Anomalous dynamics of cell migration

Data-driven classification of individual cells by their non-Markovian motion

We present a method to differentiate organisms solely by their motion based on the generalized Langevin equation (GLE) and use it to distinguish two different swimming modes of strongly confined unicellular microalgae Chlamydomonas reinhardtii. The GLE is a general model for active or passive motion of organisms and particles that can be derived from a time-dependent general many-body Hamiltonian and in particular includes non-Markovian effects (i.e., the trajectory memory of its past). We extract all GLE parameters from individual cell trajectories and perform an unbiased cluster analysis to group them into different classes. For the specific cell population employed in the experiments, the GLE-based assignment into the two different swimming modes works perfectly, as checked by control experiments. The classification and sorting of single cells and organisms is important in different areas; our method, which is based on motion trajectories, offers wide-ranging applications in biology and medicine.

Systemic cellular migration: The forces driving the directed locomotion movement of cells

Directional motility is an essential property of cells. Despite its enormous relevance in many fundamental physiological and pathological processes, how cells control their locomotion movements remains an unresolved question. Here, we have addressed the systemic processes driving the directed locomotion of cells. Specifically, we have performed an exhaustive study analyzing the trajectories of 700 individual cells belonging to three different species (Amoeba proteus, Metamoeba leningradensis, and Amoeba borokensis) in four different scenarios: in absence of stimuli, under an electric field (galvanotaxis), in a chemotactic gradient (chemotaxis), and under simultaneous galvanotactic and chemotactic stimuli. All movements were analyzed using advanced quantitative tools. The results show that the trajectories are mainly characterized by coherent integrative responses that operate at the global cellular scale. These systemic migratory movements depend on the cooperative nonlinear interaction of most, if not all, molecular components of cells.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Size-dependent self-avoidance enables superdiffusive migration in macroscopic unicellulars

Many cells face search problems, such as finding food, mates, or shelter, where their success depends on their search strategy. In contrast to other unicellular organisms, the slime mold Physarum polycephalum forms a giant network-shaped plasmodium while foraging for food. What is the advantage of the giant cell on the verge of multicellularity? We experimentally study and quantify the migration behavior of P. polycephalum plasmodia on the time scale of days in the absence and presence of food. We develop a model which successfully describes its migration in terms of ten data-derived parameters. Using the mechanistic insights provided by our data-driven model, we find that regardless of the absence or presence of food, P. polycephalum achieves superdiffusive migration by performing a self-avoiding run-and-tumble movement. In the presence of food, the run duration statistics change, only controlling the short-term migration dynamics. However, varying organism size, we find that the long-term superdiffusion arises from self-avoidance determined by cell size, highlighting the potential evolutionary advantage that this macroscopically large cell may have.

Non-Gaussian Displacements in Active Transport on a Carpet of Motile Cells

We study the dynamics of micron-sized particles on a layer of motile cells. This cell carpet acts as an active bath that propels passive tracer particles via direct mechanical contact. The resulting nonequilibrium transport shows a crossover from superdiffusive to normal-diffusive dynamics. The particle displacement distribution is distinctly non-Gaussian even at macroscopic timescales exceeding the measurement time. We obtain the distribution of diffusion coefficients from the experimental data and introduce a model for the displacement distribution that matches the experimentally observed non-Gaussian statistics. We argue why similar transport properties are expected for many composite active matter systems.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Random walk and cell morphology dynamics in Naegleria gruberi

Amoeboid cell movement and migration are wide-spread across various cell types and species. Microscopy-based analysis of the model systems Dictyostelium and neutrophils over the years have uncovered generality in their overall cell movement pattern. Under no directional cues, the centroid movement can be quantitatively characterized by their persistence to move in a straight line and the frequency of re-orientation. Mathematically, the cells essentially behave as a persistent random walker with memory of two characteristic time-scale. Such quantitative characterization is important from a cellular-level ethology point of view as it has direct connotation to their exploratory and foraging strategies. Interestingly, outside the amoebozoa and metazoa, there are largely uncharacterized species in the excavate taxon Heterolobosea including amoeboflagellate Naegleria. While classical works have shown that these cells indeed show typical amoeboid locomotion on an attached surface, their quantitative features are so far unexplored. Here, we analyzed the cell movement of Naegleria gruberi by employing long-time phase contrast imaging that automatically tracks individual cells. We show that the cells move as a persistent random walker with two time-scales that are close to those known in Dictyostelium and neutrophils. Similarities were also found in the shape dynamics which are characterized by the appearance, splitting and annihilation of the curvature waves along the cell edge. Our analysis based on the Fourier descriptor and a neural network classifier point to importance of morphology features unique to Naegleria including complex protrusions and the transient bipolar dumbbell morphologies.

