Determination of thermodynamics and kinetics of RNA reactions by force

Abstract

1. Introduction 3262. Instrumentation 3282.1 Instruments to study mechanical properties of RNA 3282.1.1 AFM 3282.1.2 Magnetic tweezers 3282.1.3 Optical tweezers 3302.2 Optical trap instrumentation 3302.3 Calibrations 3322.3.1 Calibration of trap stiffness 3322.3.2 Calibration of force 3332.3.3 Calibration of distance 3342.4 Types of experiments 3342.4.1 Force-ramp 3342.4.2 Force-clamp or constant-force experiments 3352.4.3 Extension-clamp or constant extension experiments 3352.4.4 Force-jump, Force-drop 3362.4.5 Passive mode 3363. Thermodynamics 3363.1 Reversibility 3363.2 Gibbs free energy 3373.2.1 Stretching free energy 3383.2.1.1 Rigid molecules 3383.2.1.2 Compliant or flexible molecules 3393.2.2 Free energy of a reversible unfolding transition 3393.2.3 Free energy of unfolding at zero force 3403.2.4 Free energy of an irreversible unfolding transition 3403.2.4.1 Jarzynski's method 3413.2.4.2 Crooks fluctuation theorem 3434. Kinetics 3454.1 Measuring rate constants 3454.1.1 Hopping 3454.1.2 Force-jump, Force-drop 3474.1.3 Force-ramp 3484.1.4 Instrumental effects 3504.2 Kinetic mechanisms 3514.2.1 Free-energy landscapes 3514.2.2 Kinetics of unfolding 3535. Relating force-measured data to other measurements 3545.1 Thermodynamics 3545.2 Kinetics 3576. Acknowledgements 3577. References 358Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force.