Protein mechanics probed using simple molecular models.

BACKGROUND: Single-molecule experimental techniques such as optical tweezers or atomic force microscopy are a direct probe of the mechanical unfolding/folding of individual proteins. They are also a means to investigate free energy landscapes. Protein force spectroscopy alone provides limited information; theoretical models relate measurements to thermodynamic and kinetic properties of the protein, but do not reveal atomic level information. By building a molecular model of the protein and probing its properties through numerical simulation, one can gauge the response to an external force for individual interatomic interactions and determine structures along the unfolding pathway. In combination, single-molecule force probes and molecular simulations contribute to uncover the rich behavior of proteins when subjected to mechanical force. SCOPE OF REVIEW: We focus on how simplified protein models have been instrumental in showing how general properties of the free energy landscape of a protein relate to its response to mechanical perturbations. We discuss the role of simple protein models to explore the complexity of free energy landscapes and highlight important conceptual issues that more chemically accurate models with all-atom representations of proteins and solvent cannot easily address. MAJOR CONCLUSIONS: Native-centric, coarse-grained models, despite simplifications in chemical detail compared to all-atom models, can reproduce and interpret experimental results. They also highlight instances where the theoretical framework used to interpret single-molecule data is too simple. However, these simple models are not able to reproduce experimental findings where non-native contacts are involved. GENERAL SIGNIFICANCE: Mechanical forces are ubiquitous in the cell and it is increasingly clear that the way a protein responds to mechanical perturbation is important.

Complex unfolding kinetics of single-domain proteins in the presence of force.

Single-molecule force spectroscopy is providing unique, and sometimes unexpected, insights into the free-energy landscapes of proteins. Despite the complexity of the free-energy landscapes revealed by mechanical probes, forced unfolding experiments are often analyzed using one-dimensional models that predict a logarithmic dependence of the unfolding force on the pulling velocity. We previously found that the unfolding force of the protein filamin at low pulling speed did not decrease logarithmically with the pulling speed. Here we present results from a large number of unfolding simulations of a coarse-grain model of the protein filamin under a broad range of constant forces. These show that a two-path model is physically plausible and produces a deviation from the behavior predicted by one-dimensional models analogous to that observed experimentally. We also show that the analysis of the distributions of unfolding forces (p[F]) contains crucial and exploitable information, and that a proper description of the unfolding of single-domain proteins needs to account for the intrinsic multidimensionality of the underlying free-energy landscape, especially when the applied perturbation is small.

Fluctuation power spectra reveal dynamical heterogeneity of peptides.

Characterizing the conformational properties and dynamics of biopolymers and their relation to biological activity and function is an ongoing challenge. Single molecule techniques have provided a rich experimental window on these properties, yet they have often relied on simple one-dimensional projections of a multidimensional free energy landscape for a practical interpretation of the results. Here, we study three short peptides with different structural propensity (alpha helical, beta hairpin, and random coil) in the presence (or absence) of a force applied to their ends using Langevin dynamics simulation and an all-atom model with implicit solvation. Each peptide produces fluctuation power spectra with a characteristic dynamic fingerprint consistent with persistent structural motifs of helices, hairpins, and random coils. The spectra for helix formation shows two well-defined relaxation modes, corresponding to local relaxation and cooperative coil to uncoil interconversion. In contrast, both the hairpin and random coil are polymerlike, showing a broad and continuous range of relaxation modes giving characteristic power laws of omega(-5/4) and omega(-3/2), respectively; the -5/4 power law for hairpins is robust and has not been previously observed. Langevin dynamics simulations of diffusers on a potential of mean force derived from the atomistic simulations fail to reproduce the fingerprints of each peptide motif in the power spectral density, demonstrating explicitly that such information is lacking in such one-dimensional projections. Our results demonstrate the yet unexploited potential of single molecule fluctuation spectroscopy to probe more fine scaled properties of proteins and biological macromolecules and how low dimensional projections may cause the loss of relevant information.

Direct evidence of the multidimensionality of the free-energy landscapes of proteins revealed by mechanical probes.

