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Register a new userNonlinear modeling reveals multi-timescale and higher-order effects in active tissue mechanics
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Cell proliferation, apoptosis, and myosin-dependent contraction can generate elastic stress and strain in living tissues, which may be dissipated by tissue rearrangement through cell topological transition and cytoskeletal reorganization. The present work demonstrates significant nonlinear effects in macroscopic tissue mechanics arising from the competition between force-generating and dissipating processes. We develop a mathematical model to describe the coupled dynamics of tissue activities and mechanics in the nonlinear regime. The model exhibits multi-timescale behavior when the timescale of rearrangement is much shorter than that of growth and constriction. Under this condition, tissue behaves like an active viscoelastic solid at the shorter timescale and like an active viscous fluid at the longer timescale. The accumulated prestrain due to growth and constriction can regulate its viscosity. We solve the full nonlinear system considering the local growth rate coupled with a chemical gradient within a 2D radially symmetric tissue region. We find that the elastic properties and rearrangement rate can regulate tissue size as a higher-order effect due to advection in tissue flow. Furthermore, we show that tissue mechanics nonlinear effects can increase tissue size control sensitivity via mechanical feedback mechanisms.
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We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher moments of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.
In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For the numerical solution of the coupled model, partitioned schemes, that foresee the sequential solution of the two subproblems, are often used. However, this approach may be unstable. For this reason, the coupled model is commonly solved as a unique system using Newton type algorithms, at the price, however, of high computational costs. In light of this motivation, in this paper we propose a new numerical scheme, that is numerically stable and accurate, yet within a fully partitioned (i.e. segregated) framework. Specifically, we introduce, with respect to standard segregated scheme, a numerically consistent stabilization term, capable of removing the nonphysical oscillations otherwise present in the numerical solution of the commonly used segregated scheme. Our new method is derived moving from a physics-based analysis on the microscale energetics of the force generation dynamics. By considering a model problem of active mechanics we prove that the proposed scheme is unconditionally absolutely stable (i.e. it is stable for any time step size), unlike the standard segregated scheme, and we also provide an interpretation of the scheme as a fractional step method. We show, by means of several numerical tests, that the proposed stabilization term successfully removes the nonphysical numerical oscillations characterizing the non stabilized segregated scheme solution. Our numerical tests are carried out for several force generation models available in the literature, namely the Niederer-Hunter-Smith model, the model by Land and coworkers, and the mean-field force generation model that we have recently proposed. Finally, we apply the proposed scheme [...]
Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the time scales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical patterns at integer topological defects. Our description includes three distinct sources of activity: traction forces accounting for cell-substrate interactions as well as anisotropic and isotropic active nematic stresses accounting for cell-cell interactions. We apply our approach to C2C12 cell monolayers in small circular confinements, which form isolated aster or spiral topological defects. By analyzing the velocity and orientational order fields in spirals as well as the forces and cell number density fields in asters, we determine mechanical parameters of C2C12 cell monolayers. Our work shows how topological defects can be used to fully characterize the mechanical properties of biological active matter.
We have developed a method to systematically compute the form of Rashba- and Dresselhaus-like contributions to the spin Hamiltonian of heterostructures to an arbitrary order in the wavevector k. This is achieved by using the double group representations to construct general symmetry-allowed Hamiltonians with full spin-orbit effects within the tight-binding formalism. We have computed full-zone spin Hamiltonians for [001]-, [110]- and [111]-grown zinc blende heterostructures (D_{2d},C_{4v},C_{2v},C_{3v} point group symmetries), which are commonly used in spintronics. After an expansion of the Hamiltonian up to third order in k, we are able to obtain additional terms not found previously. The present method also provides the matrix elements for bulk zinc blendes (T_d) in the anion/cation and effective bond orbital model (EBOM) basis sets with full spin-orbit effects.
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