Wouter-Jan Rappel

Single cells confined by the extracellular matrix can exhibit rotational motion, yet the physical mechanisms underlying its onset and persistence remain unclear. Here, we address this gap with a cellular phase field model that couples cell deformation, cell polarization governed by stochastic excitable dynamics, and confinement. We identify the confinement strength as a bifurcation parameter determining three regimes: Strong confinement prevents rotation through spatial constraints, intermediate confinement induces stochastic transitions between rotating and nonrotating states, and weak confinement allows persistent rotations. For the intermediate regime, we develop a semi-Markovian renewal process framework that characterizes the stochastic dynamics through dwell time statistics, transition probabilities, and first-passage times. For the weak confinement regime, we reveal that a mechanochemical feedback enables coherent rotations despite internal noise through the reduction of local excitability mediated by mechanical contraction. We formalize this feedback analytically using Kramers escape theory. Experiments on epithelial MCF10A cells in Matrigel demonstrate three types of cell dynamics that recapitulate those observed in each confinement regime. Our results establish a theoretical approach for understanding single-cell rotations under confinement, with implications for controlling single-cell dynamics by tuning extracellular matrix properties.

Single cells confined by the extracellular matrix can exhibit persistent rotational motion, yet the physical mechanisms underlying this chiral symmetry breaking remain unclear. Here, we address this gap with a cellular phase field model that couples cell deformation, cell polarization governed by stochastic excitable dynamics, and confinement. We identify the confinement strength as a bifurcation parameter determining three regimes: strong confinement prevents rotation through spatial constraints, intermediate confinement induces stochastic transitions between chiral and non-chiral states, and weak confinement allows persistent rotational motion. For the intermediate regime, we develop a semi-Markovian renewal process framework that characterizes the stochastic dynamics through dwell time statistics, transition probabilities and first-passage times. For the weak confinement regime, we reveal that a mechanochemical feedback enables coherent rotations despite internal noise through the reduction of local excitability mediated by mechanical contraction. We formalize this feedback analytically using Kramers escape theory. Experiments on epithelial MCF10A cells in Matrigel validate predictions for the weak confinement regime. Our results establish a theoretical approach for understanding single-cell chiral symmetry breaking under confinement, with implications for controlling single-cell dynamics by tuning extracellular matrix properties.

Scroll-wave instabilities in excitable domains are central to life-threatening arrhythmias, yet practical methods to stabilize these dynamics remain limited. Here, we investigate the effects of boundary layer heterogeneities in the spatiotemporal dynamics of a quasi-2D semidiscrete excitable model. We reveal that a novel boundary-driven mechanism suppresses meandering and chaotic spiral dynamics. We show how the strength of the heterogeneities mediates the emergence of this regulation through a pinning-unpinning-like transition. We derive a reduced 2D model and find that a decrease in bulk excitability and a boundary-driven delayed-feedback underlie the stabilization. Our results may point to alternative methods to control arrhythmias.

Chemotaxing Dictyostelium discoideum cells migrate in a step-wise fashion characterized by periodic protrusion, contraction, and rear retraction cycles accompanied by distinct traction force patterns. Traction force microscopy reveals two stationary force spots that exchange identity as the cell advances and generate a convergent stress pattern with both axial and lateral components. To investigate the physical origin of these traction patterns, we developed a continuum, phase-field model that couples cytosolic flow, active stresses, and substrate friction within a cell with a deformable morpholgy. The model incorporates protrusive forces at the front, contractile stresses at the rear and sides, and spatially localized adhesive regions that undergo cyclic activation. While this baseline model reproduces persistent motion, it fails to capture the experimentally observed traction force patterns and cell morphology. Guided by new experiments visualizing myosin dynamics, we extended the model to include a localized contractile myosin patch positioned between the two adhesive regions. This modification yields cell shapes, speeds, and convergent traction patterns consistent with experimental measurements. The results demonstrate that a centrally positioned myosin patch is sufficient to generate the step-wise migration cycle and the characteristic convergent traction pattern of Dictyostelium cells, providing a mechanistic link between intracellular contractility, cytosolic flow, and force transmission during amoeboid motility.

Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and drops to zero at termination. In this work, we demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In such intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. We quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. In addition, we observe that quasistable spiral waves may intermittently persist in part of the computational domain, while the rest of the domain exhibits SDC. Our results may have implications for clinical atrial fibrillation, which often shows intermittency, switching back-and-forth between fibrillation and normal sinus rhythm.

Excitable media, including a cardiac tissue, can exhibit spiral defect chaos (SDC), during which spiral waves are continuously created and annihilated. Simulating this behavior typically requires solving large-scale reaction–diffusion systems, limiting computational feasibility especially for larger model domains. To address this, we have previously developed a particle model that was capable of replicating spiral-wave annihilation via short-range attraction and diffusion. In this study, we extend that model to capture spiral-wave creation by introducing a short-lived repulsive interaction between newly formed particle pairs. Our extended model accurately reproduces the termination statistics of SDC in cardiac simulations, including mean termination time, offering a simplified yet faithful description of SDC dynamics at much lesser computational cost.

Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and eventually drops to zero, marking the termination of activity. In this work, we demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In this intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. We quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. In addition, we find that it is also possible to have intermittently present quasi-stable spiral waves in part of the computational domain while the remainder of the domain exhibits SDC. Our results may have implications for clinical atrial fibrillation, which often shows intermittency, switching back-and-forth between fibrillation and normal sinus rhythm.

The metastasis of solid tumors hinges on cancer cells navigating through complex three-dimensional tissue environments, characterized by mechanical heterogeneity and biological diversity. This process is closely linked to the dynamic migration behavior exhibited by cancer cells, which dictates the invasiveness of tumors. In our study, we investigate tumor spheroids composed of breast cancer cells embedded in three-dimensional (3D) collagen matrices. Through a combination of quantitative experiments, artificial-intelligence-driven image processing, and mathematical modeling, we uncover rapid transitions in cell phenotypes and phenotype-dependent motility among disseminating cells originating from tumor spheroids. Persistent invasion leads to continuous remodeling of the extracellular matrix surrounding the spheroids, altering the landscape of migration phenotypes. Consequently, filopodial cells emerge as the predominant phenotype across diverse extracellular matrix conditions. Our findings unveil the complex mesoscale dynamics of invading tumor spheroids, shedding light on the complex interplay between migration phenotype plasticity, microenvironment remodeling, and cell motility within 3D extracellular matrices. Published by the American Physical Society 2024

When cells of the social amoeba Dictyostelium discoideum are starved of nutrients they start to synthesize and secrete the chemical messenger and chemoattractant cyclic adenosine monophosphate (cAMP). This signal is relayed by other cells, resulting in the establishment of periodic waves. The cells aggregate through chemotaxis toward the center of these waves. We investigated the chemotactic response of individual cells to repeated exposure to waves of cAMP generated by a microfluidic device. For fast-moving waves (short period), the chemotactic ability of the cells was found to increase upon exposure to more waves, suggesting the development of a memory over several cycles. This effect was not significant for slow-moving waves (large period). We show that the experimental results are consistent with a local excitation global inhibition-based model, extended by including a component that rises and decays slowly and that is activated by the temporal gradient of cAMP concentration. The observed enhancement in chemotaxis is relevant to populations in the wild: once sustained, periodic waves of the chemoattractant are established, it is beneficial to cells to improve their chemotactic ability in order to reach the aggregation center sooner.

Pair-annihilation events are ubiquitous in a variety of spatially extended systems and are often studied using computationally expensive simulations. Here, we develop an approach in which we simulate the pair-annihilation of spiral wave tips in cardiac models using a computationally efficient particle model. Spiral wave tips are represented as particles with dynamics governed by diffusive behavior and short-ranged attraction. The parameters for diffusion and attraction are obtained by comparing particle motion to the trajectories of spiral wave tips in cardiac models during spiral defect chaos. The particle model reproduces the annihilation rates of the cardiac models and can determine the statistics of spiral wave dynamics, including its mean termination time. We show that increasing the attraction coefficient sharply decreases the mean termination time, making it a possible target for pharmaceutical intervention.