Instantaneous cell migration velocity may be ill-defined

Cell crawling is critical to biological development, homeostasis and disease. In many cases, cell trajectories are quasi-random-walk. In vitro assays on flat surfaces often described such quasi-random-walk cell trajectories as approximations to a solution of a Langevin process. However, experiments show quasi-diffusive behavior at small timescales, indicating that instantaneous velocity and velocity autocorrelations are not well-defined. We propose to characterize mean-squared cell displacement using a modified F\"urth equation with three temporal and spatial regimes: short- and long-time/range diffusion and intermediate time/range ballistic motion. This analysis collapses mean-squared displacements of previously published experimental data onto a single-parameter family of curves, allowing direct comparison between movement in different cell types, and between experiments and numerical simulations. Our method also show that robust cell-motility quantification requires an experiment with a maximum interval between images of a few percent of the cell-motion persistence time or less, and a duration of a few orders-of-magnitude longer than the cell-motion persistence time or more.Comment: 5 pages, plus Supplemental materia

Redes de neurônios

In the last ten years many scientific advances regarding neurons and the way they are interconnected has mad o it possible to study the dynamics of storage and Processing of information in the brain. In particular, the physicist J. J. Hopfield proposed a formal minimalist model to these neural networks reducing the problem to a particular case of a well – defined physical problem – the spin glass. Although the problem í s well defined, its solution is far from being trivial.Here we introduce the problem, describe Hopfield model, with its achievements and limitations, and present our contribution to the description of information storage in neural networks.Na última década várias descobertas em relação a neurônios e á maneira como estão interconectados, formando redes, possibilitaram o estudo da dinâmica do armazenamento e processamento de informação pelo cérebro. Em particular, o físico J. J. Hopfield propôs um modelo formal, minimalista para estas redes neuronais, reduzindo o problema a um caso particular de um sistema físico bem definido - o vidro de spin. Embora o problema esteja bem definido, sua solução está longe de ser trivial.Neste texto nós introduzimos o problema, descrevemos o modelo de Hopfield com seus resultados e limitações e apresentamos nossa contribuição para a descrição do armazenamento da informação em redes de neurônios

CompuCell3D Model of Cell Migration Reproduces Chemotaxis

Chemotaxis combines three processes: directional sensing, polarity reorientation and migration. Directed migration plays an important role in immune response, metastasis, wound healing and development. To describe chemotaxis, we extend a previously published computational model of a 3D single cell, that presents three compartments (lamellipodium, nucleus and cytoplasm), whose migration on a flat surface quantitatively describes experiments. The simulation is built in the framework of CompuCell3D, an environment based on the Cellular Potts Model. In our extension, we treat chemotaxis as a compound process rather than a response to a potential force. We propose robust protocols to measure cell persistence, drift speed, terminal speed, chemotactic efficiency, taxis time, and we analyse cell migration dynamics in the cell reference frame from position and polarization recordings through time. Our metrics can be applied to experimental results and allow quantitative comparison between simulations and experiments. We found that our simulated cells exhibit a trade-off between polarization stability and chemotactic efficiency. Specifically, we found that cells with lower protrusion forces and smaller lamellipodia exhibit an increased ability to undergo chemotaxis. We also noticed no significant change in cell movement due to external chemical gradient when analysing cell displacement in the cell reference frame. Our results demonstrate the importance of measuring cell polarity throughout the entire cell trajectory, and treating velocity quantities carefully when cell movement is diffusive at short time intervals. The simulation we developed is adequate to the development of new measurement protocols, and it helps paving the way to more complex multicellular simulations to model collective migration and their interaction with external fields, which are under development on this date.Comment: Download and run (in CompuCell3D version 4) the simulation at https://github.com/pdalcastel/Single_Cell_Chemotaxis_2.3 . See the supplemental materials at https://github.com/pdalcastel/CC3D-Chemotaxis-SuppMa

Geometrical distribution of Cryptococcus neoformans mediates flower-like biofilm development

