The growth and the fluid dynamics of protein crystals and soft organic tissues: models and simulations, similarities and differences

Abstract

The fluid-dynamic environment within typical growth reactors as well as the interaction of such flow with the intrinsic kinetics of the growth process are investigated in the frame of the new fields of protein crystal and tissue engineering. The paper uses available data to introduce a set of novel growth models. The surface conditions are coupled to the exchange mass flux at the specimen/culture-medium interface and lead to the introduction of a group of differential equations for the nutrient concentration around the sample and for the evolution of the construct mass displacement. These models take into account the sensitivity of the construct/liquid interface to the level of supersaturation in the case of macromolecular crystal growth and to the “direct” effect of the fluid-dynamic shear stress in the case of biological tissue growth. They then are used to show how the proposed surface kinetic laws can predict (through sophisticated numerical simulations) many of the known characteristics of protein crystals and biological tissues produced using well-known and widely used reactors. This procedure provides validation of the models and associated numerical method and at the same time gives insights into the mechanisms of the phenomena. The onset of morphological instabilities is discussed and investigated in detail. The interplay between the increasing size of the sample and the structure of the convective field established inside the reactor is analysed. It is shown that this interaction is essential in determining the time evolution of the specimen shape. Analogies about growing macromolecular crystals and growing biological tissues are pointed out in terms of behaviours and cause-and-effect relationships. These aspects lead to a common source (in terms of original mathematical models, ideas and results) made available for the scientific community under the optimistic idea that the contacts established between the “two fields of engineering” will develop into an ongoing, mutually beneficial dialogue.