Extracting the causality of correlated motions from molecular dynamics simulations

Evaluation of information flows in the RAS-MAPK system using transfer entropy measurements

The RAS-MAPK system plays an important role in regulating various cellular processes, including growth, differentiation, apoptosis, and transformation. Dysregulation of this system has been implicated in genetic diseases and cancers affecting diverse tissues. To better understand the regulation of this system, we employed information flow analysis based on transfer entropy (TE) between the activation dynamics of two key elements in cells stimulated with EGF: SOS, a guanine nucleotide exchanger for the small GTPase RAS, and RAF, a RAS effector serine/threonine kinase. TE analysis allows for model-free assessment of the timing, direction, and strength of the information flow regulating the system response. We detected significant amounts of TE in both directions between SOS and RAF, indicating feedback regulation. Importantly, the amount of TE did not simply follow the input dose or the intensity of the causal reaction, demonstrating the uniqueness of TE. TE analysis proposed regulatory networks containing multiple tracks and feedback loops and revealed temporal switching in the reaction pathway primarily responsible for reaction control. This proposal was confirmed by the effects of an MEK inhibitor on TE. Furthermore, TE analysis identified the functional disorder of a SOS mutation associated with Noonan syndrome, a human genetic disease, of which the pathogenic mechanism has not been precisely known yet. TE assessment holds significant promise as a model-free analysis method of reaction networks in molecular pharmacology and pathology.

Allostery at a Protein-Protein Interface Harboring an Intermolecular Motional Network

Motional properties of proteins govern recognition, catalysis, and regulation. The dynamics of tightly interacting residues can form intramolecular dynamic networks, dependencies fine-tuned by evolution to optimize a plethora of functional aspects. The constructive interaction of residues from different proteins to assemble intermolecular dynamic networks is a similarly likely case but has escaped thorough experimental assessment due to interfering association/dissociation dynamics. Here, we use fast-MAS solid-state 15N R1ρ NMR relaxation dispersion aided by molecular-dynamics simulations to mechanistically assess the hierarchy of individual μs timescale motions arising from a crystal-crystal contact, in the absence of translational motion. In contrast to the monomer, where particular mutations entail isolated perturbations, specific intermolecular interactions couple the motional properties between distant residues in the same protein. The mechanistic insights obtained from this conceptual work may improve our understanding on how intramolecular allostery can be tuned by intermolecular interactions via assembly of dynamic networks from previously isolated elements.

Study of Correlated Motions to Detect the Conformational Transitions of the Intrinsically Disordered Sheep Prion Peptide

Intrinsically disordered proteins (IDPs) are known for their random structural changes throughout their sequence based on the environment. The mechanism underlying these structural changes is difficult to explain. All biological processes are known to follow the direction through which they act. A study of the correlated motion can help to understand the direction of the change. Herein, we introduced the multivariate statistical analysis (MSA) technique to study the correlated motion of the peptide. The correlated motion of the sheep prion peptide was studied with the change in the temperature and solvent. These techniques helped to identify the contributing residual motions that helped to form the different secondary structures of the protein and also the triggering factors that drive these sorts of residual motions. The structural details match the experimentally reported data. It was found that the direction of the change of the secondary structure for this peptide shifted from the C-terminal to the N-terminal with an increase in the temperature. It was found that the involvement of the hydrophobic residues present at the C-terminal and the middle residues (residues 12-17) is responsible for forming a β-sheet at the normal temperature. Hydration water was found to play an important role in this change. Insights gained from this study can be used to design strategies for desirable structural changes in the IDPs.

Role of Shape Deformation of DNA-Binding Sites in Regulating the Efficiency and Specificity in Their Recognition by DNA-Binding Proteins

Accurate transcription of genetic information is crucial, involving precise recognition of the binding motifs by DNA-binding proteins. While some proteins rely on short-range hydrophobic and hydrogen bonding interactions at binding sites, others employ a DNA shape readout mechanism for specific recognition. In this mechanism, variations in DNA shape at the binding motif resulted from either inherent flexibility or binding of proteins at adjacent sites are sensed and capitalized by the searching proteins to locate them specifically. Through extensive computer simulations, we investigate both scenarios to uncover the underlying mechanism and origin of specificity in the DNA shape readout mechanism. Our findings reveal that deformation in shape at the binding motif creates an entropy funnel, allowing information about altered shapes to manifest as fluctuations in minor groove widths. This signal enhances the efficiency of nonspecific search of nearby proteins by directing their movement toward the binding site, primarily driven by a gain in entropy. We propose this as a generic mechanism for DNA shape readout, where specificity arises from the alignment between the molecular frustration of the searching protein and the ruggedness of the entropic funnel governed by molecular features of the protein and arrangement of the DNA bases at the binding site, respectively.

Berberine ameliorates the progression of primary sclerosing cholangitis by activating farnesoid X receptor

Primary sclerosing cholangitis (PSC) is a rare cholestatic disease characterized by biliary infiltration, hepatic fibrosis and bile duct destruction. To date, treatment options for PSC are very limited. Therefore, the current study is aimed to investigate the therapeutic potential of berberine (BBR) against PSC. The disease was induced by feeding the mice with 3,5-diethoxycarbonyl-1,4-dihydro-2,4,6-collidine (DDC) for four weeks. The serum biochemistry and liver histology were analyzed. Furthermore, the expression of farnesoid X receptor (FXR) was also evaluated by real-time PCR. The results indicated that berberine prevents the progression of PSC by modulating the expression of FXR which ultimately regulates other genes (including Cyp7A1 and BSEP) thus maintaining bile acids homeostasis. Furthermore, the docking analysis showed that berberine interacts with the binding pocket of FXR to activate the protein thus acting as an FXR agonist. In conclusion, data indicate that berberine protects the liver from PSC-related injury. This effect might be due to the modulation of FXR activity.

Repurposing FDA approved drugs against monkeypox virus DNA dependent RNA polymerase: virtual screening, normal mode analysis and molecular dynamics simulation studies

Zoonotic monkeypox disease, caused by the double-stranded DNA monkeypox virus, has become a global concern. Due to the absence of a specific small molecule drug for the disease, this report aims to identify potential inhibitor drugs for monkeypox. This study explores a drug repurposing strategy using virtual screening to evaluate 1615 FDA approved drugs against the monkeypox virus DNA dependent RNA polymerase subunit A6R. Normal mode analysis and molecular dynamics simulation assessed the flexibility and stability of the target protein in complex with the top screened drugs. The analysis identified Nilotinib (ZINC000006716957), Conivaptan (ZINC000012503187), and Ponatinib (ZINC000036701290) as the most potential RNA polymerase inhibitors with binding energies of - 7.5 kcal/mol. These drugs mainly established hydrogen bonds and hydrophobic interactions with the protein active sites, including LEU95, LEU90, PRO96, MET110, and VAL113, and residues nearby. Normal mode analysis and molecular dynamics simulation confirmed the stability of interactions between the top drugs and the protein. In conclusion, we have discovered promising drugs that can potentially control the monkeypox virus and should be further explored through experimental assays and clinical trials to assess their actual activity against the disease. The findings of this study could lay the foundation for screening repurposed compounds as possible antiviral treatments against various highly pathogenic viruses.

