Persistent cell motion in the absence of external signals: a search strategy for eukaryotic cells

Lung architecture amplifies tissue deposition in an agent-based model of fibrotic development

Idiopathic pulmonary fibrosis (IPF) is a progressive interstitial lung disease where excessive extracellular matrix (ECM) deposition and remodeling stiffens the lung, impeding its function. Many factors are known to contribute to the development of this fibrosis, but a lack of conclusive understanding endures because of their complex nature. The modification of ECM and the unique architecture of the lung are such factors in IPF's propagation and not solely casualties. Their effects on fibrogenesis are not known and tricky to study. We apply a computational methodology known as an agent-based model (ABM) to simulate cellular behavior as automata. Our ABM is a tissue maintenance model where agents modify tissue density to sustain a global mean and variance to represent the cyclic turnover of ECM. Agents traverse and interact with high fidelity architecture obtained through micro computed tomography (microCT) of mouse lung tissue. The properties of the ABM are validated to microCT of fibrotic mouse lung tissue. We find that increasing cell density is sufficient for fibrogenesis, but that the lung architecture led to more tissue deposition. Our model suggests that lung structure is a relevant contributor to the pathogenesis of IPF.

Formation of motile cell clusters in heterogeneous model tumors: The role of cell-cell alignment

Circulating tumor cell clusters play an important role in the metastatic cascade. These clusters can acquire a migratory and more invasive phenotype, and coordinate their motion to migrate as a collective. Before such clusters can form by collectively detaching from a primary tumor, however, the cluster must first aggregate in the tumor interior. The mechanism of this cluster formation process is still poorly understood. One of the possible ways for cells to cluster is by aligning their direction of motion with their neighboring cells. This work aims to investigate the role of this cell-cell alignment interaction on the formation of motile cell clusters inside the bulk of a tumor using computer simulations. We employ a cellular Potts model in which we model a two-dimensional heterogeneous confluent layer containing both motile and nonmotile cells. Our results indicate that the degree of clustering is governed by two distinct processes: the formation of clusters due to the presence of cell-cell alignment interactions among motile cells, and the suppression of clustering due to the presence of the dynamic cellular environment (comprising the nonmotile cells). We find that the largest motile clusters are formed for intermediate alignment strengths, contrary to what is observed for motile cells in free space (that is, unimpeded by a dense cellular environment), in which case stronger cell-cell alignment always leads to larger clustering. Our findings suggest that the presence of a densely packed cellular environment and strong cell-cell alignment inhibits the formation of large migratory clusters within the primary tumor, providing physical insight into potential factors at play during the early stages of metastasis.

Multiphoton excited polymerized biomimetic models of collagen fiber morphology to study single cell and collective migration dynamics in pancreatic cancer

The respective roles of aligned collagen fiber morphology found in the extracellular matrix (ECM) of pancreatic cancer patients and cellular migration dynamics have been gaining attention because of their connection with increased aggressive phenotypes and poor prognosis. To better understand how collagen fiber morphology influences cell-matrix interactions associated with metastasis, we used Second Harmonic Generation (SHG) images from patient biopsies with Pancreatic ductal adenocarcinoma (PDAC) as models to fabricate collagen scaffolds to investigate processes associated with motility. Using the PDAC BxPC-3 metastatic cell line, we investigated single and collective cell dynamics on scaffolds of varying collagen alignment. Collective or clustered cells grown on the scaffolds with the highest collagen fiber alignment had increased E-cadherin expression and larger focal adhesion sites compared to single cells, consistent with metastatic behavior. Analysis of single cell motility revealed that the dynamics were characterized by random walk on all substrates. However, examining collective motility over different time points showed that the migration was super-diffusive and enhanced on highly aligned fibers, whereas it was hindered and sub-diffusive on un-patterned substrates. This was further supported by the more elongated morphology observed in collectively migrating cells on aligned collagen fibers. Overall, this approach allows the decoupling of single and collective cell behavior as a function of collagen alignment and shows the relative importance of collective cell behavior as well as fiber morphology in PDAC metastasis. We suggest these scaffolds can be used for further investigations of PDAC cell biology. STATEMENT OF SIGNIFICANCE: Pancreatic ductal adenocarcinoma (PDAC) has a high mortality rate, where aligned collagen has been associated with poor prognosis. Biomimetic models representing this architecture are needed to understand complex cellular interactions. The SHG image-based models based on stromal collagen from human biopsies afford the measurements of cell morphology, cadherin and focal adhesion expression as well as detailed motility dynamics. Using a metastatic cell line, we decoupled the roles of single cell and collective cell behavior as well as that arising from aligned collagen. Our data suggests that metastatic characteristics are enhanced by increased collagen alignment and that collective cell behavior is more relevant to metastatic processes. These scaffolds provide new insight in this disease and can be a platform for further experiments such as testing drug efficacy.

