Determination of thermodynamics and kinetics of RNA reactions by force

Abstract

1. Introduction 326

2. Instrumentation 328

2.1 Instruments to study mechanical properties of RNA 328

2.1.1 AFM 328

2.1.2 Magnetic tweezers 328

2.1.3 Optical tweezers 330

2.2 Optical trap instrumentation 330

2.3 Calibrations 332

2.3.1 Calibration of trap stiffness 332

2.3.2 Calibration of force 333

2.3.3 Calibration of distance 334

2.4 Types of experiments 334

2.4.1 Force-ramp 334

2.4.2 Force-clamp or constant-force experiments 335

2.4.3 Extension-clamp or constant extension experiments 335

2.4.4 Force-jump, Force-drop 336

2.4.5 Passive mode 336

3. Thermodynamics 336

3.1 Reversibility 336

3.2 Gibbs free energy 337

3.2.1 Stretching free energy 338

3.2.1.1 Rigid molecules 338

3.2.1.2 Compliant or flexible molecules 339

3.2.2 Free energy of a reversible unfolding transition 339

3.2.3 Free energy of unfolding at zero force 340

3.2.4 Free energy of an irreversible unfolding transition 340

3.2.4.1 Jarzynski's method 341

3.2.4.2 Crooks fluctuation theorem 343

4. Kinetics 345

4.1 Measuring rate constants 345

4.1.1 Hopping 345

4.1.2 Force-jump, Force-drop 347

4.1.3 Force-ramp 348

4.1.4 Instrumental effects 350

4.2 Kinetic mechanisms 351

4.2.1 Free-energy landscapes 351

4.2.2 Kinetics of unfolding 353

5. Relating force-measured data to other measurements 354

5.1 Thermodynamics 354

5.2 Kinetics 357

6. Acknowledgements 357

7. References 358

Single-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.