(134b) Hydrodynamics and Mixing Dynamics in Droplet-Based Microfluidics for Protein Crystallization

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 1^st 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 2^nd 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 2^nd 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.