Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.     

Fluctuations of primary ubiquitin folding intermediates in a force clamp

Folding experiments of single ubiquitin molecules under force clamp using an atomic force microscope revealed a dynamic long-lived intermediate with nanometer scale end-to-end distance fluctuations along an unexpectedly complex folding pathway. To examine the nature of this intermediate at the atomic level as well as the driving forces that give rise to the observed fluctuations, we performed molecular dynamics refolding simulations of unfolded ubiquitin under constant force. After an initial fast collapse, we find a highly dynamic, broad ensemble of conformations with partial and continuously changing secondary structure and side chain interactions. This ensemble resembles a molten-globule-like state, similar in nature to the previously described non-native state of ubiquitin in solution, but stretched by the external force. The scale of the end-to-end distance fluctuations derived from the simulations compares well with experiment. Transient formation of unspecific and metastable hydrophobic clusters along the chain are found to give rise to the observed end-to-end distance fluctuations. These distinct collapses, interpreted as folding attempts, imply an upper limit for the folding attempt frequency of approximately 10 ns. Our results suggest possible relations between force-induced unfolding and temperature or chemically induced denaturation.     

Quantitative study of polymer conformation and dynamics by single-particle tracking

We present a new method for analyzing the dynamics of conformational fluctuations of individual flexible polymer molecules. In single-particle tracking (SPT), one end of the polymer molecule is tethered to an immobile substratum. A microsphere attached to the other end serves as an optical marker. The conformational fluctuations of the polymer molecule can be measured by optical microscopy via the motion of the microsphere. The bead-and-spring theory for polymer dynamics is further developed to account for the microsphere, and together the measurement and the theory yield quantitative information about molecular conformations and dynamics under nonperturbing conditions. Applying the method to measurements carried out on DNA molecules provides information complementary to recent studies of single DNA molecules under extensional force. Combining high precision measurements with the theoretical analysis presented here creates a powerful tool for studying conformational dynamics of biological and synthetic macromolecules at the single-molecule level.     

How Do We Know when Single-Molecule Force Spectroscopy Really Tests Single Bonds?

Single-molecule force spectroscopy makes it possible to measure the mechanical strength of single noncovalent receptor-ligand-type bonds. A major challenge in this technique is to ensure that measurements reflect bonds between single biomolecules because the molecules cannot be directly observed. This perspective evaluates different methodologies for identifying and reducing the contribution of multiple molecule interactions to single-molecule measurements to help the reader design experiments or assess publications in the single-molecule force spectroscopy field. We apply our analysis to the large body of literature that purports to measure the strength of single bonds between biotin and streptavidin as a demonstration that measurements are only reproducible when the most reliable methods for ensuring single molecules are used.     

Comparative energy measurements in single molecule interactions

Single molecule experiments have opened promising new avenues of investigations in biology, but the quantitative interpretation of results remains challenging. In particular, there is a need for a comparison of such experiments with theoretical methods. We experimentally determine the activation free energy for single molecule interactions between two synaptic proteins syntaxin 1A and synaptobrevin 2, using an atomic force microscope and the Jarzynski equality of nonequilibrium thermodynamics. The value obtained is shown to be reasonably consistent with that from single molecule reaction rate theory. The temperature dependence of the spontaneous dissociation lifetime along with different pulling speeds is used to confirm the approach to the adiabatic limit. This comparison of the Jarzynski equality for intermolecular interactions extends the procedure for calculation of activation energies in nonequilibrium processes.     