Computational Insights into Prostaglandin E2 Ligand Binding and Activation of G-Protein-Coupled Receptors

G-protein coupled receptors (GPCRs) are eukaryotic integral membrane proteins that regulate signal transduction cascade pathways implicated in a variety of human diseases and are consequently of interest as drug targets. For this reason, it is of interest to investigate the way in which specific ligands bind and trigger conformational changes in the receptor during activation and how this in turn modulates intracellular signaling. In the present study, we investigate the way in which the ligand Prostaglandin E2 interacts with three GPCRs in the E-prostanoid family: EP1, EP2, and EP3. We examine information transfer pathways based on long-time scale molecular dynamics simulations using transfer entropy and betweenness centrality to measure the physical transfer of information among residues in the system. We monitor specific residues involved in binding to the ligand and investigate how the information transfer behavior of these residues changes upon ligand binding. Our results provide key insights that enable a deeper understanding of EP activation and signal transduction functioning pathways at the molecular level, as well as enabling us to make some predictions about the activation pathway for the EP1 receptor, for which little structural information is currently available. Our results should advance ongoing efforts in the development of potential therapeutics targeting these receptors.

Tunnel-like region observed as a potential allosteric site in Staphylococcus aureus Glyceraldehyde-3-phosphate dehydrogenase

Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) catalyzing the sixth step of glycolysis has been investigated for allosteric features that might be used as potential target for specific inhibition of Staphylococcus aureus (S.aureus). X-ray structure of bacterial enzyme for which a tunnel-like opening passing through the center previously proposed as an allosteric site has been subjected to six independent 500 ns long Molecular Dynamics simulations. Harmonic bond restraints were employed at key residues to underline the allosteric feature of this region. A noticeable reduction was observed in the mobility of NAD+ binding domains when restrictions were applied. Also, a substantial decrease in cross-correlations between distant Cα fluctuations was detected throughout the structure. Mutual information (MI) analysis revealed a similar decrease in the degree of correspondence in positional fluctuations in all directions everywhere in the receptor. MI between backbone and side-chain torsional variations changed its distribution profile and decreased considerably around the catalytic sites when restraints were employed. Principal component analysis clearly showed that the restrained state sampled a narrower range of conformations than apo state, especially in the first principal mode due to restriction in the conformational flexibility of NAD+ binding domain. Clustering the trajectory based on catalytic site residues displayed a smaller repertoire of conformations for restrained state compared to apo. Representative snapshots subjected to k-shortest pathway analysis revealed the impact of bond restraints on the allosteric communication which displayed distinct optimal and suboptimal pathways for two states, where observed frequencies of critical residues Gln51 and Val283 at the proposed site changed considerably.

Flagellar motor protein-targeted search for the druggable site of Helicobacter pylori

The deleterious impact of Helicobacter pylori (H. pylori) on human health is contingent upon its ability to create and sustain colony structure, which in turn is dictated by the effective performance of flagella - a multi-protein rotary nanodevice. Hence, to design an effective therapeutic strategy against H. pylori, we here conducted a systematic search for an effective druggable site by focusing on the structure-dynamics-energetics-stability landscape of the junction points of three 1 : 1 protein complexes (FliFC-FliGN, FliGM-FliMM, and FliYC-FliNC) that contribute mainly to the rotary motion of the flagella via the transformation of information along the junctions over a wide range of pH values operative in the stomach (from neutral to acidic). We applied a gamut of physiologically relevant perturbations in the form of thermal scanning and mechanical force to sample the entire quasi - and non-equilibrium conformational spaces available for the protein complexes under neutral and acidic pH conditions. Our perturbation-induced magnification of conformational distortion approach identified pH-independent protein sequence-specific evolution of precise thermally labile segments, which dictate the specific thermal unfolding mechanism of each complex and this complex-specific pH-independent structural disruption notion remains consistent under mechanical stress as well. Complementing the above observations with the relative rank-ordering of estimated equilibrium binding free energies between two protein sequences of a specific complex quantifies the extent of structure-stability modulation due to pH alteration, rationalizes the exceptional stability of H. pylori under acidic pH conditions, and identifies the pH-independent complex-sequence-segment-residue diagram for targeted drug design.

Study of the Allosteric Mechanism of Human Mitochondrial Phenylalanyl-tRNA Synthetase by Transfer Entropy via an Improved Gaussian Network Model and Co-evolution Analyses

We propose an improved transfer entropy approach called the dynamic version of the force constant fitted Gaussian network model based on molecular dynamics ensemble (dfcfGNM_MD) to explore the allosteric mechanism of human mitochondrial phenylalanyl-tRNA synthetase (hmPheRS), one of the aminoacyl-tRNA synthetases that play a crucial role in translation of the genetic code. The dfcfGNM_MD method can provide reliable estimates of the transfer entropy and give new insights into the role of the anticodon binding domain in driving the catalytic domain in aminoacylation activity and into the effects of tRNA binding and residue mutation on the enzyme activity, revealing the causal mechanism of the allosteric communication in hmPheRS. In addition, we incorporate the residue dynamic and co-evolutionary information to further investigate the key residues in hmPheRS allostery. This study sheds light on the mechanisms of hmPheRS allostery and can provide important information for related drug design.

Mutual information analysis of mutation, nonlinearity, and triple interactions in proteins

Mutations are the cause of several diseases as well as the underlying force of evolution. A thorough understanding of their biophysical consequences is essential. We present a computational framework for evaluating different levels of mutual information (MI) and its dependence on mutation. We used molecular dynamics trajectories of the third PDZ domain and its different mutations. Nonlinear MI between all residue pairs are calculated by tensor Hermite polynomials up to the fifth order and compared with results from multivariate Gaussian distribution of joint probabilities. We show that MI is written as the sum of a Gaussian and a nonlinear component. Results for the PDZ domain show that the Gaussian term gives a sufficiently accurate representation of MI when compared with nonlinear terms up to the fifth order. Changes in MI between residue pairs show the characteristic patterns resulting from specific mutations. Emergence of new peaks in the MI versus residue index plots of mutated PDZ shows how mutation may change allosteric pathways. Triple correlations are characterized by evaluating MI between triplets of residues. We observed that certain triplets are strongly affected by mutation. Susceptibility of residues to perturbation is obtained by MI and discussed in terms of linear response theory.