Data-driven modelling makes quantitative predictions regarding bacteria surface motility

In this work, we quantitatively compare computer simulations and existing cell tracking data of P. aeruginosa surface motility in order to analyse the underlying motility mechanism. We present a three dimensional twitching motility model, that simulates the extension, retraction and surface association of individual Type IV Pili (TFP), and is informed by recent experimental observations of TFP. Sensitivity analysis is implemented to minimise the number of model parameters, and quantitative estimates for the remaining parameters are inferred from tracking data by approximate Bayesian computation. We argue that the motility mechanism is highly sensitive to experimental conditions. We predict a TFP retraction speed for the tracking data we study that is in a good agreement with experimental results obtained under very similar conditions. Furthermore, we examine whether estimates for biologically important parameters, whose direct experimental determination is challenging, can be inferred directly from tracking data. One example is the width of the distribution of TFP on the bacteria body. We predict that the TFP are broadly distributed over the bacteria pole in both walking and crawling motility types. Moreover, we identified specific configurations of TFP that lead to transitions between walking and crawling states.

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.

Pseudopod Tracking and Statistics During Cell Movement in Buffer and Chemotaxis

Amoeboid cells such as the protist Dictyostelium, human neutrophils, and the fungus B.d. chytrid move by extending pseudopods. The trajectories of cell movement depend on the size, rhythm, and direction of long series of pseudopods. These pseudopod properties are regulated by internal factors such as memory of previous directions and by external factors such as gradients of chemoattractants or electric currents. Here a simple method is described that defines the X, Y time coordinates of a pseudopod at the start and the end of the extension phase. The connection between the start and end of an extending pseudopod defines a vector, which is the input of different levels of analysis that defines cell movement. The primary information of the vector is its spatial length (pseudopod size), temporal length (extension time), extension rate (size divided by time), and direction. The second layer of information describes the sequence of two (or more) pseudopods: the direction of the second pseudopod relative to the direction of the first pseudopod, the start of the second pseudopod relative to the extension phase of the first pseudopod (the second starts while the first is still extending or after the first has stopped), and the alternating right/left extension of pseudopods. The third layer of information is provided by specific and detailed statistical analysis of these data and addresses question such as: is pseudopod extension in buffer in random direction or has the system internal directional memory, and how do shallow external electrical or chemical gradients bias the intrinsic pseudopod extension. The method is described for Dictyostelium, but has been used successfully for fast-moving neutrophils, slow-moving stem cells, and the fungus B.d. chytrid.

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.

Active oscillations in microscale navigation

Living organisms routinely navigate their surroundings in search of better conditions, more food, or to avoid predators. Typically, animals do so by integrating sensory cues from the environment with their locomotor apparatuses. For single cells or small organisms that possess motility, fundamental physical constraints imposed by their small size have led to alternative navigation strategies that are specific to the microscopic world. Intriguingly, underlying these myriad exploratory behaviours or sensory functions is the onset of periodic activity at multiple scales, such as the undulations of cilia and flagella, the vibrations of hair cells, or the oscillatory shape modes of migrating neutrophils. Here, I explore oscillatory dynamics in basal microeukaryotes and hypothesize that these active oscillations play a critical role in enhancing the fidelity of adaptive sensorimotor integration.

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.

Coordinated linear and rotational movements of endothelial cells compartmentalized by VE-cadherin drive angiogenic sprouting

Angiogenesis is a sequential process to extend new blood vessels from preexisting ones by sprouting and branching. During angiogenesis, endothelial cells (ECs) exhibit inhomogeneous multicellular behaviors referred to as "cell mixing," in which ECs repetitively exchange their relative positions, but the underlying mechanism remains elusive. Here we identified the coordinated linear and rotational movements potentiated by cell-cell contact as drivers of sprouting angiogenesis using in vitro and in silico approaches. VE-cadherin confers the coordinated linear motility that facilitated forward sprout elongation, although it is dispensable for rotational movement, which was synchronous without VE-cadherin. Mathematical modeling recapitulated the EC motility in the two-cell state and angiogenic morphogenesis with the effects of VE-cadherin-knockout. Finally, we found that VE-cadherin-dependent EC compartmentalization potentiated branch elongations, and confirmed this by mathematical simulation. Collectively, we propose a way to understand angiogenesis, based on unique EC behavioral properties that are partially dependent on VE-cadherin function.

Waves in a Stochastic Cell Motility Model

In Bhattacharya et al. (Sci Adv 6(32):7682, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied at two levels. The microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction-diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction-diffusion system, or chemical Langevin equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction-diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

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.

Physical biomarkers for human hematopoietic stem and progenitor cells

Adhesion of hematopoietic stem and progenitor cells (HSPCs) to the bone marrow niche plays critical roles in the maintenance of the most primitive HSPCs. The interactions of HSPC-niche interactions are clinically relevant in acute myeloid leukemia (AML), because (i) leukemia-initiating cells adhered to the marrow niche are protected from the cytotoxic effect by chemotherapy and (ii) mobilization of HSPCs from healthy donors' bone marrow is crucial for the effective stem cell transplantation. However, although many clinical agents have been developed for the HSPC mobilization, the effects caused by the extrinsic molecular cues were traditionally evaluated based on phenomenological observations. This review highlights the recent interdisciplinary challenges of hematologists, biophysicists and cell biologists towards the design of defined in vitro niche models and the development of physical biomarkers for quantitative indexing of differential effects of clinical agents on human HSPCs.