Volumetric Compression Shifts Rho GTPase Balance and Induces Mechanobiological Cell State Transition

During development and disease progression, cells are subject to osmotic and mechanical stresses that modulate cell volume, which fundamentally influences cell homeostasis and has been linked to a variety of cellular functions. It is not well understood how the mechanobiological state of cells is programmed by the interplay of intracellular organization and complex extracellular mechanics when stimulated by cell volume modulation. Here, by controlling cell volume via osmotic pressure, we evaluate physical phenotypes (including cell shape, morphodynamics, traction force, and extracellular matrix (ECM) remodeling) and molecular signaling (YAP), and we uncover fundamental transitions in active biophysical states. We demonstrate that volumetric compression shifts the ratiometric balance of Rho GTPase activities, thereby altering mechanosensing and cytoskeletal organization in a reversible manner. Specifically, volumetric compression controls cell spreading, adhesion formation, and YAP nuclear translocation, while maintaining cell contractile activity. Furthermore, we show that on physiologically relevant fibrillar collagen I matrices, which are highly non-elastic, cells exhibit additional modes of cell volume-dependent mechanosensing that are not observable on elastic substrates. Notably, volumetric compression regulates the dynamics of cell-ECM interactions and irreversible ECM remodeling via Rac-directed protrusion dynamics, at both the single-cell level and the multicellular level. Our findings support that cell volume is a master biophysical regulator and reveal its roles in cell mechanical state transition, cell-ECM interactions, and biophysical tissue programming.

Acid-base homeostasis orchestrated by NHE1 defines the pancreatic stellate cell phenotype in pancreatic cancer

Pancreatic ductal adenocarcinoma (PDAC) progresses in an organ with a unique pH landscape, where the stroma acidifies after each meal. We hypothesized that disrupting this pH landscape during PDAC progression triggers pancreatic stellate cells (PSCs) and cancer-associated fibroblasts (CAFs) to induce PDAC fibrosis. We revealed that alkaline environmental pH was sufficient to induce PSC differentiation to a myofibroblastic phenotype. We then mechanistically dissected this finding, focusing on the involvement of the Na+/H+ exchanger NHE1. Perturbing cellular pH homeostasis by inhibiting NHE1 with cariporide partially altered the myofibroblastic PSC phenotype. To show the relevance of this finding in vivo, we targeted NHE1 in murine PDAC (KPfC). Indeed, tumor fibrosis decreased when mice received the NHE1-inhibitor cariporide in addition to gemcitabine treatment. Moreover, the tumor immune infiltrate shifted from granulocyte rich to more lymphocytic. Taken together, our study provides mechanistic evidence on how the pancreatic pH landscape shapes pancreatic cancer through tuning PSC differentiation.

Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion

We use a subdiffusion equation with fractional Caputo time derivative with respect to another function g (g-subdiffusion equation) to describe a smooth transition from ordinary subdiffusion to superdiffusion. Ordinary subdiffusion is described by the equation with the "ordinary" fractional Caputo time derivative, superdiffusion is described by the equation with a fractional Riesz-type spatial derivative. We find the function g for which the solution (Green's function, GF) to the g-subdiffusion equation takes the form of GF for ordinary subdiffusion in the limit of small time and GF for superdiffusion in the limit of long time. To solve the g-subdiffusion equation we use the g-Laplace transform method. It is shown that the scaling properties of the GF for g-subdiffusion and the GF for superdiffusion are the same in the long time limit. We conclude that for a sufficiently long time the g-subdiffusion equation describes superdiffusion well, despite a different stochastic interpretation of the processes. Then, paradoxically, a subdiffusion equation with a fractional time derivative describes superdiffusion. The superdiffusive effect is achieved here not by making anomalously long jumps by a diffusing particle, but by greatly increasing the particle jump frequency which is derived by means of the g-continuous-time random walk model. The g-subdiffusion equation is shown to be quite general, it can be used in modeling of processes in which a kind of diffusion change continuously over time. In addition, some methods used in modeling of ordinary subdiffusion processes, such as the derivation of local boundary conditions at a thin partially permeable membrane, can be used to model g-subdiffusion processes, even if this process is interpreted as superdiffusion.

Quantification of cell migration: metrics selection to model application

Cell migration plays an essential role in physiological and pathological states, such as immune response, tissue generation and tumor development. This phenomenon can occur spontaneously or it can be triggered by an external stimuli, including biochemical, mechanical, or electrical cues that induce or direct cells to migrate. The migratory response to these cues is foundational to several fields including neuroscience, cancer and regenerative medicine. Various platforms are available to qualitatively and quantitatively measure cell migration, making the measurements of cell motility straight-forward. Migratory behavior must be analyzed by multiple metrics and then models to connect the measurements to physiological meaning. This review will focus on describing and quantifying cell movement for individual cell migration.

A machine learning approach to discover migration modes and transition dynamics of heterogeneous dendritic cells

Dendritic cell (DC) migration is crucial for mounting immune responses. Immature DCs (imDCs) reportedly sense infections, while mature DCs (mDCs) move quickly to lymph nodes to deliver antigens to T cells. However, their highly heterogeneous and complex innate motility remains elusive. Here, we used an unsupervised machine learning (ML) approach to analyze long-term, two-dimensional migration trajectories of Granulocyte-macrophage colony-stimulating factor (GMCSF)-derived bone marrow-derived DCs (BMDCs). We discovered three migratory modes independent of the cell state: slow-diffusive (SD), slow-persistent (SP), and fast-persistent (FP). Remarkably, imDCs more frequently changed their modes, predominantly following a unicyclic SD→FP→SP→SD transition, whereas mDCs showed no transition directionality. We report that DC migration exhibits a history-dependent mode transition and maturation-dependent motility changes are emergent properties of the dynamic switching of the three migratory modes. Our ML-based investigation provides new insights into studying complex cellular migratory behavior.

