The Role of Non-native Interactions in the Folding of Knotted Proteins

Stochastic simulations of coarse-grained protein models are used to investigate the propensity to form knots in early stages of protein folding. The study is carried out comparatively for two homologous carbamoyltransferases, a natively-knotted N-acetylornithine carbamoyltransferase (AOTCase) and an unknotted ornithine carbamoyltransferase (OTCase). In addition, two different sets of pairwise amino acid interactions are considered: one promoting exclusively native interactions, and the other additionally including non-native quasi-chemical and electrostatic interactions. With the former model neither protein show a propensity to form knots. With the additional non-native interactions, knotting propensity remains negligible for the natively-unknotted OTCase while for AOTCase it is much enhanced. Analysis of the trajectories suggests that the different entanglement of the two transcarbamylases follows from the tendency of the C-terminal to point away from (for OTCase) or approach and eventually thread (for AOTCase) other regions of partly-folded protein. The analysis of the OTCase/AOTCase pair clarifies that natively-knotted proteins can spontaneously knot during early folding stages and that non-native sequence-dependent interactions are important for promoting and disfavoring early knotting events.Comment: Accepted for publication on PLOS Computational Biolog

Folding Pathways of a Knotted Protein with a Realistic Atomistic Force Field

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native $\beta$-sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Exact Solution of the Munoz-Eaton Model for Protein Folding

A transfer-matrix formalism is introduced to evaluate exactly the partition function of the Munoz-Eaton model, relating the folding kinetics of proteins of known structure to their thermodynamics and topology. This technique can be used for a generic protein, for any choice of the energy and entropy parameters, and in principle allows the model to be used as a first tool to characterize the dynamics of a protein of known native state and equilibrium population. Applications to a $\beta$-hairpin and to protein CI-2, with comparisons to previous results, are also shown.Comment: 4 pages, 5 figures, RevTeX 4. To be published in Phys. Rev. Let

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure

Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties

Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $\mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes' blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure

Inferring the effective thickness of polyelectrolytes from stretching measurements at various ionic strengths: applications to DNA and RNA

By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA and poly-U, for different ionic strengths. Due to the very different degree of flexibility of the two molecules, the results provide insight into how the apparent diameter is influenced by the interplay between the (solution-dependent) Debye screening length and the polymers' ``bare'' thickness. For DNA, the electrostatic contribution to the effective radius, $\Delta$, is found to be about 5 times larger than the Debye screening length, consistently with previous theoretical predictions for highly-charged stiff rods. For the more flexible poly-U chains the electrostatic contribution to $\Delta$ is found to be significantly smaller than the Debye screening length.Comment: iopart, 14 pages, 13 figures, to appear in J. Phys.: Condens. Matte

Influence of conformational fluctuations on enzymatic activity: modelling the functional motion of beta-secretase

Considerable insight into the functional activity of proteins and enzymes can be obtained by studying the low-energy conformational distortions that the biopolymer can sustain. We carry out the characterization of these large scale structural changes for a protein of considerable pharmaceutical interest, the human $\beta$-secretase. Starting from the crystallographic structure of the protein, we use the recently introduced beta-Gaussian model to identify, with negligible computational expenditure, the most significant distortion occurring in thermal equilibrium and the associated time scales. The application of this strategy allows to gain considerable insight into the putative functional movements and, furthermore, helps to identify a handful of key regions in the protein which have an important mechanical influence on the enzymatic activity despite being spatially distant from the active site. The results obtained within the Gaussian model are validated through an extensive comparison against an all-atom Molecular Dynamics simulation.Comment: To be published in a special issue of J. Phys.: Cond. Mat. (Bedlewo Workshop