Particle-based model to simulate the micromechanics of biological cells

Abstract

This paper is concerned with addressing how biological cells react to mechanical impulse. We propose a particle based model to numerically study the mechanical response of these cells with subcellular detail. The model focuses on a plant cell in which two important features are present: (1) the cell's interior liquidlike phase inducing hydrodynamic phenomena, and (2) the cell wall, a viscoelastic solid membrane that encloses the protoplast. In this particle modeling framework, the cell fluid is modeled by a standard smoothed particle hydrodynamics (SPH) technique. For the viscoelastic solid phase (cell wall), a discrete element method (DEM) is proposed. The cell wall hydraulic conductivity (permeability) is built in through a constitutive relation in the SPH formulation. Simulations show that the SPH-DEM model is in reasonable agreement with compression experiments on an in vitro cell and with analytical models for the basic dynamical modes of a spherical liquid filled shell. We have performed simulations to explore more complex situations such as relaxation and impact, thereby considering two cell types: a stiff plant type and a soft animal-like type. Their particular behavior (force transmission) as a function of protoplasm and cell wall viscosity is discussed. We also show that the mechanics during and after cell failure can be modeled adequately. This methodology has large flexibility and opens possibilities to quantify problems dealing with the response of biological cells to mechanical impulses, e.g., impact, and the prediction of damage on a (sub)cellular scale.

Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results

“…Disadvantages of SPH are the requirement a relatively high number of particles to attain the same accuracy as grid-based methods, and the non-trivial boundary treatment. Based on SPH, Van Liedekerke et al [185,202] proposed model to simulate dynamics of impact an damage in tissue (Fig. 21a).…”

“…However, the latter ones are used to describe the elasticity cortical CSK, whereas the former one reflects the elasticity of the lipid bilayer of the cell. The linear spring constant for a sixfold symmetric triangulated lattice can be related approximatively to the cortex Young modulus E cor with thickness h by [185,187] …”

“…For a more a more in depth analysis relating the spring force parameters to macroscopic constants, we refer to literature [140,184,185,188]. The volume penalty forces are computed from the internal pressure using the volume change and compressibility K V .…”

“…Van Liedekerke et al [185] implemented a Neo-Hookean incompressible polymer model for a cell surface:…”

“…To analyze stress distribution and predict damage in compressed cells and impacted parenchyma tissue, Van Liedekerke et al [185,202] introduced a full Lagrangian particle model using the continuum smoothed particle hydrodynamics (SPH) technique, coupled with viscoelastic network model representing a solid hyperelastic membrane (Fig. 20), see Sect.…”