Ants combine systematic meandering and correlated random walks when searching for unknown resources

Animal search movements are typically assumed to be mostly random walks, although non-random elements may be widespread. We tracked ants (Temnothorax rugatulus) in a large empty arena, resulting in almost 5 km of trajectories. We tested for meandering by comparing the turn autocorrelations for empirical ant tracks and simulated, realistic Correlated Random Walks. We found that 78% of ants show significant negative autocorrelation around 10 mm (3 body lengths). This means that turns in one direction are likely followed by turns in the opposite direction after this distance. This meandering likely makes the search more efficient, as it allows ants to avoid crossing their own paths while staying close to the nest, avoiding return-travel time. Combining systematic search with stochastic elements may make the strategy less vulnerable to directional inaccuracies. This study is the first to find evidence for efficient search by regular meandering in a freely searching animal.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Monte Carlo Physarum Machine: Characteristics of Pattern Formation in Continuous Stochastic Transport Networks

We present Monte Carlo Physarum Machine (MCPM): a computational model suitable for reconstructing continuous transport networks from sparse 2D and 3D data. MCPM is a probabilistic generalization of Jones's (2010) agent-based model for simulating the growth of Physarum polycephalum (slime mold). We compare MCPM to Jones's work on theoretical grounds, and describe a task-specific variant designed for reconstructing the large-scale distribution of gas and dark matter in the Universe known as the cosmic web. To analyze the new model, we first explore MCPM's self-patterning behavior, showing a wide range of continuous network-like morphologies-called polyphorms-that the model produces from geometrically intuitive parameters. Applying MCPM to both simulated and observational cosmological data sets, we then evaluate its ability to produce consistent 3D density maps of the cosmic web. Finally, we examine other possible tasks where MCPM could be useful, along with several examples of fitting to domain-specific data as proofs of concept.

Oscillators and servomechanisms in orientation and navigation, and sometimes in cognition

Navigational mechanisms have been characterized as servomechanisms. A navigational servomechanism specifies a goal state to strive for. Discrepancies between the perceived current state and the goal state specify error. Servomechanisms adjust the course of travel to reduce the error. I now add that navigational servomechanisms work with oscillators, periodic movements of effectors that drive locomotion. I illustrate this concept selectively over a vast range of scales of travel from micrometres in bacteria to thousands of kilometres in sea turtles. The servomechanisms differ in sophistication, with some interrupting forward motion occasionally or changing travel speed in kineses and others adjusting the direction of travel in taxes. I suggest that in other realms of life as well, especially in cognition, servomechanisms work with oscillators.

Temperature-sensitive migration dynamics in neutrophil-differentiated HL-60 cells

Cell migration plays an essential role in wound healing and inflammatory processes inside the human body. Peripheral blood neutrophils, a type of polymorphonuclear leukocyte (PMN), are the first cells to be activated during inflammation and subsequently migrate toward an injured tissue or infection site. This response is dependent on both biochemical signaling and the extracellular environment, one aspect of which includes increased temperature in the tissues surrounding the inflammation site. In our study, we analyzed temperature-dependent neutrophil migration using differentiated HL-60 cells. The migration speed of differentiated HL-60 cells was found to correlate positively with temperature from 30 to 42 °C, with higher temperatures inducing a concomitant increase in cell detachment. The migration persistence time of differentiated HL-60 cells was higher at lower temperatures (30-33 °C), while the migration persistence length stayed constant throughout the temperature range. Coupled with the increased speed observed at high temperatures, this suggests that neutrophils are primed to migrate more effectively at the elevated temperatures characteristic of inflammation. Temperature gradients exist on both cell and tissue scales. Taking this into consideration, we also investigated the ability of differentiated HL-60 cells to sense and react to the presence of temperature gradients, a process known as thermotaxis. Using a two-dimensional temperature gradient chamber with a range of 27-43 °C, we observed a migration bias parallel to the gradient, resulting in both positive and negative thermotaxis. To better mimic the extracellular matrix (ECM) environment in vivo, a three-dimensional collagen temperature gradient chamber was constructed, allowing observation of biased neutrophil-like differentiated HL-60 migration toward the heat source.

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.

Cellular inertia

It has been experimentally reported that chemotactic cells exhibit cellular memory, that is, a tendency to maintain the migration direction despite changes in the chemoattractant gradient. In this study, we analyzed a phenomenological model assuming the presence of cellular inertia, as well as a response time in motility, resulting in the reproduction of the cellular memory observed in the previous experiments. According to the analysis, the cellular motion is described by the superposition of multiple oscillative functions induced by the multiplication of the oscillative polarity and motility. The cellular intertia generates cellular memory by regulating phase differences between those oscillative functions. By applying the theory to the experimental data, the cellular inertia was estimated at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=3-6$$\end{document}m=3-6 min. In addition, physiological parameters, such as response time in motility and intracellular processing speed, were also evaluated. The agreement between the experiemental data and theory suggests the possibility of the presence of the response time in motility, which has never been biologically verified and should be explored in the future.

