Migrating Cells: Living Liquid Crystals

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Abstract
Two conditions are necessary to built up a condensated state out of elementary units: (i) interaction between the elementary units and (ii) motion of the elementary units. A new type of liquid crystal is found by using migrating cells (human granulocytes) as elementary units. These cells show no interaction or a weak repulsion at high calcium concentration (2.5 mM). But at low calcium concentration (< nM) the cells attract each other and form a polar nematic liquid crystal. First, the machine for the directed movement is investigated phenomenologically. The direction of migration is guided by a cellular automatic controller. It can be characterized by two machine coefficients: (i) the response of the automatic controller is proportional to the strength of the extracellular guiding field times a cellular machine coefficient, and (ii) the random movement is induced by stochastic processes in the cellular machinery. These cellular stochastic processes are equivalent to the thermal motion of inert particles. The analogy to the Boltzmann statistics is evident. In the next step, the cell-cell communication is investigated. During one machine cycle, the cell can release metabolic molecules which attract other cells via chemotaxis. Galvanotaxis is another mechanism for the cell-cell interaction since every cell is surrounded by an electric field. The distance dependent cell-cell interaction is determined from the pair correlation function.