Bioconjugation of COL1 protein on liquid-like solid surfaces to study tumor invasion dynamics

Tumor invasion is likely driven by the product of intrinsic and extrinsic stresses, reduced intercellular adhesion, and reciprocal interactions between the cancer cells and the extracellular matrix (ECM). The ECM is a dynamic material system that is continuously evolving with the tumor microenvironment. Although it is widely reported that cancer cells degrade the ECM to create paths for migration using membrane-bound and soluble enzymes, other nonenzymatic mechanisms of invasion are less studied and not clearly understood. To explore tumor invasion that is independent of enzymatic degradation, we have created an open three-dimensional (3D) microchannel network using a novel bioconjugated liquid-like solid (LLS) medium to mimic both the tortuosity and the permeability of a loose capillary-like network. The LLS is made from an ensemble of soft granular microgels, which provides an accessible platform to investigate the 3D invasion of glioblastoma (GBM) tumor spheroids using in situ scanning confocal microscopy. The surface conjugation of the LLS microgels with type 1 collagen (COL1-LLS) enables cell adhesion and migration. In this model, invasive fronts of the GBM microtumor protruded into the proximal interstitial space and may have locally reorganized the surrounding COL1-LLS. Characterization of the invasive paths revealed a super-diffusive behavior of these fronts. Numerical simulations suggest that the interstitial space guided tumor invasion by restricting available paths, and this physical restriction is responsible for the super-diffusive behavior. This study also presents evidence that cancer cells utilize anchorage-dependent migration to explore their surroundings, and geometrical cues guide 3D tumor invasion along the accessible paths independent of proteolytic ability.

Bézier interpolation improves the inference of dynamical models from data

Many dynamical systems, from quantum many-body systems to evolving populations to financial markets, are described by stochastic processes. Parameters characterizing such processes can often be inferred using information integrated over stochastic paths. However, estimating time-integrated quantities from real data with limited time resolution is challenging. Here, we propose a framework for accurately estimating time-integrated quantities using Bézier interpolation. We applied our approach to two dynamical inference problems: Determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes. We found that Bézier interpolation reduces the estimation bias for both dynamical inference problems. This improvement was especially noticeable for data sets with limited time resolution. Our method could be broadly applied to improve accuracy for other dynamical inference problems using finitely sampled data.

Proper Orthogonal Decomposition Analysis Reveals Cell Migration Directionality During Wound Healing

A proper orthogonal decomposition (POD) order reduction method was implemented to reduce the full high dimensional dynamical system associated with a wound healing cell migration assay to a low-dimensional approximation that identified the prevailing cell trajectories. The POD analysis generated POD modes that were representative of the prevalent cell trajectories. The shapes of the POD modes depended on the location of the cells with respect to the wound and exposure to disturbed (DF) or undisturbed (UF) fluid flow where the net flow was in the antegrade direction with a retrograde component or fully antegrade, respectively. For DF and UF, the POD modes of the downstream cells identified trajectories that moved upstream against the flow, while upstream POD modes exhibited sideways cell migrations. In the absence of flow, no major shape differences were observed in the POD modes on either side of the wound. The POD modes also served to reconstruct the cell migration of individual cells. With as few as three modes, the predominant cell migration trajectories were reconstructed, while the level of accuracy increased with the inclusion of more POD modes. The POD order reduction method successfully identified the predominant cell migratory trajectories under static and varying pulsatile fluid flow conditions serving as a first step in the development of artificial intelligence models of cell migration in disease and development.

Distinct speed and direction memories of migrating dendritic cells diversify their search strategies

Migrating cells exhibit various motility patterns, resulting from different migration mechanisms, cell properties, or cell-environment interactions. The complexity of cell dynamics is reflected, e.g., in the diversity of the observed forms of velocity autocorrelation function-which has been widely served as a measure of diffusivity and spreading. By analyzing the dynamics of migrating dendritic cells in vitro, we disentangle the contributions of direction θ and speed v to the velocity autocorrelation. We find that the ability of cells to maintain their speed or direction of motion is unequal, reflected in different temporal decays of speed and direction autocorrelation functions, ACv(t)∼t-1.2 and ACθ(t)∼t-0.5, respectively. The larger power-law exponent of ACv(t) indicates that the cells lose their speed memory considerably faster than the direction memory. Using numerical simulations, we investigate the influence of ACθ and ACv as well as the direction-speed cross correlation Cθ-v on the search time of a persistent random walker to find a randomly located target in confinement. Although ACθ and Cθ-v play the major roles, we find that the speed autocorrelation ACv can be also tuned to minimize the search time. Adopting an optimal ACv can reduce the search time even up to 10% compared with uncorrelated spontaneous speeds. Our results suggest that migrating cells can improve their search efficiency, especially in crowded environments, through the directional or speed persistence or the speed-direction correlation.

Relevance of Abnormal KCNN1 Expression and Osmotic Hypersensitivity in Ewing Sarcoma

Simple Summary

The main oncogene in Ewing sarcoma directly drives a high expression of a previously unknown variant KCNN1 (encoding the K_Ca2.1 channel) that we also verified in samples from >200 patients. Yet, we found that the channel is not functional and does not modulate Ewing sarcoma cell behavior. We could explain this lack of functional impact by the surprising absence of any K_Ca2.1-carried K⁺ current in Ewing sarcoma cells. However, we show in a proof-of-principle study that the essential lack of a K⁺ conductance can be exploited by applying hypoosmotic stress and effectively and selectively killing the Ewing sarcoma cells.