Toward Reliable and Insightful Entropy Calculations on Flexible Molecules

The absolute entropy of a flexible molecule can be approximated by the sum of a rigid-rotor-harmonic-oscillator (RRHO) entropy and a Gibbs-Shannon entropy associated to the Boltzmann distribution for the occupation of the conformational energy levels. Herein, we show that such partitioning, which has received renewed interest, leads to accurate entropies of single molecules of increasing size provided that the conformational part is estimated by means of a set of discretization and expansion techniques that are able to capture the significant correlation effects among the torsional motions. To ensure a reliable entropy estimation, we rely on extensive sampling as that produced by classical molecular dynamics simulations on the microsecond time scale, which is currently affordable for small- and medium-sized molecules. According to test calculations, the gas-phase entropy of simple organic molecules is predicted with a mean unsigned error of 0.9 cal/(mol K) when the RRHO entropies are computed at the B3LYP-D3/cc-pVTZ level. Remarkably, the same protocol gives small errors [<1 cal/(mol K)] for the extremely flexible linear alkane molecules (C_nH_2n+2, n = 14, 16, and 18). Similarly, we obtain well-converged entropies for a more challenging test of drug molecules, which exhibit more pronounced correlation effects. We also perform equivalent entropy calculations on a 76 amino acid protein, ubiquitin, by taking advantage of the cutoff-dependent formulation of an expansion technique (correlation-consistent multibody local approximation, CC-MLA), which incorporates genuine correlation effects among the neighboring dihedral angles. Moreover, we show that insightful descriptors of the coupled torsional motions can be obtained with the CC-MLA approach.

Nucleosome breathing facilitates cooperative binding of pluripotency factors Sox2 and Oct4 to DNA

Critical lineage commitment events are staged by multiple transcription factors (TFs) binding to their cognate motifs, often positioned at nucleosome-enriched regions of chromatin. The underlying mechanism remains elusive due to difficulty in disentangling the heterogeneity in chromatin states. Using a novel coarse-grained model and molecular dynamics simulations, here we probe the association of Sox2 and Oct4 proteins that show clustered binding at the entry-exit region of a nucleosome. The model captures the conformational heterogeneity of nucleosome breathing dynamics that features repeated wrap-unwrap transitions of a DNA segment from one end of the nucleosome. During the dynamics, DNA forms bulges that diffuse stochastically and may regulate the target search dynamics of a protein by nonspecifically interacting with it. The overall search kinetics of the TF pair follows a "dissociation-compensated-association" mechanism, where Oct4 binding is facilitated by the association of Sox2. The cooperativity stems from a change in entropy caused by an alteration in the nucleosome dynamics upon TF binding. The binding pattern is consistent with a live-cell single-particle tracking experiment, suggesting the mechanism observed for clustered binding of a TF pair, which is a hallmark of cis-regulatory elements, has broader implications in understanding gene regulation in a complex chromatin environment.

Altered Dynamics of S. aureus Phosphofructokinase via Bond Restraints at Two Distinct Allosteric Binding Sites

The effect of perturbation at the allosteric site was investigated through several replicas of molecular dynamics (MD) simulations conducted on bacterial phosphofructokinase (SaPFK). In our previous work, an alternative binding site was estimated to be allosteric in addition to the experimentally reported one. To highlight the effect of both allosteric sites on receptor's dynamics, MD runs were carried out on apo forms with and without perturbation. Perturbation was achieved via incorporating multiple bond restraints for residue pairs located at the allosteric site. Restraints applied to the predicted site caused one dimer to stiffen, whereas an increase in mobility was detected in the same dimer when the experimentally resolved site was restrained. Fluctuations in C_α-C_α distances which is used to disclose residues with high potential of communication indicated a marked increase in signal transmission within each dimer as the receptor switched to a restrained state. Cross-correlation of positional fluctuations indicated an overall decrease in the magnitude of both positive and negative correlations when restraints were employed on the predicted allosteric site whereas an exact opposite effect was observed for the reported site. Finally, mutual correspondence between positional fluctuations noticeably increased with restraints on predicted allosteric site, whereas an opposite effect was observed for restraints applied on experimentally reported one. In view of these findings, it is clear that the perturbation of either one of two allosteric sites effected the dynamics of the receptor with a distinct and contrasting character.

Information Flow and Allosteric Communication in Proteins

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer in proteins is developed. The joint distribution function for residue fluctuations is expressed in terms of tensor Hermite polynomials which conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. Amount and speed of information transfer between residues, important for understanding allosteric activity in proteins, are discussed. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in Human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Estimated transfer rates are in the order of 1-20 megabits per second. Information transfer from third order contributions are one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.

Identification of allosteric fingerprints of alpha-synuclein aggregates in matrix metalloprotease-1 and substrate-specific virtual screening with single molecule insights

Alpha-synuclein (aSyn) has implications in pathological protein aggregations in neurodegeneration. Matrix metalloproteases (MMPs) are broad-spectrum proteases and cleave aSyn, leading to aggregation. Previous reports showed that allosteric communications between the two domains of MMP1 on collagen fibril and fibrin depend on substrates, activity, and ligands. This paper reports quantification of allostery using single molecule measurements of MMP1 dynamics on aSyn-induced aggregates by calculating Forster Resonance Energy Transfer (FRET) between two dyes attached to the catalytic and hemopexin domains of MMP1. The two domains of MMP1 prefer open conformations that are inhibited by a single point mutation E219Q of MMP1 and tetracycline, an MMP inhibitor. A two-state Poisson process describes the interdomain dynamics, where the two states and kinetic rates of interconversion between them are obtained from histograms and autocorrelations of FRET values. Since a crystal structure of aSyn-bound MMP1 is unavailable, binding poses were predicted by molecular docking of MMP1 with aSyn using ClusPro. MMP1 dynamics were simulated using predicted binding poses and compared with the experimental interdomain dynamics to identify an appropriate pose. The selected aSyn-MMP1 binding pose near aSyn residue K45 was simulated and analyzed to define conformational changes at the catalytic site. Allosteric residues in aSyn-bound MMP1 exhibiting strong correlations with the catalytic motif residues were compared with allosteric residues in free MMP1, and aSyn-specific residues were identified. The allosteric residues in aSyn-bound MMP1 are K281, T283, G292, G327, L328, E329, R337, F343, G345, N346, Y348, G353, Q354, D363, Y365, S366, S367, F368, P371, R372, V374, K375, A379, F391, A394, R399, M414, F419, V426, and C466. Shannon entropy was defined to quantify MMP1 dynamics. Virtual screening was performed against a site on selected aSyn-MMP1 binding poses, which showed that lead molecules differ between free MMP1 and substrate-bound MMP1. Also, identifying aSyn-specific allosteric residues in MMP1 enabled further selection of lead molecules. In other words, virtual screening needs to take substrates into account for potential substrate-specific control of MMP1 activity in the future. Molecular understanding of interactions between MMP1 and aSyn-induced aggregates may open up the possibility of degrading aggregates by targeting MMPs.

