Mathematical modelling of flows in cells

Biophysicists and cell biologists have been strongly interested recently in how spatial structures form spontaneously in cells and tissues and which physical, chemical and biological mechanisms are decisive for this process. Whereas biochemical and genetic processes have long been investigated as “driving forces”, mechanical forces and the associated flow processes inside the cell have recently moved into the focus of research. Knowing the dynamics of such mechanisms and of chemical processes in cells is important for the understanding of processes such as cell motion and the development of cell tissues.

Mechanical forces are generated by the contraction of clusters of the biopolymer actin. This motion, in turn, is generated by the activity of myosin molecules that act as molecular motors. The myosin-regulating calcium ions inside the cell have to redistribute to enable this process to create biological structures; this causes a feedback reaction towards the mechanics of the actin fibre bundles.

A model which was developed in a cooperation project between PTB and TU Berlin describes the cell as a porous and elastic (“poroelastic”) medium and has now been applied successfully to the biophysical model organism Physarum polycephalum. Physarum cells contain a great number of cell nuclei and reach macroscopic dimensions, exhibiting frequently complex geometric shapes. If a small amount of cell plasma is taken from larger cells, cylindrical microdrops form. In these drops, many different patterns of deformation waves are observed. PTB's model allows all these patterns to be reproduced successfully. In addition, the model predicts a strong coupling of the mechanical processes to the intracellular fluid dynamics and the local calcium concentration.

Such simulations can also be used for the quantitative assessment of dynamic processes in cells and may trigger new measurements of the intracellular flows and spatial distributions of calcium and actin (e.g. by means of fluorescence methods) as well as of the mechanical and elastic properties of the cell material.