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A theoretical model of collective cell polarization and alignment.

ABSTRACT: Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine the order parameter we derive two sets of governing equations, one for the force equilibrium of the system, and the other for the minimization of the system's free energy including the energy of cell polarization and alignment. By solving these coupled governing equations, we can predict the effects of substrate stiffness, geometries of cell layers, external forces and myosin activity on the direction- and position-dependent cell aspect ratio and cell orientation. Moreover, the axisymmetric problem with cells on a ring-like pattern is solved analytically, and the analytical solution for cell aspect ratio are governed by parameter groups which include the stiffness of the cell and the substrate, the strength of myosin activity and the external forces. Our predictions of the cell aspect ratio and orientation are generally comparable to experimental observations. These results show that the pattern of cell polarization is determined by the anisotropic degree of active contractile stress, and suggest a stress-driven polarization mechanism that enables cells to sense their spatial positions to develop direction- and position-dependent behavior. This, in turn, sheds light on the ways to control pattern formation in tissue engineering for potential biomedical applications.

SUBMITTER: He S

PROVIDER: S-EPMC7842695 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature

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A theoretical model of collective cell polarization and alignment.

He Shijie S Green Yoav Y Saeidi Nima N Li Xiaojun X Fredberg Jeffrey J JJ Ji Baohua B Pismen Len M LM

Journal of the mechanics and physics of solids 20191230

Collective cell polarization and alignment play important roles in tissue morphogenesis, wound healing and cancer metastasis. How cells sense the direction and position in these processes, however, has not been fully understood. Here we construct a theoretical model based on describing cell layer as a nemato-elastic medium, by which the cell polarization, cell alignment and cell active contraction are explicitly expressed as functions of components of the nematic order parameter. To determine th ...[more]

PMID: 33518805

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Project description:Rapid methods for alignment-free sequence comparison make large-scale comparisons between sequences increasingly feasible. Here we study the power of the statistic D2, which counts the number of matching k-tuples between two sequences, as well as D2*, which uses centralized counts, and D2S, which is a self-standardized version, both from a theoretical viewpoint and numerically, providing an easy to use program. The power is assessed under two alternative hidden Markov models; the first one assumes that the two sequences share a common motif, whereas the second model is a pattern transfer model; the null model is that the two sequences are composed of independent and identically distributed letters and they are independent. Under the first alternative model, the means of the tuple counts in the individual sequences change, whereas under the second alternative model, the marginal means are the same as under the null model. Using the limit distributions of the count statistics under the null and the alternative models, we find that generally, asymptotically D2S has the largest power, followed by D2*, whereas the power of D2 can even be zero in some cases. In contrast, even for sequences of length 140,000 bp, in simulations D2* generally has the largest power. Under the first alternative model of a shared motif, the power of D2*approaches 100% when sufficiently many motifs are shared, and we recommend the use of D2* for such practical applications. Under the second alternative model of pattern transfer,the power for all three count statistics does not increase with sequence length when the sequence is sufficiently long, and hence none of the three statistics under consideration canbe recommended in such a situation. We illustrate the approach on 323 transcription factor binding motifs with length at most 10 from JASPAR CORE (October 12, 2009 version),verifying that D2* is generally more powerful than D2. The program to calculate the power of D2, D2* and D2S can be downloaded from http://meta.cmb.usc.edu/d2. Supplementary Material is available at www.liebertonline.com/cmb.

Dataset Information

A theoretical model of collective cell polarization and alignment.

Publications

A theoretical model of collective cell polarization and alignment.

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