Granger Causality Analysis of Chignolin Folding

Constantly advancing computer simulations of biomolecules provide huge amounts of data that are difficult to interpret. In particular, obtaining insights into functional aspects of macromolecular dynamics, often related to cascades of transient events, calls for methodologies that depart from the well-grounded framework of equilibrium statistical physics. One of the approaches toward the analysis of complex temporal data which has found applications in the fields of neuroscience and econometrics is Granger causality analysis. It allows determining which components of multidimensional time series are most influential for the evolution of the entire system, thus providing insights into causal relations within the dynamic structure of interest. In this work, we apply Granger analysis to a long molecular dynamics trajectory depicting repetitive folding and unfolding of a mini β-hairpin protein, CLN025. We find objective, quantitative evidence indicating that rearrangements within the hairpin turn region are determinant for protein folding and unfolding. On the contrary, interactions between hairpin arms score low on the causality scale. Taken together, these findings clearly favor the concept of zipperlike folding, which is one of two postulated β-hairpin folding mechanisms. More importantly, the results demonstrate the possibility of a conclusive application of Granger causality analysis to a biomolecular system.

Molecular Insights into Phosphorylation-Induced Allosteric Conformational Changes in a β2-Adrenergic Receptor

The large conformational flexibility of G protein-coupled receptors (GPCRs) has been a puzzle in structural and pharmacological studies for the past few decades. Apart from structural rearrangements induced by ligands, enzymatic phosphorylations by GPCR kinases (GRKs) at the carboxy-terminal tail (C-tail) of a GPCR also make conformational alterations to the transmembrane helices and facilitates the binding of one of its transducer proteins named β-arrestin. The phosphorylation-induced conformational transition of the receptor that causes specific binding to β-arrestin but prevents the association of other transducers such as G proteins lacks atomistic understanding and is elusive to experimental studies. Using microseconds of all-atom conventional and Gaussian accelerated molecular dynamics (GaMD) simulations, we investigate the allosteric mechanism of phosphorylation induced-conformational changes in β₂-adrenergic receptor, a well-characterized GPCR model system. Free energy profiles reveal that the phosphorylated receptor samples a new conformational state in addition to the canonical active state corroborating with recent nuclear magnetic resonance experimental findings. The new state has a smaller intracellular cavity that is likely to accommodate β-arrestin better than G protein. Using contact map and inter-residue interaction energy calculations, we found the phosphorylated C-tail adheres to the cytosolic surface of the transmembrane domain of the receptor. Transfer entropy calculations show that the C-tail residues drive the correlated motions of TM residues, and the allosteric signal is relayed via several residues at the cytosolic surface. Our results also illustrate how the redistribution of inter-residue nonbonding interaction couples with the allosteric communication from the phosphorylated C-tail to the transmembrane. Atomistic insight into phosphorylation-induced β-arrestin specific conformation is therapeutically important to design drugs with higher efficacy and fewer side effects. Our results, therefore, open novel opportunities to fine-tune β-arrestin bias in GPCR signaling.

Substitutions at Nonconserved Rheostat Positions Modulate Function by Rewiring Long-Range, Dynamic Interactions

Amino acid substitutions at nonconserved protein positions can have noncanonical and "long-distance" outcomes on protein function. Such outcomes might arise from changes in the internal protein communication network, which is often accompanied by changes in structural flexibility. To test this, we calculated flexibilities and dynamic coupling for positions in the linker region of the lactose repressor protein. This region contains nonconserved positions for which substitutions alter DNA-binding affinity. We first chose to study 11 substitutions at position 52. In computations, substitutions showed long-range effects on flexibilities of DNA-binding positions, and the degree of flexibility change correlated with experimentally measured changes in DNA binding. Substitutions also altered dynamic coupling to DNA-binding positions in a manner that captured other experimentally determined functional changes. Next, we broadened calculations to consider the dynamic coupling between 17 linker positions and the DNA-binding domain. Experimentally, these linker positions exhibited a wide range of substitution outcomes: Four conserved positions tolerated hardly any substitutions ("toggle"), ten nonconserved positions showed progressive changes from a range of substitutions ("rheostat"), and three nonconserved positions tolerated almost all substitutions ("neutral"). In computations with wild-type lactose repressor protein, the dynamic couplings between the DNA-binding domain and these linker positions showed varied degrees of asymmetry that correlated with the observed toggle/rheostat/neutral substitution outcomes. Thus, we propose that long-range and noncanonical substitutions outcomes at nonconserved positions arise from rewiring long-range communication among functionally important positions. Such calculations might enable predictions for substitution outcomes at a range of nonconserved positions.

Calculating Transfer Entropy from Variance-Covariance Matrices Provides Insight into Allosteric Communication in ERK2

We develop an approach by which reliable estimates of the transfer entropy can be obtained from the variance-covariance matrix of atomic fluctuations, which converges quickly and retains sensitivity to the full chemical profile of the biomolecular system. We validate our method on ERK2, a well-studied kinase involved in the MAPK signaling cascade for which considerable computational, experimental, and mutation data are available. We present the results of transfer entropy analysis on data obtained from molecular dynamics simulations of wild-type active and inactive ERK2, along with mutants Q103A, I84A, L73P, and G83A. We show that our method is systematically consistent within the context of other approaches for calculating transfer entropy, and we provide a method for interpreting networks of interconnected residues in the protein from a perspective of allosteric coupling. We introduce new insights about possible allosteric activity of the extreme N-terminal region of the kinase, and we describe evidence that suggests that activation may occur by different paths or routes in different mutants. Our results highlight systematic advantages and disadvantages of each method for calculating transfer entropy and show the important role of transfer entropy analysis for understanding allosteric behavior in biomolecular systems.

Bioinformatic Analysis of Structure and Function of LIM Domains of Human Zyxin Family Proteins

Members of the human Zyxin family are LIM domain-containing proteins that perform critical cellular functions and are indispensable for cellular integrity. Despite their importance, not much is known about their structure, functions, interactions and dynamics. To provide insights into these, we used a set of in-silico tools and databases and analyzed their amino acid sequence, phylogeny, post-translational modifications, structure-dynamics, molecular interactions, and functions. Our analysis revealed that zyxin members are ohnologs. Presence of a conserved nuclear export signal composed of LxxLxL/LxxxLxL consensus sequence, as well as a possible nuclear localization signal, suggesting that Zyxin family members may have nuclear and cytoplasmic roles. The molecular modeling and structural analysis indicated that Zyxin family LIM domains share similarities with transcriptional regulators and have positively charged electrostatic patches, which may indicate that they have previously unanticipated nucleic acid binding properties. Intrinsic dynamics analysis of Lim domains suggest that only Lim1 has similar internal dynamics properties, unlike Lim2/3. Furthermore, we analyzed protein expression and mutational frequency in various malignancies, as well as mapped protein-protein interaction networks they are involved in. Overall, our comprehensive bioinformatic analysis suggests that these proteins may play important roles in mediating protein-protein and protein-nucleic acid interactions.

