Tuesday, 31 July 2018

Towards Quantitative DNA Reaction-Diffusion Chemical Networks

By Javier Cabello Garcia

Have you ever wondered how zebras got their stripes? Or why you (probably) were blessed with five toes instead of webbed feet? These and other pattern-formation phenomena in Nature are produced by reaction-diffusion systems. These systems are defined as those in which the concentration of one or more species of chemical compounds change in time and space. The change of concentration with time is not exotic, since every chemical reaction leads the transformation of one species into another during time. However, space dependency due to a diffusion factor is introduced when the system is not well stirred - i.e., concentrations are not the same in all regions of space.

Diffusion is the spontaneous spread of particles as a result of random motion in a solution. This motion produces the transition of particles from regions where they are present in high concentration to others where their concentration is lower, following concentration gradients. Concentration imbalances not only cause diffusion, but lead to different chemical reaction rates in different regions. This heterogeneity prompts the formation of patterns, which can show interesting behaviours like wave fronts or oscillations.
The pattern formation of reaction-diffusion systems is common in many biochemical processes; several lines of research have therefore addressed the design and quantitative study of these systems. DNA has been proposed several times as the ideal substrate for the production of quantitative chemical networks. The suitability of DNA comes from the predictability of the DNA interactions and the thorough characterisation of its reaction rates in well-stirred conditions. However, reaction-diffusion networks strongly depend on the diffusion speeds of each species as well. This means that for DNA networks the diffusion speed of each DNA species has to be known and tunable.

Alas, the diffusion speed of individual DNA strands is hard to control. It is largely determined by size and shape, and varies relatively little for the sort of short DNA systems typically used. Previous attempts to modify the diffusion of strands relied on making them transiently stick to a solid matrix, effectively immobilising the strands temporarily. In a recent paper, Rodjanapanyakui et al. present a matrix-free approach, were they modulate the diffusion speeds of particular DNA species in solution by specific non-covalent binding. The “modulated” strand is complementary to an “anchor” strand, which is attached to a large polymer that is free in the solution. Binding to the anchor reduces the diffusion of the modulated strand a great deal. A “competitor” strand, which can compete with the modulated strand for binding to the anchor (by a toehold exchange reaction), allows temporary release of the modulated strand from the anchor. By varying the concentration of competitors, different average diffusion rates can be obtained.

Fig. 1 Diffusion modulation system. a) Strands of the system. b) In the presence of a large excess of the competitor strand (C) the modulated strand (T) can diffuse freely. When no C is present, T binds to the anchor (A) complexes, which diffuse at a significantly slower speed. c) C release T by a toehold exchange reaction. The newly created toehold can be used by a free-in-solution T to bind again to A. Reproduced with permission from APS Physics, Diffusion modulation of DNA by toehold exchange, Rodjanapanyakul, T., Takabatake, F., Abe, K., Kawamata, I., Nomura, S. and Murata, S. Physical Review E, 97(5).

Fluorescence Recovery After Photobleaching (FRAP) was used to follow the diffusion speed variation of the modulated strand with varying concentrations of competitor and anchor. This technique involves labelling the molecule of interest (in this case the modulated strand) with fluorophores and exciting a region of the sample with a high laser intensity. This results in the bleaching of the fluorescence of the excited area. The diffusion of the labelled molecule of interest gradually restores the fluorescence in the area, and the recovery time is directly related to the diffusion speed.

Experimental data showed that by employing this diffusion modulation method, the effective average diffusion speed of a specific strand can be tuned along a sixfold variation in range. This method has even been proved to tune simultaneously the diffusion of two DNA strands without any crosstalk. The introduction of this diffusion tuning mechanism in solution opens the way for new dynamics and quantitative reaction-diffusion systems with complex behaviours and functions for DNA systems.

Read More:
-Rodjanapanyakul, T., Takabatake, F., Abe, K., Kawamata, I., Nomura, S. and Murata, S. (2018). Diffusion modulation of DNA by toehold exchange. Physical Review E, 97(5). Link:https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.052617
-Zadorin, A., Rondelez, Y., Galas, J. and Estevez-Torres, A. (2015). Synthesis of Programmable Reaction-Diffusion Fronts Using DNA Catalyzers. Physical Review Letters, 114(6). Link:https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.068301
-Kondo, S. and Miura, T. (2010). Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation. Science, 329(5999), pp.1616-1620. Link:http://science.sciencemag.org/content/329/5999/1616.long
-Allen, P., Chen, X. and Ellington, A. (2012). Spatial Control of DNA Reaction Networks by DNA Sequence. Molecules, 17(11), pp.13390-13402. Link: http://www.mdpi.com/1420-3049/17/11/13390
-Padirac, A., Fujii, T., Estévez-Torres, A. and Rondelez, Y. (2013). Spatial Waves in Synthetic Biochemical Networks. Journal of the American Chemical Society, 135(39), pp.14586-14592. Link:https://pubs.acs.org/doi/abs/10.1021/ja403584p

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