Comparative mapping of crawling-cell morphodynamics in deep learning-based feature space

Navigation of fast migrating cells such as amoeba Dictyostelium and immune cells are tightly associated with their morphologies that range from steady polarized forms that support high directionality to those more complex and variable when making frequent turns. Model simulations are essential for quantitative understanding of these features and their origins, however systematic comparisons with real data are underdeveloped. Here, by employing deep-learning-based feature extraction combined with phase-field modeling framework, we show that a low dimensional feature space for 2D migrating cell morphologies obtained from the shape stereotype of keratocytes, Dictyostelium and neutrophils can be fully mapped by an interlinked signaling network of cell-polarization and protrusion dynamics. Our analysis links the data-driven shape analysis to the underlying causalities by identifying key parameters critical for migratory morphologies both normal and aberrant under genetic and pharmacological perturbations. The results underscore the importance of deciphering self-organizing states and their interplay when characterizing morphological phenotypes.

Migratory cells that move by crawling do so by extending and retracting their plasma membrane. When and where these events take place determine the cell shape, and this is directly linked to the movement patterns. Understanding how the highly plastic and interconvertible morphologies appear from their underlying dynamics remains a challenge partly because their inherent complexity makes quantitatively comparison against the outputs of mathematical models difficult. To this end, we employed machine-learning based classification to extract features that characterize the basic migrating morphologies. The obtained features were then used to compare real cell data with outputs of a conceptual model that we introduced which describes coupling via feedback between local protrusive dynamics and polarity. The feature mapping showed that the model successfully recapitulates the shape dynamics that were not covered by previous related models and also hints at the critical parameters underlying state transitions. The ability of the present approach to compare model outputs with real cell data systematically and objectively is important as it allows outputs of future mathematical models to be quantitatively tested in an accessible and common reference frame.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

Deriving time-varying cellular motility parameters via wavelet analysis

Cell migration, which is regulated by intracellular signaling pathways (ICSP) and extracellular matrix (ECM), plays an indispensable role in many physiological and pathological process such as normal tissue development and cancer metastasis. However, there is a lack of rigorous and quantitative tools for analyzing the time-varying characteristics of cell migration in heterogeneous microenvironment, resulted from, e.g. the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop a wavelet-analysis approach to derive the time-dependent motility parameters from cell migration trajectories, based on the time-varying persistent random walk model. In particular, the wavelet denoising and wavelet transform are employed to analyze migration velocities and obtain the wavelet power spectrum. Subsequently, the time-dependent motility parameters are derived via Lorentzian power spectrum. Our results based on synthetic data indicate the superiority of the method for estimating the intrinsic transient motility parameters, robust against a variety of stochastic noises. We also carry out a systematic parameter study and elaborate the effects of parameter selection on the performance of the method. Moreover, we demonstrate the utility of our approach via analyzing experimental data ofin vitrocell migration in distinct microenvironments, including the migration of MDA-MB-231 cells in confined micro-channel arrays and correlated migration of MCF-10A cells due to ECM-mediated mechanical coupling. Our analysis shows that our approach can be as a powerful tool to accurately derive the time-dependent motility parameters, and further analyze the time-dependent characteristics of cell migration regulated by complex microenvironment.

A Novel Method for Effective Cell Segmentation and Tracking in Phase Contrast Microscopic Images

Cell migration plays an important role in the identification of various diseases and physiological phenomena in living organisms, such as cancer metastasis, nerve development, immune function, wound healing, and embryo formulation and development. The study of cell migration with a real-time microscope generally takes several hours and involves analysis of the movement characteristics by tracking the positions of cells at each time interval in the images of the observed cells. Morphological analysis considers the shapes of the cells, and a phase contrast microscope is used to observe the shape clearly. Therefore, we developed a segmentation and tracking method to perform a kinetic analysis by considering the morphological transformation of cells. The main features of the algorithm are noise reduction using a block-matching 3D filtering method, k-means clustering to mitigate the halo signal that interferes with cell segmentation, and the detection of cell boundaries via active contours, which is an excellent way to detect boundaries. The reliability of the algorithm developed in this study was verified using a comparison with the manual tracking results. In addition, the segmentation results were compared to our method with unsupervised state-of-the-art methods to verify the proposed segmentation process. As a result of the study, the proposed method had a lower error of less than 40% compared to the conventional active contour method.

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.

