Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged experimental, theoretical and computational scientists because cells can sense very small chemoattractant gradients that are tightly controlled by cell-cell interactions and the regulation of the chemoattractant distribution by the cells. Computational models of collective cell migration that offer a high-fidelity resolution of the cell motion and chemoattractant dynamics in the extracellular space have been limited to a small number of cells. Here, we present Dynamic cluster field modeling (DCF), a novel computational method that enables simulations of collective chemotaxis of cellular systems with O(1000) cells and high-resolution transport dynamics of the chemoattractant in the time-evolving extracellular space. We illustrate the efficiency and predictive capabilities of our approach by comparing our numerical simulations with experiments in multiple scenarios that involve chemoattractant secretion and uptake by the migrating cells, regulation of the attractant distribution by cell motion, and interactions of the chemoattractant with an enzyme. The proposed algorithm opens new opportunities to address outstanding problems that involve collective cell migration in the central nervous system, immune response and cancer metastasis.
We discuss recent progress in the theoretical description of chemotaxis by coupling the diffusion equation of a chemical species to equations describing the motion of sensing microorganisms. In particular, we discuss models for autochemotaxis of a single microorganism which senses its own secretion leading to phenomena such as self-localization and self-avoidance. For two heterogeneous particles, chemotactic coupling can lead to predator-prey behavior including chase and escape phenomena, and to the formation of active molecules, where motility spontaneously emerges when the particles approach…
A phase field approach is proposed to model the chemotaxis of Dictyostelium discoideum. In this framework, motion is controlled by active forces as determined by the Meinhardt model of chemical dynamics which is used to simulate directional sensing during chemotaxis. Then, the movement of the cell is achieved by the phase field dynamics, while the reaction-diffusion equations of the Meinhardt model are solved on an evolving cell boundary. This task requires the extension of the usual phase-field formulation to allow for components that are restricted to the membrane. The coupled system is nume…
Collectives of actively-moving particles can spontaneously separate into dilute and dense phases -- a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly-moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS -- in some cases, arresting or completely suppressing phase separation, or …
Collective migration -- the directed, coordinated motion of many self-propelled agents -- is a fascinating emergent behavior exhibited by active matter that has key functional implications for biological systems. Extensive studies have elucidated the different ways in which this phenomenon may arise. Nevertheless, how collective migration can persist when a population is confronted with perturbations, which inevitably arise in complex settings, is poorly understood. Here, by combining experiments and simulations, we describe a mechanism by which collectively migrating populations smooth out la…
Phase field approach for modeling intracellular dynamics
我们介绍了一个相场方法的扩散内部和外部的一个封闭的细胞与阻尼和源项在界面上。该方法相比，精确的解决方案（在可能的情况下）和更传统的有限元方法。它被证明是非常准确的，易于实现和计算成本低廉。我们将我们的方法应用于Rappel等人最近引入的趋化性模型[Biophys. J. 83，1361（2002）]。
The quest on how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource, such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins, while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but in general it features ma…
Angiogenesis is the formation of new blood vessels from the existing vessels. During tumour angiogenesis, tumour cells secret a number of chemical substrates called tumour angiogenic factors (TAFs). These factors diffuse through the extracellular matrix (ECM) and degrade the basement membrane of nearby vasculature. The TAFs also disrupt the corresponding endothelial cell receptors and form finger like capillary sprouts. These factors also create a chemical gradient (chemotaxis) between the tumour and the surrounding blood vessels. Due to the chemotactic force, the capillary sprouts migrate tow…
The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed peri…
Mathematical and Computational Modeling of Amoeboid Cell Crawling
Universitat Politècnica de Catalunya—BarcelonaTech（加泰罗尼亚理工大学）；Institute for Research and Innovation in Health (IRIS), Universitat Politècnica de Catalunya—BarcelonaTech（加泰罗尼亚理工大学健康研究与创新研究所）；Universität Potsdam（波茨坦大学）；Kanazawa University（金泽大学）
Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mec…
