Thermal modulation

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Dynamically-addressed mechanisms

Macroscopic models have been proposed to account for complex matter behavior encountered in Biology. However, those models do not correspond to the kinetic laws of the simple systems of Chemistry. They are not helpful to design and implement chemical molecules and reactions reproducing such complex behavior.

We proceeded conversely by evaluating the behavior resulting from assemblies of chemical modules: The dynamics of such assemblies can exhibit a “complex” macroscopic behavior for appropriate mechanisms and rate constants. As such conditions are difficult to fulfill by engineering, we have adopted a combinatorial strategy. In collaboration with Annie Lemarchand (LPTMC, UPMC) and Charlie Gosse (LPN, CNRS), we have introduced unprecedented approaches for identifying, quantifying and sorting targeted mechanisms defined by their dynamics. Our approach relies on maximizing the response of a given reactant or network of reactants stimulated by one or several appropriate periodic excitations.

We experimentally validated a first strategy based on applying a periodic uniform electric field for sorting a given reactant submitted to a titration reaction: When the frequency of the field is tuned to match its reactive dynamics, the desired reactant exhibits a maximized dispersion coefficient. Its dispersion can be easily controlled and allows us to collect it at the edges of the concentration distribution of the mixture.1

We also introduced new theoretical sorting protocols. In these cases, the reactive mixture is exposed to two periodic excitations at the same frequency, which is tuned to match the dynamics of the titration reaction for the reactant of interest.2, 3 In the most selective one4, we superimpose the modulation of the temperature to the oscillation of an electric field. For an appropriate phase delay between both modulations, we predict an oriented motion for the desired reactant which can be easily extracted from the other mixture components (non mobile or slower).

More recently, we evaluated how small modulations of the temperature can reveal the dynamics of a reactive system. Indeed biological networks have recently received a considerable attention to interpret the behavior of living matter. However, the available tools to analyze the dynamics of networks remain scarce, in particular in vivo and in a wild-type context. We showed that the temperature modulation provides a non invasive approach to efficiently analyze mechanisms.5 We currently implement non-invasive protocols relying on temperature modulation to image a dynamically-addressed component in a mixture (Figure 1)6

Figure 1. The equilibrium titration approach. At chemical equilibrium at temperature T0, the mixture components (geometrical figures) generate the output signal SIl0. In the displayed case, the targeted analyte (blue disk) in low amount weakly contributes to the total constant output signal (blue arrow). Its concentration cannot be reliably retrieved without further information on the contributions from interfering mixture components. In the temperature modulation and signal filtering titration, the periodic thermal excitation of small amplitude (red creneled arrow) adds to the preceding output signal a supplementary oscillating term which can be analyzed to extract the out-of-phase contributions SbIl1cos. Upon appropriate tuning of the angular frequency of the temperature modulation and of the reagent concentration, the out-of-phase contribution of the targeted analyte(blue creneled arrow) now dominates the whole response so as to extract a reliable value for its concentration, even if it is present in low amount in a complex mixture.

References

1. D. Alcor, V. Croquette, L. Jullien, A. Lemarchand, Proc. Natl. Acad. Sci. USA, 2004, 101, 8276-8280 ; D. Alcor, J.-F. Allemand, E. Cogné-Laage, V. Croquette, F. Ferrage, L. Jullien, A. Kononov, A. Lemarchand, Stochastic Resonance to Control Diffusion in Chemistry, J. Phys. Chem. B, 2005, 109, 1318-1328.

2. A. Lemarchand, L. Jullien, Symmetry-Broken Reactant Motion upon Phase-Related Symmetrically Modulated Excitations: Application to Highly Selective Molecular Sorting, J. Phys. Chem. A, 2005, 109, 5770-5776.

3. H. Berthoumieux, L. Jullien, A. Lemarchand, Temporal Modulation of a Spatially Periodic Potential for Kinetically Governed Oriented Motion, J. Phys. Chem. B, 2007, 111, 2045-2051.

4. H. Berthoumieux, L. Jullien, A. Lemarchand, Response to a Temperature Modulation a Signature of Chemical Mechanisms, Phys. Rev. E, 2007, 76, 056112.

5. H. Berthoumieux, L. Jullien, A. Lemarchand, Response to a Temperature Modulation a Signature of Chemical Mechanisms, Phys. Rev. E, 2007, 76, 056112.

6. K. Zrelli, T. Barilero, E. Cavatore, H. Berthoumieux, T. Le Saux, V. Croquette, A. Lemarchand, C. Gosse, L. Jullien, Temperature Modulation and Quadrature Detection for Selective Titration of Two-State Exchanging Reactants, Anal. Chem., 2011, 83, 2476-2484