Anomalous dynamics of cell migration

Enteropathogenic Escherichia coli induces Entamoeba histolytica superdiffusion movement on fibronectin by reducing traction forces

Amebiasis, caused by Entamoeba histolytica, is a global health concern, affecting millions and causing significant mortality, particularly in areas with poor sanitation. Although recent studies have examined E. histolytica's interaction with human intestinal microbes, the impact of bacterial presence on the parasite's motility, mechanical forces, and their potential role in altering invasiveness have not been fully elucidated. In this study, we utilized a micropillar-array system combined with live imaging to investigate the effects of enteropathogenic Escherichia coli on E. histolytica's motility characteristics, F-actin spatial localization, and traction force exerted on fibronectin-coated substrates. Our findings indicate that co-incubation with live enteropathogenic E. coli significantly enhances the motility of E. histolytica, as evidenced by superdiffusive movement-characterized by increased directionality and speed-resulting in broader dispersal and more extensive tissue/cell damage. This increased motility is accompanied by a reduction in F-actin-dependent traction forces and podosome-like structures on fibronectin-coated substrates, but with increased F-actin localization in the upper part of the cytoplasm. These findings highlight the role of physical interactions and cellular behaviors in modulating the parasite's virulence, providing new insights into the mechanistic basis of its pathogenicity.

Non-Markovian equilibrium and non-equilibrium barrier-crossing kinetics in asymmetric double-well potentials

Barrier-crossing processes in nature are often non-Markovian and typically occur over an asymmetric double-well free-energy landscape. However, most theories and numerical studies on barrier-crossing rates assume symmetric free-energy profiles. Here, we use a one-dimensional generalized Langevin equation (GLE) to investigate non-Markovian reaction kinetics in asymmetric double-well potentials. We derive a general formula, confirmed by extensive simulations, that accurately predicts mean first-passage times from well to barrier top in an asymmetric double-well potential with arbitrary memory time and reaction coordinate mass. We extend our formalism to non-equilibrium non-Markovian systems, confirming its broad applicability to equilibrium and non-equilibrium systems in biology, chemistry, and physics.

A self-assembled protein β-helix as a self-contained biofunctional motif

Nature constructs matter by employing protein folding motifs, many of which have been synthetically reconstituted to exploit function. A less understood motif whose structure-function relationships remain unexploited is formed by parallel β-strands arranged in a helical repetitive pattern, termed a β-helix. Herein we reconstitute a protein β-helix by design and endow it with biological function. Unlike β-helical proteins, which are contiguous covalent structures, this β-helix self-assembles from an elementary sequence of 18 amino acids. Using a combination of experimental and computational methods, we demonstrate that the resulting assemblies are discrete cylindrical structures exhibiting conserved dimensions at the nanoscale. We provide evidence for the structures to form a carpet-like three-dimensional scaffold promoting and inhibiting the growth of human and bacterial cells, respectively, while being able to mediate intracellular gene delivery. The study introduces a self-assembled β-helix as a self-contained bio- and multi-functional motif for exploring and exploiting mechanistic biology.

Memory and Friction: From the Nanoscale to the Macroscale

Friction is a phenomenon that manifests across all spatial and temporal scales, from the molecular to the macroscopic scale. It describes the dissipation of energy from the motion of particles or abstract reaction coordinates and arises in the transition from a detailed molecular-level description to a simplified, coarse-grained model. It has long been understood that time-dependent (non-Markovian) friction effects are critical for describing the dynamics of many systems, but that they are notoriously difficult to evaluate for complex physical, chemical, and biological systems. In recent years, the development of advanced numerical friction extraction techniques and methods to simulate the generalized Langevin equation has enabled exploration of the role of time-dependent friction across all scales. We discuss recent applications of these friction extraction techniques and the growing understanding of the role of friction in complex equilibrium and nonequilibrium dynamic many-body systems.