Abstract

Ewing sarcoma (EwS) is a rare and highly malignant bone tumor occurring mainly in childhood and adolescence. Physiologically, the bone is a central hub for Ca²⁺ homeostasis, which is severely disturbed by osteolytic processes in EwS. Therefore, we aimed to investigate how ion transport proteins involved in Ca²⁺ homeostasis affect EwS pathophysiology. We characterized the expression of 22 candidate genes of Ca²⁺-permeable or Ca²⁺-regulated ion channels in three EwS cell lines and found the Ca²⁺-activated K⁺ channel K_Ca2.1 (KCNN1) to be exceptionally highly expressed. We revealed that KCNN1 expression is directly regulated by the disease-driving oncoprotein EWSR1-FL1. Due to its consistent overexpression in EwS, KCNN1 mRNA could be a prognostic marker in EwS. In a large cohort of EwS patients, however, KCNN1 mRNA quantity does not correlate with clinical parameters. Several functional studies including patch clamp electrophysiology revealed no evidence for K_Ca2.1 function in EwS cells. Thus, elevated KCNN1 expression is not translated to K_Ca2.1 channel activity in EwS cells. However, we found that the low K⁺ conductance of EwS cells renders them susceptible to hypoosmotic solutions. The absence of a relevant K⁺ conductance in EwS thereby provides an opportunity for hypoosmotic therapy that can be exploited during tumor surgery.

Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells

Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D in vivo imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.

Myofibroblast transdifferentiation of keratocytes results in slower migration and lower sensitivity to mesoscale curvatures

Functional tissue repair after injury or disease is governed by the regenerative or fibrotic response by cells within the tissue. In the case of corneal damage, keratocytes are a key cell type that determine the outcome of the remodeling response by either adapting to a fibroblast or myofibroblast phenotype. Although a growing body of literature indicates that geometrical cues in the environment can influence Myo(fibroblast) phenotype, there is a lack of knowledge on whether and how differentiated keratocyte phenotype is affected by the curved tissue geometry in the cornea. To address this gap, in this study we characterized the phenotype of fibroblastic and transforming growth factor β (TGFβ)-induced myofibroblastic keratocytes and studied their migration behavior on curved culture substrates with varying curvatures. Immunofluorescence staining and quantification of cell morphological parameters showed that, generally, fibroblastic keratocytes were more likely to elongate, whereas myofibroblastic keratocytes expressed more pronounced α smooth muscle actin (α-SMA) and actin stress fibers as well as more mature focal adhesions. Interestingly, keratocyte adhesion on convex structures was weak and unstable, whereas they adhered normally on flat and concave structures. On concave cylinders, fibroblastic keratocytes migrated faster and with higher persistence along the longitudinal direction compared to myofibroblastic keratocytes. Moreover, this behavior became more pronounced on smaller cylinders (i.e., higher curvatures). Taken together, both keratocyte phenotypes can sense and respond to the sign and magnitude of substrate curvatures, however, myofibroblastic keratocytes exhibit weaker curvature sensing and slower migration on curved substrates compared to fibroblastic keratocytes. These findings provide fundamental insights into keratocyte phenotype after injury, but also exemplify the potential of tuning the physical cell environments in tissue engineering settings to steer towards a favorable regeneration response.

Extracellular pH Controls Chemotaxis of Neutrophil Granulocytes by Regulating Leukotriene B4 Production and Cdc42 Signaling

Neutrophil granulocytes are the first and robust responders to the chemotactic molecules released from an inflamed acidic tissue. The aim of this study was to elucidate the role of microenvironmental pH in neutrophil chemotaxis. To this end, we used neutrophils from male C57BL/6J mice and combined live cell imaging chemotaxis assays with measurements of the intracellular pH (pH_i) in varied extracellular pH (pH_e). Observational studies were complemented by biochemical analyses of leukotriene B₄ (LTB₄) production and activation of the Cdc42 Rho GTPase. Our data show that pH_i of neutrophils dose-dependently adapts to a given pH of the extracellular milieu. Neutrophil chemotaxis toward C5a has an optimum at pH_i ∼7.1, and its pH_i dependency is almost parallel to that of LTB₄ production. Consequently, a shallow pH_e gradient, resembling that encountered by neutrophils during extravasation from a blood vessel (pH ∼7.4) into the interstitium (pH ∼7.2), favors chemotaxis of stimulated neutrophils. Lowering pH_e below pH 6.8, predominantly affects neutrophil chemotaxis, although the velocity is largely maintained. Inhibition of the Na⁺/H⁺ exchanger 1 (NHE1) with cariporide drastically attenuates neutrophil chemotaxis at the optimal pH_i irrespective of the high LTB₄ production. Neutrophil migration and chemotaxis are almost completely abrogated by inhibiting LTB₄ production or blocking its receptor (BLT1). The abundance of the active GTP-bound form of Cdc42 is strongly reduced by NHE1 inhibition or pH_e 6.5. In conclusion, we propose that the pH dependence of neutrophil chemotaxis toward C5a is caused by a pH_i-dependent production of LTB₄ and activation of Cdc42. Moreover, it requires the activity of NHE1.

Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis

The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric 'memory' of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior.

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.

Exact solution for the Anisotropic Ornstein-Uhlenbeck process

Active-Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models also include random noise in particle displacement (a Wiener process), resulting in diffusive motion at short time scales. On the other hand, Ornstein-Uhlenbeck processes apply Langevin dynamics to the particles' velocity and predict motion that is not diffusive at short time scales. Experiments show that migrating cells have gradually varying speeds at intermediate and long time scales, with short-time diffusive behavior. While Ornstein-Uhlenbeck processes can describe the moderate-and long-time speed variation, Active-Matter models for over-damped particles can explain the short-time diffusive behavior. Isotropic models cannot explain both regimes, because short-time diffusion renders instantaneous velocity ill-defined, and prevents the use of dynamical equations that require velocity time-derivatives. On the other hand, both models correctly describe some of the different temporal regimes seen in migrating biological cells and must, in the appropriate limit, yield the same observable predictions. Here we propose and solve analytically an Anisotropic Ornstein-Uhlenbeck process for polarized particles, with Langevin dynamics governing the particle's movement in the polarization direction and a Wiener process governing displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in experiments in which measurements have meaningful space and time units. We also propose an approach to deal with inevitable finite-precision effects in experiments and simulations.

Fibroblast-mediated uncaging of cancer cells and dynamic evolution of the physical microenvironment

Stromal cells are prominent in solid tumor microenvironments and contribute to tumor progression. In particular, fibroblasts are common cell types in the tumor stroma that play important roles in remodeling the extracellular matrix (ECM). Here, we perform co-culture experiments with tumor cells and fibroblasts embedded in 3D collagen I matrices. We investigate the impact of fibroblasts on the migratory behavior of neighboring tumor cells and on the evolution of the surrounding ECM. We find that fibroblasts increase tumor cell motility and facilitate the transition from confined to diffusive tumor cell motions, indicative of an uncaging effect. Furthermore, the ECM is globally and locally remodeled substantially with the presence of fibroblasts. Moreover, these fibroblast-mediated phenomena are in part dependent on matrix metalloproteinases.

Ergodic property of random diffusivity system with trapping events

A Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an α-stable subordinator with α<1. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble- and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model with any kind of diffusivity, including the critical case where the model presents normal diffusion.

Orai3 Calcium Channel Regulates Breast Cancer Cell Migration through Calcium-Dependent and -Independent Mechanisms

Orai3 calcium (Ca²⁺) channels are implicated in multiple breast cancer processes, such as proliferation and survival as well as resistance to chemotherapy. However, their involvement in the breast cancer cell migration processes remains vague. In the present study, we exploited MDA-MB-231 and MDA-MB-231 BrM2 basal-like estrogen receptor-negative (ER^-) cell lines to assess the direct role of Orai3 in cell migration. We showed that Orai3 regulates MDA-MB-231 and MDA-MB-231 BrM2 cell migration in two distinct ways. First, we showed that Orai3 remodels cell adhesive capacities by modulating the intracellular Ca²⁺ concentration. Orai3 silencing (siOrai3) decreased calpain activity, cell adhesion and migration in a Ca²⁺-dependent manner. In addition, Orai3 interacts with focal adhesion kinase (FAK) and regulates the actin cytoskeleton, in a Ca²⁺-independent way. Thus, siOrai3 modulates cell morphology by altering F-actin polymerization via a loss of interaction between Orai3 and FAK. To summarize, we demonstrated that Orai3 regulates cell migration through a Ca²⁺-dependent modulation of calpain activity and, in a Ca²⁺-independent manner, the actin cytoskeleton architecture via FAK.

Single-cell tracking reveals super-spreading brain cancer cells with high persistence

Cell migration is a fundamental characteristic of vital processes such as tissue morphogenesis, wound healing and immune cell homing to lymph nodes and inflamed or infected sites. Therefore, various brain defect diseases, chronic inflammatory diseases as well as tumor formation and metastasis are associated with aberrant or absent cell migration. We embedded multicellular brain cancer spheroids in Matrigel™ and utilized single-particle tracking to extract the paths of cells migrating away from the spheroids. We found that - in contrast to local invasion - single cell migration is independent of Matrigel™ concentration and is characterized by high directionality and persistence. Furthermore, we identified a subpopulation of super-spreading cells with >200-fold longer persistence times than the majority of cells. These results highlight yet another aspect of cell heterogeneity in tumors.

Alignment interactions drive structural transitions in biological tissues

Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a nonequilibrium phase transition into a quasihexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of the alignment coupling. In this regime, the dynamics of cell centers and shape fluctuation show features typical of glassy systems.

Neurotransmitter signaling regulates distinct phases of multimodal human interneuron migration

Inhibitory GABAergic interneurons migrate over long distances from their extracortical origin into the developing cortex. In humans, this process is uniquely slow and prolonged, and it is unclear whether guidance cues unique to humans govern the various phases of this complex developmental process. Here, we use fused cerebral organoids to identify key roles of neurotransmitter signaling pathways in guiding the migratory behavior of human cortical interneurons. We use scRNAseq to reveal expression of GABA, glutamate, glycine, and serotonin receptors along distinct maturation trajectories across interneuron migration. We develop an image analysis software package, TrackPal, to simultaneously assess 48 parameters for entire migration tracks of individual cells. By chemical screening, we show that different modes of interneuron migration depend on distinct neurotransmitter signaling pathways, linking transcriptional maturation of interneurons with their migratory behavior. Altogether, our study provides a comprehensive quantitative analysis of human interneuron migration and its functional modulation by neurotransmitter signaling.

