Inferring a weighted elastic network from partial unfolding with coarse‐grained simulations

A number of studies have demonstrated that simple elastic network models can reproduce experimental B‐factors, providing insights into the structure–function properties of proteins. Here, we report a study on how to improve an elastic network model and explore its performance by predicting the experimental B‐factors. Elastic network models are built on the experimental coordinates, and they only take the pairs of atoms within a given cutoff distance r_c into account. These models describe the interactions by elastic springs with the same force constant. We have developed a method based on numerical simulations with a simple coarse‐grained force field, to attribute weights to these spring constants. This method considers the time that two atoms remain connected in the network during partial unfolding, establishing a means of measuring the strength of each link. We examined two different coarse‐grained force fields and explored the computation of these weights by unfolding the native structures. Proteins 2014; 82:119–129. © 2013 Wiley Periodicals, Inc.     

Archaea S‐layer nanotube from a “black smoker” in complex with cyclo‐octasulfur (S8) rings

Elemental sulfur exists primarily as an ring and serves as terminal electron acceptor for a variety of sulfur‐fermenting bacteria. Hyperthermophilic archaea from black smoker vents are an exciting research tool to advance our knowledge of sulfur respiration under extreme conditions. Here, we use a hybrid method approach to demonstrate that the proteinaceous cavities of the S‐layer nanotube of the hyperthermophilic archaeon Staphylothermus marinus act as a storage reservoir for cyclo‐octasulfur . Fully atomistic molecular dynamics (MD) simulations were performed and the method of multiconfigurational thermodynamic integration was employed to compute the absolute free energy for transferring a ring of elemental sulfur from an aqueous bath into the largest hydrophobic cavity of a fragment of archaeal tetrabrachion. Comparisons with earlier MD studies of the free energy of hydration as a function of water occupancy in the same cavity of archaeal tetrabrachion show that the sulfur ring is energetically favored over water.     

pKa predictions for proteins,RNAs, and DNAs with the Gaussian dielectric function using DelPhi pKa

We developed a Poisson‐Boltzmann based approach to calculate the values of protein ionizable residues (Glu, Asp, His, Lys and Arg), nucleotides of RNA and single stranded DNA. Two novel features were utilized: the dielectric properties of the macromolecules and water phase were modeled via the smooth Gaussian‐based dielectric function in DelPhi and the corresponding electrostatic energies were calculated without defining the molecular surface. We tested the algorithm by calculating values for more than 300 residues from 32 proteins from the PPD dataset and achieved an overall RMSD of 0.77. Particularly, the RMSD of 0.55 was achieved for surface residues, while the RMSD of 1.1 for buried residues. The approach was also found capable of capturing the large shifts of various single point mutations in staphylococcal nuclease (SNase) from ‐cooperative dataset, resulting in an overall RMSD of 1.6 for this set of pKa's. Investigations showed that predictions for most of buried mutant residues of SNase could be improved by using higher dielectric constant values. Furthermore, an option to generate different hydrogen positions also improves predictions for buried carboxyl residues. Finally, the calculations on two RNAs demonstrated the capability of this approach for other types of biomolecules. Proteins 2015; 83:2186–2197. © 2015 Wiley Periodicals, Inc.     

Investigating the linkage between disease‐causing amino acid variants and their effect on protein stability and binding

Single amino acid variations (SAV) occurring in human population result in natural differences between individuals or cause diseases. It is well understood that the molecular effect of SAV can be manifested as changes of the wild type characteristics of the corresponding protein, among which are the protein stability and protein interactions. Typically the effect of SAV on protein stability and interactions was assessed via the changes of the wild type folding and binding free energies. However, in terms of SAV affecting protein functionally and disease susceptibility, one wants to know to what extend the wild type function is perturbed by the SAV. Here it is demonstrated that relative, rather than the absolute, change of the folding and binding free energy serves as a good indicator for SAV association with disease. Using HumVar as a source for disease‐causing SAV and experimentally determined free energy changes from ProTherm and SKEMPI databases, correlation coefficients (CC) between the disease index and relative folding and binding probability indexes, respectively, was achieved. The obtained CCs demonstrated the applicability of the proposed approach and it served as good indicator for SAV association with disease. Proteins 2016; 84:232–239. © 2015 Wiley Periodicals, Inc.     