Massively Parallel Single-Molecule Manipulation Using Centrifugal Force

Precise manipulation of single molecules has already led to remarkable insights in physics, chemistry, biology, and medicine. However, widespread adoption of single-molecule techniques has been impeded by equipment cost and the laborious nature of making measurements one molecule at a time. We have solved these issues by developing an approach that enables massively parallel single-molecule force measurements using centrifugal force. This approach is realized in an instrument that we call the centrifuge force microscope in which objects in an orbiting sample are subjected to a calibration-free, macroscopically uniform force-field while their micro-to-nanoscopic motions are observed. We demonstrate high-throughput single-molecule force spectroscopy with this technique by performing thousands of rupture experiments in parallel, characterizing force-dependent unbinding kinetics of an antibody-antigen pair in minutes rather than days. Additionally, we verify the force accuracy of the instrument by measuring the well-established DNA overstretching transition at 66 ± 3 pN. With significant benefits in efficiency, cost, simplicity, and versatility, single-molecule centrifugation has the potential to expand single-molecule experimentation to a wider range of researchers and experimental systems.     

Mechanical Coupling between Myosin Molecules Causes Differences between Ensemble and Single-Molecule Measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.     

Sub-angstrom conformational changes of a single molecule captured by AFM variance analysis

A system's equilibrium variance can be analyzed to probe its underlying dynamics at higher resolution. Here, using single-molecule atomic-force microscope techniques, we show how the variance in the length of a single dextran molecule can be used to establish thermodynamic equilibrium and to detect conformational changes not directly observable with other methods. Dextran is comprised of a chain of pyranose rings that each undergoes an Angstrom-scale transition from a chair to boat conformation under a stretching force. Our analysis of the variance of the molecule's fluctuations verifies equilibrium throughout the force-extension curve, consistent with the expected thermodynamic ensemble. This validates further analysis of the variance in the transition region, which reveals an intermediate conformation between the chair and the boat on the sub-Angstrom scale. Our test of thermal equilibrium as well as our variance analysis can be readily extended to a wide variety of molecules, including proteins.     

Investigating Single Molecule Adhesion by Atomic Force Spectroscopy

Atomic force spectroscopy is an ideal tool to study molecules at surfaces and interfaces. An experimental protocol to couple a large variety of single molecules covalently onto an AFM tip is presented. At the same time the AFM tip is passivated to prevent unspecific interactions between the tip and the substrate, which is a prerequisite to study single molecules attached to the AFM tip. Analyses to determine the adhesion force, the adhesion length, and the free energy of these molecules on solid surfaces and bio-interfaces are shortly presented and external references for further reading are provided. Example molecules are the poly(amino acid) polytyrosine, the graft polymer PI-g-PS and the phospholipid POPE (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine). These molecules are desorbed from different surfaces like CH₃-SAMs, hydrogen terminated diamond and supported lipid bilayers under various solvent conditions. Finally, the advantages of force spectroscopic single molecule experiments are discussed including means to decide if truly a single molecule has been studied in the experiment.     

Single molecule thermodynamics in biological motors

Biological molecular machines use thermal activation energy to carry out various functions. The process of thermal activation has the stochastic nature of output events that can be described according to the laws of thermodynamics. Recently developed single molecule detection techniques have allowed each distinct enzymatic event of single biological machines to be characterized providing clues to the underlying thermodynamics. In this study, the thermodynamic properties in the stepping movement of a biological molecular motor have been examined. A single molecule detection technique was used to measure the stepping movements at various loads and temperatures and a range of thermodynamic parameters associated with the production of each forward and backward step including free energy, enthalpy, entropy and characteristic distance were obtained. The results show that an asymmetry in entropy is a primary factor that controls the direction in which the motor will step. The investigation on single molecule thermodynamics has the potential to reveal dynamic properties underlying the mechanisms of how biological molecular machines work.     

Intramolecular dynamics of chain molecules monitored by fluctuations in efficiency of excitation energy transfer. A theoretical study.

The fluorescence quantum yield of a polymer molecule to which an energy donor chromophore and an energy acceptor chromophore are attached depends on the distance between the donor and acceptor chromophores. If this distance fluctuates with time, the fluorescence intensity is expected to fluctuate as well, and the time course of the intensity fluctuations will be correlated with the time course of the changes in the interchromophore distance. The intensity fluctuations are experimentally measurable if the number of illuminated molecules is small. A theoretical treatment of such fluorescence intensity fluctuations is presented in terms of a parameter that describes the polymer chain dynamics. Computer simulations were performed to illustrate the dependence of the autocorrelation function of the intensity fluctuations on the polymer chain conformation, the interchromophore energy transfer properties, and the macromolecular dynamics. These simulations demonstrate that the intensity fluctuations due to nonradiative energy transfer between chromophores attached to polymer chains can be large enough to be experimentally useful in the study of intramolecular dynamics of macromolecules.     

Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics

During the last 15 years, scientists have developed methods that permit the direct mechanical manipulation of individual molecules. Using this approach, they have begun to investigate the effect of force and torque in chemical and biochemical reactions. These studies span from the study of the mechanical properties of macromolecules, to the characterization of molecular motors, to the mechanical unfolding of individual proteins and RNA. Here I present a review of some of our most recent results using mechanical force to unfold individual molecules of RNA. These studies make it possible to follow in real time the trajectory of each molecule as it unfolds and characterize the various intermediates of the reaction. Moreover, if the process takes place reversibly it is possible to extract both kinetic and thermodynamic information from these experiments at the same time that we characterize the forces that maintain the three-dimensional structure of the molecule in solution. These studies bring us closer to the biological unfolding processes in the cell as they simulate in vitro, the mechanical unfolding of RNAs carried out in the cell by helicases. If the unfolding process occurs irreversibly, I show here that single-molecule experiments can still provide equilibrium, thermodynamic information from non-equilibrium data by using recently discovered fluctuation theorems. Such theorems represent a bridge between equilibrium and non-equilibrium statistical mechanics. In fact, first derived in 1997, the first experimental demonstration of the validity of fluctuation theorems was obtained by unfolding mechanically a single molecule of RNA. It is perhaps a sign of the times that important physical results are these days used to extract information about biological systems and that biological systems are being used to test and confirm fundamental new laws in physics.     

Force spectroscopy with single bio-molecules

For many biological molecules, force is an important functional and structural parameter. With the rapidly growing knowledge about the relation between structure, function, and force, single-molecule force spectroscopy has become a versatile analytical tool for the structural and functional investigation of single bio-molecules in their native environments. Within the past year, detailed insights into binding potentials of receptor ligand pairs, protein folding pathways, molecular motors, DNA mechanics and the functioning of DNA-binding agents (such as proteins and drugs), as well as the function of molecular motors, have been obtained.     

Measurement of Mesoscale Conformational Dynamics of Freely Diffusing Molecules with Tracking FCS

Few techniques are suited to probe the structure and dynamics of molecular complexes at the mesoscale level ($～$100–1000 nm). We have developed a single-molecule technique that uses tracking fluorescence correlation spectroscopy (tFCS) to probe the conformation and dynamics of mesoscale molecular assemblies. tFCS measures the distance fluctuations between two fluorescently labeled sites within an untethered, freely diffusing biomolecule. To achieve subdiffraction spatial resolution, we developed a feedback scheme that allows us to maintain the molecule at an optimal position within the laser intensity gradient for fluorescence correlation spectroscopy. We characterized tFCS spatial sensitivity by measuring the Brownian end-to-end dynamics of DNA molecules as short as 1000 bp. We demonstrate that tFCS detects changes in the compaction of reconstituted nucleosome arrays and can assay transient protein-mediated interactions between distant sites in an individual DNA molecule. Our measurements highlight the applicability of tFCS to a wide variety of biochemical processes involving mesoscale conformational dynamics.     

