Uncovering multiscale structure in the variability of larval zebrafish navigation

Animals chain movements into long-lived motor strategies, resulting in variability that ultimately reflects the interplay between internal states and environmental cues. To reveal structure in such variability, we build models that bridges across time scales that enable a quantitative comparison of behavioral phenotypes among individuals. Applied to larval zebrafish exposed to diverse sensory cues, we uncover a hierarchy of long-lived motor strategies, dominated by changes in orientation distinguishing cruising and wandering strategies. Environmental cues induce preferences along these modes at the population level: while fish cruise in the light, they wander in response to aversive (dark) stimuli or in search for prey. Our method enables us to encode the behavioral dynamics of each individual fish in the transitions among coarse-grained motor strategies. By doing so, we uncover a hierarchical structure to the phenotypic variability that corresponds to exploration-exploitation trade-offs. Within a wide range of sensory cues, a major source of variation among fish is driven by prior and immediate exposure to prey that induces exploitation phenotypes. However, a large degree of variability is unexplained by environmental cues, pointing to hidden states that override the sensory context to induce contrasting exploration-exploitation phenotypes. Altogether, our approach extracts the timescales of motor strategies deployed during navigation, exposing undiscovered structure among individuals and pointing to internal states tuned by prior experience.

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.

Geometry-Sensitive Protrusion Growth Directs Confined Cell Migration

The migratory dynamics of cells can be influenced by the complex microenvironment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their microenvironment. Here, we propose a biophysical mechanism for a geometry-dependent coupling between cellular protrusions and the nucleus that leads to directed migration. We apply our model to geometry-guided cell migration to obtain insights into the origin of directed migration on asymmetric adhesive micropatterns and the polarization enhancement of cells observed under strong confinement. Remarkably, for cells that can choose between channels of different size, our model predicts an intricate dependence for cellular decision making as a function of the two channel widths, which we confirm experimentally.

Model for active particles confined in a two-state micropattern

We propose a model, based on active Brownian particles, for the dynamics of cells confined in a two-state micropattern, composed of two rectangular boxes connected by a bridge, and investigate the transition statistics. A transition between boxes occurs when the active particle crosses the center of the bridge, and the time between subsequent transitions is the dwell time. By assuming that the rotational diffusion time τ is a function of the position, some experimental observations are qualitatively recovered as, for example, the shape of the survival function. τ controls the transition from a ballistic regime at short time scales to a diffusive regime at long time scales, with an effective diffusion coefficient proportional to τ. For small values of τ, the dwell time is determined by the characteristic diffusion timescale which is constant for very low values of τ, when the rotational diffusion is much faster than the translational one and decays with τ for intermediate values of τ. For large values of τ, the interaction with the walls dominates and the particle stays mostly at the corners of the boxes increasing the dwell time. We find that there is an optimal τ for which the dwell time is minimal and its value can be tuned by changing the geometry of the pattern.

Modeling ATP-mediated endothelial cell elongation on line patterns

Endothelial cell (EC) migration is crucial for a wide range of processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. We have previously demonstrated that ECs cultured on 15-μm wide adhesive line patterns exhibit three distinct migration phenotypes: (a) “running” cells that are polarized and migrate continuously and persistently on the adhesive lines with possible spontaneous directional changes, (b) “undecided” cells that are highly elongated and exhibit periodic changes in the direction of their polarization while maintaining minimal net migration, and (c) “tumbling-like” cells that migrate persistently for a certain amount of time but then stop and round up for a few hours before spreading again and resuming migration. Importantly, the three migration patterns are associated with distinct profiles of cell length. Because of the impact of adenosine triphosphate (ATP) on cytoskeletal organization and cell polarization, we hypothesize that the observed differences in EC length among the three different migration phenotypes are driven by differences in intracellular ATP levels. In the present work, we develop a mathematical model that incorporates the interactions between cell length, cytoskeletal (F-actin) organization, and intracellular ATP concentration. An optimization procedure is used to obtain the model parameter values that best fit the experimental data on EC lengths. The results indicate that a minimalist model based on differences in intracellular ATP levels is capable of capturing the different cell length profiles observed experimentally.