Quasi-Diffusion Imaging: Application to Ultra-High b-Value and Time-Dependent Diffusion Images of Brain Tissue

We demonstrate that quasi-diffusion imaging (QDI) is a signal representation that extends towards the negative power law regime. We evaluate QDI for in vivo human and ex vivo fixed rat brain tissue acrossb $$ b $$ -value ranges from 0 to 25,000 s mm-2, determine whether accurate parameter estimates can be acquired from clinically feasible scan times and investigate their diffusion time-dependence. Several mathematical properties of the QDI representation are presented. QDI describes diffusion magnetic resonance imaging (dMRI) signal attenuation by two fitting parameters within a Mittag-Leffler function (MLF). We present its asymptotic properties at low and highb $$ b $$ -values and define the inflection point (IP) above which the signal tends to a negative power law. To show that QDI provides an accurate representation of dMRI signal, we apply it to two human brain datasets (Dataset 1:0 ≤ b ≤ 15,000 $$ 0\le b\le \mathrm{15,000} $$ s mm-2; Dataset 2:0 ≤ b ≤ 17,800 $$ 0\le b\le \mathrm{17,800} $$  s mm-2) and an ex vivo fixed rat brain (Dataset 3:0 ≤ b ≤ 25,000 $$ 0\le b\le \mathrm{25,000} $$  s mm-2, diffusion times17.5 ≤ ∆ ≤ 200 $$ 17.5\le \Delta \le 200 $$  ms). A clinically feasible 4b $$ b $$ -value subset of Dataset 1 (0 ≤ b ≤ 15,000 $$ 0\le b\le \mathrm{15,000} $$  s mm-2) is also analysed (acquisition time 6 min and 16 s). QDI showed excellent fits to observed signal attenuation, identified signal IPs and provided an apparent negative power law. Stable parameter estimates were identified upon increasing the maximumb $$ b $$ -value of the fitting range to near and above signal IPs, suggesting QDI is a valid signal representation within in vivo and ex vivo brain tissue across largeb $$ b $$ -value ranges with multiple diffusion times. QDI parameters were accurately estimated from clinically feasible shorter data acquisition, and time-dependence was observed with parameters approaching a Gaussian tortuosity limit with increasing diffusion time. In conclusion, QDI provides a parsimonious representation of dMRI signal attenuation in brain tissue that is sensitive to tissue microstructural heterogeneity and cell membrane permeability.

Decoupling of Density-Dependent Migration/Proliferation Dichotomy on Surface Potential Gradient

The reciprocal connection between cell migration and proliferation relies on the intertwined contributions from substrate-associated and intercellular cues in the microenvironment. However, how cells perceive the substrates, make contact with their neighbors, and switch phenotypes under different trade-off conditions are still not fully understood. Here, we designed a distinct heterogeneous electric surface potential gradient of piezoelectric biomaterials to decouple the density-dependent migration/proliferation dichotomy. We found that the surface potential gradient accelerated both individual and collective cell migration but reduced proliferation through G0/G1 cell cycle arrest via the integrin/cytoskeleton signaling axis in low density. Interestingly, the initial cell density encodes the proliferative potential independent of the substrate feature. While in high density, the surface potential gradient ceased cell proliferation mainly via the E-cadherin/β-catenin signaling axis. Taken together, these results shed light on the underlying mechanism of the intertwined contributions of cell-material and cell-cell cross-links on migration and proliferation and also provide a new paradigm of materiobiology.

Glassy Adhesion Dynamics Govern Transitions Between Sub-Diffusive and Super-Diffusive Cell Migration on Viscoelastic Substrates

Cell migration is pivotal in cancer metastasis, where cells navigate the extracellular matrix (ECM) and invade distant tissues. While the ECM is viscoelastic-exhibiting time-dependent stress relaxation-its influence on cell migration remains poorly understood. Here, we employ an integrated experimental and modeling approach to investigate filopodial cancer cell migration on viscoelastic substrates and uncover a striking transition from sub-diffusive to super-diffusive behavior driven by the substrate's viscous relaxation timescale. Conventional motor-clutch based migration models fail to capture these anomalous migration modes, as they overlook the complex adhesion dynamics shaped by broad distribution of adhesion lifetimes. To address this, we develop a glassy motor-clutch model that incorporates the rugged energy landscape of adhesion clusters, where multiple metastable states yield long-tailed adhesion timescales. Our model reveals that migration dynamics are governed by the interplay between cellular and substrate timescales: slow-relaxing substrates prolong trapping, leading to sub-diffusion, while fast-relaxing substrates promote larger steps limiting trapping, leading to super-diffusion. Additionally, we uncover the role of actin polymerization and contractility in modulating adhesion dynamics and driving anomalous migration. These findings establish a mechanistic framework linking substrate viscoelasticity to cell motility, with implications for metastasis and cancer progression.

