Specific Rate of Protein Crystallization Determined by the Guggenheim Method

Abstract

The biological function of a protein is intimately related to its three-dimensional molecular structure. Although X-ray diffraction from single crystals can be employed to solve for the molecular structure, use of this method is often impeded by the slow rate of precipitation of crystals from the pH buffered, aqueous solutions of strong electrolytes which ordinarily serve as growth media. The rate of crystallization can be measured as a function of growth solution conditions by growing the crystals in a dilatometer. As the crystallization progresses, the rate of change of the system volume caused by the difference in density between the crystals and the solution is reflected in the rate of change of the height of the fluid in the capillary side arm of the dilatometer. In the case of the proteins, lysozyme, and canavalin, this height changes exponentially with time, which serves to define a first-order rate constant or specific crystallization rate, k. A dozen such experiments may be needed to determine how $k$ depends upon pH, electrolyte concentration, and temperature. Each experiment can require 4 or 5 days to reach equilibrium. If height measurements are made equally spaced in time, however, early time data can be combined according to the Guggenheim procedure, and the value of k can be determined without the experiment having to reach equilibrium. By using this method, the time required to complete an experiment can be reduced by as much as 50 %.