A Probabilistic Model for Crystal Growth Applied to Protein Deposition at the Microscale
Abstract
:1. Introduction
2. The Model
2.1. Structure
- If a cell is occupied, it cannot be occupied again, i.e., if , then .
- If a cell is occupied, then the probability of occupation of the adjacent free cells is increased, see Equation (1).
2.2. Kinetics
3. The Parameters
3.1. Structural Parameters
- : the “difficulty of filling” parameter, see Equation (2). It ranges from 0 to 1 and determines the importance of the maximum effective radius in the model. It is also related to the rate at which void regions are filled. Setting means that the probability of occupation of a cell does not depend on the maximum effective radius. In Figure 6 how this parameter (along with ) affects the shape of the crystal is shown.
- : the “effective dimension” parameter, see Equation (2). It must be positive and, as explained before, in our model, is set to 2. It also determines how the maximum effective radius affects the crystal growth.
3.2. Kinetic Parameters
- : parameters of the Gompertz function in Equation (6) that models the last stages of the process.
4. Results
4.1. Protein Recrystallization
4.2. Influence of the Contour Regularity
5. Discussion
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Bolos, V.J.; Benitez, R.; Eleta-Lopez, A.; Toca-Herrera, J.L. A Probabilistic Model for Crystal Growth Applied to Protein Deposition at the Microscale. Materials 2019, 12, 479. https://doi.org/10.3390/ma12030479
Bolos VJ, Benitez R, Eleta-Lopez A, Toca-Herrera JL. A Probabilistic Model for Crystal Growth Applied to Protein Deposition at the Microscale. Materials. 2019; 12(3):479. https://doi.org/10.3390/ma12030479
Chicago/Turabian StyleBolos, Vicente J., Rafael Benitez, Aitziber Eleta-Lopez, and Jose L. Toca-Herrera. 2019. "A Probabilistic Model for Crystal Growth Applied to Protein Deposition at the Microscale" Materials 12, no. 3: 479. https://doi.org/10.3390/ma12030479
APA StyleBolos, V. J., Benitez, R., Eleta-Lopez, A., & Toca-Herrera, J. L. (2019). A Probabilistic Model for Crystal Growth Applied to Protein Deposition at the Microscale. Materials, 12(3), 479. https://doi.org/10.3390/ma12030479