Heat flow random walks in biomolecular systems using symbolic transfer entropy and graph theory

This study combines the information- and graph-theoretic measures to investigate the cluster modulation of the amino acid residues and nucleotides at complex biomolecular interfaces. The symbolic transfer entropy is used as an information-theoretic measure. I also used graph theory to obtain information and heat flow weighted digraph models used to study the topology of information and heat flow paths at complex biomolecular interfaces. I introduce the graph-theoretic measures, such as the influence score and betweenness centrality, to identify the most influential amino acid and nucleotide sequences as sources of the information and absorb centers of the structure's heat flow. PageRank-like random walks algorithm is used to analyze the network of amino acid and nucleotide sequences at the protein-RNA interface combined with weighted digraph models. The cluster analysis using graph-theoretic measures revealed the modular molecular structure and the mechanism of the binding interface. In this study, the first benchmark system is an intuitive directed information flow network used to test the algorithms, and the second benchmark is a protein-RNA complex system. The approach was able to identify the most influential amino acid residues and nucleotides. Furthermore, the statistical cluster analysis using graph-theoretic measures revealed the modular molecular structure and the binding mechanism at the interface.

Distinctive communication networks in inactive states of β2 -adrenergic receptor: Mutual information and entropy transfer analysis

Mutual information and entropy transfer analysis employed on two inactive states of human beta-2 adrenergic receptor (β₂ -AR) unraveled distinct communication pathways. Previously, a so-called "highly" inactive state of the receptor was observed during 1.5 microsecond long molecular dynamics simulation where the largest intracellular loop (ICL3) was swiftly packed onto the G-protein binding cavity, becoming entirely inaccessible. Mutual information quantifying the degree of correspondence between backbone-C_α fluctuations was mostly shared between intra- and extra-cellular loop regions in the original inactive state, but shifted to entirely different regions in this latest inactive state. Interestingly, the largest amount of mutual information was always shared among the mobile regions. Irrespective of the conformational state, polar residues always contributed more to mutual information than hydrophobic residues, and also the number of polar-polar residue pairs shared the highest degree of mutual information compared to those incorporating hydrophobic residues. Entropy transfer, quantifying the correspondence between backbone-C_α fluctuations at different timesteps, revealed a distinctive pathway directed from the extracellular site toward intracellular portions in this recently exposed inactive state for which the direction of information flow was the reverse of that observed in the original inactive state where the mobile ICL3 and its intracellular surroundings drove the future fluctuations of extracellular regions.

Long-range Regulation of Partially Folded Amyloidogenic Peptides

Neurodegeneration involves abnormal aggregation of intrinsically disordered amyloidogenic peptides (IDPs), usually mediated by hydrophobic protein-protein interactions. There is mounting evidence that formation of α-helical intermediates is an early event during self-assembly of amyloid-β42 (Aβ42) and α-synuclein (αS) IDPs in Alzheimer’s and Parkinson’s disease pathogenesis, respectively. However, the driving force behind on-pathway molecular assembly of partially folded helical monomers into helical oligomers assembly remains unknown. Here, we employ extensive molecular dynamics simulations to sample the helical conformational sub-spaces of monomeric peptides of both Aβ42 and αS. Our computed free energies, population shifts, and dynamic cross-correlation network analyses reveal a common feature of long-range intra-peptide modulation of partial helical folds of the amyloidogenic central hydrophobic domains via concerted coupling with their charged terminal tails (N-terminus of Aβ42 and C-terminus of αS). The absence of such inter-domain fluctuations in both fully helical and completely unfolded (disordered) states suggests that long-range coupling regulates the dynamicity of partially folded helices, in both Aβ42 and αS peptides. The inter-domain coupling suggests a form of intra-molecular allosteric regulation of the aggregation trigger in partially folded helical monomers. This approach could be applied to study the broad range of amyloidogenic peptides, which could provide a new path to curbing pathogenic aggregation of partially folded conformers into oligomers, by inhibition of sites far from the hydrophobic core.

Spectral analysis of molecular dynamics simulations on PDZ: MD sectors

The idea of protein "sectors" posits that sparse subsets of amino acid residues form cooperative networks that are key elements of protein stability, ligand binding, and allosterism. To date, protein sectors have been calculated by the statistical coupling analysis (SCA) method of Ranganathan and co-workers via the spectral analysis of conservation-weighted evolutionary covariance matrices obtained from a multiple sequence alignments of homologous families of proteins. SCA sectors, a knowledge-based protocol, have been indentified with functional properties and allosterism for a number of systems. In this study, we investigate the utility of the sector idea for the analysis of physics-based molecular dynamics (MD) trajectories of proteins. Our test case for this procedure is PSD95- PDZ3, one of the smallest proteins for which allosterism has been observed. It has served previously as a model system for a number of prediction algorithms, and is well characterized by X-ray crystallography, NMR spectroscopy and site specific mutagenisis. All-atom MD simulations were performed for a total of 500 nanoseconds using AMBER, and MD-calculated covariance matrices for the fluctuations of residue displacements and non-bonded interaction energies were subjected to spectral analysis in a manner analogous to that of SCA. The composition of MD sectors was compared with results from SCA, site specific mutagenesis, and allosterism. The concordance indicates that MD sectors are a viable protocol for analyzing MD trajectories and provide insight into the physical origin of the phenomenon.Communicated by Ramaswamy H. Sarma.

Structural and dynamic origins of ESR lineshapes in spin-labeled GB1 domain: the insights from spin dynamics simulations based on long MD trajectories

Site-directed spin labeling (SDSL) ESR is a valuable tool to probe protein systems that are not amenable to characterization by x-ray crystallography, NMR or EM. While general principles that govern the shape of SDSL ESR spectra are known, its precise relationship with protein structure and dynamics is still not fully understood. To address this problem, we designed seven variants of GB1 domain bearing R1 spin label and recorded the corresponding MD trajectories (combined length 180 μs). The MD data were subsequently used to calculate time evolution of the relevant spin density matrix and thus predict the ESR spectra. The simulated spectra proved to be in good agreement with the experiment. Further analysis confirmed that the spectral shape primarily reflects the degree of steric confinement of the R1 tag and, for the well-folded protein such as GB1, offers little information on local backbone dynamics. The rotameric preferences of R1 side chain are determined by the type of the secondary structure at the attachment site. The rotameric jumps involving dihedral angles χ1 and χ2 are sufficiently fast to directly influence the ESR lineshapes. However, the jumps involving multiple dihedral angles tend to occur in (anti)correlated manner, causing smaller-than-expected movements of the R1 proxyl ring. Of interest, ESR spectra of GB1 domain with solvent-exposed spin label can be accurately reproduced by means of Redfield theory. In particular, the asymmetric character of the spectra is attributable to Redfield-type cross-correlations. We envisage that the current MD-based, experimentally validated approach should lead to a more definitive, accurate picture of SDSL ESR experiments.

