Equilibrium and kinetic factors in protein crystal growth

Abstract

Diseases such as Alzheimer’s, Parkinson’s, eye lens cataracts, and Type 2 diabetes are the results of protein aggregation. Protein aggregation is also a problem in pharmaceutical industry for designing protein based drugs for long term stability. Disordered states such as precipitates and gels and ordered states such as crystals, micro tubules and capsids are both possible outcomes of protein–protein interaction. To understand the outcomes of protein–protein interaction and to find the ways to control forces, it is required to study both kinetic and equilibrium factors in protein–protein interactions. Salting in/salting out and Hofmeister effects are familiar terminologies used in protein science field from more than a century to represent the effects of salt on protein solubility, but they are yet to be understood theoretically. Here, we build a theory accounting both attractive and repulsive electrostatic interactions via the Poisson Boltzmann equation, ion–protein binding via grand cannonical partition function and implicit ion–water interaction using hydrated ion size, for describing salting in/salting out phenomena and Hofmeister and/or salt specific effect. Our model free energy includes Coulomb energy, salt entropy and ion–protein binding free energy. We find that the salting in behavior seen at low salt concentration near the isoelectric point of the protein is the output of Coulomb energy such that the addition of salt not only screens dipole attraction but also it enhances the monopole repulsion due to anion binding. The salting out behavior appearing after salting in at high salt concentration is due to a salt mediated depletion interaction. We also find that the salting out seen far from the isoelectric point of the protein is dominated by the salt entropy term. At low salt, the dominant effect comes from the entropic cost of confining ions within the aggregates and at high salt, the dominant effect comes from the entropy gain by ions in solution by enhancing the depletion attraction. The ion size has significant effects on the entropic term which leads to the salt specificity in the protein solubility. Crystal growth of anisotropic and fragile molecules such as proteins is a challenging task because kinetics search for a molecule having the correct binding state from a large ensemble of molecules. In the search process, crystal growth might suffer from a kinetic trap called self–poisoning. Here, we use Monte Carlo simulation to show why protein crystallization is vulnerable to the poisoning and how one can avoid such trap or recover crystal growth from such trap during crystallization. We show that self–poisoning requires only three minimal ingredients and these are related to the binding affinity of a protein molecule and its probability of occurrence. If a molecule attaches to the crystal in the crystallographic state then its binding energy will be high but in protein system this happens with very low probability (≈ 10−5). On the other hand, non–crystallographic binding is energetically weak, but it is highly probable to happen. If these things are realized, then it will not be surprising to encounter with self–poisoning during protein crystallization. The only way to recover or avoid poisoning is to alter the solution condition slightly such as by changing temperature or salt concentration or protein concentration etc.