Synthesis of Programmable Reaction-Diffusion Fronts Using DNA Catalyzers

Abstract : We introduce a DNA-based reaction-diffusion (RD) system in which reaction and diffusion terms can be precisely and independently controlled. The effective diffusion coefficient of an individual reaction component, as we demonstrate on a traveling wave, can be reduced up to 2.7-fold using a self-assembled hydrodynamic drag. The intrinsic programmability of this RD system allows us to engineer, for the first time, orthogonal autocatalysts that counter-propagate with minimal interaction. Our results are in excellent quantitative agreement with predictions of the Fisher-Kolmogorov-Petrovskii-Piscunov model. These advances open the way for the rational engineering of pattern formation in pure chemical RD systems. Reaction-diffusion (RD) models are a rich source of spatiotemporal pattern formation phenomena. Not only is this mechanism relevant to biological morphogene-sis [1], but it is one of the few conceptualizations that physics can offer for the spontaneous emergence of order in molecular systems [2]. Traveling waves [3], spirals [4] and Turing patterns [5], among other structures [6, 7], have been observed experimentally. However, in contrast to pattern formation in hydrodynamics, few of these studies are quantitative [8, 9]. The reason is that we lack a fully controllable and easily modeled experimental RD system. In addition, to generate arbitrary spatiotemporal patterns the following properties need to be programmable: i) the topology of the chemical reaction network (CRN), ii) the reaction rates, and iii) the diffusion coefficients of individual species D i. The majority of attempts to achieve these goals concern redox or acid-base reactions related to the Belousov-Zhabotinsky (BZ) reaction [10–12]. Our current understanding does not allow to engineer CRNs with such chemistries in a rational way. Although semi-heuristic methods have been developed [13–15], they are neither general nor modular. Particular solutions to control diffusion have been devised for BZ-related reactions [5, 16] but no general strategy is available. DNA-based chemical reaction networks provide an interesting solution to the issues mentioned above. Due to base complementarity, the kinetics of the DNA hybridiza-tion reaction can be predicted from the sequence [17, 18]. Recent advances in DNA nanotechnology allow us to program the topology of quite complex CRNs. Enzyme-free DNA circuits have been used for producing tunable cascading reactions [19] and encoding edge detection algorithms [20]. In combination with enzymatic reactions, non-equilibrium dissipative behaviors with DNA circuits have been obtained, such as non-linear oscillators [21– 23], memory switches [24], and propagating waves and spirals [25]. Here we introduce a general method to control specifically the reaction and diffusion rates of DNA species involved in such programmable reaction networks. We demonstrate this on the minimal reaction capable of self-organization in space: an autocatalytic front propagating in a 1-dimensional reactor. As such, we used an auto-catalytic node of the DNA polymerase exonuclease nicking enzyme (PEN) toolbox, that works as follows [21]. Species A, an 11-mer single-stranded DNA (ssDNA), cat-alyzes its own growth in the presence of a template strand T, a 22-mer that carries two contiguous domains complementary to A: species A reversibly hybridizes with T on either of these domains and one of the resulting complexes can be extended by a polymerase (pol), which is the rate-limiting step in our conditions. The resulting double-stranded DNA (dsDNA) complex carries a recognition site for a nicking enzyme (nick) such that the upper strand is cut at its midpoint, releasing two molecules of A and the intact T. The kinetics of this process is captured by the simplified mechanism sketched in (FIG. 1a, for details refer to [21, 25]). The total concentration of each species, free or bound, is noted in italics in the following. In a one dimensional reactor the evolution of A is described by the reaction-diffusion equation ∂A ∂t = r(A) + ∂ ∂x D eff (A) ∂A ∂x , (1) where r(A) is the reaction term, and we have made explicit that the effective diffusion coefficient D eff (A) depends on A. This reflects the existence of A in states with different diffusion coefficients (free and bound to T). When D eff (A) = D, equation (1) together with reasonable assumptions about r(A) [26], form the Fisher-Kolmogorov-Petrovskii-Piscunov (Fisher-KPP) case: there exists a single stable asymp-totic traveling wave solution A(x, t) = A(x − v m t), where v m = 2 r (0)D depends neither on other details of the growth function r(A) nor on the shape of the initial condition [27, 28]. In our case, if the front propagation is controlled by the growth at the leading edge, where A 0,
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Physical Review Letters, American Physical Society, 2015, 114 (6), pp.55 - 66. 〈10.1103/PhysRevLett.114.068301〉
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Anton Zadorin, Yannick Rondelez, Jean-Christophe Galas, André Estévez-Torres. Synthesis of Programmable Reaction-Diffusion Fronts Using DNA Catalyzers. Physical Review Letters, American Physical Society, 2015, 114 (6), pp.55 - 66. 〈10.1103/PhysRevLett.114.068301〉. 〈hal-01623547〉

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