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.

A mathematical framework for modelling 3D cell motility: applications to glioblastoma cell migration

The collection of 3D cell tracking data from live images of micro-tissues is a recent innovation made possible due to advances in imaging techniques. As such there is increased interest in studying cell motility in 3D in vitro model systems but a lack of rigorous methodology for analysing the resulting data sets. One such instance of the use of these in vitro models is in the study of cancerous tumours. Growing multicellular tumour spheroids in vitro allows for modelling of the tumour microenvironment and the study of tumour cell behaviours, such as migration, which improves understanding of these cells and in turn could potentially improve cancer treatments. In this paper, we present a workflow for the rigorous analysis of 3D cell tracking data, based on the persistent random walk model, but adaptable to other biologically informed mathematical models. We use statistical measures to assess the fit of the model to the motility data and to estimate model parameters and provide confidence intervals for those parameters, to allow for parametrization of the model taking correlation in the data into account. We use in silico simulations to validate the workflow in 3D before testing our method on cell tracking data taken from in vitro experiments on glioblastoma tumour cells, a brain cancer with a very poor prognosis. The presented approach is intended to be accessible to both modellers and experimentalists alike in that it provides tools for uncovering features of the data set that may suggest amendments to future experiments or modelling attempts.

Rab40-Cullin5 complex regulates EPLIN and actin cytoskeleton dynamics during cell migration

Rab40b is a SOCS box–containing protein that regulates the secretion of MMPs to facilitate extracellular matrix remodeling during cell migration. Here, we show that Rab40b interacts with Cullin5 via the Rab40b SOCS domain. We demonstrate that loss of Rab40b–Cullin5 binding decreases cell motility and invasive potential and show that defective cell migration and invasion stem from alteration to the actin cytoskeleton, leading to decreased invadopodia formation, decreased actin dynamics at the leading edge, and an increase in stress fibers. We also show that these stress fibers anchor at less dynamic, more stable focal adhesions. Mechanistically, changes in the cytoskeleton and focal adhesion dynamics are mediated in part by EPLIN, which we demonstrate to be a binding partner of Rab40b and a target for Rab40b–Cullin5-dependent localized ubiquitylation and degradation. Thus, we propose a model where Rab40b–Cullin5-dependent ubiquitylation regulates EPLIN localization to promote cell migration and invasion by altering focal adhesion and cytoskeletal dynamics.

Study of Wound Healing Dynamics by Single Pseudo-Particle Tracking in Phase Contrast Images Acquired in Time-Lapse

Cellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities self-aligning in time. The presence of a dense agglomerate of cells makes the application of single particle tracking techniques to define cells dynamics difficult, especially in the case of phase contrast images. Here, we propose an original pipeline for the analysis of phase contrast images of the wound healing scratch assay acquired in time-lapse, with the aim of extracting single particle trajectories describing the dynamics of the wound closure. In such an approach, the membrane of the cells at the border of the wound is taken as a unicum, i.e., the wound edge, and the dynamics is described by the stochastic motion of an ensemble of points on such a membrane, i.e., pseudo-particles. For each single frame, the pipeline of analysis includes: first, a texture classification for separating the background from the cells and for identifying the wound edge; second, the computation of the coordinates of the ensemble of pseudo-particles, chosen to be uniformly distributed along the length of the wound edge. We show the results of this method applied to a glioma cell line (T98G) performing a wound healing scratch assay without external stimuli. We discuss the efficiency of the method to assess cell motility and possible applications to other experimental layouts, such as single cell motion. The pipeline is developed in the Python language and is available upon request.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Non-Markovian data-driven modeling of single-cell motility

Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extracted memory function we formulate a generalized exactly solvable cell migration model which indicates that negative friction generates cell persistence over long timescales. The nonequilibrium character of cell motion is investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model that involves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process.

Advances in fluorescence microscopy techniques to study kidney function

Fluorescence microscopy, in particular immunofluorescence microscopy, has been used extensively for the assessment of kidney function and pathology for both research and diagnostic purposes. The development of confocal microscopy in the 1950s enabled imaging of live cells and intravital imaging of the kidney; however, confocal microscopy is limited by its maximal spatial resolution and depth. More recent advances in fluorescence microscopy techniques have enabled increasingly detailed assessment of kidney structure and provided extraordinary insights into kidney function. For example, nanoscale precise imaging by rapid beam oscillation (nSPIRO) is a super-resolution microscopy technique that was originally developed for functional imaging of kidney microvilli and enables detection of dynamic physiological events in the kidney. A variety of techniques such as fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS) and Förster resonance energy transfer (FRET) enable assessment of interaction between proteins. The emergence of other super-resolution techniques, including super-resolution stimulated emission depletion (STED), photoactivated localization microscopy (PALM), stochastic optical reconstruction microscopy (STORM) and structured illumination microscopy (SIM), has enabled functional imaging of cellular and subcellular organelles at ≤50 nm resolution. The deep imaging via emission recovery (DIVER) detector allows deep, label-free and high-sensitivity imaging of second harmonics, enabling assessment of processes such as fibrosis, whereas fluorescence lifetime imaging microscopy (FLIM) enables assessment of metabolic processes.