Microbial biofilms are highly structured and dynamic communities in which phenotypic diversification allows microorganisms to adapt to different environments under distinct conditions. The environmentally ubiquitous pathogen Cryptococcus neoformans colonizes many niches of the human body and implanted medical devices in the form of biofilms, an important virulence factor. A new approach was used to characterize the underlying geometrical distribution of C. neoformans cells during the adhesion stage of biofilm formation. Geometrical aspects of adhered cells were calculated from the Delaunay triangulation and Voronoi diagramobtained fromscanning electronmicroscopy images (SEM). A correlation between increased biofilm formation and higher ordering of the underlying cell distribution was found. Mature biofilm aggregates were analyzed by applying an adapted protocol developed for ultrastructure visualization of cryptococcal cells by SEM. Flower-like clusters consisting of cells embedded in a dense layer of extracellular matrix were observed as well as distinct levels of spatial organization: adhered cells, clusters of cells and community of clusters. The results add insights into yeast motility during the dispersion stage of biofilm formation. This study highlights the importance of cellular organization for biofilm growth and presents a novel application of the geometrical method of analysis

Shape-velocity correlation defines polarization in migrating cell simulations

Cell migration plays essential roles in development, wound healing, diseases, and in the maintenance of a complex body. Experiments in collective cell migration generally measure quantities such as cell displacement and velocity. The observed short-time diffusion regime for mean square displacement in single-cell migration experiments on flat surfaces calls into question the definition of cell velocity and the measurement protocol. Theoretical results in stochastic modeling for single-cell migration have shown that this fast diffusive regime is explained by a white noise acting on displacement on the direction perpendicular to the migrating cell polarization axis (not on velocity). The prediction is that only the component of velocity parallel to the polarization axis is a well-defined quantity, with a robust measurement protocol. Here, we ask whether we can find a definition of a migrating-cell polarization that is able to predict the cell's subsequent displacement, based on measurements of its shape. Supported by experimental evidence that cell nucleus lags behind the cell center of mass in a migrating cell, we propose a robust parametrization for cell migration where the distance between cell nucleus and the cell's center of mass defines cell shape polarization. We tested the proposed methods by applying to a simulation model for three-dimensional cells performed in the CompuCell3D environment, previously shown to reproduce biological cells kinematics migrating on a flat surface

Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits

We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant bubble characteristics are the Plateau border radius and a new variable, the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau borders interfaces. The resulting prediction is successfully tested, without adjustable parameter, using extensive bidimensional Potts model simulations. Simulations also show that a selfsimilar growth regime is observed at any liquid fraction and determine how the average size growth exponent, side number distribution and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals and other domains with coarsening driven by curvature

Velocities of Mesenchymal Cells May be Ill-Defined

The dynamics of single cell migration on flat surfaces is usually modeled by a Langevin-like problem consisting of ballistic motion for short periods and random walk. for long periods. Conversely, recent studies have revealed a previously neglected random motion at very short intervals, what would rule out the possibility of defining the cell instantaneous velocity and a robust measurement procedure. A previous attempt to address this issue considered an anisotropic migration model, which takes into account a polarization orientation along which the velocity is well-defined, and a direction orthogonal to the polarization vector that describes the random walk. Although the numerically and analytically calculated mean square displacement and auto-correlation agree with experimental data for that model, the velocity distribution peaks at zero, which contradicts experimental observations of a constant drift in the polarization direction. Moreover, Potts model simulations indicate that instantaneous velocity cannot be measured for any direction. Here, we consider dynamical equations for cell polarization, which is measurable and introduce a polarization-dependent displacement, circumventing the problem of ill defined instantaneous velocity. Polarization is a well-defined quantity, preserves memory for short intervals, and provides a robust measurement procedure for characterizing cell migration. We consider cell polarization dynamics to follow a modified Langevin equation that yields cell displacement distribution that peaks at positive values, in agreement with experiments and Potts model simulations. Furthermore, displacement autocorrelation functions present two different time scales, improving the agreement between theoretical fits and experiments or simulations