Ribonucleic acids (RNAs) play essential roles in living cells. Many of them fold into defined three-dimensional (3D) structures to perform functions. Recent advances in single-particle cryo-electron microscopy (cryo-EM) have enabled structure determinations of RNA to atomic resolutions. However, most RNA molecules are structurally flexible, limiting the resolution of their structures solved by cryo-EM. In modeling these molecules, several computational methods are limited by the requirement of massive computational resources and/or the low efficiency in exploring large-scale structural variations. Here we use hierarchical natural move Monte Carlo (HNMMC), which takes advantage of collective motions for groups of nucleic acid residues, to refine RNA structures into their cryo-EM maps, preserving atomic details in the models. After validating the method on a simulated density map of tRNA, we applied it to objectively obtain the model of the folding intermediate for the specificity domain of ribonuclease P from Bacillus subtilis and refine a flexible ribosomal RNA (rRNA) expansion segment from the Mycobacterium tuberculosis (Mtb) ribosome in different conformational states. Finally, we used HNMMC to model atomic details and flexibility for two distinct conformations of the complete genomic RNA (gRNA) inside MS2, a single-stranded RNA virus, revealing multiple pathways for its capsid assembly.

MHC class II molecules bind peptides derived from extracellular proteins that have been ingested by antigen-presenting cells and display them to the immune system. Peptide loading occurs within the antigen-presenting cell and is facilitated by HLA-DM. HLA-DM stabilizes the open conformation of the MHCII binding groove when no peptide is bound. While a structure of the MHCII/HLA-DM complex exists, the mechanism of stabilization is still largely unknown. Here, we applied customized Natural Move Monte Carlo to investigate this interaction. We found a possible longrange mechanism that implicates the configuration of the membrane-proximal globular domains in stabilizing the open state of the empty MHCII binding groove.

There are four known epigenetic cytosine modifications in mammals: methylation (5mC), hydroxymethylation (5hmC), formylation (5fC) and carboxylation (5caC). The biological effects of 5mC are well understood but the roles of the remaining modifications remain elusive. Experimental and computational studies suggest that a single epigenetic mark has little structural effect but six of them can radically change the structure of DNA to a new form, F-DNA. Investigating the collective effect of multiple epigenetic marks requires the ability to interrogate all possible combinations of epigenetic states (e.g. methylated/non-methylated) along a stretch of DNA. Experiments on such complex systems are only feasible on small, isolated examples and there currently exist no systematic computational solutions to this problem. We address this issue by extending the use of Natural Move Monte Carlo to simulate the conformations of epigenetic marks. We validate our protocol by reproducing in silico experimental observations from two recently published highresolution crystal structures that contain epigenetic marks 5hmC and 5fC. We further demonstrate that our protocol correctly finds either the F-DNA or the B-DNA states more energetically favorable depending on the configuration of the epigenetic marks. We hope that the computational efficiency and ease of use of this novel simulation framework would form the basis for future protocols and facilitate our ability to rapidly interrogate diverse epigenetic systems.

HIV-1 replication requires binding to occur between Transactivation Response Element (TAR) RNA and the TAT protein. This TAR TAT binding depends on the conformation of TAR, and therapeutic development has attempted to exploit this dynamic behavior. Here we simulate TAR dynamics in the context of mutations inhibiting TAR binding. We find that two tertiary elements, the apical loop and the bulge, can interact directly, and this interaction may be linked to the affinity of TAR for TAT.

Simulating the functional motions of biomolecular systems requires large computational resources. We introduce a computationally inexpensive protocol for the systematic testing of hypotheses regarding the dynamic behavior of proteins and nucleic acids. The protocol is based on natural move Monte Carlo, a highly efficient conformational sampling method with built-in customization capabilities that allows researchers to design and perform a large number of simulations to investigate functional motions in biological systems. We demonstrate the use of this protocol on both a protein and a DNA case study. Firstly, we investigate the plasticity of a class II major histocompatibility complex in the absence of a bound peptide. Secondly, we study the effects of the epigenetic mark 5-hydroxymethyl on cytosine on the structure of the Dickerson-Drew dodecamer. We show how our customized natural moves protocol can be used to investigate causal relationships of functional motions in biological systems.

The binding between a peptide and a major histocompatibility complex (MHC) is one of the most important processes for the induction of an adaptive immune response. Many algorithms have been developed to predict peptide/MHC (pMHC) binding. However, no approach has yet been able to give structural insight into how peptides detach from the MHC. In this study, we used a combination of coarse graining, hierarchical natural move Monte Carlo and stochastic conformational optimization to explore the detachment processes of 32 different peptides from HLA-A*02:01. We performed 100 independent repeats of each stochastic simulation and found that the presence of experimentally known anchor amino acids affects the detachment trajectories of our peptides. Comparison with experimental binding affinity data indicates the reliability of our approach (area under the receiver operating characteristic curve 0.85). We also compared to a 1000 ns molecular dynamics simulation of a non-binding peptide (AAAKTPVIV) and HLA-A*02:01. Even in this simulation, the longest published for pMHC, the peptide does not fully detach. Our approach is orders of magnitude faster and as such allows us to explore pMHC detachment processes in a way not possible with all-atom molecular dynamics simulations.

