Kristopher Opron

Multiscale multiphysics and multidomain models—Flexibility and rigidity

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRIs computational complexity is of O(N(2)) at most, where N is the number of atoms or residues, in contrast to O(N(3)) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

Molecular dynamics and mutational analysis of the catalytic and translocation cycle of RNA polymerase

BackgroundDuring elongation, multi-subunit RNA polymerases (RNAPs) cycle between phosphodiester bond formation and nucleic acid translocation. In the conformation associated with catalysis, the mobile “trigger loop” of the catalytic subunit closes on the nucleoside triphosphate (NTP) substrate. Closing of the trigger loop is expected to exclude water from the active site, and dehydration may contribute to catalysis and fidelity. In the absence of a NTP substrate in the active site, the trigger loop opens, which may enable translocation. Another notable structural element of the RNAP catalytic center is the “bridge helix” that separates the active site from downstream DNA. The bridge helix may participate in translocation by bending against the RNA/DNA hybrid to induce RNAP forward movement and to vacate the active site for the next NTP loading. The transition between catalytic and translocation conformations of RNAP is not evident from static crystallographic snapshots in which macromolecular motions may be restrained by crystal packing.ResultsAll atom molecular dynamics simulations of Thermus thermophilus (Tt) RNAP reveal flexible hinges, located within the two helices at the base of the trigger loop, and two glycine hinges clustered near the N-terminal end of the bridge helix. As simulation progresses, these hinges adopt distinct conformations in the closed and open trigger loop structures. A number of residues (described as “switch” residues) trade atomic contacts (ion pairs or hydrogen bonds) in response to changes in hinge orientation. In vivo phenotypes and in vitro activities rendered by mutations in the hinge and switch residues in Saccharomyces cerevisiae (Sc) RNAP II support the importance of conformational changes predicted from simulations in catalysis and translocation. During simulation, the elongation complex with an open trigger loop spontaneously translocates forward relative to the elongation complex with a closed trigger loop.ConclusionsSwitching between catalytic and translocating RNAP forms involves closing and opening of the trigger loop and long-range conformational changes in the atomic contacts of amino acid side chains, some located at a considerable distance from the trigger loop and active site. Trigger loop closing appears to support chemistry and the fidelity of RNA synthesis. Trigger loop opening and limited bridge helix bending appears to promote forward nucleic acid translocation.

Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

Protein structural fluctuation, typically measured by Debye-Waller factors, or B-factors, is a manifestation of protein flexibility, which strongly correlates to protein function. The flexibility-rigidity index (FRI) is a newly proposed method for the construction of atomic rigidity functions required in the theory of continuum elasticity with atomic rigidity, which is a new multiscale formalism for describing excessively large biomolecular systems. The FRI method analyzes protein rigidity and flexibility and is capable of predicting protein B-factors without resorting to matrix diagonalization. A fundamental assumption used in the FRI is that protein structures are uniquely determined by various internal and external interactions, while the protein functions, such as stability and flexibility, are solely determined by the structure. As such, one can predict protein flexibility without resorting to the protein interaction Hamiltonian. Consequently, bypassing the matrix diagonalization, the original FRI has a computational complexity of O(N(2)). This work introduces a fast FRI (fFRI) algorithm for the flexibility analysis of large macromolecules. The proposed fFRI further reduces the computational complexity to O(N). Additionally, we propose anisotropic FRI (aFRI) algorithms for the analysis of protein collective dynamics. The aFRI algorithms permit adaptive Hessian matrices, from a completely global 3N × 3N matrix to completely local 3 × 3 matrices. These 3 × 3 matrices, despite being calculated locally, also contain non-local correlation information. Eigenvectors obtained from the proposed aFRI algorithms are able to demonstrate collective motions. Moreover, we investigate the performance of FRI by employing four families of radial basis correlation functions. Both parameter optimized and parameter-free FRI methods are explored. Furthermore, we compare the accuracy and efficiency of FRI with some established approaches to flexibility analysis, namely, normal mode analysis and Gaussian network model (GNM). The accuracy of the FRI method is tested using four sets of proteins, three sets of relatively small-, medium-, and large-sized structures and an extended set of 365 proteins. A fifth set of proteins is used to compare the efficiency of the FRI, fFRI, aFRI, and GNM methods. Intensive validation and comparison indicate that the FRI, particularly the fFRI, is orders of magnitude more efficient and about 10% more accurate overall than some of the most popular methods in the field. The proposed fFRI is able to predict B-factors for α-carbons of the HIV virus capsid (313 236 residues) in less than 30 seconds on a single processor using only one core. Finally, we demonstrate the application of FRI and aFRI to protein domain analysis.

Communication: Capturing protein multiscale thermal fluctuations

Existing elastic network models are typically parametrized at a given cutoff distance and often fail to properly predict the thermal fluctuation of many macromolecules that involve multiple characteristic length scales. We introduce a multiscale flexibility-rigidity index (mFRI) method to resolve this problem. The proposed mFRI utilizes two or three correlation kernels parametrized at different length scales to capture protein interactions at corresponding scales. It is about 20% more accurate than the Gaussian network model (GNM) in the B-factor prediction of a set of 364 proteins. Additionally, the present method is able to deliver accurate predictions for some large macromolecules on which GNM fails to produce accurate predictions. Finally, for a protein of N residues, mFRI is of linear scaling (O(N)) in computational complexity, in contrast to the order of O(N(3)) for GNM.

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions.

