Kinetic factors may reshape the dependence of crystal nucleation rate on temperature in protein bulk solution
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Kinetic factors may reshape the dependence of crystal nucleation rate on temperature in protein bulk solution Ivaylo L. Dimitrov 1 Received: 29 June 2020 / Accepted: 15 September 2020/ # Springer Nature B.V. 2020
Abstract
Here we provide an analysis of primary results obtained from a study of apoferritin crystal nucleation in compositionally invariant bulk solution at constant supersaturation ratio of the protein. The temperature dependence of the stationary crystal nucleation rate in the protein bulk solution is obtained with the help of experimentally determined probability for detection of at least one crystal per solution volume until a given time. The stationary crystal nucleation rate demonstrates unusual behavior with temperature. We emphasize that this is caused by kinetic factors that are often disregarded in the frame of the classical nucleation theory but can certainly affect the nucleation kinetics. Keywords Kinetic factors . Crystal nucleation rate . Protein crystals . Temperature
1 Introduction An important task in the studies of nucleation of protein crystals is to quantify the stationary nucleation rate J (m−3 s−1) in the bulk solution of the crystallizing substance [1–4]. Commonly, this can be done in three distinct cases: (i) changing the protein concentration to adjust the supersaturation at constant temperature, pH, and constant salt (precipitant) concentration used to initiate the crystallization; (ii) changing the salt (precipitant) concentration to adjust the supersaturation via modifying the protein solubility (equilibrium concentration) at constant temperature, pH, and constant protein concentration; and (iii) changing the temperature to adjust the protein solubility at constant protein concentration, pH, and constant salt concentration. All of these cases require knowledge about the protein solubility dependence either of salt concentration or temperature for estimation of the supersaturation in buffered solutions. Usually, higher nucleation rate is observed for solutions of higher protein or salt concentration because the supersaturation rises. On the other hand, the majority of proteins exhibit normal
* Ivaylo L. Dimitrov [email protected]
1
Institute of Physical Chemistry “Rostislaw Kaischew”, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 11, 1113 Sofia, Bulgaria
I. L. Dimitrov
dependence of their solubility on temperature [5], which means that the solubility is higher at higher temperatures. This, in turn, leads to higher nucleation rate at lower temperatures because the supersaturation again rises as a result of significant change in the ratio of actual and equilibrium protein concentration (the supersaturation ratio). And this ratio may quite overpower the dependence of the supersaturation itself on temperature, despite the ratio’s logarithmic scale. In the present study, we obtain and analyze the nucleation rate of apoferritin crystals in the bulk solution in a wide temperature range under the constraint of constant supersaturation ratio [6] with a stress on
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