Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration

Making the cut: Multiscale simulation of membrane remodeling

Biological membranes are dynamic heterogeneous materials, and their shape and organization are tightly coupled to the properties of the proteins in and around them. However, the length scales of lipid and protein dynamics are far below the size of membrane-bound organelles, much less an entire cell. Therefore, multiscale modeling approaches are often necessary to build a comprehensive picture of the interplay of these factors, and have provided critical insights into our understanding of membrane dynamics. Here, we review computational methods for studying membrane remodeling, as well as passive and active examples of protein-driven membrane remodeling. As the field advances towards the modeling of key aspects of organelles and whole cells - an increasingly accessible regime of study - we summarize here recent successes and offer comments on future trends.

Active viscoelastic models for cell and tissue mechanics

Living cells are out of equilibrium active materials. Cell-generated forces are transmitted across the cytoskeleton network and to the extracellular environment. These active force interactions shape cellular mechanical behaviour, trigger mechano-sensing, regulate cell adaptation to the microenvironment and can affect disease outcomes. In recent years, the mechanobiology community has witnessed the emergence of many experimental and theoretical approaches to study cells as mechanically active materials. In this review, we highlight recent advancements in incorporating active characteristics of cellular behaviour at different length scales into classic viscoelastic models by either adding an active tension-generating element or adjusting the resting length of an elastic element in the model. Summarizing the two groups of approaches, we will review the formulation and application of these models to understand cellular adaptation mechanisms in response to various types of mechanical stimuli, such as the effect of extracellular matrix properties and external loadings or deformations.

Modelling cell shape in 3D structured environments: A quantitative comparison with experiments

Cell shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.

Three-component contour dynamics model to simulate and analyze amoeboid cell motility in two dimensions

Amoeboid cell motility is relevant in a wide variety of biomedical processes such as wound healing, cancer metastasis, and embryonic morphogenesis. It is characterized by pronounced changes of the cell shape associated with expansions and retractions of the cell membrane, which result in a crawling kind of locomotion. Despite existing computational models of amoeboid motion, the inference of expansion and retraction components of individual cells, the corresponding classification of cells, and the a priori specification of the parameter regime to achieve a specific motility behavior remain challenging open problems. We propose a novel model of the spatio-temporal evolution of two-dimensional cell contours comprising three biophysiologically motivated components: a stochastic term accounting for membrane protrusions and two deterministic terms accounting for membrane retractions by regularizing the shape and area of the contour. Mathematically, these correspond to the intensity of a self-exciting Poisson point process, the area-preserving curve-shortening flow, and an area adjustment flow. The model is used to generate contour data for a variety of qualitatively different, e.g., polarized and non-polarized, cell tracks that visually resemble experimental data very closely. In application to experimental cell tracks, we inferred the protrusion component and examined its correlation to common biomarkers: the F-actin density close to the membrane and its local motion. Due to the low model complexity, parameter estimation is fast, straightforward, and offers a simple way to classify contour dynamics based on two locomotion types: the amoeboid and a so-called fan-shaped type. For both types, we use cell tracks segmented from fluorescence imaging data of the model organism Dictyostelium discoideum. An implementation of the model is provided within the open-source software package AmoePy, a Python-based toolbox for analyzing and simulating amoeboid cell motility.

CellularPotts.jl: simulating multiscale cellular models in Julia

SUMMARY

CellularPotts.jl is a software package written in Julia to simulate biological cellular processes such as division, adhesion, and signaling. Accurately modeling and predicting these simple processes is crucial because they facilitate more complex biological phenomena related to important disease states like tumor growth, wound healing, and infection. Here we take advantage of Cellular Potts Modeling to simulate cellular interactions and combine them with differential equations to model dynamic cell signaling patterns. These models are advantageous over other approaches because they retain spatial information about each cell while remaining computationally efficient at larger scales. Users of this package define three key inputs to create valid model definitions: a 2- or 3-dimensional space, a table describing the cells to be positioned in that space, and a list of model penalties that dictate cell behaviors. Models can then be evolved over time to collect statistics, simulated repeatedly to investigate how changing a specific property impacts cellular behavior, and visualized using any of the available plotting libraries in Julia.