Comparing side chain packing in soluble proteins,protein‐protein interfaces,and transmembrane proteins

We compare side chain prediction and packing of core and non‐core regions of soluble proteins, protein‐protein interfaces, and transmembrane proteins. We first identified or created comparable databases of high‐resolution crystal structures of these 3 protein classes. We show that the solvent‐inaccessible cores of the 3 classes of proteins are equally densely packed. As a result, the side chains of core residues at protein‐protein interfaces and in the membrane‐exposed regions of transmembrane proteins can be predicted by the hard‐sphere plus stereochemical constraint model with the same high prediction accuracies (>90%) as core residues in soluble proteins. We also find that for all 3 classes of proteins, as one moves away from the solvent‐inaccessible core, the packing fraction decreases as the solvent accessibility increases. However, the side chain predictability remains high (80% within ) up to a relative solvent accessibility, , for all 3 protein classes. Our results show that % of the interface regions in protein complexes are “core”, that is, densely packed with side chain conformations that can be accurately predicted using the hard‐sphere model. We propose packing fraction as a metric that can be used to distinguish real protein‐protein interactions from designed, non‐binding, decoys. Our results also show that cores of membrane proteins are the same as cores of soluble proteins. Thus, the computational methods we are developing for the analysis of the effect of hydrophobic core mutations in soluble proteins will be equally applicable to analyses of mutations in membrane proteins.     

Nucleotide‐dependent structural fluctuations and regulation of microtubule‐binding affinity of KIF1A

Molecular motors such as kinesin regulate affinity to a rail protein during the ATP hydrolysis cycle. The regulation mechanism, however, is yet to be determined. To understand this mechanism, we investigated the structural fluctuations of the motor head of the single‐headed kinesin called KIF1A in different nucleotide states using molecular dynamics simulations of a Gō‐like model. We found that the helix at the microtubule (MT) binding site intermittently exhibits a large structural fluctuation when MT is absent. Frequency of this fluctuation changes systematically according to the nucleotide states and correlates strongly with the experimentally observed binding affinity to MT. We also showed that thermal fluctuation enhances the correlation and the interaction with the nucleotide suppresses the fluctuation of the helix . These results suggest that KIF1A regulates affinity to MT by changing the flexibility of the helix during the ATP hydrolysis process: the binding site becomes more flexible in the strong binding state than in the weak binding state. Proteins 2015; 83:809–819. © 2015 Wiley Periodicals, Inc.     

Roles of conserved tryptophans in trimerization of HIV‐1 membrane‐proximal external regions: Implications for virucidal design via alchemical free‐energy molecular simulations

The Dual‐Action Virolytic Entry Inhibitors, or “DAVEI's,” are a class of recombinant fusions of a lectin, a linker polypeptide, and a 15‐residue fragment from the membrane‐proximal external region (MPER) of HIV‐1 gp41. DAVEI's trigger rupture of HIV‐1 virions, and the interaction site between DAVEI MPER and HIV‐1 lies in the gp41 component of the envelope glycoprotein Env. Here, we explore the hypothesis that DAVEI MPER engages Env gp41 in a mode structurally similar to a crystallographic MPER trimer. We used alchemical free‐energy perturbation to assess the thermodynamic roles of each of the four conserved tryptophan residues on each protomer of MPER₃. We found that a W666A mutation had a large positive for all three protomers, while W672A had a large positive for only two of the three protomers, with the other tryptophans remaining unimportant contributors to MPER₃ stability. The protomer for which W672 is not important is unique in the placement of its W666 sidechain between the other two protomers. We show that the unique orientation of this W666 sidechain azimuthally rotates its protomer away from the orientation it would have if the trimer were symmetric, resulting in the diminished interaction of this W672 with the rest of MPER₃. Our findings are consistent with our previous experimental study of W‐to‐A mutants of DAVEI. This suggests that DAVEI MPER may engage HIV‐1 Env to form a mixed trimer state in which one DAVEI MPER forms a trimer by displacing a more weakly interacting protomer of the endogenous Env MPER trimer.     

