Sub Cellular Elements (SCE).

My interest is to modeling multi-cellular systems using sub-cellular elements (SCEM). In contrast to the Cellular Potts models (CPM), a dynamical system is developed that defines cellular shape and elasticity, by emulating the cytoskeleton, and uses the Lennard-Jones potential, to mimic cellular adhesion, giving more realistic simulations. The current methods use harmonic restraints between the sub-cellular elements (SCE) to give the correct shape and elasticity, extensions of the model to cell division allows the restraint to be removed beyond a given distance. A schematic representation for two cells, i and j can be seen in Figure 1, where the internal (cytoskeleton) and external (adhesion) forces are shown.

SCE network

Since the SCEM method derives a biologically relevant potential, the inter SCE forces can be found by taking the derivative w.r.t. the positions.

Since the blood cells and platelets are not expected to divide we propose to model the cells using a central SCE connected to SCE representing the surface of the cell, by harmonic restraints. The surface SCE will be coupled to their nearest surface neighbors by harmonic restraints. The length and ‘stiffness’ of the restraints will define the shape and elasticity of the cells. The Figure below depicts our proposed cell structure, the blue SCE represents the center of the cell and the surface is defined by the red SCE. The transparent spheres show the effective Lennard-Jones or Morse potential minima where the effective cell surface is defined (the minimum potential energy corresponding to the cell adhesion value). The cell consists of 21 SCE in this representation, and is rendered using VMD and psf/pdb files generated for the cell.

SCE

Results.

We have simulated collisions and flow coupling to prove the relevant concepts as seen in the following Figures for Platelets and Blood cells. Click on the Platelet or Blood cell picture to view the simulation.

Cells Blood cell

Blood vessel Blood vessels

Preliminary results can be found here.

Latest Results.

The latest simulations represent a platelet in a blood flow that impacts the vessel wall. It then proceeds to roll along the vessel due to the impact of the flow and the adhesion to the vessel. Click the following image to show the simulation.

Rolling cell