Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers.

In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and ß-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.

Introduction of Phosphorylated Residues into the UNRES Coarse-Grained Model: Toward Modeling of Signaling Processes.

Phosphorylated proteins take part in many signaling pathways and play a key role in homeostasis regulation. The all-atom force fields enable us to study the systems containing phosphorylated proteins, but they are limited to short time scales. In this paper, we report the extension of the physics-based coarse-grained UNRES force field to treat systems with phosphorylated amino-acid residues. To derive the respective potentials, appropriate physics-based analytical expressions were fitted to the potentials of mean force of systems modeling phosphorylated amino-acid residues computed in our previous work and implemented in UNRES. The extended UNRES performed well in ab initio simulations of two miniproteins containing phosphorylated residues, strongly suggesting that realistic large-scale simulations of processes involving phosphorylated proteins, especially signaling processes, are now possible.

Local and long range potentials for heparin-protein systems for coarse-grained simulations.

Heparin belongs to glycosaminoglycans (GAGs), a class of periodic linear anionic polysaccharides, which are functionally important components of the extracellular matrix owing to their interactions with various protein targets. Heparin is known to be involved in many cell signaling processes, while the experimental data available for heparin are significantly more abundant than for other GAGs. At the same time, the length and conformational flexibility of the heparin represent major challenges for its theoretical analysis. Coarse-grained (CG) approaches, which enable us to extend the size- and time-scale by orders of magnitude owing to reduction of system representation, appear, therefore, to be useful in simulating these systems. In this work, by using umbrella-sampling molecular dynamics simulations, we derived and parameterized the CG backbone-local potentials of heparin chains and the orientational potentials for the interactions of heparin with amino acid side chains to be further included in the physics-based Unified Coarse-Grained Model of biological macromolecules. With these potentials, simulations of extracellular matrix processes where both heparin and multiple proteins participate will be possible.

An analysis and evaluation of the WeFold collaborative for protein structure prediction and its pipelines in CASP11 and CASP12.

Every two years groups worldwide participate in the Critical Assessment of Protein Structure Prediction (CASP) experiment to blindly test the strengths and weaknesses of their computational methods. CASP has significantly advanced the field but many hurdles still remain, which may require new ideas and collaborations. In 2012 a web-based effort called WeFold, was initiated to promote collaboration within the CASP community and attract researchers from other fields to contribute new ideas to CASP. Members of the WeFold coopetition (cooperation and competition) participated in CASP as individual teams, but also shared components of their methods to create hybrid pipelines and actively contributed to this effort. We assert that the scale and diversity of integrative prediction pipelines could not have been achieved by any individual lab or even by any collaboration among a few partners. The models contributed by the participating groups and generated by the pipelines are publicly available at the WeFold website providing a wealth of data that remains to be tapped. Here, we analyze the results of the 2014 and 2016 pipelines showing improvements according to the CASP assessment as well as areas that require further adjustments and research.

Performance of protein-structure predictions with the physics-based UNRES force field in CASP11.

Participating as the Cornell-Gdansk group, we have used our physics-based coarse-grained UNited RESidue (UNRES) force field to predict protein structure in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11). Our methodology involved extensive multiplexed replica exchange simulations of the target proteins with a recently improved UNRES force field to provide better reproductions of the local structures of polypeptide chains. All simulations were started from fully extended polypeptide chains, and no external information was included in the simulation process except for weak restraints on secondary structure to enable us to finish each prediction within the allowed 3-week time window. Because of simplified UNRES representation of polypeptide chains, use of enhanced sampling methods, code optimization and parallelization and sufficient computational resources, we were able to treat, for the first time, all 55 human prediction targets with sizes from 44 to 595 amino acid residues, the average size being 251 residues. Complete structures of six single-domain proteins were predicted accurately, with the highest accuracy being attained for the T0769, for which the CαRMSD was 3.8 Å for 97 residues of the experimental structure. Correct structures were also predicted for 13 domains of multi-domain proteins with accuracy comparable to that of the best template-based modeling methods. With further improvements of the UNRES force field that are now underway, our physics-based coarse-grained approach to protein-structure prediction will eventually reach global prediction capacity and, consequently, reliability in simulating protein structure and dynamics that are important in biochemical processes. AVAILABILITY AND IMPLEMENTATION: Freely available on the web at http://www.unres.pl/ CONTACT: has5@cornell.edu.

Approach for the Simulation and Modeling of Flexible Rings: Application to the α-D-Arabinofuranoside Ring, a Key Constituent of Polysaccharides from Mycobacterium tuberculosis.

A number of lower organisms (bacteria, fungi, and parasites) produce glycoconjugates that contain furanose rings. Of particular interest to our group are cell wall polysaccharides from mycobacteria, including the human pathogen, Mycobacterium tuberculosis, which contain a large number of arabinofuranose resides. As part of a larger project on the conformational analysis of these molecules, we report here molecular dynamics simulations on methyl α-D-arabinofuranoside (1) using the AMBER force field and the GLYCAM carbohydrate parameter set. We initially studied the ability of this method to predict rotamer populations about the hydroxymethyl group (C4-C5) bond. Importantly, we show that simulation times of up to 200 ns are required in order to obtain convergence of the rotamer populations for this ring system. We also propose a new charge derivation approach that accounts for the flexibility of the furanoside ring by taking an average of the charges from a large number of conformers across the psuedorotational itinerary. The approach yields rotamer populations that are in good agreement with available NMR data and, in addition, provides insight into the nature of the puckering angle and amplitude in 1.