A Fully Integrated Arduino-Based System for the Application of Stretching Stimuli to Living Cells and Their Time-Lapse Observation: A Do-It-Yourself Biology Approach

Mechanobiology has nowadays acquired the status of a topic of fundamental importance in a degree in Biological Sciences. It is inherently a multidisciplinary topic where biology, physics and engineering competences are required. A course in mechanobiology should include lab experiences where students can appreciate how mechanical stimuli from outside affect living cell behaviour. Here we describe all the steps to build a cell stretcher inside an on-stage cell incubator. This device allows exposing living cells to a periodic mechanical stimulus similar to what happens in physiological conditions such as, for example, in the vascular system or in the lungs. The reaction of the cells to the periodic mechanical stretching represents a prototype of a mechanobiological signal integrated by living cells. We also provide the theoretical and experimental aspects related to the calibration of the stretcher apparatus at a level accessible to researchers not used to dealing with topics like continuum mechanics and analysis of deformations. We tested our device by stretching cells of two different lines, U87-MG and Balb-3T3 cells, and we analysed and discussed the effect of the periodic stimulus on both cell reorientation and migration. We also discuss the basic aspects related to the quantitative analysis of the reorientation process and of cell migration. We think that the device we propose can be easily reproduced at low-cost within a project-oriented course in the fields of biology, biotechnology and medical engineering.

Enhanced persistence and collective migration in cooperatively aligning cell clusters

Most cells possess the capacity to locomote. Alone or collectively, this allows them to adapt, to rearrange, and to explore their surroundings. The biophysical characterization of such motile processes, in health and in disease, has so far focused mostly on two limiting cases: single-cell motility on the one hand and the dynamics of confluent tissues such as the epithelium on the other. The in-between regime of clusters, composed of relatively few cells moving as a coherent unit, has received less attention. Such small clusters are, however, deeply relevant in development but also in cancer metastasis. In this work, we use cellular Potts models and analytical active matter theory to understand how the motility of small cell clusters changes with N, the number of cells in the cluster. Modeling and theory reveal our two main findings: cluster persistence time increases with N, whereas the intrinsic diffusivity decreases with N. We discuss a number of settings in which the motile properties of more complex clusters can be analytically understood, revealing that the focusing effects of small-scale cooperation and cell-cell alignment can overcome the increased bulkiness and internal disorder of multicellular clusters to enhance overall migrational efficacy. We demonstrate this enhancement for small-cluster collective durotaxis, which is shown to proceed more effectively than for single cells. Our results may provide some novel, to our knowledge, insights into the connection between single-cell and large-scale collective motion and may point the way to the biophysical origins of the enhanced metastatic potential of small tumor cell clusters.

Short- and long-term memory of moving amoeboid cells

Amoeboid cells constantly change shape and extend protrusions. The direction of movement is not random, but is correlated with the direction of movement in the preceding minutes. The basis of this correlation is an underlying memory of direction. The presence of memory in movement is known for many decades, but its molecular mechanism is still largely unknown. This study reports in detail on the information content of directional memory, the kinetics of learning and forgetting this information, and the molecular basis for memory using Dictyostelium mutants. Two types of memory were characterized. A short-term memory stores for ~20 seconds the position of the last pseudopod using a local modification of the branched F-actin inducer SCAR/WAVE, which enhances one new pseudopod to be formed at the position of the previous pseudopod. A long term memory stores for ~2 minutes the activity of the last ~10 pseudopods using a cGMP-binding protein that induces myosin filaments in the rear of the cell; this inhibits pseudopods in the rear and thereby enhances pseudopods in the global front. Similar types of memory were identified in human neutrophils and mesenchymal stem cells, the protist Dictyostelium and the fungus B.d. chytrid. The synergy of short- and long-term memory explains their role in persistent movement for enhanced cell dispersal, food seeking and chemotaxis.

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.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

Bioimage Analysis and Cell Motility

Bioimage analysis (BIA) has historically helped study how and why cells move; biological experiments evolved in intimate feedback with the most classical image processing techniques because they contribute objectivity and reproducibility to an eminently qualitative science. Cell segmentation, tracking, and morphology descriptors are all discussed here. Using ameboid motility as a case study, these methods help us illustrate how proper quantification can augment biological data, for example, by choosing mathematical representations that amplify initially subtle differences, by statistically uncovering general laws or by integrating physical insight. More recently, the non-invasive nature of quantitative imaging is fertilizing two blooming fields: mechanobiology, where many biophysical measurements remain inaccessible, and microenvironments, where the quest for physiological relevance has exploded data size. From relief to remedy, this trend indicates that BIA is to become a main vector of biological discovery as human visual analysis struggles against ever more complex data.

Unified control of amoeboid pseudopod extension in multiple organisms by branched F-actin in the front and parallel F-actin/myosin in the cortex

The trajectory of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. The direction of pseudopods has been well studied to unravel mechanisms for chemotaxis, wound healing and inflammation. However, the kinetics of pseudopod extension-when and why do pseudopods start and stop- is equally important, but is largely unknown. Here the START and STOP of about 4000 pseudopods was determined in four different species, at four conditions and in nine mutants (fast amoeboids Dictyostelium and neutrophils, slow mesenchymal stem cells, and fungus B.d. chytrid with pseudopod and a flagellum). The START of a first pseudopod is a random event with a probability that is species-specific (23%/s for neutrophils). In all species and conditions, the START of a second pseudopod is strongly inhibited by the extending first pseudopod, which depends on parallel filamentous actin/myosin in the cell cortex. Pseudopods extend at a constant rate by polymerization of branched F-actin at the pseudopod tip, which requires the Scar complex. The STOP of pseudopod extension is induced by multiple inhibitory processes that evolve during pseudopod extension and mainly depend on the increasing size of the pseudopod. Surprisingly, no differences in pseudopod kinetics are detectable between polarized, unpolarized or chemotactic cells, and also not between different species except for small differences in numerical values. This suggests that the analysis has uncovered the fundament of cell movement with distinct roles for stimulatory branched F-actin in the protrusion and inhibitory parallel F-actin in the contractile cortex.