Disentangling cadherin-mediated cell-cell interactions in collective cancer cell migration

Cell dispersion from a confined area is fundamental in a number of biological processes, including cancer metastasis. To date, a quantitative understanding of the interplay of single-cell motility, cell proliferation, and intercellular contacts remains elusive. In particular, the role of E- and N-cadherin junctions, central components of intercellular contacts, is still controversial. Combining theoretical modeling with in vitro observations, we investigate the collective spreading behavior of colonies of human cancer cells (T24). The spreading of these colonies is driven by stochastic single-cell migration with frequent transient cell-cell contacts. We find that inhibition of E- and N-cadherin junctions decreases colony spreading and average spreading velocities, without affecting the strength of correlations in spreading velocities of neighboring cells. Based on a biophysical simulation model for cell migration, we show that the behavioral changes upon disruption of these junctions can be explained by reduced repulsive excluded volume interactions between cells. This suggests that in cancer cell migration, cadherin-based intercellular contacts sharpen cell boundaries leading to repulsive rather than cohesive interactions between cells, thereby promoting efficient cell spreading during collective migration.

Correlated escape of active particles across a potential barrier

We study the dynamics of one-dimensional active particles confined in a double-well potential, focusing on the escape properties of the system, such as the mean escape time from a well. We first consider a single-particle both in near and far-from-equilibrium regimes by varying the persistence time of the active force and the swim velocity. A non-monotonic behavior of the mean escape time is observed with the persistence time of the activity, revealing the existence of an optimal choice of the parameters favoring the escape process. For small persistence times, a Kramers-like formula with an effective potential obtained within the unified colored noise approximation is shown to hold. Instead, for large persistence times, we developed a simple theoretical argument based on the first passage theory, which explains the linear dependence of the escape time with the persistence of the active force. In the second part of the work, we consider the escape on two active particles mutually repelling. Interestingly, the subtle interplay of active and repulsive forces may lead to a correlation between particles, favoring the simultaneous jump across the barrier. This mechanism cannot be observed in the escape process of two passive particles. Finally, we find that in the small persistence regime, the repulsion favors the escape, such as in passive systems, in agreement with our theoretical predictions, while for large persistence times, the repulsive and active forces produce an effective attraction, which hinders the barrier crossing.

Combining experiments and in silico modeling to infer the role of adhesion and proliferation on the collective dynamics of cells

The collective dynamics of cells on surfaces and interfaces poses technological and theoretical challenges in the study of morphogenesis, tissue engineering, and cancer. Different mechanisms are at play, including, cell–cell adhesion, cell motility, and proliferation. However, the relative importance of each one is elusive. Here, experiments with a culture of glioblastoma multiforme cells on a substrate are combined with in silico modeling to infer the rate of each mechanism. By parametrizing these rates, the time-dependence of the spatial correlation observed experimentally is reproduced. The obtained results suggest a reduction in cell–cell adhesion with the density of cells. The reason for such reduction and possible implications for the collective dynamics of cancer cells are discussed.

The role of vimentin-nuclear interactions in persistent cell motility through confined spaces

The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is composed of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. Here, we develop a minimal model of a cell moving through a microchannel that incorporates explicit effects of actin and vimentin and implicit effects of microtubules. Specifically, the model consists of a cell with an actomyosin cortex and a deformable cell nucleus and mechanical linkages between the two. By decreasing the amount of vimentin, we find that the cell speed increases for vimentin-null cells compared to cells with vimentin. The loss of vimentin increases nuclear deformation and alters nuclear positioning in the cell. Assuming nuclear positioning is a read-out for cell polarity, we propose a new polarity mechanism which couples cell directional motion with cytoskeletal strength and nuclear positioning and captures the abnormally persistent motion of vimentin-null cells, as observed in experiments. The enhanced persistence indicates that the vimentin-null cells are more controlled by the confinement and so less autonomous, relying more heavily on external cues than their wild-type counterparts. Our modeling results present a quantitative interpretation for recent experiments and have implications for understanding the role of vimentin in the epithelial-mesenchymal transition.