Mechanism of cognate sequence discrimination by the ETS-family transcription factor ETS-1

Functional evidence increasingly implicates low-affinity DNA recognition by transcription factors as a general mechanism for the spatiotemporal control of developmental genes. Although the DNA sequence requirements for affinity are well-defined, the dynamic mechanisms that execute cognate recognition are much less resolved. To address this gap, here we examined ETS1, a paradigm developmental transcription factor, as a model for which cognate discrimination remains enigmatic. Using molecular dynamics simulations, we interrogated the DNA-binding domain of murine ETS1 alone and when bound to high-and low-affinity cognate sites or to nonspecific DNA. The results of our analyses revealed collective backbone and side-chain motions that distinguished cognate versus nonspecific as well as high- versus low-affinity cognate DNA binding. Combined with binding experiments with site-directed ETS1 mutants, the molecular dynamics data disclosed a triad of residues that respond specifically to low-affinity cognate DNA. We found that a DNA-contacting residue (Gln-336) specifically recognizes low-affinity DNA and triggers the loss of a distal salt bridge (Glu-343/Arg-378) via a large side-chain motion that compromises the hydrophobic packing of two core helices. As an intact Glu-343/Arg-378 bridge is the default state in unbound ETS1 and maintained in high-affinity and nonspecific complexes, the low-affinity complex represents a unique conformational adaptation to the suboptimization of developmental enhancers.

Allosterism and signal transfer in DNA

We analysed the basic mechanisms of signal transmission in DNA and the origins of the allostery exhibited by systems such as the ternary complex BAMHI-DNA-GRDBD. We found that perturbation information generated by a primary protein binding event travels as a wave to distant regions of DNA following a hopping mechanism. However, such a structural perturbation is transient and does not lead to permanent changes in the DNA geometry and interaction properties at the secondary binding site. The BAMHI-DNA-GRDBD allosteric mechanism does not occur through any traditional models: direct (protein-protein), indirect (reorganization of the secondary site) readout or solvent-release. On the contrary, it is generated by a subtle and less common entropy-mediated mechanism, which might have an important role to explain other DNA-mediated cooperative effects.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

How proteins bind to DNA: target discrimination and dynamic sequence search by the telomeric protein TRF1

Target search as performed by DNA-binding proteins is a complex process, in which multiple factors contribute to both thermodynamic discrimination of the target sequence from overwhelmingly abundant off-target sites and kinetic acceleration of dynamic sequence interrogation. TRF1, the protein that binds to telomeric tandem repeats, faces an intriguing variant of the search problem where target sites are clustered within short fragments of chromosomal DNA. In this study, we use extensive (>0.5 ms in total) MD simulations to study the dynamical aspects of sequence-specific binding of TRF1 at both telomeric and non-cognate DNA. For the first time, we describe the spontaneous formation of a sequence-specific native protein-DNA complex in atomistic detail, and study the mechanism by which proteins avoid off-target binding while retaining high affinity for target sites. Our calculated free energy landscapes reproduce the thermodynamics of sequence-specific binding, while statistical approaches allow for a comprehensive description of intermediate stages of complex formation.

Molecular determinants for the thermodynamic and functional divergence of uniporter GLUT1 and proton symporter XylE

GLUT1 facilitates the down-gradient translocation of D-glucose across cell membrane in mammals. XylE, an Escherichia coli homolog of GLUT1, utilizes proton gradient as an energy source to drive uphill D-xylose transport. Previous studies of XylE and GLUT1 suggest that the variation between an acidic residue (Asp27 in XylE) and a neutral one (Asn29 in GLUT1) is a key element for their mechanistic divergence. In this work, we combined computational and biochemical approaches to investigate the mechanism of proton coupling by XylE and the functional divergence between GLUT1 and XylE. Using molecular dynamics simulations, we evaluated the free energy profiles of the transition between inward- and outward-facing conformations for the apo proteins. Our results revealed the correlation between the protonation state and conformational preference in XylE, which is supported by the crystal structures. In addition, our simulations suggested a thermodynamic difference between XylE and GLUT1 that cannot be explained by the single residue variation at the protonation site. To understand the molecular basis, we applied Bayesian network models to analyze the alteration in the architecture of the hydrogen bond networks during conformational transition. The models and subsequent experimental validation suggest that multiple residue substitutions are required to produce the thermodynamic and functional distinction between XylE and GLUT1. Despite the lack of simulation studies with substrates, these computational and biochemical characterizations provide unprecedented insight into the mechanistic difference between proton symporters and uniporters.

We seek to address one intriguing question, the mechanistic distinction between active proton-coupled symporters and passive uniporters that are related in evolution. Proton-coupled symporters harness the transmembrane proton gradient to drive the substrate transport, while uniporters can only facilitate the passive substrate translocation. In this work, we focus on two sugar transporters GLUT1 and XylE, which belong to symporters and uniporters respectively but have high sequence similarity. We first applied molecular dynamics simulations to characterize the thermodynamic behaviors of apo GLUT1 and XylE, which are supposed to provide prominent details of mechanisms. From the identified difference in thermodynamics, we concluded that neutralizing protonation site in XylE is insufficient for its conversion to GLUT1 analog. To pinpoint extra elements contributing to their evolutionary divergence, we developed a novel network modeling scheme based on Bayesian network which shows impressive predictive power on residue mutations. Our models suggested the detailed mechanism of proton coupling in XylE and molecular basis of symporter/uniporter discrepancy. Furthermore, the modeling scheme could help to guide the design of biomolecules for desired functions.

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

In heme proteins, the efficient transport of ligands such as NO or O₂ to the binding site is achieved via ligand migration networks. A quantitative assessment of ligand diffusion in these networks is thus essential for a better understanding of the function of these proteins. For this, Xe migration in truncated hemoglobin N (trHbN) of Mycobacterium Tuberculosis was studied using molecular dynamics simulations. Transitions between pockets of the migration network and intra-pocket relaxation occur on similar time scales (10 ps and 20 ps), consistent with low free energy barriers (1-2 kcal/mol). Depending on the pocket from where Xe enters a particular transition, the conformation of the side chains lining the transition region differs which highlights the coupling between ligand and protein degrees of freedom. Furthermore, comparison of transition probabilities shows that Xe migration in trHbN is a non-Markovian process. Memory effects arise due to protein rearrangements and coupled dynamics as Xe moves through it.

Binding and transport of ligands in proteins is essential, in particular in globular proteins which often exhibit internal cavities. In truncated Hemoglobin N (trHbN) these cavities are arranged as a network with particular connectivities. The present work supports the notion that ligand diffusion in trHbN is an active process and coupled to the protein dynamics. Furthermore, transition probabilities between neighboring pockets depend on the location from where the ligand entered the transition, which is typical for non-Markovian processes. Hence, ligand migration in trHbN exhibits memory effects due to dynamical coupling between the protein and ligand motion.

Causality, transfer entropy, and allosteric communication landscapes in proteins with harmonic interactions

A fast and approximate method of generating allosteric communication landscapes in proteins is presented by using Schreiber's entropy transfer concept in combination with the Gaussian Network Model of proteins. Predictions of the model and the allosteric communication landscapes generated show that information transfer in proteins does not necessarily take place along a single path, but an ensemble of pathways is possible. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations should be introduced, which leads to the presence of causality in proteins. The model provides a simple tool for mapping entropy sink-source relations into pairs of residues. By this approach, residues that should be manipulated to control protein activity may be determined. This should be of great importance for allosteric drug design and for understanding the effects of mutations on function. The model is applied to determine allosteric communication in three proteins, Ubiquitin, Pyruvate Kinase, and the PDZ domain. Predictions are in agreement with molecular dynamics simulations and experimental evidence. Proteins 2017; 85:1056-1064. © 2017 Wiley Periodicals, Inc.