A model for genesis of transcription systems

ABSTRACT Repeating sequences generated from RNA gene fusions/ligations dominate ancient life, indicating central importance of building structural complexity in evolving biological systems. A simple and coherent story of life on earth is told from tracking repeating motifs that generate α/β proteins, 2-double-Ψ−β-barrel (DPBB) type RNA polymerases (RNAPs), general transcription factors (GTFs), and promoters. A general rule that emerges is that biological complexity that arises through generation of repeats is often bounded by solubility and closure (i.e., to form a pseudo-dimer or a barrel). Because the first DNA genomes were replicated by DNA template-dependent RNA synthesis followed by RNA template-dependent DNA synthesis via reverse transcriptase, the first DNA replication origins were initially 2-DPBB type RNAP promoters. A simplifying model for evolution of promoters/replication origins via repetition of core promoter elements is proposed. The model can explain why Pribnow boxes in bacterial transcription (i.e., −12TATAATG−6) so closely resemble TATA boxes (i.e., −31TATAAAAG−24) in archaeal/eukaryotic transcription. The evolution of anchor DNA sequences in bacterial (i.e., −35TTGACA−30) and archaeal (BREup; BRE for TFB recognition element) promoters is potentially explained. The evolution of BREdown elements of archaeal promoters is potentially explained.

Five checkpoints maintaining the fidelity of transcription by RNA polymerases in structural and energetic details

Transcriptional fidelity, which prevents the misincorporation of incorrect nucleoside monophosphates in RNA, is essential for life. Results from molecular dynamics (MD) simulations of eukaryotic RNA polymerase (RNAP) II and bacterial RNAP with experimental data suggest that fidelity may involve as many as five checkpoints. Using MD simulations, the effects of different active site NTPs in both open and closed trigger loop (TL) structures of RNAPs are compared. Unfavorable initial binding of mismatched substrates in the active site with an open TL is proposed to be the first fidelity checkpoint. The leaving of an incorrect substrate is much easier than a correct one energetically from the umbrella sampling simulations. Then, the closing motion of the TL, required for catalysis, is hindered by the presence of mismatched NTPs. Mismatched NTPs also lead to conformational changes in the active site, which perturb the coordination of magnesium ions and likely affect the ability to proceed with catalysis. This step appears to be the most important checkpoint for deoxy-NTP discrimination. Finally, structural perturbations in the template DNA and the nascent RNA in the presence of mismatches likely hinder nucleotide addition and provide the structural foundation for backtracking followed by removing erroneously incorporated nucleotides during proofreading.

Flexibility–rigidity index for protein–nucleic acid flexibility and fluctuation analysis

Protein–nucleic acid complexes are important for many cellular processes including the most essential functions such as transcription and translation. For many protein–nucleic acid complexes, flexibility of both macromolecules has been shown to be critical for specificity and/or function. The flexibility‐rigidity index (FRI) has been proposed as an accurate and efficient approach for protein flexibility analysis. In this article, we introduce FRI for the flexibility analysis of protein–nucleic acid complexes. We demonstrate that a multiscale strategy, which incorporates multiple kernels to capture various length scales in biomolecular collective motions, is able to significantly improve the state of art in the flexibility analysis of protein–nucleic acid complexes. We take the advantage of the high accuracy and O(N) computational complexity of our multiscale FRI method to investigate the flexibility of ribosomal subunits, which are difficult to analyze by alternative approaches. An anisotropic FRI approach, which involves localized Hessian matrices, is utilized to study the translocation dynamics in an RNA polymerase.

A topological approach for protein classification

Abstract Protein function and dynamics are closely related to its sequence and structure.However, prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity between proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an independent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically,we construct machine learning feature vectors solely fromprotein topological fingerprints,which are topological invariants generated during the filtration process. To validate the presentMTF-SVMapproach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Secondly, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. Thirdly, the identification of all alpha, all beta, and alpha-beta protein domains is carried out using 900 proteins.We have found a 85% success in this identification. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples and 246 tasks over 11944 samples. Average accuracies of 82% and 73% are attained. The present study establishes computational topology as an independent and effective alternative for protein classification.

Hinge action versus grip in translocation by RNA polymerase

ABSTRACT Based on molecular dynamics simulations and functional studies, a conformational mechanism is posited for forward translocation by RNA polymerase (RNAP). In a simulation of a ternary elongation complex, the clamp and downstream cleft were observed to close. Hinges within the bridge helix and trigger loop supported generation of translocation force against the RNA–DNA hybrid resulting in opening of the furthest upstream i−8 RNA–DNA bp, establishing conditions for RNAP sliding. The β flap tip helix and the most N-terminal β′ Zn finger engage the RNA, indicating a path of RNA threading out of the exit channel. Because the β flap tip connects to the RNAP active site through the β subunit double-Ψ–β-barrel and the associated sandwich barrel hybrid motif (also called the flap domain), the RNAP active site is coupled to the RNA exit channel and to the translocation of RNA–DNA. Using an exonuclease III assay to monitor translocation of RNAP elongation complexes, we show that K+ and Mg2+ and also an RNA 3′-OH or a 3′-H2 affect RNAP sliding. Because RNAP grip to template suggests a sticky translocation mechanism, and because grip is enhanced by increasing K+ and Mg2+concentration, biochemical assays are consistent with a conformational change that drives forward translocation as observed in simulations. Mutational analysis of the bridge helix indicates that 778-GARKGL-783 (Escherichia coli numbering) is a homeostatic hinge that undergoes multiple bends to compensate for complex conformational dynamics during phosphodiester bond formation and translocation.