A Unified Theory of Liquid-Liquid Demixing and Polymer Formation Kinetics

Abstract

Sickle hemoglobin is a natural hemoglobin mutation with a hydrophobic replacement of a charged aminoacid on the molecular surface. This leads to aggregation into rigid helical structures (“polymerization”), the underlying cause of sickle cell disease. It has also been shown that polymerization occurs in close correspondence with the phase transition of liquid-liquid demixing , or with the critically diverging fluctuations of local concentration occurring in its proximity. Due to this correspondence, polymerization kinetics remarkably appear to exhibit, with respect to demixing temperature, the same universal scaling features shown by amplitudes and lifetimes of fluctuations occurring in proximity of phase transitions. Thus, it is important to understand the relation between polymer formation and liquid-liquid demuxing (LLD). Nucleation kinetics have been described by a relatively complete theory, that until now does not include LLD. We present here a way to incorporate LLD seamlessly into such theory, so as to have a description in terms of the concurrence and interaction of the two processes. In addition, we present new light scattering data supporting the theory. The theory provides a more in-depth understanding of aggregation and crystallization.