Generalization Of The Gibbs-Thomson Equation And Predicting Melting Temperatures Of Biomacromolecules In Confined Geometries

The Gibbs-Thomson equation has found successful applications in many subfields of physics. The Gibbs-Thomson effect 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, as given by the Gibbs Thomson equation. This phenomena can be reformulated for Gaussian maps of macromolecules and can be asked following question: can one use Gibbs-Thomson equation for predicting melting temperature of macromolecules in confined geometries? Of course the answer is no for many reasons and also because macromolecules form highly curved surfaces (Gaussian maps) and Gibbs-Thomson equation holds only for simple geometries (sphere, plane or cylinder). We have already solved the generalization problem of the Kelvin equation and after that the generalization of the Gibbs-Thomson equation is not conceptually difficult. In the upcoming conference we will present beautiful derivation of the equation and put forward some basic analyses and its applicability to predicting melting temperatures of biomacromolecules in confined geometries. As far as proteins fold in vivo in highly jammed and therefore confined geometries it is predicted that the equation will improve our understanding of two basic questions: how narrow, jammed and confined geometries help proteins to fold to certain shape and how the melting temperature is modulated in such confined geometries. Consequently we predict that melting temperatures of biomacromolecules, which is the temperature for “statistical polymer chain” - “folded polymer chain” phase transition significantly differs from temperatures in non-confined geometries.