Exploration of conformational changes in lactose permease upon sugar binding and proton transfer through coarse‐grained simulations

Escherichia coli lactose permease (LacY) actively transports lactose and other galactosides across cell membranes through lactose/H⁺ symport process. Lactose/H⁺ symport is a highly complex process that involves sugar translocation, H⁺ transfer, and large‐scale protein conformational changes. The complete picture of lactose/H⁺ symport is largely unclear due to the complexity and multiscale nature of the process. In this work, we develop the force field for sugar molecules compatible with PACE, a hybrid and coarse‐grained force field that couples the united‐atom protein models with the coarse‐grained MARTINI water/lipid. After validation, we implement the new force field to investigate the binding of a ‐d ‐galactopyranosyl‐1‐thio‐ ‐d ‐galactopyranoside (TDG) molecule to a wild‐type LacY. Results show that the local interactions between TDG and LacY at the binding pocket are consistent with the X‐ray experiment. Transitions from inward‐facing to outward‐facing conformations upon TDG binding and protonation of Glu269 have been achieved from ～5.5 µs simulations. Both the opening of the periplasmic side and closure of the cytoplasmic side of LacY are consistent with double electron–electron resonance and thiol cross‐linking experiments. Our analysis suggests that the conformational changes of LacY are a cumulative consequence of interdomain H‐bonds breaking at the periplasmic side, interdomain salt‐bridge formation at the cytoplasmic side, and the TDG orientational changes during the transition.     

Banding 2of NMR‐derived methyl order parameters: Implications for protein dynamics

Our understanding of protein folding, stability, and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site‐resolved insight into protein motion. It has been observed that methyl‐group motion tends to cluster into three “classes” when expressed in terms of the popular Lipari‐Szabo model‐free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O² and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function. Proteins 2014; 82:2106–2117. © 2014 Wiley Periodicals, Inc.     

Molprobity's ultimate rotamer‐library distributions for model validation

Here we describe the updated MolProbity rotamer‐library distributions derived from an order‐of‐magnitude larger and more stringently quality‐filtered dataset of about 8000 (vs. 500) protein chains, and we explain the resulting changes and improvements to model validation as seen by users. To include only side‐chains with satisfactory justification for their given conformation, we added residue‐specific filters for electron‐density value and model‐to‐density fit. The combined new protocol retains a million residues of data, while cleaning up false‐positive noise in the multi‐ datapoint distributions. It enables unambiguous characterization of conformational clusters nearly 1000‐fold less frequent than the most common ones. We describe examples of local interactions that favor these rare conformations, including the role of authentic covalent bond‐angle deviations in enabling presumably strained side‐chain conformations. Further, along with favored and outlier, an allowed category (0.3–2.0% occurrence in reference data) has been added, analogous to Ramachandran validation categories. The new rotamer distributions are used for current rotamer validation in MolProbity and PHENIX, and for rotamer choice in PHENIX model‐building and refinement. The multi‐dimensional distributions and Top8000 reference dataset are freely available on GitHub. These rotamers are termed “ultimate” because data sampling and quality are now fully adequate for this task, and also because we believe the future of conformational validation should integrate side‐chain with backbone criteria. Proteins 2016; 84:1177–1189. © 2016 Wiley Periodicals, Inc.     

Princeton_TIGRESS 2.0: High refinement consistency and net gains through support vector machines and molecular dynamics in double‐blind predictions during the CASP11 experiment

Protein structure refinement is the challenging problem of operating on any protein structure prediction to improve its accuracy with respect to the native structure in a blind fashion. Although many approaches have been developed and tested during the last four CASP experiments, a majority of the methods continue to degrade models rather than improve them. Princeton_TIGRESS (Khoury et al., Proteins 2014;82:794–814) was developed previously and utilizes separate sampling and selection stages involving Monte Carlo and molecular dynamics simulations and classification using an SVM predictor. The initial implementation was shown to consistently refine protein structures 76% of the time in our own internal benchmarking on CASP 7‐10 targets. In this work, we improved the sampling and selection stages and tested the method in blind predictions during CASP11. We added a decomposition of physics‐based and hybrid energy functions, as well as a coordinate‐free representation of the protein structure through distance‐binning distances to capture fine‐grained movements. We performed parameter estimation to optimize the adjustable SVM parameters to maximize precision while balancing sensitivity and specificity across all cross‐validated data sets, finding enrichment in our ability to select models from the populations of similar decoys generated for targets in CASPs 7‐10. The MD stage was enhanced such that larger structures could be further refined. Among refinement methods that are currently implemented as web‐servers, Princeton_TIGRESS 2.0 demonstrated the most consistent and most substantial net refinement in blind predictions during CASP11. The enhanced refinement protocol Princeton_TIGRESS 2.0 is freely available as a web server at http://atlas.engr.tamu.edu/refinement/ . Proteins 2017; 85:1078–1098. © 2017 Wiley Periodicals, Inc.     

THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, in finite populations under weak stabilizing selection for triallelic loci and for an infinite “rare alleles” model. These are compared to results for neutral characters, to the “Gaussian allelic” model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in . While it is easier to maintain absolute when alleles interact to yield dominance or overdominance for fitness, less additivity also makes more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and . This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed . The dependence of on N could be used to test the adequacy of mutation-selection balance models.     

Methane yield and species diversity dynamics of perennial wild plant mixtures established alone,under cover crop maize (Zea mays L.), and after spring barley (Hordeum vulgare L.)

The cultivation of perennial wild plant mixtures (WPMs) in biogas cropping systems dominated by maize (Zea mays L.) restores numerous ecosystem functions and improves both spatial and temporal agrobiodiversity. In addition, the colorful appearance of WPM can help enhance landscape beauty. However, their methane yield per hectare (MYH) varies greatly and amounts to only about 50% that of maize. This study aimed at decreasing MYH variability and increasing accumulated MYH of WPM by optimizing the establishment method. A field trial was established in southwest Germany in 2014, and is still running. It tested the effects of three WPM establishment procedures (E1: alone [without maize, in May], E2: undersown in cover crop maize [in May], E3: WPM sown after whole‐crop harvest of spring barley [Hordeum vulgare L.] in June) on both MYH and species diversity of two WPMs [S1, S2]). Mono‐cropped maize and cup plant (Silphium perfoliatum L.) were used as reference crops. Of the WPM treatments tested, S2E2 achieved the highest (19,296 , 60.5% of maize) and S1E1 the lowest accumulated MYH (8,156 , 25.6% of maize) in the years 2014–2018. Cup plant yielded slightly higher than S2E2 (19,968 , 62.6% of maize). In 2014, the WPM sown under maize did not significantly affect the cover crop performance. From 2015 onward, E1 and E2 had comparable average annual MYH and average annual number of WPM species. With a similar accumulated MYH but significantly higher number of species (3.5–10.2), WPM S2E2 outperformed cup plant. Overall, the long‐term MYH performance of WPM cultivation for biogas production can be significantly improved by undersowing with maize as cover crop. This improved establishment method could help facilitate the implementation of WPM cultivation for biogas production and thus reduce the trade‐off between bioenergy and biodiversity.     

Antibody side chain conformations are position‐dependent

Side chain prediction is an integral component of computational antibody design and structure prediction. Current antibody modelling tools use backbone‐dependent rotamer libraries with conformations taken from general proteins. Here we present our antibody‐specific rotamer library, where rotamers are binned according to their immunogenetics (IMGT) position, rather than their local backbone geometry. We find that for some amino acid types at certain positions, only a restricted number of side chain conformations are ever observed. Using this information, we are able to reduce the breadth of the rotamer sampling space. Based on our rotamer library, we built a side chain predictor, position‐dependent antibody rotamer swapper (PEARS). On a blind test set of 95 antibody model structures, PEARS had the highest average χ₁ and accuracy (78.7% and 64.8%) compared to three leading backbone‐dependent side chain predictors. Our use of IMGT position, rather than backbone ϕ/ψ, meant that PEARS was more robust to errors in the backbone of the model structure. PEARS also achieved the lowest number of side chain–side chain clashes. PEARS is freely available as a web application at http://opig.stats.ox.ac.uk/webapps/pears .     

Collagen chirality and three‐dimensional orientation studied with polarimetric second‐harmonic generation microscopy

Polarization‐dependent second‐harmonic generation (P‐SHG) microscopy is used to characterize molecular nonlinear optical properties of collagen and determine a three‐dimensional (3D) orientation map of collagen fibers within a pig tendon. C₆ symmetry is used to determine the nonlinear susceptibility tensor components ratios in the molecular frame of reference and , where the latter is a newly extracted parameter from the P‐SHG images and is related to the chiral structure of collagen. The is observed for collagen fibers tilted out of the image plane, and can have positive or negative values, revealing the relative polarity of collagen fibers within the tissue. The P‐SHG imaging was performed using a linear polarization‐in polarization‐out (PIPO) method on thin sections of pig tendon cut at different angles. The nonlinear chiral properties of collagen can be used to construct the 3D organization of collagen in the tissue and determine the orientation‐independent molecular susceptibility ratios of collagen fibers in the molecular frame of reference.      