Super-Gaussian, superdiffusive transport of multimode active matter

Living matter often exhibits multimode transport that switches between an active, self-propelled motion and a seemingly passive, random motion. Here, we investigate an exactly solvable model of multimode active matter, such as living cells and motor proteins, which alternatingly undergoes active and passive motion. Our model study shows that the reversible transition between a passive mode and an active mode causes super-Gaussian transport dynamics, observed in various experiments. We find the non-Gaussian character of the matter's displacement distribution is essentially determined by the population ratio between active and passive motion. Interestingly, under a certain population ratio of the active and passive modes, the displacement distribution changes from sub-Gaussian to super-Gaussian as time increases. The mean-square displacement of our model exhibits transient superdiffusive dynamics, yet recovers diffusive behavior at both the short- and long-time limits. We finally generalize our model to encompass complex, multimode active matter in an arbitrary spatial dimension.

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.

Symmetry Breaking during Cell Movement in the Context of Excitability, Kinetic Fine-Tuning and Memory of Pseudopod Formation

The path of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. Amoeboid cells constantly change their shape with pseudopods extending in different directions. Detailed analysis has revealed that time, place and direction of pseudopod extension are not random, but highly ordered with strong prevalence for only one extending pseudopod, with defined life-times, and with reoccurring events in time and space indicative of memory. Important components are Ras activation and the formation of branched F-actin in the extending pseudopod and inhibition of pseudopod formation in the contractile cortex of parallel F-actin/myosin. In biology, order very often comes with symmetry. In this essay, I discuss cell movement and the dynamics of pseudopod extension from the perspective of symmetry and symmetry changes of Ras activation and the formation of branched F-actin in the extending pseudopod. Combining symmetry of Ras activation with kinetics and memory of pseudopod extension results in a refined model of amoeboid movement that appears to be largely conserved in the fast moving Dictyostelium and neutrophils, the slow moving mesenchymal stem cells and the fungus B.d. chytrid.

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.

Hydrodynamics, superfluidity, and giant number fluctuations in a model of self-propelled particles

We derive hydrodynamics of a prototypical one-dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients-the hardcore interaction and the competing mechanisms of short- and long-range hopping. We calculate two density-dependent transport coefficients-the bulk-diffusion coefficient and the conductivity, the ratio of which, despite violation of detailed balance, is connected to particle-number fluctuation by an Einstein relation. In the limit of infinite-range hopping, the model exhibits, upon tuning density ρ (or activity), a "superfluidlike" transition from a finitely conducting fluid phase to an infinitely conducting "superfluid" phase, characterized by a divergence in conductivity χ(ρ)∼(ρ-ρ_{c})^{-1} with ρ_{c} being the critical density. The diverging conductivity greatly increases particle (or vacancy) mobility and thus induces "giant" number fluctuations in the system.

The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells

Movement of cells and tissues is essential at various stages during the lifetime of an organism, including morphogenesis in early development, in the immune response to pathogens, and during wound-healing and tissue regeneration. Individual cells are able to move in a variety of microenvironments (MEs) (A glossary of the acronyms used herein is given at the end) by suitably adapting both their shape and how they transmit force to the ME, but how cells translate environmental signals into the forces that shape them and enable them to move is poorly understood. While many of the networks involved in signal detection, transduction and movement have been characterized, how intracellular signals control re-building of the cyctoskeleton to enable movement is not understood. In this review we discuss recent advances in our understanding of signal transduction networks related to direction-sensing and movement, and some of the problems that remain to be solved.

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.

Replicative senescence in MSCWJ-1 human umbilical cord mesenchymal stem cells is marked by characteristic changes in motility, cytoskeletal organization, and RhoA localization

Here, we document changes in cell motility and organization of the contractile apparatus of human umbilical cord Wharton's jelly mesenchymal stem cells (MSCWJ-1) in the process of replicative senescence. Colocalization dynamics of F-actin and actin-binding proteins (myosin-9, α-actinin-4, RhoA) were examined in the MSCWJ-1 cell line. The results show that nuclear-cytoplasmic redistribution of RhoA occurs during replicative senescence, with maximal RhoA/nucleus colocalization evident at passage 15. At that time point, decreases in colocalization, namely myosin-9/F-actin and α-actinin-4/F-actin, were seen and myosin-9 was found in cytosolic extracts in the assembly-incompetent form. Using an automated intravital confocal cytometry system and quantitative analysis of MSCWJ-1 movements, we found that changes in cytoskeletal organization correlate with cell motility characteristics over a time period from passages 9 to 38. The factors examined (cytoskeleton structure, cell motility) indicate that the process by which cells transition to replicative senescence is best represented as three stages. The first stage lasts from cell culture isolation to passage 15 and is characterized by: accumulation of actin-binding proteins in assembly-incompetent forms; nuclear RhoA accumulation; and an increase in movement tortuosity. The second stage extends from passages 15 to 28 and is characterized by: an increase in the structural integrity of the actin cytoskeleton; exit of RhoA and alpha-actinin-4 from the nucleus; and a decrease in path tortuosity. The third stage extends from passage 28 to 38 and is marked by: a plateau in actin cytoskeleton structural integrity; significant decreases in nuclear RhoA levels; and decreases in cell speed.

