Kink kinetics, exchange fluxes, 1D `nucleation' and adsorption on the (010) face of orthorhombic lysozyme crystals

Abstract

Rare kinks (1.74 × 10-3 kinks nm-1) on the otherwise molecularly straight 001 growth steps on the (010) face of orthorhombic lysozyme were studied. These straight steps are generated at the edge between the (010) and (110) faces. Each step is assumed to propagate by creation of one-dimensional (1D) `nuclei' - the segments of a new molecular rows irreversibly attached to the straight step in the course of a trial and error process. Each `nucleus' is built of two neighbouring unit cells and is thus limited by two kinks possessing opposite signs. The steps move along the face at a rate ~0.19 nm s-1, at relative supersaturation about unity. Kink statistics and step rate measurements allowed us to evaluate the velocity of the kink along the step to be 19.3 nm s-1, and corresponding average frequencies at which attachment to and detachment from a kink occur to be 50 and 25 molecules s-1, respectively. The rate at which the 1D `nuclei' appear at a step was found experimentally to be J = 2.7 × 10-5 nm-1 s-1. This rate was also calculated as a probability that a sole molecular species adsorbed at the otherwise straight step will stay there forever. The rate of an arbitrarily oriented step driven by the 1D nucleation was also theoretically found to have a non-singular minimum at the close-packed orientation. On this theoretical basis, the coverage of the 001 step by unit cells was extracted from experimental data to be 6.5 × 10-6. Taking into account translational, rotational and vibrational partition functions flat face coverage with adsorbed molecules was estimated. The calculated adsorption coverage fits with the experimental data if the molecular detachment energy from a kink is ~6.6 kcal mol-1. The terrace adsorption coverage is ~10-3. The same approach is used to outline simple equations for protein solubility. The predicted solubility either rises with rising temperature - at a higher ratio of intermolecular binding energy to kT - or diminishes as the temperature rises - in the opposite case. The latter retrograde solubility comes from a high entropy loss associated with crystallization.