Role of active‐site residues Tyr55 and Tyr114 in catalysis and substrate specificity of Corynebacterium diphtheriae C‐S lyase

In recent years, there has been increased interest in bacterial methionine biosynthesis enzymes as antimicrobial targets because of their pivotal role in cell metabolism. C‐S lyase from Corynebacterium diphtheriae is a pyridoxal 5′‐phosphate‐dependent enzyme in the transsulfuration pathway that catalyzes the α,β‐elimination of sulfur‐containing amino acids, such as l ‐cystathionine, to generate ammonia, pyruvate, and homocysteine, the immediate precursor of L ‐methionine. In order to gain deeper insight into the functional and dynamic properties of the enzyme, mutants of two highly conserved active‐site residues, Y55F and Y114F, were characterized by UV‐visible absorbance, fluorescence, and CD spectroscopy in the absence and presence of substrates and substrate analogs, as well as by steady‐state kinetic studies. Substitution of Tyr55 with Phe apparently causes a 130‐fold decrease in at pH 8.5 providing evidence that Tyr55 plays a role in cofactor binding. Moreover, spectral data show that the mutant accumulates the external aldimine intermediate suggesting that the absence of interaction between the hydroxyl moiety and PLP‐binding residue Lys222 causes a decrease in the rate of substrate deprotonation. Mutation of Tyr114 with Phe slightly influences hydrolysis of l ‐cystathionine, and causes a change in substrate specificity towards l ‐serine and O‐acetyl‐l ‐serine compared to the wild type enzyme. These findings, together with computational data, provide useful insights in the substrate specificity of C‐S lyase, which seems to be regulated by active‐site architecture and by the specific conformation in which substrates are bound, and will aid in development of inhibitors. Proteins 2015; 83:78–90. © 2014 Wiley Periodicals, Inc.     

Norovirus RNA‐dependent RNA polymerase: A computational study of metal‐binding preferences

Norovirus (NV) RNA‐dependent RNA polymerase (RdRP) is essential for replicating the genome of the virus, which makes this enzyme a key target for the development of antiviral agents against NV gastroenteritis. In this work, a complex of NV RdRP bound to manganese ions and an RNA primer‐template duplex was investigated using X‐ray crystallography and hybrid quantum chemical/molecular mechanical simulations. Experimentally, the complex crystallized in a tetragonal crystal form. The nature of the primer/template duplex binding in the resulting structure indicates that the complex is a closed back‐tracked state of the enzyme, in which the ‐end of the primer occupies the position expected for the post‐incorporated nucleotide before translocation. Computationally, it is found that the complex can accept a range of divalent metal cations without marked distortions in the active site structure. The highest binding energy is for copper, followed closely by manganese and iron, and then by zinc, nickel, and cobalt. Proteins 2017; 85:1435–1445. © 2017 Wiley Periodicals, Inc.     

Rate limiting step of the allosteric activation of the bacterial adhesin FimH investigated by molecular dynamics simulations

The bacterial adhesin FimH is a model for the study of protein allostery because its structure has been resolved in multiple configurations, including the active and the inactive state. FimH consists of a pilin domain (PD) that anchors it to the rest of the fimbria and an allosterically regulated lectin domain (LD) that binds mannose on the surface of infected cells. Under normal conditions, the two domains are docked to each other and LD binds mannose weakly. However, in the presence of tensile force generated by shear the domains separate and conformational changes propagate across LD resulting in a stronger bond to mannose. Recently, the crystallographic structure of a variant of FimH has been resolved, called ${\text{FimH}}^{\text{FocH}}$, where PD contains 10 mutations near the inter-domain interface. Although the X-ray structures of FimH and ${\text{FimH}}^{\text{FocH}}$ are almost identical, experimental evidence shows that ${\text{FimH}}^{\text{FocH}}$ is activated even in the absence of shear. Here, molecular dynamics simulations combined with the Jarzynski equality were used to investigate the discrepancy between the crystallographic structures and the functional assays. The results indicate that the free energy barrier of the unbinding process between LD and PD is drastically reduced in ${\text{FimH}}^{\text{FocH}}$. Rupture of inter-domain hydrogen bonds involving R166 constitutes a rate limiting step of the domain separation process and occurs more readily in ${\text{FimH}}^{\text{FocH}}$ than FimH. In conclusion, the mutations in ${\text{FimH}}^{\text{FocH}}$ shift the equilibrium toward an equal occupancy of bound and unbound states for LD and PD by reducing a rate limiting step.