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

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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 analyzed. 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.
LanguageEnglish
Pages225-240
Number of pages16
JournalJournal of Theoretical Biology
Volume224
Issue number2
DOIs
Publication statusPublished - 30 Sep 2003

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crystal proteins
Biological Tissue
Fluid Dynamics
Fluid dynamics
Reactor
fluid mechanics
Crystal
Tissue
Proteins
Protein
Crystals
crystals
Growth
Kinetics
Crystal growth
Tissue Engineering
kinetics
tissue engineering
Mass flux
Simulation

Keywords

  • growth kinetics
  • fluid motion
  • mathematical models
  • moving boundary method
  • morphology evolution
  • protein crystals
  • macromolecular crystal growth

Cite this

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title = "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 analyzed. 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.",
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author = "Marcello Lappa",
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