populations using a system of coupled semi-linear ordinary differential equations and derive general results for the optimal solutions. We then apply this framework to three canonical examples and discuss the wider question of how to relate mathematical optimality to clinically observable outcomes, introducing a systematic approach to propose qualitatively different classes of drug dosing inspired by optimal control.

q-bio.QM↗