Multi-scale analysis and modelling of collective migration in biological systems

Collective migration has become a paradigm for emergent behaviour in systems of moving and interacting individual units resulting in coherent motion. In biology, these units are cells or organisms. Collective cell migration is important in embryonic development, where it underlies tissue and organ formation, as well as pathological processes, such as cancer invasion and metastasis. In animal groups, collective movements may enhance individuals' decisions and facilitate navigation through complex environments and access to food resources. Mathematical models can extract unifying principles behind the diverse manifestations of collective migration. In biology, with a few exceptions, collective migration typically occurs at a 'mesoscopic scale' where the number of units ranges from only a few dozen to a few thousands, in contrast to the large systems treated by statistical mechanics. Recent developments in multi-scale analysis have allowed linkage of mesoscopic to micro- and macroscopic scales, and for different biological systems. The articles in this theme issue on 'Multi-scale analysis and modelling of collective migration' compile a range of mathematical modelling ideas and multi-scale methods for the analysis of collective migration. These approaches (i) uncover new unifying organization principles of collective behaviour, (ii) shed light on the transition from single to collective migration, and (iii) allow us to define similarities and differences of collective behaviour in groups of cells and organisms. As a common theme, self-organized collective migration is the result of ecological and evolutionary constraints both at the cell and organismic levels. Thereby, the rules governing physiological collective behaviours also underlie pathological processes, albeit with different upstream inputs and consequences for the group. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

A Stochastic Modelling Framework for Single Cell Migration: Coupling Contractility and Focal Adhesions

The interaction of the actin cytoskeleton with cell–substrate adhesions is necessary for cell migration. While the trajectories of motile cells have a stochastic character, investigations of cell motility mechanisms rarely elaborate on the origins of the observed randomness. Here, guided by a few fundamental attributes of cell motility, I construct a minimal stochastic cell migration model from ground-up. The resulting model couples a deterministic actomyosin contractility mechanism with stochastic cell–substrate adhesion kinetics, and yields a well-defined piecewise deterministic process. Numerical simulations reproduce several experimentally observed results, including anomalous diffusion, tactic migration and contact guidance. This work provides a basis for the development of cell–cell collision and population migration models.

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion

Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.

Alternating regimes of motion in a model with cell-cell interactions

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra- and extracellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases, cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we have considered a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolve according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In one case, the next orientation of the driving field depends on the previous direction of the field. In the other case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Different cell densities are considered to reveal the effect of cell-cell interactions. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction-coefficient and cell-density-dependent manner. Furthermore, we observe alternating regimes in the mean-square displacement, with normal and anomalous diffusion. The crossovers between diffusive and directed motion regimes are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement, the duration of the diffusive regime decreases, particularly in high-density cultures.

Stochastic Methods for Inferring States of Cell Migration

Cell migration refers to the ability of cells to translocate across a substrate or through a matrix. To achieve net movement requires spatiotemporal regulation of the actin cytoskeleton. Computational approaches are necessary to identify and quantify the regulatory mechanisms that generate directed cell movement. To address this need, we developed computational tools, based on stochastic modeling, to analyze time series data for the position of randomly migrating cells. Our approach allows parameters that characterize cell movement to be efficiently estimated from cell track data. We applied our methods to analyze the random migration of Mouse Embryonic Fibroblasts (MEFS) and HeLa cells. Our analysis revealed that MEFs exist in two distinct states of migration characterized by differences in cell speed and persistence, whereas HeLa cells only exhibit a single state. Further analysis revealed that the Rho-family GTPase RhoG plays a role in determining the properties of the two migratory states of MEFs. An important feature of our computational approach is that it provides a method for predicting the current migration state of an individual cell from time series data. Finally, we applied our computational methods to HeLa cells expressing a Rac1 biosensor. The Rac1 biosensor is known to perturb movement when expressed at overly high concentrations; at these expression levels the HeLa cells showed two migratory states, which correlated with differences in the spatial distribution of active Rac1.

CompuCell3D Simulations Reproduce Mesenchymal Cell Migration on Flat Substrates

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The Fürth equation, the usual characterization of mean-squared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time- and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longer-time cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.

Adhesion modulates cell morphology and migration within dense fibrous networks

One of the most fundamental abilities required for the sustainability of complex life forms is active cell migration, since it is essential in diverse processes from morphogenesis to leukocyte chemotaxis in immune response. The movement of a cell is the result of intricate mechanisms, that involve the coordination between mechanical forces, biochemical regulatory pathways and environmental cues. In particular, epithelial cancer cells have to employ mechanical strategies in order to migrate through the tissue's basement membrane and infiltrate the bloodstream during the invasion stage of metastasis. In this work we explore how mechanical interactions such as spatial restriction and adhesion affect migration of a self-propelled droplet in dense fibrous media. We have performed a systematic analysis using a phase-field model and we propose a novel approach to simulate cell migration with dissipative particle dynamics modelling. With this purpose we have measured in our simulation the cell's velocity and quantified its morphology as a function of the fibre density and of its adhesiveness to the matrix fibres. Furthermore, we have compared our results to a previousin vitromigration assay of fibrosarcoma cells in fibrous matrices. The results show good agreement between the two methodologies and experiments in the literature, which indicates that these minimalist descriptions are able to capture the main features of the system. Our results indicate that adhesiveness is critical for cell migration, by modulating cell morphology in crowded environments and by enhancing cell velocity. In addition, our analysis suggests that matrix metalloproteinases (MMPs) play an important role as adhesiveness modulators. We propose that new assays should be carried out to address the role of adhesion and the effect of different MMPs in cell migration under confined conditions.

