A protein is a biological macromolecule with a complex three-dimensional (3D) structure, involving one or more polypeptide chains. Proteins are the building blocks of all cells in all living creatures and given the fact that all their functions are dependent on their structure, one can easily understand the importance of determining their 3D structure (Walsh 2015). Indeed, knowledge of protein structure has a huge impact on fundamental research in biochemistry and biology, and has led to tremendous progress in molecular biology (Ducruix & Giegé 1999). That is the reason why it is so important to solve protein structures by electron diffraction from 3D crystals. However, the insights into protein crystallization are still limited. Due to the highly variable nature of protein crystallization, it is often a matter of trial-and-error to successfully crystallize a protein, without systematic methodologies.
This study aims at improving our comprehension of the fundamentals of protein crystallization, in particular the effect of mass transfer and mixing on the nucleation phenomena, using numerical approaches. Numerical simulations provide an alternative tool to understand the fundamental fluid dynamics, avoiding long and costly experimental procedures (Li & Ismagilov 2010). There are only a few number of studies in this research field, especially compared to the large number of publications for the prediction of droplets generation. Besides that, these works are not applied in protein crystallization.
In this context, we propose to study protein crystallization in droplet-based microfluidic devices, which are attractive tools for high-throughput screening. Each droplet is defined as a microreactor, allowing to carry out a large number of experiments under identical conditions, offering thus more flexibility and using a minimal protein consumption (Yamaguchi et al. 2013). Further, they provide unique experimental conditions to study the fundamentals of protein crystallization mechanisms, as they offer enhanced heat and mass transfer, including control of molecular diffusion, manipulation of operating parameters, and optical access for in situ characterization (Squires & Quake 2005).
Microbatch lysozyme crystallization trials will be carried out following the double pulse technique reported by Galkin & Vekilov (Galkin & Vekilov 1999). For the temperatures selection, a two-dimensional (2D) phase diagram, representing the protein concentration as a function of the temperature, will be drawn in order to depict the metastability zone and thereby the temperatures that should be used in the double pulse technique. This procedure will be applied for different droplet sizes within a range of low values of the Capillary number (Ca). Based on the dimensions and/or boundary-conditions of this study, the continuum approach is assumed valid. The governing equations in fluid dynamics are coupled with the Level-Set equation. The velocity field generated in single-field momentum equation (Navier-Stokes equation) is applied within the interface evolution equation. Macromolecule and precipitant agent solutions have different values of physical properties, but attending to the fact that the molar concentrations are lower than 10%, Fick’s 1st law can be used to describe the diffusive transport (Howard et al. 2009; García-Ruiz et al. 2016) and the fluid properties can be assumed identical to the values for water. The Nernst-Planck equation combines diffusion and convection mechanisms, where the Transport of Diluted Species model is applied to solve the transport mechanisms generated by the solved velocity field, where the concentrations of protein and precipitant agent are defined, as well as the respective diffusion coefficients.
Using this numerical approach, we obtain the concentration profiles inside the droplets for different droplet sizes. This information aides in the understanding of how mass transport and mixing affect protein crystallization, including crystal growth (crystal size, morphology and quality), crystal distribution and orientation, and complex phenomena at the interface between the protein and precipitant agent solutions upon mixing (García-Ruiz et al. 2016). Furthermore, it will also be helpful to establish a compromise between the mass transport mechanisms in order to determine the optimum conditions (concentration ratios of protein and precipitant agent solutions, flow rate of both phases, and characteristic dimension of the microchannel) to enhance protein crystallization and obtain high quality crystals.
References
Ducruix, A. & Giegé, R., 1999. Crystallization of Nucleic Acids and Proteins: A Practical Approach 2nd edition., Oxford University Press.
Galkin, O. & Vekilov, P.G., 1999. Direct Determination of the Nucleation Rates of Protein Crystals. The Journal of Physical: Chemistry B, 103(49), pp.10965–10971.
García-Ruiz, J.M., Otálora, F. & García-Caballero, A., 2016. The role of mass transport in protein crystallization. Acta Crystallographica Section F Structural Biology Communications, 72(2), pp.96–104.
Howard, E.I., Fernandez, J.M. & Garcia-Ruiz, J.M., 2009. On the mixing of protein crystallization cocktails. Crystal Growth and Design, 9(6), pp.2707–2712.
Li, L. & Ismagilov, R.F., 2010. Protein Crystallization Using Microfluidic Technologies Based on Valves, Droplets, and SlipChip. In Annual Review of Biophysics. New York, pp. 139–158.
Squires, T.M. & Quake, S.R., 2005. Microfluidics: Fluid physics at the nanoliter scale. Reviews of Modern Physics, 77(3), pp.977–1026.
Walsh, G., 2015. Proteins: Biochemistry and Biotechnology 2nd edition., Wiley.
Yamaguchi, H. et al., 2013. Controlling one protein crystal growth by droplet-based microfluidic system. Journal of Biochemistry, 153(4), pp.339-346.
Acknowledgements
This work was financially supported by: Project POCI-01-0145-FEDER-006939 (Laboratory for Process Engineering, Environment, Biotechnology and Energy – LEPABE funded by FEDER funds through COMPETE2020 – Programa Operacional Competitividade e Internacionalização (POCI) – and by national funds through FCT - Fundação para a Ciência e a Tecnologia. Thanks are due to Fonds Wetenschappelijk Onderzoek (FWO) by financial support of the author J. Ferreira and to Fundação para a Ciência e Tecnologia (FCT) of the author F. Castro by means of scholarship SFRH/BDP/96132/2013.