The study of mechanical unfolding, through the combined efforts of atomic force microscopy and simulation, is yielding fresh insights into the free-energy landscapes of proteins. Thus far, experiments have been mostly analyzed with one-dimensional models of the free-energy landscape. We show that as the two ends of a protein, filamin, are pulled apart at a speed tending to zero, the measured mechanical strength plateaus at approximately 30 pN instead of going toward zero, deviating from the Bell model. The deviation can only be explained by a switch between parallel pathways. Insightful analysis of mechanical unfolding kinetics needs to account for the multidimensionality of the free-energy landscapes of proteins, which are crucial for understanding the behavior of proteins under the small forces experienced in vivo.

Non-native interactions are critical for mechanical strength in PKD domains.

Experimental observation has led to the commonly held view that native state protein topology is the principle determinant of mechanical strength. However, the PKD domains of polycystin-1 challenge this assumption: they are stronger than predicted from their native structure. Molecular dynamics simulations suggest that force induces rearrangement to an intermediate structure, with nonnative hydrogen bonds, that resists unfolding. Here we test this hypothesis directly by introducing mutations designed to prevent formation of these nonnative interactions. We find that these mutations, which only moderately destabilize the native state, reduce the mechanical stability dramatically. The results demonstrate that nonnative interactions impart significant mechanical stability, necessary for the mechanosensor function of polycystin-1. Remarkably, such nonnative interactions result from force-induced conformational change: the PKD domain is strengthened by the application of force.

New dynamical window onto the landscape for forced protein unfolding.

The unfolding of a protein by the application of an external force pulling two atoms of the protein can be detected by atomic force and optical tweezers technologies as have been broadly demonstrated in the past decade. Variation of the applied force results in a modulation of the free-energy barrier to unfolding and thus, the rate of the process, which is often assumed to have single exponential kinetics. It has been recently shown that it is experimentally feasible, through the use of force clamps, to estimate the distribution of unfolding times for a population of proteins initially in the native state. In this Letter we show how the analysis of such distributions under a range of forces can provide unique information about the underlying free-energy surface such as the height of the free-energy barrier, the preexponential factor and the force dependence of the unfolding kinetics without resorting to ad hoc kinetic models.

Free-energy landscapes of proteins in the presence and absence of force.

The equilibrium properties of the fourth immunoglobulin domain of filamin from Dictyostelium discoideum (ddFLN4) in the absence and presence of a small force (0-6 pN) pulling the termini apart is characterized through atomistic numerical simulation. The equilibrium free-energy landscape of ddFLN4 is found to change in a complex fashion that cannot be described in terms of one-dimensional projections as usually done in the interpretation of mechanical (un)folding experiments. Nonequilibrium unfolding simulations reveal that the major unfolding intermediate corresponds to a marginally populated state at equilibrium that only appears when a force larger than 4 pN is applied. Finally, we show that if the free-energy difference between states is taken to be linear in the applied force, the proportionality coefficient is not the difference in the end-to-end distance between pair of states as generally assumed even though the data can be reasonably fitted. The present results suggest that mechanical unfolding experiments may reveal states that are not accessible in the absence of force. Thus, special care should be taken when trying to interpret both equilibrium and nonequilibrium mechanical (un)folding experiments in light of the (un)folding properties in the absence of a force.

The structure of a folding intermediate provides insight into differences in immunoglobulin amyloidogenicity.

Folding intermediates play a key role in defining protein folding and assembly pathways as well as those of misfolding and aggregation. Yet, due to their transient nature, they are poorly accessible to high-resolution techniques. Here, we made use of the intrinsically slow folding reaction of an antibody domain to characterize its major folding intermediate in detail. Furthermore, by a single point mutation we were able to trap the intermediate in equilibrium and characterize it at atomic resolution. The intermediate exhibits the basic beta-barrel topology, yet some strands are distorted. Surprisingly, two short strand-connecting helices conserved in constant antibody domains assume their completely native structure already in the intermediate, thus providing a scaffold for adjacent strands. By transplanting these helical elements into beta(2)-microglobulin, a highly homologous member of the same superfamily, we drastically reduced its amyloidogenicity. Thus, minor structural differences in an intermediate can shape the folding landscape decisively to favor either folding or misfolding.