Helicase processivity and not the unwinding velocity exhibits universal increase with force.

Helicases, involved in a number of cellular functions, are motors that translocate along single-stranded nucleic acid and couple the motion to unwinding double-strands of a duplex nucleic acid. The junction between double- and single-strands creates a barrier to the movement of the helicase, which can be manipulated in vitro by applying mechanical forces directly on the nucleic acid strands. Single-molecule experiments have demonstrated that the unwinding velocities of some helicases increase dramatically with increase in the external force, while others show little response. In contrast, the unwinding processivity always increases when the force increases. The differing responses of the unwinding velocity and processivity to force have lacked explanation. By generalizing a previous model of processive unwinding by helicases, we provide a unified framework for understanding the dependence of velocity and processivity on force and the nucleic acid sequence. We predict that the sensitivity of unwinding processivity to external force is a universal feature that should be observed in all helicases. Our prediction is illustrated using T7 and NS3 helicases as case studies. Interestingly, the increase in unwinding processivity with force depends on whether the helicase forces basepair opening by direct interaction or if such a disruption occurs spontaneously due to thermal fluctuations. Based on the theoretical results, we propose that proteins like single-strand binding proteins associated with helicases in the replisome may have coevolved with helicases to increase the unwinding processivity even if the velocity remains unaffected.

Force-induced unzipping transitions in an athermal crowded environment.

Using theoretical arguments and extensive Monte Carlo (MC) simulations of a coarse-grained three-dimensional off-lattice model of a ß-hairpin, we demonstrate that the equilibrium critical force, Fc, needed to unfold the biopolymer increases nonlinearly with increasing volume fraction occupied by the spherical macromolecular crowding agent. Both scaling arguments and MC simulations show that the critical force increases as Fc ≈ φc(α). The exponent α is linked to the Flory exponent relating the size of the unfolded state of the biopolymer and the number of amino acids. The predicted power law dependence is confirmed in simulations of the dependence of the isothermal extensibility and the fraction of native contacts on φc. We also show using MC simulations that Fc is linearly dependent on the average osmotic pressure (P) exerted by the crowding agents on the ß-hairpin. The highly significant linear correlation coefficient of 0.99657 between Fc and P makes it straightforward to predict the dependence of the critical force on the density of crowders. Our predictions are amenable to experimental verification using laser optical tweezers.

Refolding dynamics of stretched biopolymers upon force quench.

Single-molecule force spectroscopy methods can be used to generate folding trajectories of biopolymers from arbitrary regions of the folding landscape. We illustrate the complexity of the folding kinetics and generic aspects of the collapse of RNA and proteins upon force quench by using simulations of an RNA hairpin and theory based on the de Gennes model for homopolymer collapse. The folding time, tau(F), depends asymmetrically on deltaf(S) = f (S) - f (m) and deltaf (Q) = f (m) - f (Q) where f (S) (f (Q)) is the stretch (quench) force and f (m) is the transition midforce of the RNA hairpin. In accord with experiments, the relaxation kinetics of the molecular extension, R(t), occurs in three stages: A rapid initial decrease in the extension is followed by a plateau and finally, an abrupt reduction in R(t) occurs as the native state is approached. The duration of the plateau increases as lambda = tau (Q)/tau (F) decreases (where tau (Q) is the time in which the force is reduced from f (S) to f (Q)). Variations in the mechanisms of force-quench relaxation as lambda is altered are reflected in the experimentally measurable time-dependent entropy, which is computed directly from the folding trajectories. An analytical solution of the de Gennes model under tension reproduces the multistage stage kinetics in R(t). The prediction that the initial stages of collapse should also be a generic feature of polymers is validated by simulation of the kinetics of toroid (globule) formation in semiflexible (flexible) homopolymers in poor solvents upon quenching the force from a fully stretched state. Our findings give a unified explanation for multiple disparate experimental observations of protein folding.

Assembly mechanisms of RNA pseudoknots are determined by the stabilities of constituent secondary structures.

Understanding how RNA molecules navigate their rugged folding landscapes holds the key to describing their roles in a variety of cellular functions. To dissect RNA folding at the molecular level, we performed simulations of three pseudoknots (MMTV and SRV-1 from viral genomes and the hTR pseudoknot from human telomerase) using coarse-grained models. The melting temperatures from the specific heat profiles are in good agreement with the available experimental data for MMTV and hTR. The equilibrium free energy profiles, which predict the structural transitions that occur at each melting temperature, are used to propose that the relative stabilities of the isolated helices control their folding mechanisms. Kinetic simulations, which corroborate the inferences drawn from the free energy profiles, show that MMTV folds by a hierarchical mechanism with parallel paths, i.e., formation of one of the helices nucleates the assembly of the rest of the structure. The SRV-1 pseudoknot, which folds in a highly cooperative manner, assembles in a single step in which the preformed helices coalesce nearly simultaneously to form the tertiary structure. Folding occurs by multiple pathways in the hTR pseudoknot, the isolated structural elements of which have similar stabilities. In one of the paths, tertiary interactions are established before the formation of the secondary structures. Our work shows that there are significant sequence-dependent variations in the folding landscapes of RNA molecules with similar fold. We also establish that assembly mechanisms can be predicted using the stabilities of the isolated secondary structures.

Crowding effects on the mechanical stability and unfolding pathways of ubiquitin.

