Quantitative Perspectives of Biomolecular Crystallization Kinetics

As crystallization kinetics determines important characteristics of the resulting crystalline product, such as number of crystals, polydispersity, and crystal size distribution (CSD), the study of the biomolecular crystallization kinetics is of importance not only from scientific but also from practical perspective. And while the number of crystals depends on the kinetics and duration of the nucleation process, the sizes of the crystals and CSD depend on the growth rate. (Of course, if present, agglomeration and oriented attachment of nanocrystals, as well as crystal breakage, may evoke changes in these characteristics.) In this chapter, first, rates of homogeneous and heterogeneous crystal nucleation are overviewed theoretically, and it is emphasized that the surface of the protein molecule dictates its ability to bind to partners: the exact meeting of the binding patches on the molecule surface is a must and explains why the kinetics of biomolecular crystal nucleation is slower compared to that one of small molecules. (That is why, albeit peculiarities of proteins' behavior in solutions are already covered in Chapter " The Starting Point for Biomolecular Crystallisation " of this book, here some peculiarities that are important for the kinetics of the protein crystal nucleation are considered again.) Second, the mechanism of growth of biomolecular crystals is discussed, and it is emphasized that their growth rate is slower than the one of crystals constituted of small molecules. Third, special attention is paid in this chapter to experimental methods for studying the kinetics of the origin and growth of biomolecular crystals. The most used methods for measuring crystal nucleation rates (such as measurement of induction time for nucleation and the so-called double-pulse technique) and the techniques for their implementation are discussed in detail; the apparatuses/devices through which these measurements are performed are also indicated. Quantitative estimation of the variables governing crystal nucleation, such as energy barrier and numbers of molecules constituting the critical nucleus, is reported. In addition, methods used to measure/evaluate growth rates of biomolecular crystals are also considered, and quantitative data on the step kinetic coefficients that determines these rates is presented. Importantly, a comparison between techniques for measuring growth rates is also reported; it is hoped that this can make it easier to choose the most suitable technique for a given purpose. Finally, recommendations are given for growing biomolecular crystals with desired characteristics.