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The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note we discuss why lag time of the operator being approximated must be held constant in the variational approach.
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We introduce the SPlit-and-conQueR (SPQR) model, a coarse-grained representation of RNA designed for structure prediction and refinement. In our approach, the representation of a nucleotide consists of a point particle for the phosphate group and an anisotropic particle for the nucleoside. The interactions are, in principle, knowledge-based potentials inspired by the ESCORE function, a base-centered scoring function. However, a special treatment is given to base-pairing interactions and certain geometrical conformations which are lost in a raw knowledge-base model. This results in a representation able to describe planar canonical and non-canonical base pairs and base-phosphate interactions and to distinguish sugar puckers and glycosidic torsion conformations. The model is applied to the folding of several structures, including duplexes with internal loops of non-canonical base pairs, tetraloops, junctions and a pseudoknot. For the majority of these systems, experimental structures are correctly predicted at the level of individual contacts. We also propose a method for efficiently reintroducing atomistic detail from the coarse-grained representation.
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Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to parallelization to novel uses of hardware. Special focus is placed on classifying algorithms -- most of which are underpinned by a few key ideas -- in order to understand their fundamental strengths and limitations. Although algorithms have proliferated, progress resulting from novel hardware use appears to be more clear-cut than from algorithms alone, partly due to the lack of widely used sampling measures.
No existing algorithm can start with arbitrary RNA sequences and return the precise, three-dimensional structures that ensures their biological function. This chapter outlines current algorithms for automated RNA structure prediction (including our own FARNA-FARFAR), highlights their successes, and dissects their limitations, using a tetraloop and the sarcin/ricin motif as examples. The barriers to future advances are considered in light of three particular challenges: improving computational sampling, reducing reliance on experimentally solved structures, and avoiding coarse-grained representations of atomic-level interactions. To help meet these challenges and better understand the current state of the field, we propose an ongoing community-wide CASP-style experiment for evaluating the performance of current structure prediction algorithms.
A complete macromolecule modeling package must be able to solve the simplest structure prediction problems. Despite recent successes in high resolution structure modeling and design, the Rosetta software suite fares poorly on deceptively small protein and RNA puzzles, some as small as four residues. To illustrate these problems, this manuscript presents extensive Rosetta results for four well-defined test cases: the 20-residue mini-protein Trp cage, an even smaller disulfide-stabilized conotoxin, the reactive loop of a serine protease inhibitor, and a UUCG RNA tetraloop. In contrast to previous Rosetta studies, several lines of evidence indicate that conformational sampling is not the major bottleneck in modeling these small systems. Instead, approximations and omissions in the Rosetta all-atom energy function currently preclude discriminating experimentally observed conformations from de novo models at atomic resolution. These molecular puzzles should serve as useful model systems for developers wishing to make foundational improvements to this powerful modeling suite.
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