AVAILABILITY AND IMPLEMENTATION

The CellularPotts.jl package is released under the MIT license and is available at https://github.com/RobertGregg/CellularPotts.jl. An archived version of the code (v0.3.2) at time of submission can also be found at https://doi.org/10.5281/zenodo.10407783.

Crawling, waving, inch worming, dilating, and pivoting mechanics of migrating cells: Lessons from Ken Jacobson

Research on the locomotion of single cells on hard, flat surfaces brought insight into the mechanisms of leading-edge protrusion, spatially graded adhesion, front-rear coordination, and how intracellular and traction forces are harnessed to execute various maneuvers. Here, we highlight how, by studying a variety of cell types, shapes, and movements, Ken Jacobson and his collaborators made several discoveries that triggered the mechanistic understanding of cell motility. We then review the recent advancements and current perspectives in this field.

Adhesion tunes speed and persistence by coordinating protrusions and extracellular matrix remodeling

Cell migration through 3D environments is essential to development, disease, and regeneration processes. Conceptual models of migration have been developed primarily on the basis of 2D cell behaviors, but a general understanding of 3D cell migration is still lacking due to the added complexity of the extracellular matrix. Here, using a multiplexed biophysical imaging approach for single-cell analysis of human cell lines, we show how the subprocesses of adhesion, contractility, actin cytoskeletal dynamics, and matrix remodeling integrate to produce heterogeneous migration behaviors. This single-cell analysis identifies three modes of cell speed and persistence coupling, driven by distinct modes of coordination between matrix remodeling and protrusive activity. The framework that emerges establishes a predictive model linking cell trajectories to distinct subprocess coordination states.

Mesenchymal Migration on Adhesive-Nonadhesive Alternate Surfaces in Macrophages

Mesenchymal migration usually happens on adhesive substrates, while cells adopt amoeboid migration on low/nonadhesive surfaces. Protein-repelling reagents, e.g., poly(ethylene) glycol (PEG), are routinely employed to resist cell adhering and migrating. Contrary to these perceptions, this work discovers a unique locomotion of macrophages on adhesive-nonadhesive alternate substrates in vitro that they can overcome nonadhesive PEG gaps to reach adhesive regions in the mesenchymal mode. Adhering to extracellular matrix regions is a prerequisite for macrophages to perform further locomotion on the PEG regions. Podosomes are found highly enriched on the PEG region in macrophages and support their migration across the nonadhesive regions. Increasing podosome density through myosin IIA inhibition facilitates cell motility on adhesive-nonadhesive alternate substrates. Moreover, a developed cellular Potts model reproduces this mesenchymal migration. These findings together uncover a new migratory behavior on adhesive-nonadhesive alternate substrates in macrophages.

Interpreting T-cell search "strategies" in the light of evolution under constraints

Two decades of in vivo imaging have revealed how diverse T-cell motion patterns can be. Such recordings have sparked the notion of search "strategies": T cells may have evolved ways to search for antigen efficiently depending on the task at hand. Mathematical models have indeed confirmed that several observed T-cell migration patterns resemble a theoretical optimum; for example, frequent turning, stop-and-go motion, or alternating short and long motile runs have all been interpreted as deliberately tuned behaviours, optimising the cell's chance of finding antigen. But the same behaviours could also arise simply because T cells cannot follow a straight, regular path through the tight spaces they navigate. Even if T cells do follow a theoretically optimal pattern, the question remains: which parts of that pattern have truly been evolved for search, and which merely reflect constraints from the cell's migration machinery and surroundings? We here employ an approach from the field of evolutionary biology to examine how cells might evolve search strategies under realistic constraints. Using a cellular Potts model (CPM), where motion arises from intracellular dynamics interacting with cell shape and a constraining environment, we simulate evolutionary optimization of a simple task: explore as much area as possible. We find that our simulated cells indeed evolve their motility patterns. But the evolved behaviors are not shaped solely by what is functionally optimal; importantly, they also reflect mechanistic constraints. Cells in our model evolve several motility characteristics previously attributed to search optimisation-even though these features are not beneficial for the task given here. Our results stress that search patterns may evolve for other reasons than being "optimal". In part, they may be the inevitable side effects of interactions between cell shape, intracellular dynamics, and the diverse environments T cells face in vivo.

