Anomalous diffusion and q-Weibull velocity distributions in epithelial cell migration.
ABSTRACT: In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, the control of cell motion is a major demand in the creation of artificial tissues and organs. Here, cell migration assays on plastic 2D surfaces involving normal (MDCK) and tumoral (B16F10) epithelial cell lines were performed varying the initial density of plated cells. Through time-lapse microscopy quantities such as speed distributions, velocity autocorrelations and spatial correlations, as well as the scaling of mean-squared displacements were determined. We find that these cells exhibit anomalous diffusion with q-Weibull speed distributions that evolves non-monotonically to a Maxwellian distribution as the initial density of plated cells increases. Although short-ranged spatial velocity correlations mark the formation of small cell clusters, the emergence of collective motion was not observed. Finally, simulational results from a correlated random walk and the Vicsek model of collective dynamics evidence that fluctuations in cell velocity orientations are sufficient to produce q-Weibull speed distributions seen in our migration assays.
Project description:Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart. While the phase transition has been thoroughly studied, the conditions to keep the flock cohesive in open space are still poorly understood. Here we extend the Vicsek model of collective motion by introducing long-range alignment interactions between the particles. We show that just a small number of these interactions is enough for the system to build up long lasting ordered states of collective motion in open space and in the presence of noise. This finding was verified for other models in addition to the Vicsek one, suggesting its generality and revealing the importance that long-range interactions can have for the cohesion of the flock.
Project description:We study how the structure of the interaction network affects self-organized collective motion in two minimal models of self-propelled agents: the Vicsek model and the Active-Elastic (AE) model. We perform simulations with topologies that interpolate between a nearest-neighbour network and random networks with different degree distributions to analyse the relationship between the interaction topology and the resilience to noise of the ordered state. For the Vicsek case, we find that a higher fraction of random connections with homogeneous or power-law degree distribution increases the critical noise, and thus the resilience to noise, as expected due to small-world effects. Surprisingly, for the AE model, a higher fraction of random links with power-law degree distribution can decrease this resilience, despite most links being long-range. We explain this effect through a simple mechanical analogy, arguing that the larger presence of agents with few connections contributes localized low-energy modes that are easily excited by noise, thus hindering the collective dynamics. These results demonstrate the strong effects of the interaction topology on self-organization. Our work suggests potential roles of the interaction network structure in biological collective behaviour and could also help improve decentralized swarm robotics control and other distributed consensus systems.
Project description:For a given multi-agent system where the local interaction rule of the existing agents can not be re-designed, one way to intervene the collective behavior of the system is to add one or a few special agents into the group which are still treated as normal agents by the existing ones. We study how to lead a Vicsek-like flocking model to reach synchronization by adding special agents. A popular method is to add some simple leaders (fixed-headings agents). However, we add one intelligent agent, called 'shill', which uses online feedback information of the group to decide the shill's moving direction at each step. A novel strategy for the shill to coordinate the group is proposed. It is strictly proved that a shill with this strategy and a limited speed can synchronize every agent in the group. The computer simulations show the effectiveness of this strategy in different scenarios, including different group sizes, shill speed, and with or without noise. Compared to the method of adding some fixed-heading leaders, our method can guarantee synchronization for any initial configuration in the deterministic scenario and improve the synchronization level significantly in low density groups, or model with noise. This suggests the advantage and power of feedback information in intervention of collective behavior.
Project description:Collective migration is commonly observed in groups of migrating cells, in the form of swarms or aggregates. Mechanistic models have proven very useful in understanding collective cell migration. Such models, either explicitly consider the forces involved in the interaction and movement of individuals or phenomenologically define rules which mimic the observed behavior of cells. However, mechanisms leading to collective migration are varied and specific to the type of cells involved. Additionally, the precise and complete dynamics of many important chemomechanical factors influencing cell movement, from signalling pathways to substrate sensing, are typically either too complex or largely unknown. The question is how to make quantitative/qualitative predictions of collective behavior without exact mechanistic knowledge. Here we propose the least microenvironmental uncertainty principle (LEUP) that may serve as a generative model of collective migration without precise incorporation of full mechanistic details. Using statistical physics tools, we show that the famous Vicsek model is a special case of LEUP. Finally, to test the biological applicability of our theory, we apply LEUP to construct a model of the collective behavior of spherical Serratia marcescens bacteria, where the underlying migration mechanisms remain elusive.
Project description:During cell migration, cell-substrate binding is required for pseudopod anchoring to move the cell forward, yet the interactions with the substrate must be sufficiently weak to allow parts of the cell to de-adhere in a controlled manner during typical protrusion/retraction cycles. Mammalian cells actively control cell-substrate binding and respond to extracellular conditions with localized integrin-containing focal adhesions mediating mechanotransduction. We asked whether mechanotransduction also occurs during non-integrin mediated migration by examining the motion of the social amoeba Dictyostelium discoideum, which is thought to bind non-specifically to surfaces. We discovered that Dictyostelium cells are able to regulate forces generated by the actomyosin cortex to maintain optimal cell-surface contact area and adhesion on surfaces of various chemical composition and that individual cells migrate with similar speed and contact area on the different surfaces. In contrast, during collective migration, as observed in wound healing and metastasis, the balance between surface forces and protrusive forces is altered. We found that Dictyostelium collective migration dynamics are strongly affected when cells are plated on different surfaces. These results suggest that the presence of cell-cell contacts, which appear as Dictyostelium cells enter development, alter the mechanism cells use to migrate on surfaces of varying composition.