Synthetic ligands called diabodies can change the amplitude and nature of signal activation, or counteract oncogenic ligand-independent intracellular signaling, by re-orienting the geometry of receptor dimerization.

Nucleosomes alter gene expression by preventing transcription factors from occupying binding sites along DNA. DNA methylation can affect nucleosome positioning and so alter gene expression epigenetically (without changing DNA sequence). Conventional methods to predict nucleosome occupancy are trained on observed DNA sequence patterns or known DNA oligonucleotide structures. They are statistical and lack the physics needed to predict subtle epigenetic changes due to DNA methylation. The training-free method presented here uses physical principles and state-of-the-art all-atom force fields to predict both nucleosome occupancy along genomic sequences as well as binding to known positioning sequences. Our method calculates the energy of both nucleosomal and linear DNA of the given sequence. Based on the DNA deformation energy, we accurately predict the in vitro occupancy profile observed experimentally for a 20,000-bp genomic region as well as the experimental locations of nucleosomes along 13 well-established positioning sequence elements. DNAwith all C bases methylated at the 5 position shows less variation of nucleosome binding: Strong binding is weakened and weak binding is strengthened compared with normal DNA. Methylation also alters the preference of nucleosomes for some positioning sequences but not others.

The method presented here refines molecular conformations directly against projections of single particles measured by electron microscopy. By optimizing the orientation of the projection at the same time as the conformation, the method is well-suited to twodimensional class averages from cryoelectron microscopy. Such direct use of two-dimensional images circumvents the need for a three-dimensional density map, which may be difficult to reconstruct from projections due to structural heterogeneity or preferred orientations of the sample on the grid. Our refinement protocol exploits Natural Move Monte Carlo to model a macromolecule as a small number of segments connected by flexible loops, on multiple scales. After tests on artificial data from lysozyme, we applied the method to the Methonococcus maripaludis chaperonin. We successfully refined its conformation from a closed-state initial model to an open-state final model using just one class-averaged projection. We also used Natural Moves to iteratively refine against heterogeneous projection images of Methonococcus maripaludis chaperonin in a mix of open and closed states. Our results suggest a general method for electron microscopy refinement specially suited to macromolecules with significant conformational flexibility. The algorithm is available in the program Methodologies for Optimization and Sampling In Computational Studies.

We develop a unique algorithm implemented in the program MOSAICS (Methodologies for Optimization and Sampling in Computational Studies) that is capable of nanoscale modeling without compromising the resolution of interest. This is achieved by modeling with customizable hierarchical degrees of freedom, thereby circumventing major limitations of conventional molecular modeling. With the emergence of RNA-based nanotechnology, large RNAs in all-atom representation are used here to benchmark our algorithm. Our method locates all favorable structural states of a model RNA of significant complexity while improving sampling accuracy and increasing speed many fold over existing all-atom RNA modeling methods. We also modeled the effects of sequence mutations on the structural building blocks of tRNA-based nanotechnology. With its flexibility in choosing arbitrary degrees of freedom as well as in allowing different all-atom energy functions, MOSAICS is an ideal tool to model and design biomolecules of the nanoscale.

Nucleic acids are an important class of biological macromolecules that carry out a variety of cellular roles. For many functions, naturally occurring DNA and RNA molecules need to fold into precise three-dimensional structures. Due to their self-assembling characteristics, nucleic acids have also been widely studied in the field of nanotechnology, and a diverse range of intricate three-dimensional nanostructures have been designed and synthesized. Different physical terms such as base-pairing and stacking interactions, tertiary contacts, electrostatic interactions and entropy all affect nucleic acid folding and structure. Here we review general computational approaches developed to model nucleic acid systems. We focus on four key areas of nucleic acid modeling: molecular representation, potential energy function, degrees of freedom and sampling algorithm. Appropriate choices in each of these key areas in nucleic acid modeling can effectively combine to aid interpretation of experimental data and facilitate prediction of nucleic acid structure.

The present article introduces a set of novel methods that facilitate the use of ‘‘natural moves’’ or arbitrary degrees of freedom that can give rise to collective rearrangements in the structure of biological macromolecules. While such ‘‘natural moves’’ may spoil the stereochemistry and even break the bonded chain at multiple locations, our new method restores the correct chain geometry by adjusting bond and torsion angles in an arbitrary defined molten zone. This is done by successive stages of partial closure that propagate the location of the chain break backwards along the chain. At the end of these stages, the size of the chain break is generally reduced so much that it can be repaired by adjusting the position of a single atom. Our chain closure method is efficient with a computational complexity of O(Nd), where Nd is the number of degrees of freedom used to repair the chain break. The new method facilitates the use of arbitrary degrees of freedom including the ‘‘natural’’ degrees of freedom inferred from analyzing experimental (X-ray crystallography and nuclear magnetic resonance [NMR]) structures of nucleic acids and proteins. In terms of its ability to generate large conformational moves and its effectiveness in locating low energy states, the new method is robust and computationally efficient.