The NHSL1-A complex interacts with the Arp2/3 complex and controls cell migration efficiency and chemotaxis

Cell migration is crucial for development and deregulation causes diseases. The Scar/WAVE complex promotes mesenchymal cell migration through Arp2/3 mediated lamellipodia protrusion. We previously discovered that all isoforms of Nance-Horan Syndrome-like 1 (NHSL1) protein interact directly with the Scar/WAVE complex and the NHSL1-F1 isoform negatively regulates Scar/WAVE-Arp2/3 activity thereby inhibiting 2D random cell migration. Here, we investigate the NHSL1-A1 isoform, which contains a Scar homology domain (SHD). The SHD in Scar/WAVE mediates the formation of the Scar/WAVE complex. We found that the SHD of NHLS1-A is sufficient for the formation of an NHSL1-A complex composed of the same proteins as the Scar/WAVE complex, but NHSL1-A replaces Scar/WAVE. NHSL1-A SHD recruits the NHSL1-A complex to lamellipodia, where also the Scar/WAVE complex resides. Scar/WAVE contains a WCA domain, which is phosphorylated by CK2 and recruits and activates the Arp2/3 complex to nucleate branched actin networks supporting lamellipodial protrusion. We identified a WCA domain in NHSL1 which interacts with the Arp2/3 complex. The NHSL1 WCA domain is phosphorylated by GSK3, and this increases the interaction with the Arp2/3 complex. In contrast to NHSL1-F1, the NHSL1-A complex promotes cell migration speed but not cell persistence via the Scar/WAVE complex and potentially via its WCA domain. In addition, the NHSL1-A complex is required for chemotaxis. Mechanistically, the NHSL1-A complex may increase lamellipodial Arp2/3 activity and lamellipodial speed while reducing lamellipodial persistence. Our findings reveal an additional layer of Arp2/3 complex control essential for mesenchymal cell migration highly relevant for development and disease.

Correction: Microglia are essential for tissue contraction in wound closure after brain injury in zebrafish larvae

Although in humans, the brain fails to heal after an injury, young zebrafish are able to restore tissue structural integrity in less than 24 h, thanks to the mechanical action of microglia.

Microglia are essential for tissue contraction in wound closure after brain injury in zebrafish larvae

Wound closure after brain injury is crucial for tissue restoration but remains poorly understood at the tissue level. We investigated this process using in vivo observations of larval zebrafish brain injury. Our findings show that wound closure occurs within the first 24 h through global tissue contraction, as evidenced by live-imaging and drug inhibition studies. Microglia accumulate at the wound site before closure, and computational models suggest that their physical traction could drive this process. Depleting microglia genetically or pharmacologically impairs tissue repair. At the cellular level, live imaging reveals centripetal deformation of astrocytic processes contacted by migrating microglia. Laser severing of these contacts causes rapid retraction of microglial processes and slower retraction of astrocytic processes, indicating tension. Disrupting the lcp1 gene, which encodes the F-actin-stabilising protein L-plastin, in microglia results in failed wound closure. These findings support a mechanical role of microglia in wound contraction and suggest that targeting microglial mechanics could offer new strategies for treating traumatic brain injury.

The maximum size of cell-aggregates is determined by the competition between the strain energy and the binding energy of cells

The development of tissues and organs is affected by how cells interact with each other to form aggregates. Such an interaction is in turn determined by several different factors, such as inter-cellular attractive forces, cell motility, and the strain energy of cells. Here, we have used mathematical modelling and numerical simulations to explore how the interplay between these factors can influence the formation and stability of 2D cell aggregates. Cell aggregates were created by incrementally accumulating cells over an initial seed. The binding energy density of these aggregates was determined using the harmonic approximation and was integrated into a probabilistic model to estimate the maximum cluster size, beyond which the aggregate becomes unstable and breaks into smaller fragments. Our simulations reveal that the ratio of strain energy to internal adhesive energy (U s / U b ) critically impacts cell aggregation; smaller ratios allow for larger cluster sizes. These findings have significant implications for tissue engineering, in-vitro modeling, the study of neurodegenerative diseases, and tissue regeneration, providing insights into how physical and biological characteristics of cells influence their aggregation and stability.