Deterministic actin waves as generators of cell polarization cues

Dendritic cells "patrol" the human body to detect pathogens. In their search, dendritic cells perform a random walk by amoeboid migration. The efficiency of pathogen detection depends on the properties of the random walk. It is not known how the dendritic cells control these properties. Here, we quantify dendritic cell migration under well-defined 2-dimensional confinement and in a 3-dimensional collagen matrix through recording their long-term trajectories. We find 2 different migration states: persistent migration, during which the dendritic cells move along curved paths, and diffusive migration, which is characterized by successive sharp turns. These states exhibit differences in the actin distributions. Our theoretical and experimental analyses indicate that this kind of motion can be generated by spontaneous actin polymerization waves that contribute to dendritic cell polarization and migration. The relative distributions of persistent and diffusive migration can be changed by modification of the molecular actin filament nucleation and assembly rates. Thus, dendritic cells can control their migration patterns and adapt to specific environments. Our study offers an additional perspective on how dendritic cells tune their searches for pathogens.

Modeling and analysis of melanoblast motion

Melanoblast migration is important for embryogenesis and is a key feature of melanoma metastasis. Many studies have characterized melanoblast movement, focusing on statistical properties and have highlighted basic mechanisms of melanoblast motility. We took a slightly different and complementary approach: we previously developed a mathematical model of melanoblast motion that enables the testing of biological assumptions about the displacement of melanoblasts and we created tests to analyze the geometric features of cell trajectories and the specific issue of trajectory interactions. Within this model, we performed simulations and compared the results with experimental data using geometric tests. In this paper, we developed the associated mathematical model and the main focus is to study the crossings between trajectories with new theoretical results about the variation of number of intersection points with respect to the crossing times. Using these results it is possible to study the random nature of displacements and the interactions between trajectories. This analysis has raised new questions, leading to the generation of strong arguments in favor of a trail left behind each moving melanoblast.

Two distinct actin waves correlated with turns-and-runs of crawling microglia

Freely crawling cells are often viewed as randomly moving Brownian particles but they generally exhibit some directional persistence. This property is often related to their zigzag motile behaviors that can be described as a noisy but temporally structured sequence of "runs" and "turns." However, its underlying biophysical mechanism is largely unexplored. Here, we carefully investigate the collective actin wave dynamics associated with the zigzag-crawling movements of microglia (as primary brain immune cells) employing a number of different quantitative imaging modalities including synthetic aperture microscopy and optical diffraction tomography, as well as conventional fluorescence imaging and scanning electron microscopy. Interestingly, we find that microglia exhibit two distinct types of actin waves working at two quite different time scales and locations, and they seem to serve different purposes. One type of actin waves is fast "peripheral ruffles" arising spontaneously with an oscillating period of about 6 seconds at some portion of the leading edge of crawling microglia, where the vigorously biased peripheral ruffles seem to set the direction of a new turn (in 2-D free space). When the cell turning events are inhibited with a physical confinement (in 1-D track), the peripheral ruffles still exist at the leading edge with no bias but showing phase coherence in the cell crawling direction. The other type is "dorsal actin waves" which also exhibits an oscillatory behavior but with a much longer period of around 2 minutes compared to the fast "peripheral ruffles". Dorsal actin waves (whether the cell turning events are inhibited or not) initiate in the lamellipodium just behind the leading edge, travelling down toward the core region of the cell and disappear. Such dorsal wave propagations seem to be correlated with migration of the cell. Thus, we may view the dorsal actin waves are connected with the "run" stage of cell body, whereas the fast ruffles at the leading front are involved in the "turn" stage.

Collective regulation of cell motility using an accurate density-sensing system

The capacity of living cells to sense their population density and to migrate accordingly is essential for the regulation of many physiological processes. However, the mechanisms used to achieve such functions are poorly known. Here, based on the analysis of multiple trajectories of vegetative Dictyostelium discoideum cells, we investigate such a system extensively. We show that the cells secrete a high-molecular-weight quorum-sensing factor (QSF) in their medium. This extracellular signal induces, in turn, a reduction of the cell movements, in particular, through the downregulation of a mode of motility with high persistence time. This response appears independent of cAMP and involves a G-protein-dependent pathway. Using a mathematical analysis of the cells' response function, we evidence a negative feedback on the QSF secretion, which unveils a powerful generic mechanism for the cells to detect when they exceed a density threshold. Altogether, our results provide a comprehensive and dynamical view of this system enabling cells in a scattered population to adapt their motion to their neighbours without physical contact.

