Study of the reaction mechanism in Mandelate racemase enzyme: reaction path and dynamical sampling approaches

En aquesta tesi s'ha dissenyat i aplicat diferents eines teoriques i computacionals per a l'estudi de la reactivitat de l'enzim Mandelat Racemasa. L'enzim Mandelat Racemasa catalitza la interconversio dels dos enantiomers (S) i (R) de l'acid mandelic a una velocitat semblant. El mecanisme de reaccio que es postula experimentalment passa per l'abstraccio d'un proto molt poc acid. Aquesta reaccio molt poc favorable en medi aquos l'enzim la catalitza a una velocitat sorprenentment alta. Fent un estudi Mecanica Quantica / Mecanica Molecular (QM/MM) de la reactivitat de l'enzim s'han trobat els intermedis i les barreres de reaccio que permeten deduir tres mecanismes a traves dels quals el substracte natural mandelat i altres dos substractes analegs poden racemitzar. Expliquem de quina manera l'enzim pot fer la catalisi tant efectiva i equivalent per als dos enantiomers. Partint de la necessitat de millorar l'estudi QM/MM anterior, sobretot pel que fa a l'acurada localitzacio dels estats de transicio (barreres reaccio), s'ha dissenyat un metode d'optimitzacio d'estructures per ser aplicat a sistemes de milers d'atoms com ho es el nostre enzim. El metode anomenat micro-iteratiu es basa en una cerca segons les equacions Rational Function Optimization (RFO) en una zona reduida mentre es minimitza l'entorn amb un metode computacionalment barat com el LBFGS. Aquest metode micro-iteratiu ha estat formulat, implementat i testejat en sistemes moleculars grans i petits. Se n'ha estudiat les diferents opcions donant una recepta practica per al seu us en altres reaccions. Tambe se n'ha justificat el seu desenvolupament posant de relleu les millores obtingudes amb aquest nou metode quan es comparen els nous resultats amb els obtinguts en l'estudi QM/MM inicial. Finalment, l'energia lliure de la reaccio enzimatica s'ha calculat amb tecniques de la dinamica molecular i de l'Umbrella Sampling. Per aquest tipus de calcul es imprescindible escollir a priori una coordenada de reaccio que permeti anar de reactius a productes, en altres paraules, es necessari saber com te lloc la reaccio. Gracies a la previa localitzacio d'estats de transicio amb el metode micro-iteratiu podem coneixer el mecanisme de reaccio. I per tant podem emprar una coordenada de reaccio adequada que ens permet calcular l'energia lliure de reaccio de forma efectiva. In this thesis several theoretical techniques to study the Mandelate Racemase enzyme reactivity are designed and used. The Mandelate Racemase enzyme catalyses the interconversion of both enantiomers (S) and (R) of mandelic acid at apparently the same rate. Experimental results suggest that the reaction mechanism takes place through the abstraction of a non-acid hydrogen. This reaction is very low in aqueous media but the enzyme catalyzes it at an extremely fast rate. We carry out a QM/MM study of the enzyme reativity. We have found the intermediate structures and the energy barriers corresponding to three proposed mechanisms that the natural substrate mandelate and two other substrate analogues may undergo. We are able to explain how the the efficient catalysis is performed for the two enantiomers. Due to the lack in the previous QM/MM study of an efficient method to locate transition state structures (energy barriers) we have designed an structure optimization method to be applied to systems constituted by thousands of atoms such as our enzyme. The so-called micro-iterative method consists in a search based on the Rational Function Optimization (RFO) equations applied in a core zone while the environment is minimized through a computationally affordable method such as LBFGS. The micro-iterative method has been formulated, implemented and tested for small and big molecular systems. We have studied several possible options giving as a result a practical guide for its usage in other reactions. Comparing the results coming from the initial QM/MM study with the ones found by this micro-iterative method we show an improvement that justifies the development. Finally, the free energy corresponding to the enzymatic reaction is calculated by means of Molecular Dynamics and Umbrella Sampling techniques. The free energy computation requires the a priori election of a reaction coordinate that allows the system to go from reactants to products. In other words, it is essential to know how the reaction takes place. Thanks to the accurate search of transition states performed previously by the micro-iterative we can find the reaction mechanism. In this sense we can use an adequate reaction coordinate that permits us an efficient calculation of the reaction free energy.