Center for Systems Biology Dresden

Dresden, Germany

Center for Systems Biology Dresden

Dresden, Germany

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Aland S.,TU Dresden | Hatzikirou H.,TU Dresden | Lowengrub J.,University of California at Irvine | Voigt A.,TU Dresden | Voigt A.,Center for Systems Biology Dresden
Biophysical Journal | Year: 2015

We present a mechanistic hybrid continuum-discrete model to simulate the dynamics of epithelial cell colonies. Collective cell dynamics are modeled using continuum equations that capture plastic, viscoelastic, and elastic deformations in the clusters while providing single-cell resolution. The continuum equations can be viewed as a coarse-grained version of previously developed discrete models that treat epithelial clusters as a two-dimensional network of vertices or stochastic interacting particles and follow the framework of dynamic density functional theory appropriately modified to account for cell size and shape variability. The discrete component of the model implements cell division and thus influences cell size and shape that couple to the continuum component. The model is validated against recent in vitro studies of epithelial cell colonies using Madin-Darby canine kidney cells. In good agreement with experiments, we find that mechanical interactions and constraints on the local expansion of cell size cause inhibition of cell motion and reductive cell division. This leads to successively smaller cells and a transition from exponential to quadratic growth of the colony that is associated with a constant-thickness rim of growing cells at the cluster edge, as well as the emergence of short-range ordering and solid-like behavior. A detailed analysis of the model reveals a scale invariance of the growth and provides insight into the generation of stresses and their influence on the dynamics of the colonies. Compared to previous models, our approach has several advantages: it is independent of dimension, it can be parameterized using classical elastic properties (Poisson's ratio and Young's modulus), and it can easily be extended to incorporate multiple cell types and general substrate geometries. © 2015 Biophysical Society.

Marth W.,Institute For Wissenschaftliches Rechnen | Voigt A.,Institute For Wissenschaftliches Rechnen | Voigt A.,TU Dresden | Voigt A.,Center for Systems Biology Dresden
Interface Focus | Year: 2016

We consider a generic model for cell motility. Even if a comprehensive understanding of cell motility remains elusive, progress has been achieved in its modelling using a whole-cell physical model. The model takes into account the main mechanisms of cell motility, actin polymerization, actin–myosin dynamics and substrate mediated adhesion (if applicable), and combines them with steric cell–cell and hydrodynamic interactions. The model predicts the onset of collective cell migration, which emerges spontaneously as a result of inelastic collisions of neighbouring cells. Each cell here modelled as an active polar gel is accomplished with two vortices if it moves. Upon collision of two cells, the two vortices which come close to each other annihilate. This leads to a rotation of the cells and together with the deformation and the reorientation of the actin filaments in each cell induces alignment of these cells and leads to persistent translational collective migration. The effect for low Reynolds numbers is as strong as in the non-hydrodynamic model, but it decreases with increasing Reynolds number. © 2016 The Author(s) Published by the Royal Society. All rights reserved.

Marth W.,TU Dresden | Aland S.,TU Dresden | Voigt A.,TU Dresden | Voigt A.,Center for Systems Biology Dresden
Journal of Fluid Mechanics | Year: 2016

We numerically investigate margination of white blood cells and demonstrate the dependency on a number of conditions including haematocrit, the deformability of the cells and the Reynolds number. The approach, which is based on a mesoscopic hydrodynamic Helfrich-type model, reproduces previous results, e.g. a decreasing tendency for margination with increasing deformability and a non-monotonic dependency on haematocrit. The consideration of inertia effects, which may be of relevance in various parts of the cardiovascular system, indicates a decreasing tendency for margination with increasing Reynolds number. The effect is discussed by analysing inertial and non-inertial lift forces for single cells under different flow conditions and large-scale two-dimensional simulations of interacting red blood cells and white blood cells in an idealized blood vessel. © 2016 Cambridge University Press.

Reuther S.,TU Dresden | Voigt A.,TU Dresden | Voigt A.,Center for Systems Biology Dresden
Journal of Computational Physics | Year: 2016

We introduce a diffuse interface approximation for an incompressible two-phase flow problem with an inextensible Newtonian fluid interface. This approach allows to model lipid membranes as viscous fluids. In the present setting the membranes are assumed to be stationary. We validate the model and the numerical approach, which is based on a stream function formulation for the surface flow problem, an operator splitting approach and a semi-implicit adaptive finite element discretization, against observed flow patterns in vesicles, which are adhered to a solid surface and are subjected to shear flow. The influence of the Gaussian curvature on the surface flow pattern is discussed. © 2016 Elsevier Inc.

Ramaswamy R.,Max Planck Institute for the Physics of Complex Systems | Ramaswamy R.,TU Dresden | Ramaswamy R.,Center for Systems Biology Dresden | Bourantas G.,TU Dresden | And 6 more authors.
Journal of Computational Physics | Year: 2015

We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded in a viscous medium, in which stresses are induced through constant consumption of energy. The numerical method is based on Lagrangian particles and staggered Cartesian finite-difference meshes. We show that the method is second-order and first-order accurate with respect to grid and time-step sizes, respectively. Using the present method, we simulate the hydrodynamics in rectangular geometries, of a passive liquid crystal, of an active polar film and of active gels with topological defects in polarization. We show the emergence of spontaneous flow due to Fréedericksz transition, and transformation in the nature of topological defects by tuning the activity of the system. © 2015 Elsevier Inc.

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