Publication: Models for chiral amplification in spontaneous mirror symmetry breaking
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2014-10-30
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Universidad Complutense de Madrid
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Abstract
Es un hecho empírico que hay un desequilibrio quiral absoluto (o ruptura de simetría especular) en todos los sistemas biológicos conocidos, dónde los procesos cruciales para la vida, como la replicación, implican estructuras supramoleculares que comparten el mismo signo quiral (homoquiralidad). Estas estructuras quirales son proteinas, compuestas de amino ácidos encontrados como L-enantiómeros; y polímeros de ADN y ARN y azúcares, compuestos de R-monocarbohidratos. Basándonos en el hecho de que es quimicamente imposible lograr una mezcla perfectamente racémica por motivos puramente estadísticos, podemos asumir la presencia de un pequeño exceso enantiomérico inevitable incluso en una mezcla racémica ’perfecta’. Entonces, en principio, el origen y la evolución de la homoquiralidad biológica y de la ruptura espontánea de simetría especular (Spontaneous Mirror Symmetry Breaking, SMSB) en los sistemas químicos y biológicos podrían explicarse teóricamente mediante un modelo en el cual un pequeño desequilibrio entre enantiómeros es amplificado, y el camino más probable para ello es mediante reacciones autocatalíticas. Nuestro principal propósito aquí es probar la capacidad de varios modelos autocatalíticos diferentes de amplificar un exceso enantiomérico inicial, ee0, incluso por debajo del desequilibrio esperado (es decir, ee0 < eest). En este contexto, introducimos y estudiamos el sistema autocatálitico más básico conocido conducente a la amplificación quiral - modelo de Frank - y su capacidad para amplificar las pequeñas desviaciones estadísticas iniciales respecto de la composición racémica ideal. Dependiendo las condiciones, esta amplificación puede ser sólo temporal, y puede ser interpretada como una excursión quiral en un espacio de fases dinámicas. Estas excursiones quirales se pueden estudiar a través de una combinación de análisis del espacio de fases, análisis de estabilidad y simulaciones numéricas, con el fin de determinar la forma en que dependen de si el sistema es abierto, semiabierto o cerrado. También la emergencia de homoquiralidad en autocatálisis enantioselectiva de compuestos que no pueden transformarse según el conjunto de reacciones de tipo Frank es discutida, con respecto al controvertido modelo de enantioselectividad ( Limited Enantioselectivity, LES ), integrado por autocatálisis enantioselectiva y no enantioselectiva copladas, y que no puede conducir a SMSB en sistemas cerrados. Ya que la homoquiralidad biológica de los sistemas vivos implica grandes macromoléculas, la capacidad de amplificar (y transmitir a todo el sistema)esos pequeños excesos enantioméricos es estudiada para dos modelos cinéticos diferentes de polimerización y copolimerización quiral en sistemas cerrados al flujo de materia y de energía, y mostramos los resultados de ajustar el modelo de copolimerización a los datos experimentales de amplificación quiral de oligopéptidos.Por último, tanto un modelo de equilibrio químico de copolimerización por control de plantillas como un enfoque probabilístico se presentan para describir los resultados de los escenarios experimentales de desimetrización inducida propuestos recientemente por Lahav y su grupo; estos mecanismos de amplificación quirales tienen lugar mediante polimerización controlada por láminas β racémicas, tanto en cristalitos en superficie como en solución. En este caso, la ruptura de simetráa surge de la combinatoria, y no de fenómenos espontáneos (bifurcación). Estos efectos estadísticos /combinatorios/estocásticos no se deben a las pequeñas fluctuaciones inherentes quirales presentes en todos los sistemas químicos reales, sino a la oclusión aleatoria de aminoácidos anfitriones y huéspedes por los sitios quirales de la plantilla: los mecanismos propuestos aquí funcionan aún para las mezclas racémicas idealmente
It is an empirical fact that there is an absolute chiral imbalance (or mirror symmetry breaking) in all known biological systems, where processes crucial for life such as replication, imply chiral supramolecular structures, sharing the same chiral sign (homochirality). These chiral structures are proteins, composed of amino acids found as the left-handed enantiomers (L); and DNA, and RNA polymers and sugars, composed of right-handed (R) monocarbohydrates. Based on the fact that a perfect racemic mixture is chemically impossible to achieve on purely statistical grounds alone, we can assume the presence of an unavoidable tiny enantiomeric excess even in a ’perfect’ racemic mixture. Then, in principle, the origin and evolution of biological homochirality and Spontaneous Mirror Symmetry Breaking (SMSB) in chemical and biological systems could be theoretically explained by a model in which a tiny imbalance of one enantiomer was amplified, and the most likely path for this is by autocatalytic reactions. Our main purpose here is to test the ability of some different autocatalytic models to amplify a tiny initial enantiomeric excess, ee0, even lower than the expected inherent imbalance (i.e., using ee0 < eest). Then, in this context, we introduce and study the most basic known