High anisotropy and frustration: the keys to regulating protein function efficiently in crowded environments

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

Inhibition of the hexamerization of SARS-CoV-2 endoribonuclease and modeling of RNA structures bound to the hexamer

Non-structural protein 15 (Nsp15) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) forms a homo hexamer and functions as an endoribonuclease. Here, we propose that Nsp15 activity may be inhibited by preventing its hexamerization through drug binding. We first explored the stable conformation of the Nsp15 monomer as the global free energy minimum conformation in the free energy landscape using a combination of parallel cascade selection molecular dynamics (PaCS-MD) and the Markov state model (MSM), and found that the Nsp15 monomer forms a more open conformation with larger druggable pockets on the surface. Targeting the pockets with high druggability scores, we conducted ligand docking and identified compounds that tightly bind to the Nsp15 monomer. The top poses with Nsp15 were subjected to binding free energy calculations by dissociation PaCS-MD and MSM (dPaCS-MD/MSM), indicating the stability of the complexes. One of the identified pockets, which is distinctively bound by inosine analogues, may be an alternative binding site to stabilize viral RNA binding and/or an alternative catalytic site. We constructed a stable RNA structure model bound to both UTP and alternative binding sites, providing a reasonable proposed model of the Nsp15/RNA complex.

Clusters of hairpins induce intrinsic transcription termination in bacteria

Intrinsic transcription termination (ITT) sites are currently identified by locating single and double-adjacent RNA hairpins downstream of the stop codon. ITTs for a limited number of genes/operons in only a few bacterial genomes are currently known. This lack of coverage is a lacuna in the existing ITT inference methods. We have studied the inter-operon regions of 13 genomes covering all major phyla in bacteria, for which good quality public RNA-seq data exist. We identify ITT sites in 87% of cases by predicting hairpin(s) and validate against 81% of cases for which the RNA-seq derived sites could be calculated. We identify 72% of these sites correctly, with 98% of them located ≤ 80 bases downstream of the stop codon. The predicted hairpins form a cluster (when present < 15 bases) in two-thirds of the cases, the remaining being single hairpins. The largest number of clusters is formed by two hairpins, and the occurrence decreases exponentially with an increasing number of hairpins in the cluster. Our study reveals that hairpins form an effective ITT unit when they act in concert in a cluster. Their pervasiveness along with single hairpin terminators corroborates a wider utilization of ITT mechanisms for transcription control across bacteria.

Edge expansion parallel cascade selection molecular dynamics simulation for investigating large-amplitude collective motions of proteins

We propose edge expansion parallel cascade selection molecular dynamics (eePaCS-MD) as an efficient adaptive conformational sampling method to investigate the large-amplitude motions of proteins without prior knowledge of the conformational transitions. In this method, multiple independent MD simulations are iteratively conducted from initial structures randomly selected from the vertices of a multi-dimensional principal component subspace. This subspace is defined by an ensemble of protein conformations sampled during previous cycles of eePaCS-MD. The edges and vertices of the conformational subspace are determined by solving the "convex hull problem." The sampling efficiency of eePaCS-MD is achieved by intensively repeating MD simulations from the vertex structures, which increases the probability of rare event occurrence to explore new large-amplitude collective motions. The conformational sampling efficiency of eePaCS-MD was assessed by investigating the open-close transitions of glutamine binding protein, maltose/maltodextrin binding protein, and adenylate kinase and comparing the results to those obtained using related methods. In all cases, the open-close transitions were simulated in ∼10 ns of simulation time or less, offering 1-3 orders of magnitude shorter simulation time compared to conventional MD. Furthermore, we show that the combination of eePaCS-MD and accelerated MD can further enhance conformational sampling efficiency, which reduced the total computational cost of observing the open-close transitions by at most 36%.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Origins of biological function in DNA and RNA hairpin loop motifs from replica exchange molecular dynamics simulation

Temperature REMD reveals how local chemical changes can result in markedly differing conformational landscapes for DNA and RNA hairpin loops.

Resolving the NFκB Heterodimer Binding Paradox: Strain and Frustration Guide the Binding of Dimeric Transcription Factors

Many eukaryotic transcription factors function after forming oligomers. The choice of protein partners is a nonrandom event that has distinct functional consequences for gene regulation. In the present work we examine three dimers of transcription factors in the NFκB family: p50p50, p50p65, and p65p65. The NFκB dimers bind to a myriad of genomic sites and switch the targeted genes on or off with precision. The p65p50 heterodimer of NFκB is the strongest DNA binder, and its unbinding is controlled kinetically by molecular stripping from the DNA induced by IκB. In contrast, the homodimeric forms of NFκB, p50p50 and p65p65, bind DNA with significantly less affinity, which places the DNA residence of the homodimers under thermodynamic rather than kinetic control. It seems paradoxical that the heterodimer should bind more strongly than either of the symmetric homodimers since DNA is a nearly symmetric target. Using a variety of energy landscape analysis tools, here we uncover the features in the molecular architecture of NFκB dimers that are responsible for these drastically different binding free energies. We show that frustration in the heterodimer interface gives the heterodimer greater conformational plasticity, allowing the heterodimer to better accommodate the DNA. We also show how the elastic energy and mechanical strain in NFκB dimers can be found by extracting the principal components of the fluctuations in Cartesian coordinates as well as fluctuations in the space of physical contacts, which are sampled via simulations with a predictive energy landscape Hamiltonian. These energetic contributions determine the specific detailed mechanisms of binding and stripping for both homo- and heterodimers.

Molecular dynamics simulation of bacterial flagella

The bacterial flagellum is a biological nanomachine for the locomotion of bacteria, and is seen in organisms like Salmonella and Escherichia coli. The flagellum consists of tens of thousands of protein molecules and more than 30 different kinds of proteins. The basal body of the flagellum contains a protein export apparatus and a rotary motor that is powered by ion motive force across the cytoplasmic membrane. The filament functions as a propeller whose helicity is controlled by the direction of the torque. The hook that connects the motor and filament acts as a universal joint, transmitting torque generated by the motor to different directions. This report describes the use of molecular dynamics to study the bacterial flagellum. Molecular dynamics simulation is a powerful method that permits the investigation, at atomic resolution, of the molecular mechanisms of biomolecular systems containing many proteins and solvent. When applied to the flagellum, these studies successfully unveiled the polymorphic supercoiling and transportation mechanism of the filament, the universal joint mechanism of the hook, the ion transfer mechanism of the motor stator, the flexible nature of the transport apparatus proteins, and activation of proteins involved in chemotaxis.

Frustration, function and folding

Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful catalysis, are examples of basic chemical activities that the great majority of polypeptides do not display, and are thought to be the outcome of the natural history of proteins. Function, a concept genuine to Biology, is at the core of evolution and often conflicts with the physical constraints. Locating the frustration between discrepant goals in a recurrent system leads to fundamental insights about the chances and necessities that shape the encoding of biological information.