Assessing cell migration in hydrogels: An overview of relevant materials and methods

Cell migration is essential in numerous living processes, including embryonic development, wound healing, immune responses, and cancer metastasis. From individual cells to collectively migrating epithelial sheets, the locomotion of cells is tightly regulated by multiple structural, chemical, and biological factors. However, the high complexity of this process limits the understanding of the influence of each factor. Recent advances in materials science, tissue engineering, and microtechnology have expanded the toolbox and allowed the development of biomimetic in vitro assays to investigate the mechanisms of cell migration. Particularly, three-dimensional (3D) hydrogels have demonstrated a superior ability to mimic the extracellular environment. They are therefore well suited to studying cell migration in a physiologically relevant and more straightforward manner than in vivo approaches. A myriad of synthetic and naturally derived hydrogels with heterogeneous characteristics and functional properties have been reported. The extensive portfolio of available hydrogels with different mechanical and biological properties can trigger distinct biological responses in cells affecting their locomotion dynamics in 3D. Herein, we describe the most relevant hydrogels and their associated physico-chemical characteristics typically employed to study cell migration, including established cell migration assays and tracking methods. We aim to give the reader insight into existing literature and practical details necessary for performing cell migration studies in 3D environments.

Listeria motility increases the efficiency of epithelial invasion during intestinal infection

Listeria monocytogenes (Lm) is a food-borne pathogen that causes severe bacterial gastroenteritis, with high rates of hospitalization and mortality. Lm is ubiquitous in soil, water and livestock, and can survive and proliferate at low temperatures. Following oral ingestion of contaminated food, Lm crosses the epithelium through intestinal goblet cells in a mechanism mediated by Lm InlA binding host E-cadherin. Importantly, human infections typically occur with Lm growing at or below room temperature, which is flagellated and motile. Even though many important human bacterial pathogens are flagellated, little is known regarding the effect of Lm motility on invasion and immune evasion. Here, we used complementary imaging and computer modeling approaches to test the hypothesis that bacterial motility helps Lm locate and engage target cells permissive for invasion. Imaging explanted mouse and human intestine, we showed that Lm grown at room temperature uses motility to scan the epithelial surface and preferentially attach to target cells. Furthermore, we integrated quantitative parameters from our imaging experiments to construct a versatile "layered" cellular Potts model (L-CPM) that simulates host-pathogen dynamics. Simulated data are consistent with the hypothesis that bacterial motility enhances invasion by allowing bacteria to search the epithelial surface for their preferred invasion targets. Indeed, our model consistently predicts that motile bacteria invade twice as efficiently over the first hour of infection. We also examined how bacterial motility affected interactions with host cellular immunity. In a mouse model of persistent infection, we found that neutrophils migrated to the apical surface of the epithelium 5 hours post infection and interacted with Lm. Yet in contrast to the view that neutrophils "hunt" for bacteria, we found that these interactions were driven by motility of Lm-which moved at least ~50x faster than neutrophils. Furthermore, our L-CPM predicts that motile bacteria maintain their invasion advantage even in the presence of host phagocytes, with the balance between invasion and phagocytosis governed almost entirely by bacterial motility. In conclusion, our simulations provide insight into host pathogen interaction dynamics at the intestinal epithelial barrier early during infection.

Numerical Study on Dynamics of Blood Cell Migration and Deformation in Atherosclerotic Vessels

A phase field model is used to study the effect of atherosclerotic plaque on hemodynamics. The migration of cells in blood flows is described by a set of multiple phase field equations, which incorporate elastic energies and the interacting effects of cells. Several simulations are carried out to reveal the influences of initial velocities of blood cells, cellular elasticity and block rates of hemodynamic vessels. The results show that the cell deformation increases with the growth of the initial active velocity and block rate but with the decrease of the cellular elasticity. The atherosclerotic plaque not only affects the deformation and migration of cells but also can promote the variation in hemodynamic properties. The atherosclerotic plaque causes a burst in cell velocity, and the greater the block rate and cellular elasticity, the more dramatic the variation of instantaneous velocity. The present work demonstrates that the phase field method could be extended to reveal formation atherosclerosis at the microscopic level from the perspective of hemodynamics.