Shannon entropy for time-varying persistence of cell migration

Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and pathological processes. Cell migration is typically modeled as a persistent random walk, which depends on two critical motility parameters, i.e., migration speed and persistence time. It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data. Here, we introduce the normalized Shannon entropy (SE) based on the FPS of cellular velocity autocovariance function to quantify migration dynamics. The SE introduced here possesses a similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration, attaining the maximal value of unity for purely diffusive migration (i.e., SE = 1 for the most "random" dynamics) and the minimal value of 0 for purely ballistic dynamics (i.e., SE = 0 for the most "ordered" dynamics). We also find that SE is strongly correlated with the migration persistence but is less sensitive to the migration speed. Moreover, we introduce the time-varying SE based on the WPS of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which typically results from complex and time-varying intra- or extracellular mechanisms. We employ our approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the SE and wavelet transform (i.e., SE-based approach) offers a simple and efficient tool to quantify cell migration dynamics in complex microenvironment.

Learning the dynamics of cell-cell interactions in confined cell migration

The migratory dynamics of cells in physiological processes, ranging from wound healing to cancer metastasis, rely on contact-mediated cell-cell interactions. These interactions play a key role in shaping the stochastic trajectories of migrating cells. While data-driven physical formalisms for the stochastic migration dynamics of single cells have been developed, such a framework for the behavioral dynamics of interacting cells still remains elusive. Here, we monitor stochastic cell trajectories in a minimal experimental cell collider: a dumbbell-shaped micropattern on which pairs of cells perform repeated cellular collisions. We observe different characteristic behaviors, including cells reversing, following, and sliding past each other upon collision. Capitalizing on this large experimental dataset of coupled cell trajectories, we infer an interacting stochastic equation of motion that accurately predicts the observed interaction behaviors. Our approach reveals that interacting noncancerous MCF10A cells can be described by repulsion and friction interactions. In contrast, cancerous MDA-MB-231 cells exhibit attraction and antifriction interactions, promoting the predominant relative sliding behavior observed for these cells. Based on these experimentally inferred interactions, we show how this framework may generalize to provide a unifying theoretical description of the diverse cellular interaction behaviors of distinct cell types.

The Role of Microenvironmental Cues and Mechanical Loading Milieus in Breast Cancer Cell Progression and Metastasis

Cancer can disrupt the microenvironments and mechanical homeostatic actions in multiple scales from large tissue modification to altered cellular signaling pathway in mechanotransduction. In this review, we highlight recent progresses in breast cancer cell mechanobiology focusing on cell-microenvironment interaction and mechanical loading regulation of cells. First, the effects of microenvironmental cues on breast cancer cell progression and metastasis will be reviewed with respect to substrate stiffness, chemical/topographic substrate patterning, and 2D vs. 3D cultures. Then, the role of mechanical loading situations such as tensile stretch, compression, and flow-induced shear will be discussed in relation to breast cancer cell mechanobiology and metastasis prevention. Ultimately, the substrate microenvironment and mechanical signal will work together to control cancer cell progression and metastasis. The discussions on breast cancer cell responsiveness to mechanical signals, from static substrate and dynamic loading, and the mechanotransduction pathways involved will facilitate interdisciplinary knowledge transfer, enabling further insights into prognostic markers, mechanically mediated metastasis pathways for therapeutic targets, and model systems required to advance cancer mechanobiology.

Inferring the Dynamics of Underdamped Stochastic Systems

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.