Protein folding tames chaos

Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderliness and relative energies of folded, misfolded and unfolded protein states. Finally, we exploit chaos for protein flexibility analysis and develop a robust chaotic algorithm for the prediction of Debye-Waller factors, or temperature factors, of protein structures

Computational structure‐based drug design: Predicting target flexibility

The role of molecular modeling in drug design has experienced a significant revamp in the last decade. The increase in computational resources and molecular models, along with software developments, is finally introducing a competitive advantage in early phases of drug discovery. Medium and small companies with strong focus on computational chemistry are being created, some of them having introduced important leads in drug design pipelines. An important source for this success is the extraordinary development of faster and more efficient techniques for describing flexibility in three‐dimensional structural molecular modeling. At different levels, from docking techniques to atomistic molecular dynamics, conformational sampling between receptor and drug results in improved predictions, such as screening enrichment, discovery of transient cavities, etc. In this review article we perform an extensive analysis of these modeling techniques, dividing them into high and low throughput, and emphasizing in their application to drug design studies. We finalize the review with a section describing our Monte Carlo method, PELE, recently highlighted as an outstanding advance in an international blind competition and industrial benchmarks.We acknowledge the BSC-CRG-IRB Joint Research Program in Computational Biology. This work was supported by a grant from the Spanish Government CTQ2016-79138-R.J.I. acknowledges support from SVP-2014-068797, awarded by the Spanish Government.Peer ReviewedPostprint (author's final draft

Monte Carlo algorithm based on internal bridging moves for the atomistic simulation of thiophene oligomers and polymers

We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as linear and branched polyethylene, to account for the ring structure of the thiophene monomer. Elementary MC moves implemented include bias reptation of an end thiophene ring, flip of an internal thiophene ring, rotation of an end thiophene ring, concerted rotation of three thiophene rings, rigid translation of an entire molecule, rotation of an entire molecule and volume fluctuation. In the implementation of all moves we assume that thiophene ring atoms remain rigid and strictly co-planar; on the other hand, inter-ring torsion and bond bending angles remain fully flexible subject to suitable potential energy functions. Test simulations with the new algorithm of an important thiophene oligomer, {\alpha}-sexithiophene ({\alpha}-6T), at a high enough temperature (above its isotropic-to-nematic phase transition) using a new united atom model specifically developed for the purpose of this work provide predictions for the volumetric, conformational and structural properties that are remarkably close to those obtained from detailed atomistic Molecular Dynamics (MD) simulations using an all-atom model. The new algorithm is particularly promising for exploring the rich (and largely unexplored) phase behavior and nanoscale ordering of very long (also more complex) thiophene-based polymers which cannot be addressed by conventional MD methods due to the extremely long relaxation times characterizing chain dynamics in these systems

A physically meaningful method for the comparison of potential energy functions

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semi-quantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root mean square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined which overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2.Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's name has been corrected. v3: A new application of the method has been added at the end of section 9 and minor modifications have also been made in other sections. v4: Journal reference and minor corrections adde