Free energy and information-content measurements in thermodynamic and molecular ensembles

Abstract

Single-molecule experiments have emerged as a powerful tool that allow researchers to investigate the physical behavior of individual molecules with unprecedented resolution. The feasibility exerting forces at the piconewton scale (10^-12 N) and measuring nanometric displacements in the sub-millisecond scale, offer a widespread range of exciting possibilities. The major part of this thesis is devoted to address fundamental topics of statistical physics using single-molecule experiments. In particular, in the first part of the thesis, we aimed to study one of the eldest questions in statistical mechanics: the issue of ensemble inequivalence. By performing single- molecule experiments on a well-known molecule (the CD4 DNA hairpin), we have been able of exploring two conjugate ensembles: the fixed-extension and the force-fixed ensemble. Both ensembles are conjugate with respect to energy since the product force times extension equals has energy dimensions. We carried out experiments in the fixed-force ensemble using both optical tweezers and magnetic tweezers, and in the fixed-extension using optical tweezers. We have found that these two conjugate ensembles are not equivalent at the level of thermodynamics nor in kinetics. Moreover, we showed that the often-neglected boundary terms in the definition of the thermodynamic work are essential to the validity of the fluctuation theorem. The second part of this thesis is also merely theoretical. Recent single-molecule assays confirmed the connection between information theory and statistical physics. Single- molecule experiments have turned out to be the perfect playground to explore the thermodynamic implications of having —or lacking— information. It is worthwhile to mention the experimental realization of the Szilard engine and the experimental verification of Landauer’s limit. With the current existing results, the information-to- energy connection is well established. We have been able to experimentally demonstrate, for the first time, the reversed implication. We have been able to quantify the information-content of neutral molecular ensembles by means of thermodynamic measurements. That is, we experimentally demonstrated the energy- to-information conversion. Our works are built on what we call ensemble force spectroscopy, a systematic procedure capable of obtaining a robust characterization of molecular ensembles in the best tradition of statistical physics, by measuring few tens of molecules. In the final part of the thesis we aimed to measure the specific binding energy of a metallic ion to the tertiary structure of a three-way RNA junction belonging

to the central domain of the 16S ribosomal RNA (rRNA). From the physics perspective, to the best of our knowledge, first time we have been able to discern the free energy contribution due to the specific binding of magnesium ions to an RNA substrate by means of single-molecule assays. On the other hand, such molecule is able to form, besides its native conformation, a force-induced misfolded state. Despite this fact was already pointed out in previous single-molecule studies, there was a lack of knowledge regarding the molecular kinetics and the folding pathway. Aiming to fill this gap, we performed a thorough study of the three-helix RNA junction using dynamic force spectroscopy. As a result, we have characterized the full folding pathway of the molecule, including both the native and the misfolded structure. Furthermore, we have experimentally confirmed the fact that the presence of magnesium promotes the stabilization of the native structure and we have measured this contribution. We have found that magnesium is able to rescue the native structure from the misfolded structure via electrostatic interactions due to magnesium binding. This fact is biologically relevant, since we have been able to characterize the conditions in which a misfolded molecule is able to recover its native conformation.

En esta tesis hemos abordado cuestiones fundamentales de la física estadística. En particular, hemos estudiado el problema de la equivalencia entre colectivos estadísticos, la conversión de energía a información y el estudio de las energías específicas de unión de iones metálicos a sustratos de RNA. Esta tesis doctoral se ha llevado a cabo empleando dos de los instrumentos de molécula individual más conocidos, las pinzas ópticas y las pinzas magnéticas. Ambas son técnicas que permiten la aplicación controlada de fuerzas mecánicas a los extremos de una molécula individual. El poder aplicar fuerzas a sistemas moleculares permite llevar a cabo una profunda caracterización de las propiedades físicas de los llamados sistemas pequeños. Las dimensiones de estos sistemas abarcan desde unos pocos nanómetros —una millonésima parte del metro— hasta varios cientos de nanómetros. Además, los sistemas pequeños están lejos del llamado límite termodinámico y están dominados por las fluctuaciones térmicas del entorno. Por lo tanto, debido a estas peculiaridades, el estudio de sistemas pequeños mediante los instrumentos de molécula individual permite impulsar y extender los horizontes de la física de no equilibrio.