Density-Dependent Migration Characteristics of Cancer Cells Driven by Pseudopod Interaction

The ability of cancer cells to invade neighboring tissue from primary tumors is an important determinant of metastatic behavior. Quantification of cell migration characteristics such as migration speed and persistence helps to understand the requirements for such invasiveness. One factor that may influence invasion is how local tumor cell density shapes cell migration characteristics, which we here investigate with a combined experimental and computational modeling approach. First, we generated and analyzed time-lapse imaging data on two aggressive Triple-Negative Breast Cancer (TNBC) cell lines, HCC38 and Hs578T, during 2D migration assays at various cell densities. HCC38 cells exhibited a counter-intuitive increase in speed and persistence with increasing density, whereas Hs578T did not exhibit such an increase. Moreover, HCC38 cells exhibited strong cluster formation with active pseudopod-driven migration, especially at low densities, whereas Hs578T cells maintained a dispersed positioning. In order to obtain a mechanistic understanding of the density-dependent cell migration characteristics and cluster formation, we developed realistic spatial simulations using a Cellular Potts Model (CPM) with an explicit description of pseudopod dynamics. Model analysis demonstrated that pseudopods exerting a pulling force on the cell and interacting via increased adhesion at pseudopod tips could explain the experimentally observed increase in speed and persistence with increasing density in HCC38 cells. Thus, the density-dependent migratory behavior could be an emergent property of single-cell characteristics without the need for additional mechanisms. This implies that pseudopod dynamics and interaction may play a role in the aggressive nature of cancers through mediating dispersal.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

During immunosurveillance, lymphocytes patrol through tissues to interact with cancer cells, other immune cells, and pathogens. The efficiency of this process depends on the kinds of trajectories taken, ranging from simple Brownian walks to Lévy walks. The composition of the extracellular matrix (ECM), a network of macromolecules, affects the formation of cell-matrix adhesions, thus strongly influencing the way lymphocytes move. Here, we present a model of lymphocyte motility driven by adhesions that grow, shrink and rupture in response to the ECM and cellular forces. Compared to other models, our model is computationally light making it suitable for generating long term cell track data, while still capturing actin dynamics and adhesion turnover. Our model suggests that cell motility is affected by the force required to break adhesions and the rate at which new adhesions form. Adhesions can promote cell protrusion by inhibiting retrograde actin flow. After introducing this effect into the model, we found that it reduces the cellular diffusivity and that it promotes stick-slip behaviour. Furthermore, location and size of adhesion clusters determined cell persistence. Overall, our model explains the plasticity of lymphocyte behaviour in response to the ECM.

Neighbor-enhanced diffusivity in dense, cohesive cell populations

The dispersal or mixing of cells within cellular tissue is a crucial property for diverse biological processes, ranging from morphogenesis, immune action, to tumor metastasis. With the phenomenon of ‘contact inhibition of locomotion,’ it is puzzling how cells achieve such processes within a densely packed cohesive population. Here we demonstrate that a proper degree of cell-cell adhesiveness can, intriguingly, enhance the super-diffusive nature of individual cells. We systematically characterize the migration trajectories of crawling MDA-MB-231 cell lines, while they are in several different clustering modes, including freely crawling singles, cohesive doublets of two cells, quadruplets, and confluent population on two-dimensional substrate. Following data analysis and computer simulation of a simple cellular Potts model, which faithfully recapitulated all key experimental observations such as enhanced diffusivity as well as periodic rotation of cell-doublets and cell-quadruplets with mixing events, we found that proper combination of active self-propelling force and cell-cell adhesion is sufficient for generating the observed phenomena. Additionally, we found that tuning parameters for these two factors covers a variety of different collective dynamic states.

Dispersal or movement of cells within dense biological tissue is essential for diverse biological processes, ranging from pattern formation, immune action, to tumor metastasis. However, it is quite puzzling how cells acquire such ability when they are supposedly “caged” by neighboring cells. Here, we report an unusual property of (MDA-MB-231) breast cancer cells that diffuse more persistently within a densely packed population than when they are free to crawl around with little interference. This property is rather surprising since they prefer to stick together, forming clusters. Interestingly, however, we find that having sticky neighbors not only makes two active cells in contact periodically rotate, reminiscent of a ballroom dance, but also enhances the persistence of the cells within a dense population. These intriguing phenomena appear to be universal as they can be generated by a simple cellular Potts model with appropriate combination of active self-propulsion and cell-cell adhesion force.