[Proton migration in a stack of tyrosine molecules induced by Mg(2+) ion and electric field. Mathematical model]. / Migratsiia protonov v stopke molekul tirozina pod vozdeistviem iona Mg(2+) i élektricheskogo polia. Matematicheskaia model'.

Quantum chemistry methods (ab initio, RHF + MP2(FULL), 6-31G** basis set) were used to study proton migration in tyrosine stacks mimicking the proton channel in tubulin and other proteins. When bound to guanosine-5'-triphosphate, Mg2+ favors the dissociation of water in its first coordination shell, thus initiating subsequent proton shifts in the tyrosine chain composed of spatially remote tyrosine residues of tubulin. The process appears to be thermodynamically allowed, delta G298 < 0, with a potential barrier along the proton shift of no more than 0.75 kcal/mol. The exposure to external electrical field of low intensity, which simulates the electric properties of tubulin, promotes proton migration over long distances.

A new point of view on the problem of G-protein aggregation. Assembly-disassembly of tubulin as an oscillation process.

Basic principles of nonlinear thermodynamics are used to develop a theory of tubulin assembly. The presence of GTP/GDP switch provides different ways for tubulin aggregation. The GTP-tubulin assembly results in determining the regime of limit cycle favoring growth of tubulin spiral with the formation of microtubules. The GDP-tubulin assembly, on the contrary, results in forming double rings. The difference between the GTP- and GDP-tubulin assemblies is that the former is a dynamical oscillation process while the latter is no more than a transition from a weakly nonequilibrium point to the equilibrium state along a thermodynamical path. Corresponding equations for the GTP- and GDP-tubulin assemblies are proposed.