The interiors of cells are crowded, thus making it important to assess the effects of macromolecules on the folding of proteins. Using the self-organized polymer (SOP) model, which is a coarse-grained representation of polypeptide chains, we probe the mechanical stability of ubiquitin (Ub) monomers and trimers ((Ub)(3)) in the presence of monodisperse spherical crowding agents. Crowding increases the volume fraction (Phi(c))-dependent average force (f(u)(Phi(c))), relative to the value at Phi(c) = 0, needed to unfold Ub and the polyprotein. For a given Phi(c), the values of f(u)(Phi(c)) increase as the diameter (sigma(c)) of the crowding particles decreases. The average unfolding force f(u)(Phi(c)) depends on the ratio D/R(g), where D approximately sigma(c)(pi/6Phi(c))(1/3), with R(g) being the radius of gyration of Ub (or (Ub)(3)) in the unfolded state. Examination of the unfolding pathways shows that, relative to Phi(c) = 0, crowding promotes reassociation of ruptured secondary structural elements. Both the nature of the unfolding pathways and f(u)(Phi(c)) for (Ub)(3) are altered in the presence of crowding particles, with the effect being most dramatic for the subunit that unfolds last. We predict, based on SOP simulations and theoretical arguments, that f(u)(Phi(c)) approximately Phi(c)(1/3nu), where nu is the Flory exponent that describes the unfolded (random coil) state of the protein.

Effects of trimethylamine N-oxide (TMAO) and crowding agents on the stability of RNA hairpins.

We study the effect of the osmolyte, Trimethylamine N-Oxide (TMAO), which accumulates in cells in response to osmotic stress, on the stability of RNA hairpins. All atom molecular dynamics (MD) simulations of a nucleotide and the 22-nucleotide RNA hairpin P5GA in an aqueous TMAO solution show that TMAO preferentially interacts with the base through the formation of a single hydrogen bond. To circumvent the difficulties of adequately sampling the conformational space of polynucleotides, we used coarse-grained models (including one that is inspired by the results of all-atom MD simulations of a single nucleotide) to probe the effects of osmoyltes on the stability of P5GA. If, as revealed by our MD simulations, the cosolute specifically interacts with only one base at a time, then we find practically no change in hairpin stability as measured by Delta T m = T m(Phi) - T m, where T m(Phi) and T m are the melting temperatures at volume fraction Phi of the osmolyte and Phi = 0, respectively. This finding is in qualitative agreement with recent experiments. If the interactions between the RNA and osmolytes are repulsive, which is appropriate for mimicking the effects of crowding, Delta T m can vary from 5 to 15 K depending on the size of the osmolyte and the nature of RNA-osmolyte interactions. Cosolutes that interact favorably with multiple bases simultaneously can stabilize the hairpin more than a crowding agent of the same size. The implications of our predictions for experiments are briefly outlined.

Long loop prediction using the protein local optimization program.

We have developed an improved sampling algorithm and energy model for protein loop prediction, the combination of which has yielded the first methodology capable of achieving good results for the prediction of loop backbone conformations of 11 residue length or greater. Applied to our newly constructed test suite of 104 loops ranging from 11 to 13 residues, our method obtains average/median global backbone root-mean-square deviations (RMSDs) to the native structure (superimposing the body of the protein, not the loop itself) of 1.00/0.62 A for 11 residue loops, 1.15/0.60 A for 12 residue loops, and 1.25/0.76 A for 13 residue loops. Sampling errors are virtually eliminated, while energy errors leading to large backbone RMSDs are very infrequent compared to any previously reported efforts, including our own previous study. We attribute this success to both an improved sampling algorithm and, more critically, the inclusion of a hydrophobic term, which appears to approximately fix a major flaw in SGB solvation model that we have been employing. A discussion of these results in the context of the general question of the accuracy of continuum solvation models is presented.

A hierarchical approach to all-atom protein loop prediction.

The application of all-atom force fields (and explicit or implicit solvent models) to protein homology-modeling tasks such as side-chain and loop prediction remains challenging both because of the expense of the individual energy calculations and because of the difficulty of sampling the rugged all-atom energy surface. Here we address this challenge for the problem of loop prediction through the development of numerous new algorithms, with an emphasis on multiscale and hierarchical techniques. As a first step in evaluating the performance of our loop prediction algorithm, we have applied it to the problem of reconstructing loops in native structures; we also explicitly include crystal packing to provide a fair comparison with crystal structures. In brief, large numbers of loops are generated by using a dihedral angle-based buildup procedure followed by iterative cycles of clustering, side-chain optimization, and complete energy minimization of selected loop structures. We evaluate this method by using the largest test set yet used for validation of a loop prediction method, with a total of 833 loops ranging from 4 to 12 residues in length. Average/median backbone root-mean-square deviations (RMSDs) to the native structures (superimposing the body of the protein, not the loop itself) are 0.42/0.24 A for 5 residue loops, 1.00/0.44 A for 8 residue loops, and 2.47/1.83 A for 11 residue loops. Median RMSDs are substantially lower than the averages because of a small number of outliers; the causes of these failures are examined in some detail, and many can be attributed to errors in assignment of protonation states of titratable residues, omission of ligands from the simulation, and, in a few cases, probable errors in the experimentally determined structures. When these obvious problems in the data sets are filtered out, average RMSDs to the native structures improve to 0.43 A for 5 residue loops, 0.84 A for 8 residue loops, and 1.63 A for 11 residue loops. In the vast majority of cases, the method locates energy minima that are lower than or equal to that of the minimized native loop, thus indicating that sampling rarely limits prediction accuracy. The overall results are, to our knowledge, the best reported to date, and we attribute this success to the combination of an accurate all-atom energy function, efficient methods for loop buildup and side-chain optimization, and, especially for the longer loops, the hierarchical refinement protocol.