Seminar by David V. Svintradze

Generalizing the Gibbs-Thomson equation and defining thermal stabilities of proteins, viruses and lipid vesicles in confined spaces.

Prof. David V. Svintradze

New Vision University, Tbilisi, Georgia

We solve a generalized version of the problem of the Kelvin and the Gibbs -- Thomson equations, named after Gibbs and Thomson (Lord Kelvin). The Kelvin and the Gibbs-Thomson equations were proposed to describe capillary condensation and variations in pressure or chemical potential across a curved surface or interface. The Gibbs -- Thomson effect, for example, predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing / melting temperatures and the increment of the temperature is inversely proportional to the pore size. The equations have found vast applications in many subfields of physics, chemistry and biophysics, but are constrained by limitations. Namely, they are only applicable to interfaces with trivial geometries such are sphere, cylinder and plane, therefore its usability for defining thermal stabilities of proteins, viruses, lipid vesicles etc. has been largely omitted. The generalization of the equations for arbitrarily curved surfaces, remained as severe problem. By the solving the generalization problem we theoretically show that Gaussian maps of proteins (folded polymers in general), viruses, vesicles and more broadly defined living systems’ thermal-stabilities are strongly influenced by geometries of confined spaces. The Gaussian maps (shapes) are defined by local the internal/external pressure difference. If the difference is positive then the systems shape is mostly defined by the internal interactions (internal hydrogen bonding for instance), while if it is negative then the shape is defined by the interface of the confined space. For instance, stable proteins control their shape by relatively strong internal interactions, while a shape of intrinsically disordered proteins are mostly controlled by the interface of the confined spaces. Same applies to cell motility and shape: cell controls its shape by overcoming environmental stress by building internal cytoskeleton, but in some particular cases, despite of overdamp nature of cells, environmental pressure forces it to change shape. Same analyses apply to shape of vesicles, viruses and shape of any system in general. If despite of environmental stress systems shape is conserved then the systems thermal stability drastically decreases, while otherwise significantly increases. Note here that the Gibbs-Thomson equation only predicts decrease of thermal stability in confined spaces, while generalized one points to possibilities of all changes and strong dependence on the systems boundary’s curvature. Theoretical conclusions, due to the generality are applicable to any nano/micro/macro systems such are: shape of proteins, shape of micelles or vesicles, shape of viruses, shape of cells in confined spaces, shape of cloud etc.