Analysis of Initial Cell Spreading Using Mechanistic Contact Formulations for a Deformable Cell Model

Abstract

Adhesion governs to a large extent the mechanical interaction between a cell and its microenvironment. As initial cell spreading is purely adhesion driven, understanding this phenomenon leads to profound insight in both cell adhesion and cell-substrate interaction. It has been found that across a wide variety of cell types, initial spreading behavior universally follows the same power laws. The simplest cell type providing this scaling of the radius of the spreading area with time are modified red blood cells (RBCs), whose elastic responses are well characterized. Using a mechanistic description of the contact interaction between a cell and its substrate in combination with a deformable RBC model, we are now able to investigate in detail the mechanisms behind this universal power law. The presented model suggests that the initial slope of the spreading curve with time results from a purely geometrical effect facilitated mainly by dissipation upon contact. Later on, the spreading rate decreases due to increasing tension and dissipation in the cell's cortex as the cell spreads more and more. To reproduce this observed initial spreading, no irreversible deformations are required. Since the model created in this effort is extensible to more complex cell types and can cope with arbitrarily shaped, smooth mechanical microenvironments of the cells, it can be useful for a wide range of investigations where forces at the cell boundary play a decisive role.

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

“…27, we arrive at a linear problem described by a sparse symmetric matrix, which can be solved efficiently by a Conjugate Gradient method [140,141]. Note that the above system of equations of motion (Eq.…”

“…In some cases however, it is necessary to incorporate nonlinear elastic behavior which better describe the polymeric molecular structures [140,184]. A well-known model for this is the Finitely Extensible Nonlinear Elastic (FENE) force which behaves soft at low stretch but become very stiff at high stretches (similar to uncoiling a rope):…”

“…19). The forces F a are then applied in the plane of each triangle in the direction from the barycenter of the triangle [140]. Note that the area conservation forces contribute to the membrane/cortex stiffness in a similar way as the spring forces in Eqs.…”

“…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 .…”

The effect of cortical elasticity and active tension on cell adhesion mechanics

“…Cells are represented as spherical elastic shells that maintain internal volume and for which adhesive/repulsive contact is described using a Dugdale approach (11). Active contractility is explicitly introduced through a contractile tension, and acts similar to an additional surface tension (see Fig.…”