Sacrificial bonds and hidden length: unraveling molecular mesostructures in tough materials

Sacrificial bonds and hidden length in structural molecules and composites have been found to greatly increase the fracture toughness of biomaterials by providing a reversible, molecular-scale energy-dissipation mechanism. This mechanism relies on the energy, of order 100 eV, needed to reduce entropy and increase enthalpy as molecular segments are stretched after being released by the breaking of weak bonds, called sacrificial bonds. This energy is relatively large compared to the energy needed to break the polymer backbone, of order a few eV. In many biological cases, the breaking of sacrificial bonds has been found to be reversible, thereby additionally providing a "self-healing" property to the material. Due to the nanoscopic nature of this mechanism, single molecule force spectroscopy using an atomic force microscope has been a useful tool to investigate this mechanism. Especially when investigating natural molecular constructs, force versus distance curves quickly become very complicated. In this work we propose various types of sacrificial bonds, their combination, and how they appear in single molecule force spectroscopy measurements. We find that by close analysis of the force spectroscopy curves, additional information can be obtained about the molecules and their bonds to the native constructs.     

Multi-nanopore force spectroscopy for DNA analysis

The need for low-cost DNA sequence detection in clinical applications is driving development of new technologies. We demonstrate a method for detection of mutations in a DNA sequence purely by electronic means, and without need for fluorescent labeling. Our method uses an array of nanopores to perform synchronized single-molecule force spectroscopy measurements over many molecules in parallel, yielding detailed information on the kinetics of hundreds of molecule dissociations in a single measurement.     

Localization accuracy in single-molecule microscopy

One of the most basic questions in single-molecule microscopy concerns the accuracy with which the location of a single molecule can be determined. Using the Fisher information matrix it is shown that the limit of the localization accuracy for a single molecule is given by, lambda(em)/2pi n(a) square root of gammaAt, where lambda(em), n(a), gamma, A, and t denote the emission wavelength of the single molecule, the numerical aperture of the objective, the efficiency of the optical system, the emission rate of the single molecule and the acquisition time, respectively. Using Monte Carlo simulations it is shown that estimation algorithms can come close to attaining the limit given in the expression. Explicit quantitative results are also provided to show how the limit of the localization accuracy is reduced by factors such as pixelation of the detector and noise sources in the detection system. The results demonstrate what is achievable by single-molecule microscopy and provide guidelines for experimental design.     

Force spectroscopy of the double-tethered concanavalin-A mannose bond

We present the measurement of the force required to rupture a single protein-sugar bond using a methodology that provides selective discrimination between specific and nonspecific binding events and helps verify the presence of a single functional molecule on the atomic force microscopy tip. In particular, the interaction force between a polymer-tethered concanavalin-A protein (ConA) and a similarly tethered mannose carbohydrate was measured as 47 +/- 9 pN at a bond loading rate of approximately 10 nN/s. Computer simulations of the polymer molecular configurations were used to determine the angles that the polymers could sweep out during binding and, in conjunction with mass spectrometry, used to separate the angular effects from the effects due to a distribution of tether lengths. We find that when using commercially available polymer tethers that vary in length from 19 to 29 nm, the angular effects are relatively small and the rupture distributions are dominated by the 10-nm width of the tether length distribution. In all, we show that tethering both a protein and its ligand allows for the determination of the single-molecule bond rupture force with high sensitivity and includes some validation for the presence of a single-tethered functional molecule on the atomic force microscopy tip.     

The effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.     

Mechanical design of proteins studied by single-molecule force spectroscopy and protein engineering

Mechanical unfolding and refolding may regulate the molecular elasticity of modular proteins with mechanical functions. The development of the atomic force microscopy (AFM) has recently enabled the dynamic measurement of these processes at the single-molecule level. Protein engineering techniques allow the construction of homomeric polyproteins for the precise analysis of the mechanical unfolding of single domains. alpha-Helical domains are mechanically compliant, whereas beta-sandwich domains, particularly those that resist unfolding with backbone hydrogen bonds between strands perpendicular to the applied force, are more stable and appear frequently in proteins subject to mechanical forces. The mechanical stability of a domain seems to be determined by its hydrogen bonding pattern and is correlated with its kinetic stability rather than its thermodynamic stability. Force spectroscopy using AFM promises to elucidate the dynamic mechanical properties of a wide variety of proteins at the single molecule level and provide an important complement to other structural and dynamic techniques (e.g., X-ray crystallography, NMR spectroscopy, patch-clamp).