73. How eukaryotic cells feel direction
Save This Post as PDFEukaryotic cells present in both plants and animals are cells bounded by membranes and containing nuclei.
Often they contain other organelles such as mitochondria or chloroplasts, but this is not what will interest us at this time – let us focus on membranes.
Properties of these membranes are rather peculiar: they actually represent a nice chemical compass. Concentration differences of certain chemicals between different sides of the membrane lead to its chemical polarization followed by the migration of the cell when these differences are at the level of few percent. This directional sensing is necessary, for example, for embryo development, and in fact, no multicellular organism can exist without it.
There is a known chain of chemical reactions that leads to directional sensing. The chemical factors that cluster on different sides of the membrane are called phospholipids PIP2 and PIP3. Two different enzymes can transform these lipids into each other. While phospholipids are bound to the membrane, enzymes can diffuse inside the volume of the cell. Enzymes become active only after they are getting absorbed by the membrane. Absorption of the first enzyme is activated by the extracellular signal (change of concentraction of the reactant inside the cell), and that is how the membrane feels the reactant. Absorption of the second enzyme is due to the coupling to PIP2, and that is how backreaction is introduced into the system.
After one understands this chain, one is ready to construct the quantitative theory of the membrane polarization. Suppose that 
is the radius of the PIP2 patch. This radius is essentially determined by the Langevin-type equation (we discussed the latter multiple times in the context of eternal inflation on this blog, as you will see in a monent, here we have a kind of eternal inflation of PIP2 patches inside the cell 
):
,
where 
is the function of the concentration of one of the enzymes, 
is the linear tension of the interface with surrounding PIP3 phase and 
is the thermal noise. From the Langevin equation above one immediately derives the Fokker-Planck equation for the stochastic distribution of patches:
.
The physical picture is the following. The volume of different PIP2 patches grows stochastically, and eventually a single PIP2 phase survives, and its orientation determines the reaction of the cell to the external reactant. The process of patch formation is not actually very rapid, and so is the reaction of the cell. Since the mechanism of patch formation is diffusive, one gets the diffusive law of the form
,
and the corresponding time scale is the diffusion time essentially determined by the strength of thermal fluctuations. So, what your cells to be reactive? Heat them up 
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