autocatalytic system leading to chiral amplification- the Frank model - and its ability to amplify the initial small statistical deviations from the idealized racemic composition. Depending on the conditions, this amplification can be just temporary, and it can be interpreted as a chiral excursion in a dynamic phase space. These chiral excursions can be studied through a combination of phase space analysis, stability analysis and numerical simulations in order to determine how they depend on whether the system is open, semi-open or closed. Also the emergence of homochirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non- nantioselective autocatalyses, which cannot lead to SMSB in closed systems. Since biological homochirality of living systems involves large macromolecules, the ability to amplify (and transmit to the entire system) those small initial enantiomeric excesses is studied for two different kinetic models of chiral polymerization and copolymerization in systems closed to matter and energy flow, and the results from fitting the copolymerization model to the experimental data on chiral amplification of oligopeptides are shown. Finally, both a chemical equilibrium model of template-controlled copolymerization and a probabilistic approach are presented for describing the outcome of the experimental induced desymmetrization scenarios recently proposed by Lahav and co-workers; these chiral amplification mechanisms proceed through racemic β-sheet controlled polymerization operative in both surface crystallites as well as in solution. In this case, the symmetry breaking arises from combinatorics, not from spontaneous (bifurcation) phenomena. These stochastic/statistical/combinatorial effects are not due to the inherent tiny chiral fluctuations present in all real chemical systems, but are due rather to the random occlusion of host and guest amino acids by the chiral sites of the template: the mechanisms proposed here work even for ideally racemic mixtures.
It is an empirical fact that there is an absolute chiral imbalance (or mirror symmetry breaking) in all known biological systems, where processes crucial for life such as replication, imply chiral supramolecular structures, sharing the same chiral sign (homochirality). These chiral structures are proteins, composed of amino acids found as the left-handed enantiomers (L); and DNA, and RNA polymers and sugars, composed of right-handed (R) monocarbohydrates. Based on the fact that a perfect racemic mixture is chemically impossible to achieve on purely statistical grounds alone, we can assume the presence of an unavoidable tiny enantiomeric excess even in a ’perfect’ racemic mixture. Then, in principle, the origin and evolution of biological homochirality and Spontaneous Mirror Symmetry Breaking (SMSB) in chemical and biological systems could be theoretically explained by a model in which a tiny imbalance of one enantiomer was amplified, and the most likely path for this is by autocatalytic reactions. Our main purpose here is to test the ability of some different autocatalytic models to amplify a tiny initial enantiomeric excess, ee0, even lower than the expected inherent imbalance (i.e., using ee0 < eest). Then, in this context, we introduce and study the most basic known autocatalytic system leading to chiral amplification- the Frank model - and its ability to amplify the initial small statistical deviations from the idealized racemic composition. Depending on the conditions, this amplification can be just temporary, and it can be interpreted as a chiral excursion in a dynamic phase space. These chiral excursions can be studied through a combination of phase space analysis, stability analysis and numerical simulations in order to determine how they depend on whether the system is open, semi-open or closed. Also the emergence of homochirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non- nantioselective autocatalyses, which cannot lead to SMSB in closed systems. Since biological homochirality of living systems involves large macromolecules, the ability to amplify (and transmit to the entire system) those small initial enantiomeric excesses is studied for two different kinetic models of chiral polymerization and copolymerization in systems closed to matter and energy flow, and the results from fitting the copolymerization model to the experimental data on chiral amplification of oligopeptides are shown. Finally, both a chemical equilibrium model of template-controlled copolymerization and a probabilistic approach are presented for describing the outcome of the experimental induced desymmetrization scenarios recently proposed by Lahav and co-workers; these chiral amplification mechanisms proceed through racemic β-sheet controlled polymerization operative in both surface crystallites as well as in solution. In this case, the symmetry breaking arises from combinatorics, not from spontaneous (bifurcation) phenomena. These stochastic/statistical/combinatorial effects are not due to the inherent tiny chiral fluctuations present in all real chemical systems, but are due rather to the random occlusion of host and guest amino acids by the chiral sites of the template: the mechanisms proposed here work even for ideally racemic mixtures.
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Óptica, leída el 23-05-2014. Tesis formato europeo (compendio de artículos)