Unravelling a fulvene based Replicator: Experiment and Theory in Interplay
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A self-replicating system based on a cycloaddition of a fulvene derivative and a maleinimide is investigated using a two-pronged approach combining NMR spectroscopy with computer simulations. In the course of the reaction, two diastereomers are formed with identical rates in the absence of replication. When replication is enabled, a network emerges in which one diastereomer takes over the resources as a "selfish" autocatalyst while exploiting the competitor as a weak "altruist". The structure and dynamics of the reaction network is studied using 1 D and 2 D NMR techniques supported by dynamically averaged ab initio chemical shifts and ab initio molecular dynamics simulations. It is shown that this combination is a powerful means to understand the observed experimental behaviour in great detail.
KeywordsHigh Performance Liquid Chromatography Autocatalytic Reaction Fulvene Background Reaction Free Energy Profile
As most signals of different product isomers in the autocatalytic reaction overlapped due to structural similarities, it was impossible to determine the composition of the product mixture from 1D-NMR. Again, we applied ROESY after the reaction was completed (see Fig. 2c). The obtained spectra clearly showed that the amide NH-proton of one isomer does not undergo chemical exchange, while it was observable for the remaining two isomers. Only XX is expected to exhibit intramolecular hydrogen bonding and therefore no chemical exchange; its existence in the mixture was further supported by cross peaks indicating an exo-Diels-Alder product. The presence of XN could be ruled out by the following reasoning: ROESY spectra and HPLC plots of the background reaction using methylester A' did not show any exo-products. The occurence of an exo-product in the presence of recognition sites then means that a recognition-mediated reaction pathway is exploited. Such a pathway is only available for the XX isomer via an A·B-complex. The remaining two products were identified as the NN (main product) and NX isomers (side product).
Although the composition of the experimental product mixture could be elucidated by 2D-NMR and calculated free energy profiles, an assignment of isomers to 1D-NMR signals was still necessary for a kinetic modelling of the system. The assignment of the NN isomer is straightforward, as it is the main product, but it is difficult to distinguish between the NX and XX isomer on the basis of the available data. For a direct assignment of the experimental NMR spectra we calculated thermally averaged ab initio chemical shifts. A comparison of calculated and experimental shifts for the set of non-overlapping protons used to extract time-dependent concentrations (see Fig. 2a/b) shows a remarkable agreement for both isomers with a deviation of just 0.05 ppm for XX and 0.03 ppm for NX, respectively. Our final assignment was supported by these shifts and corroborated by the fact that an inverse assignment did not allow for a good fit of the experimental kinetic data to models that were in accordance with results from our calculations. A 16:1 diastereoselectivity for NN was determined by integration of the respective NMR peaks, which is a true emergent property, as it results exclusively from the interactions between templates and precursors. It even reverses the slight selectivity for NX in the background reaction.
Our kinetic model was constructed based on information about possible reaction channels from AIMD simulations (see Figs. 1 and 4). Complex equilibria of A·B·NN and A·B·NX complexes were modeled with the same association constant, while A·B·NX* was modeled with a separate association constant to account for different relative complex energies. For the same reason all three duplex equilibria were attributed different association constants. Different rate constants were assigned to autocatalytic and crosscatalytic ligations. The rate constant for uncatalyzed reactions to NN and NX was known from separate measurements of the background reaction. Complex associations were assumed to be limited only by diffusion. In order to quantify the rate constants for these processes separate classical MD simulations of A, B and NN in chloroform were performed and the diffusion constant -- which is proportional to the rate constant in this scenario -- was determined from the center-of-mass mean square displacement via the Einstein relation. Thus we arrived at rate constants of the order of 1010 M-1s -1 for all diffusion limited processes. Kinetic data was fitted to the model using Simfit  to obtain rate and equilibrium constants. According to the model, the cycloaddition of A+B is rather efficiently catalyzed in the presence of NN or NX, the rate constant kauto being about 50 times larger than knon for a non-catalyzed background reaction (corresponding to an effective kinetic molarity of 50 M). The crosscatalytic mechanism is less efficient, its rate constant kcross is predicted to be approximately one half of kauto, which is in agreement with our calculated free energy profiles. Furthermore, kauto is four orders of magnitude larger than the rate constant kXX of the XX formation via an AB channel. This means, although still present, this undesirable pathway is sufficiently suppressed. Template duplexes are predicted to be more stable than termolecular complexes, suggesting that the system suffers from product inhibition. Interestingly, association constants for different termolecular complexes and duplexes reflect the relative order of calculated complex energies. All in all, the model is able to describe the dynamic behaviour of the system very well. Nevertheless, one has to keep in mind the system's complexity and very limited amount of accessible observables. As a consequence, kinetic and thermodynamic parameters obtained by kinetic fitting cannot be expected to be highly accurate. On the other hand, our method allowed us to construct a meaningful model in the first place, which would have been impossible without access to free energy profiles of all major reaction paths.
Complex reaction networks with interesting dynamic signatures in which obstacles like chemical lability or similarity lead to an incomplete base of solid chemical knowledge are expected to challenge chemistry in the future. Our approach of merging experimental NMR kinetics with ab initio dynamical chemical shifts and free energy landscapes enabled us to comprehend a dynamic puzzle which otherwise would have had to remain unsolved.
This work was supported by FP6-IST/FET IP "Pace", COST Action CM0703 "Systems Chemistry", FP7-IST/FET Projects ECCELL, MATCHIT and Thomas Young Centre, London.
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