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Normal mode analysis offers an efficient way of modeling the conformational flexibility of protein structures. Simple models defined by contact topology, known as elastic network models, have been used to model a variety of systems, but the validation is typically limited to individual modes for a single protein. We use anisotropic displacement parameters from crystallography to test the quality of prediction of both the magnitude and directionality of conformational variance. Normal modes from four simple elastic network model potentials and from the CHARMM forcefield are calculated for a data set of 83 diverse, ultrahigh resolution crystal structures. While all five potentials provide good predictions of the magnitude of flexibility, the methods that consider all atoms have a clear edge at prediction of directionality, and the CHARMM potential produces the best agreement. The low-frequency modes from different potentials are similar, but those computed from the CHARMM potential show the greatest difference from the elastic network models. This was illustrated by computing the dynamic correlation matrices from different potentials for a PDZ domain structure. Comparison of normal mode results with anisotropic temperature factors opens the possibility of using ultrahigh resolution crystallographic data as a quantitative measure of molecular flexibility. The comprehensive evaluation demonstrates the costs and benefits of using normal mode potentials of varying complexity. Comparison of the dynamic correlation matrices suggests that a combination of topological and chemical potentials may help identify residues in which chemical forces make large contributions to intramolecular coupling.
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The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a major worldwide public health emergency that has infected over $1.5$ million people. The partially open state of S1 subunit in spike glycoprotein is considered vital for its infection with host cell and is represented as a key target for neutralizing antibodies. However, the mechanism elucidating the transition from the closed state to the partially open state still remains unclear. Here, we applied a combination of Markov state model, transition path theory and random forest to analyze the S1 motion. Our results explored a promising complete conformational movement of receptor-binding domain, from buried, partially open, to detached states. We also numerically confirmed the transition probability between those states. Based on the asymmetry in both the dynamics behavior and backbone C$alpha$ importance, we further suggested a relation between chains in the trimer spike protein, which may help in the vaccine design and antibody neutralization.
Although the importance of protein dynamics in protein function is generally recognized, the role of protein fluctuations in allosteric effects scarcely has been considered. To address this gap, the Kullback-Leibler divergence (Dx) between protein conformational distributions before and after ligand binding was proposed as a means of quantifying allosteric effects in proteins. Here, previous applications of Dx to methods for analysis and simulation of proteins are first reviewed, and their implications for understanding aspects of protein function and protein evolution are discussed. Next, equations for Dx suggest that k_{B}TDx should be interpreted as an allosteric free energy -- the free energy associated with changing the ligand-free protein conformational distribution to the ligand-bound conformational distribution. This interpretation leads to a thermodynamic model of allosteric transitions that unifies existing perspectives on the relation between ligand binding and changes in protein conformational distributions. The definition of Dx is used to explore some interesting mathematical relations among commonly recognized thermodynamic and biophysical quantities, such as the total free energy change upon ligand binding, and ligand-binding affinities for individual protein conformations. These results represent the beginnings of a theoretical framework for considering the full protein conformational distribution in modeling allosteric transitions. Early applications of the framework have produced results with implications both for methods for coarsed-grained modeling of proteins, and for understanding the relation between ligand binding and protein dynamics.
The flexibility in gap cost enjoyed by Hidden Markov Models (HMMs) is expected to afford them better retrieval accuracy than position-specific scoring matrices (PSSMs). We attempt to quantify the effect of more general gap parameters by separately examining the influence of position- and composition-specific gap scores, as well as by comparing the retrieval accuracy of the PSSMs constructed using an iterative procedure to that of the HMMs provided by Pfam and SUPERFAMILY, curated ensembles of multiple alignments. We found that position-specific gap penalties have an advantage over uniform gap costs. We did not explore optimizing distinct uniform gap costs for each query. For Pfam, PSSMs iteratively constructed from seeds based on HMM consensus sequences perform equivalently to HMMs that were adjusted to have constant gap transition probabilities, albeit with much greater variance. We observed no effect of composition-specific gap costs on retrieval performance.
We consider multi-chain protein native structures and propose a criterion that determines whether two chains in the system are entangled or not. The criterion is based on the behavior observed by pulling at both temini of each chain simultaneously in the two chains. We have identified about 900 entangled systems in the Protein Data Bank and provided a more detailed analysis for several of them. We argue that entanglement enhances the thermodynamic stability of the system but it may have other functions: burying the hydrophobic residues at the interface, and increasing the DNA or RNA binding area. We also study the folding and stretching properties of the knotted dimeric proteins MJ0366, YibK and bacteriophytochrome. These proteins have been studied theoretically in their monomer
Proteins perform critical processes in all living systems: converting solar energy into chemical energy, replicating DNA, as the basis of highly performant materials, sensing and much more. While an incredible range of functionality has been sampled in nature, it accounts for a tiny fraction of the possible protein universe. If we could tap into this pool of unexplored protein structures, we could search for novel proteins with useful properties that we could apply to tackle the environmental and medical challenges facing humanity. This is the purpose of protein design. Sequence design is an important aspect of protein design, and many successful methods to do this have been developed. Recently, deep-learning methods that frame it as a classification problem have emerged as a powerful approach. Beyond their reported improvement in performance, their primary advantage over physics-based methods is that the computational burden is shifted from the user to the developers, thereby increasing accessibility to the design method. Despite this trend, the tools for assessment and comparison of such models remain quite generic. The goal of this paper is to both address the timely problem of evaluation and to shine a spotlight, within the Machine Learning community, on specific assessment criteria that will accelerate impact. We present a carefully curated benchmark set of proteins and propose a number of standard tests to assess the performance of deep learning based methods. Our robust benchmark provides biological insight into the behaviour of design methods, which is essential for evaluating their performance and utility. We compare five existing models with two novel models for sequence prediction. Finally, we test the designs produced by these models with AlphaFold2, a state-of-the-art structure-prediction algorithm, to determine if they are likely to fold into the intended 3D shapes.
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