A lumped parameter model of endoplasm flow in Physarum polycephalum explains migration and polarization-induced asymmetry during the onset of locomotion

The plasmodial slime mold Physarum polycephalum exhibits strong, periodic flow of cytoplasm through the veins of its network. In the special case of mesoplasmodia, a newly described starvation-induced, shape-constant morphotype, this periodic endoplasm streaming is the basis of locomotion. Furthermore, we presume that cytoplasm flow is also involved in signal transmission and signal processing. Mesoplasmodia motility resembles amoeboid locomotion. In contrast to other amoebae, however, mesoplasmodia move without extending pseudopods and retain a coherent, fan-shaped morphology throughout their steady locomotion. Attaining sizes of up to 2 mm², mesoplasmodia are also much bigger than other amoebae. We characterize this particular type of locomotion and identify patterns of movement. By using the analogy between pulsatile fluid flow through a network of elastic tubes and electrical circuits, we build a lumped model that explains observed fluid flow patterns. Essentially, the mesoplasmodium acts as a low-pass filter, permitting only low-frequency oscillations to propagate from back to front. This frequency selection serves to optimize flow and reduces power dissipation. Furthermore, we introduce a distributed element into the lumped model to explain cell polarization during the onset of chemotaxis: Biochemical cues (internal or external) lead to a local softening of the actin cortex, which in turn causes an increased flow of cytoplasm into that area and, thus, a net forward movement. We conclude that the internal actin-enclosed vein network gives the slime mold a high measure of control over fluid transport, especially by softening or hardening, which in turn leads to polarization and net movement.

Positioning of the Centrosome and Golgi Complex

For over a century, the centrosome has been an organelle more easily tracked than understood, and the study of its peregrinations within the cell remains a chief underpinning of its functional investigation. Increasing attention and new approaches have been brought to bear on mechanisms that control centrosome localization in the context of cleavage plane determination, ciliogenesis, directional migration, and immunological synapse formation, among other cellular and developmental processes. The Golgi complex, often linked with the centrosome, presents a contrasting case of a pleiomorphic organelle for which functional studies advanced somewhat more rapidly than positional tracking. However, Golgi orientation and distribution has emerged as an area of considerable interest with respect to polarized cellular function. This chapter will review our current understanding of the mechanism and significance of the positioning of these organelles.

Multi-scale computational study of the Warburg effect, reverse Warburg effect and glutamine addiction in solid tumors

Cancer metabolism has received renewed interest as a potential target for cancer therapy. In this study, we use a multi-scale modeling approach to interrogate the implications of three metabolic scenarios of potential clinical relevance: the Warburg effect, the reverse Warburg effect and glutamine addiction. At the intracellular level, we construct a network of central metabolism and perform flux balance analysis (FBA) to estimate metabolic fluxes; at the cellular level, we exploit this metabolic network to calculate parameters for a coarse-grained description of cellular growth kinetics; and at the multicellular level, we incorporate these kinetic schemes into the cellular automata of an agent-based model (ABM), iDynoMiCS. This ABM evaluates the reaction-diffusion of the metabolites, cellular division and motion over a simulation domain. Our multi-scale simulations suggest that the Warburg effect provides a growth advantage to the tumor cells under resource limitation. However, we identify a non-monotonic dependence of growth rate on the strength of glycolytic pathway. On the other hand, the reverse Warburg scenario provides an initial growth advantage in tumors that originate deeper in the tissue. The metabolic profile of stromal cells considered in this scenario allows more oxygen to reach the tumor cells in the deeper tissue and thus promotes tumor growth at earlier stages. Lastly, we suggest that glutamine addiction does not confer a selective advantage to tumor growth with glutamine acting as a carbon source in the tricarboxylic acid (TCA) cycle, any advantage of glutamine uptake must come through other pathways not included in our model (e.g., as a nitrogen donor). Our analysis illustrates the importance of accounting explicitly for spatial and temporal evolution of tumor microenvironment in the interpretation of metabolic scenarios and hence provides a basis for further studies, including evaluation of specific therapeutic strategies that target metabolism.

Cancer metabolism is an emerging hallmark of cancer. In the past decade, a renewed focus on cancer metabolism has led to several distinct hypotheses describing the role of metabolism in cancer. To complement experimental efforts in this field, a scale-bridging computational framework is needed to allow rapid evaluation of emerging hypotheses in cancer metabolism. In this study, we present a multi-scale modeling platform and demonstrate the distinct outcomes in population-scale growth dynamics under different metabolic scenarios: the Warburg effect, the reverse Warburg effect and glutamine addiction. Within this modeling framework, we confirmed population-scale growth advantage enabled by the Warburg effect, provided insights into the symbiosis between stromal cells and tumor cells in the reverse Warburg effect and argued that the anaplerotic role of glutamine is not exploited by tumor cells to gain growth advantage under resource limitations. We point to the opportunity for this framework to help understand tissue-scale response to therapeutic strategies that target cancer metabolism while accounting for the tumor complexity at multiple scales.

Lévy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long "flights". Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for "reprogramming" the Lévy walks into either diffusive or ballistic movements.

Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM

We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.