Protonation of Piezo1 Impairs Cell-Matrix Interactions of Pancreatic Stellate Cells

Pancreatic ductal adenocarcinoma (PDAC) is characterized by an acidic and fibrotic stroma. The extracellular matrix (ECM) causing the fibrosis is primarily formed by pancreatic stellate cells (PSCs). The effects of the altered biomechanics and pH landscape in the pathogenesis of PDAC, however, are poorly understood. Mechanotransduction in cells has been linked to the function of mechanosensitive ion channels such as Piezo1. Here, we tested whether this channel plays crucial roles in transducing mechanical signals in the acidic PDAC microenvironment. We performed immunofluorescence, Ca²⁺ influx and intracellular pH measurements in PSCs and complemented them by live-cell imaging migration experiments in order to assess the function of Piezo1 channels in PSCs. We evaluated whether Piezo1 responds to changes of extracellular and/or intracellular pH in the pathophysiological range (pH 6.6 and pH 6.9, respectively). We validated our results using Piezo1-transfected HEK293 cells as a model system. Indeed, acidification of the intracellular space severely inhibits Piezo1-mediated Ca²⁺ influx into PSCs. In addition, stimulation of Piezo1 channels with its activator Yoda1 accelerates migration of PSCs on a two-dimensional ECM as well as in a 3D setting. Furthermore, Yoda1-activated PSCs transmit more force to the surrounding ECM under physiological pH, as revealed by measuring the dislocation of microbeads embedded in the surrounding matrix. This is paralleled by an enhanced phosphorylation of myosin light chain isoform 9 after Piezo1 stimulation. Intriguingly, upon acidification, Piezo1 activation leads to the initiation of cell death and disruption of PSC spheroids. In summary, stimulating Piezo1 activates PSCs by inducing Ca²⁺ influx which in turn alters the cytoskeletal architecture. This results in increased cellular motility and ECM traction, which can be useful for the cells to invade the surroundings and to detach from the tissue. However, in the presence of an acidic extracellular pH, although net Ca²⁺ influx is reduced, Piezo1 activation leads to severe cell stress also limiting cellular viability. In conclusion, our results indicate a strong interdependence between environmental pH, the mechanical output of PSCs and stromal mechanics, which promotes early local invasion of PDAC cells.

The recent advances in the mathematical modelling of human pluripotent stem cells

Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop non-invasive prognostic modelling tools to assist in the optimisation of laboratory experiments. Here, the recent advances in the mathematical modelling of hPSCs are discussed, including cell kinematics, cell proliferation and colony formation, and pluripotency and differentiation.

MMP3 activity rather than cortical stiffness determines NHE1-dependent invasiveness of melanoma cells

Background

Both cell adhesion and matrix metalloproteinase (MMP) activity depend on pH at the cell surface. By regulating extracellular juxtamembrane pH, the Na⁺/H⁺ exchanger NHE1 plays a significant part in human melanoma (MV3) cell migration and invasion. Because NHE1, besides its pH-regulatory transport function, also serves as a structural element tying the cortical actin cytoskeleton to the plasma membrane, we investigated whether NHE1 affects cortical stiffness of MV3 cells, and how this makes an impact on their invasiveness.

Methods

NHE1 overexpressing MV3 cells were compared to the corresponding mock-transfected control cells. NHE1 expression was verified by Western blotting, cariporide (HOE642) was used to inhibit NHE1 activity, cell stiffness was determined by atomic force microscopy, and F-actin was visualized by phalloidin-staining. Migration on, and invasion of, native and glutaraldehyde-fixed collagen I substrates were analyzed using time-lapse video microscopy and Boyden-chamber assays, respectively. MMP secretion and activity were detected by Western blot and zymography, respectively. MMP activity was inhibited with NNGH.

Results

The cortical, but not the bulk stiffness, was significantly higher in NHE1 overexpressing cells. This increase in cortical stiffness was accompanied by a reorganization of the cortical cytoskeleton, i.e. a condensation of F-actin underneath and along the plasma membrane. However, it was not affected by NHE1 inhibition. Nevertheless, actin dynamics is required for cell invasion as demonstrated with the application of cytochalasin D. NHE1 overexpression was associated with an elevated MMP3 secretion and an increase in the invasion of a native matrix. This increase in invasiveness could be antagonized by the MMP inhibitor NNGH. Transmigration through a glutaraldehyde-fixed, indigestible substrate was not affected by NHE1 overexpression.

Conclusion

NHE1, as a structural element and independently of its transport activity, contributes to the organization of the cortical F-actin meshwork and thus impacts cortical stiffness. Since NHE1 overexpression stimulates MMP3 secretion but does not change transmigration through a fixed substrate, MV3 cell invasion of a native substrate depends on MMP activity rather than on a modifiable cortical stiffness.