The Levinthal paradox: yesterday and today

A change in the perception of the protein folding problem has taken place recently. The nature of the change is outlined and the reasons for it are presented. An essential element is the recognition that a bias toward the native state over much of the effective energy surface may govern the folding process. This has replaced the random search paradigm of Levinthal and suggests that there are many ways of reaching the native state in a reasonable time so that a specific pathway does not have to be postulated. The change in perception is due primarily to the application of statistical mechanical models and lattice simulations to protein folding. Examples of lattice model results on protein folding are presented. It is pointed out that the new optimism about the protein folding problem must be complemented by more detailed studies to determine the structural and energetic factors that introduce the biases which make possible the folding of real proteins

The nature of the ion binding interactions in EF-hand peptide analogs: free energy simulation of Asp to Asn mutations

The binding of the La3+ ion to a tridecapeptide, which is a model for the EF-hand in calcium-binding proteins, is studied hi solution by free energy simulations. The calculations analyze the effect on the La3+ ion binding of the mutation of Asp to Asn for side chains that interact directly with the ion. The results are compared with the measurements of Marsden.B.J., Hodges, R.S. and Sykes, B.D. (1989) Biochemistry, 28,8839, on the same system. They found that the Asp to Asn mutation has only a small effect on the binding; the observed differences in the free energies on changing one Asp to an Asn are between -0.3 and 1.8 kcal/ mol. This result is analyzed by alchemical simulations for the tridecapeptide in the bound Qoop) structure and free (extended) form. The free energy changes due to the mutation of an Asp to an Asn are large and positive for both the bound and free forms. However, since the values of the free energy changes are calculated to be similar hi the two forms, the difference in the binding free energy of Asp and Asn peptides is found to be small, in agreement with experiment. By use of thermodynamic integration, the various contributions to the free energy changes are estimated. In the com-plexed form, the Asp to Asn mutation is favored by the reduction in the repulsive interaction with other charged residues of the peptide; it is disfavored by the reduction of the stabilization of the ion and the surrounding water has a small effect. When the peptide adopts an extended conformation in the absence of the ion, the mutation Asp to Asn is strongly disfavored by the interactions with the water and is favored by the interactions within the peptide. The results demonstrate the essential role of contributions to the binding of EF-hands from interactions other than those between the ion and the charged amino acid side chains. The results obtained from the simulations suggest, in accord with crystal structures of La3+ bound to various ligands, that the calcium-binding loop complexed with La3+ in solution has a significantly different structure from that observed hi protein

Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise

The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not previously been considered. Here, we present a Bayesian formalism for estimating free-energy changes from non-equilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise, and therefore provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with AFM, optical, and magnetic tweezers.Comment: 8 page

Many-Body Perturbation Theory Applied to Molecules: Analysis and Correlation Energy Calculation for Li\u3csub\u3e2\u3c/sub\u3e, N\u3csub\u3e2\u3c/sub\u3e, and H\u3csub\u3e3\u3c/sub\u3e

The correlation problem is analyzed in terms of Goldstone diagrammatic perturbation theory. A hole-line expansion for the correlation energy is defined and used with matrix partitioning techniques to determine the diagrams contributing to various forms of pair theory and to configuration interaction treatments of the usual type. The presence of certain terms in the double excitation configuration interaction formulation that cancel in higher order is demonstrated. The nature of various approximations to the correlation correction is determined. To illustrate the analysis. certain of the approximations are used in correlation energy calculations with multicenter Slater basis sets on Li2, N2, and H3.Comparison with complete configuration interaction calculations are made for Li2, and H3; the diagrammatic calculation. which is much simpler than a full CI treatment. is found to be a good approximation to the latter

Mechanical Coupling in Myosin V: A Simulation Study

Myosin motor function depends on the interaction between different domains that transmit information from one part of the molecule to another. The interdomain coupling in myosin V is studied with restrained targeted molecular dynamics using an all-atom representation in explicit solvent. To elucidate the origin of the conformational change due to the binding of ATP, targeting forces are applied to small sets of atoms (the forcing sets, FSs) in the direction of their displacement from the rigor conformation, which has a closed actin-binding cleft, to the post-rigor conformation, in which the cleft is open. The “minimal” FS that results in extensive structural changes in the overall myosin conformation is composed of ATP, switch 1, and the nearby HF, HG, and HH helices. Addition of switch 2 to the FS is required to achieve a complete opening of the actin-binding cleft. The restrained targeted molecular dynamics simulations reveal the mechanical coupling pathways between (i) the nucleotide-binding pocket (NBP) and the actin-binding cleft, (ii) the NBP and the converter, and (iii) the actin-binding cleft and the converter. Closing of the NBP due to ATP binding is tightly coupled to the opening of the cleft and leads to the rupture of a key hydrogen bond (F441N/A684O) between switch 2 and the SH1 helix. The actin-binding cleft may mediate the rupture of this bond via a connection between the HW helix, the relay helix, and switch 2. The findings are consistent with experimental studies and a recent normal mode analysis. The present method is expected to be useful more generally in studies of interdomain coupling in proteins

Force Generation in Kinesin Hinges on Cover-Neck Bundle Formation

SummaryIn kinesin motors, a fundamental question concerns the mechanism by which ATP binding generates the force required for walking. Analysis of available structures combined with molecular dynamics simulations demonstrates that the conformational change of the neck linker involves the nine-residue-long N-terminal region, the cover strand, as an element that is essential for force generation. Upon ATP binding, it forms a β sheet with the neck linker, the cover-neck bundle, which induces the forward motion of the neck linker, followed by a latch-type binding to the motor head. The estimated stall force and anisotropic response to external loads calculated from the model agree with force-clamp measurements. The proposed mechanism for force generation by the cover-neck bundle formation appears to apply to several kinesin families. It also elucidates the design principle of kinesin as the smallest known processive motor

Improving protein secondary structure prediction using a simple k-mer model

Motivation: Some first order methods for protein sequence analysis inherently treat each position as independent. We develop a general framework for introducing longer range interactions. We then demonstrate the power of our approach by applying it to secondary structure prediction; under the independence assumption, sequences produced by existing methods can produce features that are not protein like, an extreme example being a helix of length 1. Our goal was to make the predictions from state of the art methods more realistic, without loss of performance by other measures