Project description:Motivated by the wealth of experimental data recently available, we present a cellular-automaton-based modeling framework focussing on high-level cell functions and their concerted effect on cellular migration patterns. Specifically, we formulate a coarse-grained description of cell polarity through self-regulated actin organization and its response to mechanical cues. Furthermore, we address the impact of cell adhesion on collective migration in cell cohorts. The model faithfully reproduces typical cell shapes and movements down to the level of single cells, yet allows for the efficient simulation of confluent tissues. In confined circular geometries, we find that specific properties of individual cells (polarizability; contractility) influence the emerging collective motion of small cell cohorts. Finally, we study the properties of expanding cellular monolayers (front morphology; stress and velocity distributions) at the level of extended tissues.
Project description:In this paper, the normal and extreme wind conditions for power at 12 coastal locations along China's coastline were investigated. For this purpose, the daily meteorological data measured at the standard 10-m height above ground for periods of 40-62 years are statistically analyzed. The East Asian Monsoon that affects almost China's entire coastal region is considered as the leading factor determining wind energy resources. For most stations, the mean wind speed is higher in winter and lower in summer. Meanwhile, the wind direction analysis indicates that the prevalent winds in summer are southerly, while those in winter are northerly. The air densities at different coastal locations differ significantly, resulting in the difference in wind power density. The Weibull and lognormal distributions are applied to fit the yearly wind speeds. The lognormal distribution performs better than the Weibull distribution at 8 coastal stations according to two judgement criteria, the Kolmogorov-Smirnov test and absolute error (AE). Regarding the annual maximum extreme wind speed, the generalized extreme value (GEV) distribution performs better than the commonly-used Gumbel distribution. At these southeastern coastal locations, strong winds usually occur in typhoon season. These 4 coastal provinces, that is, Guangdong, Fujian, Hainan, and Zhejiang, which have abundant wind resources, are also prone to typhoon disasters.
Project description:Collective cell migration plays crucial roles in tissue remodeling, wound healing, and cancer cell invasion. However, its underlying mechanism remains unknown. Previously, we showed that the RhoA-targeting guanine nucleotide exchange factor Solo (ARHGEF40) is required for tensile force-induced RhoA activation and proper organization of keratin-8/keratin-18 (K8/K18) networks. Here, we demonstrate that Solo knockdown significantly increases the rate at which Madin-Darby canine kidney cells collectively migrate on collagen gels. However, it has no apparent effect on the migratory speed of solitary cultured cells. Therefore, Solo decelerates collective cell migration. Moreover, Solo localized to the anteroposterior regions of cell-cell contact sites in collectively migrating cells and was required for the local accumulation of K8/K18 filaments in the forward areas of the cells. Partial Rho-associated protein kinase (ROCK) inhibition or K18 or plakoglobin knockdown also increased collective cell migration velocity. These results suggest that Solo acts as a brake for collective cell migration by generating pullback force at cell-cell contact sites via the RhoA-ROCK pathway. It may also promote the formation of desmosomal cell-cell junctions related to K8/K18 filaments and plakoglobin.
Project description:A long-standing question in collective cell migration has been what might be the relative advantage of forming a cluster over migrating individually. Does an increase in the size of a collectively migrating group of cells enable them to sample the chemical gradient over a greater distance because the difference between front and rear of a cluster would be greater than for single cells? We combined theoretical modeling with experiments to study collective migration of the border cells in-between nurse cells in the Drosophila egg chamber. We discovered that cluster size is positively correlated with migration speed, up to a particular point above which speed plummets. This may be due to the effect of viscous drag from surrounding nurse cells together with confinement of all of the cells within a stiff extracellular matrix. The model predicts no relationship between cluster size and velocity for cells moving on a flat surface, in contrast to movement within a 3D environment. Our analyses also suggest that the overall chemoattractant profile in the egg chamber is likely to be exponential, with the highest concentration in the oocyte. These findings provide insights into collective chemotaxis by combining theoretical modeling with experimentation.
Project description:BACKGROUND: We establish that the occurrence of protein folds among genomes can be accurately described with a Weibull function. Systems which exhibit Weibull character can be interpreted with reliability theory commonly used in engineering analysis. For instance, Weibull distributions are widely used in reliability, maintainability and safety work to model time-to-failure of mechanical devices, mechanisms, building constructions and equipment. RESULTS: We have found that the Weibull function describes protein fold distribution within and among genomes more accurately than conventional power functions which have been used in a number of structural genomic studies reported to date. It has also been found that the Weibull reliability parameter beta for protein fold distributions varies between genomes and may reflect differences in rates of gene duplication in evolutionary history of organisms. CONCLUSIONS: The results of this work demonstrate that reliability analysis can provide useful insights and testable predictions in the fields of comparative and structural genomics.