Binding Site Configurations Probe the Structure and Dynamics of the Zinc Finger of NEMO (NF-κB Essential Modulator)

Zinc-finger proteins are regulators of critical signaling pathways for various cellular functions, including apoptosis and oncogenesis. Here, we investigate how binding site protonation states and zinc coordination influence protein structure, dynamics, and ultimately function, as these pivotal regulatory proteins are increasingly important for protein engineering and therapeutic discovery. To better understand the thermodynamics and dynamics of the zinc finger of NEMO (NF-κB essential modulator), as well as the role of zinc, we present results of 20 μs molecular dynamics trajectories, 5 μs for each of four active site configurations. Consistent with experimental evidence, the zinc ion is essential for mechanical stabilization of the functional, folded conformation. Hydrogen bond motifs are unique for deprotonated configurations yet overlap in protonated cases. Correlated motions and principal component analysis corroborate the similarity of the protonated configurations and highlight unique relationships of the zinc-bound configuration. We hypothesize a potential mechanism for zinc binding from results of the thiol configurations. The deprotonated, zinc-bound configuration alone predominantly maintains its tertiary structure throughout all 5 μs and alludes rare conformations potentially important for (im)proper zinc-finger-related protein-protein or protein-DNA interactions.

Entropy Transfer between Residue Pairs and Allostery in Proteins: Quantifying Allosteric Communication in Ubiquitin

It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.

Spatio-temporal coordination among functional residues in protein

The microscopic basis of communication among the functional sites in bio-macromolecules is a fundamental challenge in uncovering their functions. We study the communication through temporal cross-correlation among the binding sites. We illustrate via Molecular Dynamics simulations the properties of the temporal cross-correlation between the dihedrals of a small protein, ubiquitin which participates in protein degradation in eukaryotes. We show that the dihedral angles of the residues possess non-trivial temporal cross-correlations with asymmetry with respect to exchange of the dihedrals, having peaks at low frequencies with time scales in nano-seconds and an algebraic tail with a universal exponent for large frequencies. We show the existence of path for temporally correlated degrees of freedom among the functional residues. We explain the qualitative features of the cross-correlations through a general mathematical model. The generality of our analysis suggests that temporal cross-correlation functions may provide convenient theoretical framework to understand bio-molecular functions on microscopic basis.

Excess positional mutual information predicts both local and allosteric mutations affecting beta lactamase drug resistance

MOTIVATION

Bacterial resistance to antibiotics, particularly plasmid-encoded resistance to beta lactam drugs, poses an increasing threat to human health. Point mutations to beta-lactamase enzymes can greatly alter the level of resistance conferred, but predicting the effects of such mutations has been challenging due to the large combinatorial space involved and the subtle relationships of distant residues to catalytic function. Therefore we desire an information-theoretic metric to sensitively and robustly detect both local and distant residues that affect substrate conformation and catalytic activity.

RESULTS

Here, we report the use of positional mutual information in multiple microsecond-length molecular dynamics (MD) simulations to predict residues linked to catalytic activity of the CTX-M9 beta lactamase. We find that motions of the bound drug are relatively isolated from motions of the protein as a whole, which we interpret in the context of prior theories of catalysis. In order to robustly identify residues that are weakly coupled to drug motions but nonetheless affect catalysis, we utilize an excess mutual information metric. We predict 31 such residues for the cephalosporin antibiotic cefotaxime. Nine of these have previously been tested experimentally, and all decrease both enzyme rate constants and empirical drug resistance. We prospectively validate our method by testing eight high-scoring mutations and eight low-scoring controls in bacteria. Six of eight predicted mutations decrease cefotaxime resistance greater than 2-fold, while only one control shows such an effect. The ability to prospectively predict new variants affecting bacterial drug resistance is of great interest to clinical and epidemiological surveillance.

AVAILABILITY AND IMPLEMENTATION

Excess mutual information code is available at https://github.com/kassonlab/positionalmi CONTACT: kasson@virginia.edu.

Intrinsic K-Ras dynamics: A novel molecular dynamics data analysis method shows causality between residue pair motions

K-Ras is the most frequently mutated oncogene in human cancers, but there are still no drugs that directly target it in the clinic. Recent studies utilizing dynamics information show promising results for selectively targeting mutant K-Ras. However, despite extensive characterization, the mechanisms by which K-Ras residue fluctuations transfer allosteric regulatory information remain unknown. Understanding the direction of information flow can provide new mechanistic insights for K-Ras targeting. Here, we present a novel approach –conditional time-delayed correlations (CTC) – using the motions of all residue pairs of a protein to predict directionality in the allosteric regulation of the protein fluctuations. Analyzing nucleotide-dependent intrinsic K-Ras motions with the new approach yields predictions that agree with the literature, showing that GTP-binding stabilizes K-Ras motions and leads to residue correlations with relatively long characteristic decay times. Furthermore, our study is the first to identify driver-follower relationships in correlated motions of K-Ras residue pairs, revealing the direction of information flow during allosteric modulation of its nucleotide-dependent intrinsic activity: active K-Ras Switch-II region motions drive Switch-I region motions, while α-helix-3L7 motions control both. Our results provide novel insights for strategies that directly target mutant K-Ras.

Oscillatory Diffusion and Second-Order Cyclostationarity in Alanine Tripeptide from Molecular Dynamics Simulation

Molecular dynamics (MD) simulation distinctly describes motions of biomolecules at high resolution and can potentially be used to explain allosteric mechanism in subcellular processes. Statistical methods are necessary to realize this potential because MD simulations generate a large volume of data and because the analysis is never efficient, objective, or thorough without using appropriate statistical approaches. Tracing the flow of information within a biomolecule requires not only a description of an overall mechanism but also a multiscale statistical description from atomic interactions to the overall mechanism. The foundation of this multiscale description, in general, is a measure of correlation between motions of atoms or residues, as reflected by dynamic cross-correlation, Pearson correlation, or mutual information. However, these correlations can be inadequate because they assume wide sense stationarity, which means that the instantaneous average and correlation of a particular property are time-independent. Consequently, these measures of correlation cannot account for correlation between motions of different frequencies, since frequency implies oscillation and variation over time. Here, we characterize the nonstationarity in the form of pure oscillatory instantaneous variance in the signed dihedral angular accelerations (SDAA) along the main chain of alanine tripeptide in MD simulations by power spectrum, corrected squared envelope spectrum (CSES), and cross-CSES. This oscillation has a physical interpretation of an oscillatory diffusion. The fraction of this oscillation in all motions is as high as about 40% at some frequencies. This shows that oscillatory instantaneous variance exists in the SDAA and that significant correlation may not be accounted for in current correlation analysis. This oscillation is also found to transmit between dihedral angles. These results could have implications in the understanding of the dynamics of biomolecules.