Elastic interactions compete with persistent cell motility to drive durotaxis

Many animal cells that crawl on extracellular substrates exhibit durotaxis, i.e., directed migration toward stiffer substrate regions. This has implications in several biological processes including tissue development and tumor progression. Here, we introduce a phenomenological model for single-cell durotaxis that incorporates both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by a key observation in an early demonstration of durotaxis: a single, contractile cell at a sharp interface between a softer and a stiffer region of an elastic substrate reorients and migrates toward the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile traction forces on their elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential. The dynamics is determined by two crucial parameters: the strength of the cellular traction-induced boundary elastic interaction (A), and the persistence of cell motility (Pe). Elastic forces and torques resulting from the potential orient cells perpendicular (parallel) to the boundary and accumulate (deplete) them at the clamped (free) boundary. Thus, a clamped boundary induces an attractive potential that drives durotaxis, while a free boundary induces a repulsive potential that prevents antidurotaxis. By quantifying the steady-state position and orientation probability densities, we show how the extent of accumulation (depletion) depends on the strength of the elastic potential and motility. We compare and contrast crawling cells with biological microswimmers and other synthetic active particles, where accumulation at confining boundaries is well known. We define metrics quantifying boundary accumulation and durotaxis, and present a phase diagram that identifies three possible regimes: durotaxis, and adurotaxis with and without motility-induced accumulation at the boundary. Overall, our model predicts how durotaxis depends on cell contractility and motility, successfully explains some previous observations, and provides testable predictions to guide future experiments.

Human Pluripotent Stem Cell Colony Migration Is Related to Culture Environment and Morphological Phenotype

Human pluripotent stem cells (hPSCs) are an important tool in the field of regenerative medicine due to their ability to differentiate towards all tissues of the adult organism. An important task in the study of hPSCs is to understand the factors that influence the maintenance of pluripotent and clonal characteristics of colonies represented by their morphological phenotype. Such factors include the ability of colonies to migrate during growth. In this work, we measured and analyzed the migration trajectories of hPSC colonies obtained from bright-field images of three cell lines, including induced hPSC lines AD3 and HPCASRi002-A (CaSR) and human embryonic stem cell line H9. To represent the pluripotent status, the colonies were visually phenotyped into two classes having a "good" or "bad" morphological phenotype. As for the migration characteristics, we calculated the colony speed and distance traveled (mobility measures), meandering index (motion persistence measures), outreach ratio (trajectory tortuosity characteristic), as well as the velocity autocorrelation function. The analysis revealed that the discrimination of phenotypes by the migration characteristics depended on both the cell line and growth environment. In particular, when the mTESR1/Matrigel culture environment was used, "good" AD3 colonies demonstrated a higher average migration speed than the "bad" ones. The reverse relationship between average speeds of "good" and "bad" colonies was found for the H9 line. The CaSR cell line did not show significant differences in the migration speed between the "good" and "bad" phenotypes. We investigated the type of motion exhibited by the colonies by applying two diffusion models to the mean squared displacement dynamics, one model corresponding to normal and the other to anomalous diffusion. The type of diffusion and diffusion parameter values resulting from the model fitting to data demonstrated a similar cell line, environment, and phenotype dependency. Colonies mainly showed a superdiffusive behavior for the mTESR1/Matrigel culture conditions, characterized by longer migration steps compared to the normal random walk. The specific properties of migration features and the patterns of their variation demonstrated in our work can be useful for the development and/or improvement of automated solutions for quality control of hPSCs.

Aggregation of adult parasitic nematodes in sex-mixed groups analysed by transient anomalous diffusion formalism

Intestinal parasitic worms are widespread throughout the world, causing chronic infections in humans and animals. However, very little is known about the locomotion of the worms in the host gut. We studied the movement of Heligmosomoides bakeri, naturally infecting mice, and used as an animal model for roundworm infections. We investigated the locomotion of H. bakeri in simplified environments mimicking key physical features of the intestinal lumen, i.e. medium viscosity and intestinal villi topology. We found that the motion sequence of these nematodes is non-periodic, but the migration could be described by transient anomalous diffusion. Aggregation as a result of biased, enhanced-diffusive locomotion of nematodes in sex-mixed groups was detected. This locomotion is probably stimulated by mating and reproduction, while single nematodes move randomly (diffusive). Natural physical obstacles such as high mucus-like viscosity or villi topology slowed down but did not entirely prevent nematode aggregation. Additionally, the mean displacement rate of nematodes in sex-mixed groups of 3.0 × 10-3 mm s-1 in a mucus-like medium is in good agreement with estimates of migration velocities of 10-4 to 10-3 mm s-1 in the gut. Our data indicate H. bakeri motion to be non-periodic and their migration random (diffusive-like), but triggerable by the presence of kin.

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

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 KCa2.1 (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 KCa2.1 function in EwS cells. Thus, elevated KCNN1 expression is not translated to KCa2.1 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.