Preferred conformations of N-glycan core pentasaccharide in solution and in glycoproteins

N-linked glycans are on protein surfaces and have direct and water/ion-mediated interactions with surrounding amino acids. Such contacts could restrict their conformational freedom compared to the same glycans free in solution. In this work, we have examined the conformational freedom of the N-glycan core pentasaccharide moiety in solution using standard molecular dynamics (MD) simulations as well as temperature replica-exchange MD simulations. Both simulations yield the comparable conformational variability of the pentasaccharide in solution, indicating the convergence of both simulations. The glycoprotein crystal structures are analyzed to compare the conformational freedom of the N-glycan on the protein surface with the simulation result. Surprisingly, the pentasaccharide free in solution shows more restricted conformational variability than the N-glycan on the protein surface. The interactions between the carbohydrate and the protein side chain appear to be responsible for the increased conformational diversity of the N-glycan on the protein surface. Finally, the transfer entropy analysis of the simulation trajectory also reveals an unexpected causality relationship between intramolecular hydrogen bonds and the conformational states in that the hydrogen bonds play a role in maintaining the conformational states rather than driving the change in glycosidic torsional states.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

Recovery of the poisoned topoisomerase II for DNA religation: coordinated motion of the cleavage core revealed with the microsecond atomistic simulation

Type II topoisomerases resolve topological problems of DNA double helices by passing one duplex through the reversible double-stranded break they generated on another duplex. Despite the wealth of information in the cleaving operation, molecular understanding of the enzymatic DNA ligation remains elusive. Topoisomerase poisons are widely used in anti-cancer and anti-bacterial therapy and have been employed to entrap the intermediates of topoisomerase IIβ with religatable DNA substrate. We removed drug molecules from the structure and conducted molecular dynamics simulations to investigate the enzyme-mediated DNA religation. The drug-unbound intermediate displayed transitions toward the resealing-compliant configuration: closing distance between the cleaved DNA termini, B-to-A transformation of the double helix, and restoration of the metal-binding motif. By mapping the contact configurations and the correlated motions between enzyme and DNA, we identified the indispensable role of the linker preceding winged helix domain (WHD) in coordinating the movements of TOPRIM, the nucleotide-binding motifs, and the bound DNA substrate during gate closure. We observed a nearly vectorial transition in the recovery of the enzyme and identified the previously uncharacterized roles of Asn508 and Arg677 in DNA rejoining. Our findings delineate the dynamic mechanism of the DNA religation conducted by type II topoisomerases.

Computing ensembles of transitions with molecular dynamics simulations

A molecular understanding of conformational change is important for connecting structure and function. Without the ability to sample on the meaningful large-scale conformational changes, the ability to infer biological function and to understand the effect of mutations and changes in environment is not possible. Our Dynamic Importance Sampling method (DIMS), part of the CHARMM simulation package, is a method that enables sampling over ensembles of transition intermediates. This chapter outlines the context for the method and the usage within the program.

New insights into the meaning and usefulness of principal component analysis of concatenated trajectories

A comparison between different conformations of a given protein, relating both structure and dynamics, can be performed in terms of combined principal component analysis (combined-PCA). To that end, a trajectory is obtained by concatenating molecular dynamics trajectories of the individual conformations under comparison. Then, the principal components are calculated by diagonalizing the correlation matrix of the concatenated trajectory. Since the introduction of this approach in 1995 it has had a large number of applications. However, the interpretation of the eigenvectors and eigenvalues so obtained is based on intuitive foundations, because analytical expressions relating the concatenated correlation matrix with those of the individual trajectories under consideration have not been provided yet. In this article, we present such expressions for the cases of two, three, and an arbitrary number of concatenated trajectories. The formulas are simple and show what is to be expected and what is not to be expected from a combined-PCA. Their correctness and usefulness is demonstrated by discussing some representative examples. The results can be summarized in a simple sentence: the correlation matrix of a concatenated trajectory is given by the average of the individual correlation matrices plus the correlation matrix of the individual averages. From this it follows that the combined-PCA of trajectories belonging to different free energy basins provides information that could also be obtained by alternative and more straightforward means.

Coupled binding-bending-folding: The complex conformational dynamics of protein-DNA binding studied by atomistic molecular dynamics simulations

BACKGROUND

Protein-DNA binding often involves dramatic conformational changes such as protein folding and DNA bending. While thermodynamic aspects of this behavior are understood, and its biological function is often known, the mechanism by which the conformational changes occur is generally unclear. By providing detailed structural and energetic data, molecular dynamics simulations have been helpful in elucidating and rationalizing protein-DNA binding.

SCOPE OF REVIEW

This review will summarize recent atomistic molecular dynamics simulations of the conformational dynamics of DNA and protein-DNA binding. A brief overview of recent developments in DNA force fields is given as well.

MAJOR CONCLUSIONS

Simulations have been crucial in rationalizing the intrinsic flexibility of DNA, and have been instrumental in identifying the sequence of binding events, the triggers for the conformational motion, and the mechanism of binding for a number of important DNA-binding proteins.

GENERAL SIGNIFICANCE

Molecular dynamics simulations are an important tool for understanding the complex binding behavior of DNA-binding proteins. With recent advances in force fields and rapid increases in simulation time scales, simulations will become even more important for future studies. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Structure and dynamics analysis on plexin-B1 Rho GTPase binding domain as a monomer and dimer

Plexin-B1 is a single-pass transmembrane receptor. Its Rho GTPase binding domain (RBD) can associate with small Rho GTPases and can also self-bind to form a dimer. In total, more than 400 ns of NAMD molecular dynamics simulations were performed on RBD monomer and dimer. Different analysis methods, such as root mean squared fluctuation (RMSF), order parameters (S(2)), dihedral angle correlation, transfer entropy, principal component analysis, and dynamical network analysis, were carried out to characterize the motions seen in the trajectories. RMSF results show that after binding, the L4 loop becomes more rigid, but the L2 loop and a number of residues in other regions become slightly more flexible. Calculating order parameters (S(2)) for CH, NH, and CO bonds on both backbone and side chain shows that the L4 loop becomes essentially rigid after binding, but part of the L1 loop becomes slightly more flexible. Backbone dihedral angle cross-correlation results show that loop regions such as the L1 loop including residues Q25 and G26, the L2 loop including residue R61, and the L4 loop including residues L89-R91, are highly correlated compared to other regions in the monomer form. Analysis of the correlated motions at these residues, such as Q25 and R61, indicate two signal pathways. Transfer entropy calculations on the RBD monomer and dimer forms suggest that the binding process should be driven by the L4 loop and C-terminal. However, after binding, the L4 loop functions as the motion responder. The signal pathways in RBD were predicted based on a dynamical network analysis method using the pathways predicted from the dihedral angle cross-correlation calculations as input. It is found that the shortest pathways predicted from both inputs can overlap, but signal pathway 2 (from F90 to R61) is more dominant and overlaps all of the routes of pathway 1 (from F90 to P111). This project confirms the allosteric mechanism in signal transmission inside the RBD network, which was in part proposed in the previous experimental study.