Conventional NMA as a better standard for evaluating elastic network models

Normal mode analysis (NMA) is an important tool for studying protein dynamics. Because of the complexity of conventional NMA that uses an all‐atom model and a semi‐empirical force field, many simplified NMA models have been developed, some of which are known as elastic network models. The quality of these simplified NMA models was assessed mostly by evaluating their predictions against experimental B‐factors, and rarely by comparing them with the original NMA. In this work, we take the effort to create a publicly accessible dataset of proteins with their minimized structures, NMA modes, and mean‐square fluctuations. Then, for the first time, we evaluate the quality of individual normal modes of several widely used elastic network models by comparing them with the conventional NMA. Our results demonstrate that the conventional NMA presents a better and more complete evaluation measure of the quality of elastic network models. This realization should be very helpful in improving current or designing new, higher quality elastic network models. Moreover, using the conventional NMA as the standard of evaluation, a number of interesting and significant insights into the elastic network models are gained. Proteins 2015; 83:259–267. © 2014 Wiley Periodicals, Inc.     

Bridging between normal mode analysis and elastic network models

Normal mode analysis (NMA) has been a powerful tool for studying protein dynamics. Elastic network models (ENM), through their simplicity, have made normal mode computations accessible to a much broader research community and for many more biomolecular systems. The drawback of ENMs, however, is that they are less accurate than NMA. In this work, through steps of simplification that starts with NMA and ends with ENMs we build a tight connection between NMA and ENMs. In the process of bridging between the two, we have also discovered several high‐quality simplified models. Our best simplified model has a mean correlation with the original NMA that is as high as 0.88. In addition, the model is force‐field independent and does not require energy minimization, and thus can be applied directly to experimental structures. Another benefit of drawing the connection is a clearer understanding why ENMs work well and how it can be further improved. We discovered that can be greatly enhanced by including an additional torsional term and a geometry term. Proteins 2014; 82:2157–2168. © 2014 Wiley Periodicals, Inc.     

Tensorial elastic network model for protein dynamics: Integration of the anisotropic network model with bond‐bending and twist elasticities

We present a tensorial elastic network model (TNM) to describe the equilibrium fluctuations of proteins near their native fold structure. The model combines the anisotropic network model (ANM), bond bending elasticity, and backbone twist elasticity, and can predict both the isotropic fluctuations, similar to the Gaussian network model (GNM), and anisotropic fluctuations, similar to the ANM. TNM performs equally well for B‐factor predictions as GNM and predicts the anisotropy of B‐factors better than ANM. The model also outperforms the ANM in its predictability of the complete anisotropic displacement parameters. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

Application of multivariate analysis and mass transfer principles for refinement of a 3‐L bioreactor scale‐down model—when shake flasks mimic 15,000‐L bioreactors better

Characterization of manufacturing processes is key to understanding the effects of process parameters on process performance and product quality. These studies are generally conducted using small‐scale model systems. Because of the importance of the results derived from these studies, the small‐scale model should be predictive of large scale. Typically, small‐scale bioreactors, which are considered superior to shake flasks in simulating large‐scale bioreactors, are used as the scale‐down models for characterizing mammalian cell culture processes. In this article, we describe a case study where a cell culture unit operation in bioreactors using one‐sided pH control and their satellites (small‐scale runs conducted using the same post‐inoculation cultures and nutrient feeds) in 3‐L bioreactors and shake flasks indicated that shake flasks mimicked the large‐scale performance better than 3‐L bioreactors. We detail here how multivariate analysis was used to make the pertinent assessment and to generate the hypothesis for refining the existing 3‐L scale‐down model. Relevant statistical techniques such as principal component analysis, partial least square, orthogonal partial least square, and discriminant analysis were used to identify the outliers and to determine the discriminatory variables responsible for performance differences at different scales. The resulting analysis, in combination with mass transfer principles, led to the hypothesis that observed similarities between 15,000‐L and shake flask runs, and differences between 15,000‐L and 3‐L runs, were due to pCO₂ and pH values. This hypothesis was confirmed by changing the aeration strategy at 3‐L scale. By reducing the initial sparge rate in 3‐L bioreactor, process performance and product quality data moved closer to that of large scale. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:1370–1380, 2015     

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.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

Opening and closing of a toroidal group II chaperonin revealed by a symmetry constrained elastic network model

Recently, the atomic structures of both the closed and open forms of Group 2 chaperonin protein Mm‐cpn were revealed through crystallography and cryo‐electron microscopy. This toroidal‐like chaperonin is composed of two eightfold rings that face back‐to‐back. To gain a computational advantage, we used a symmetry constrained elastic network model (SCENM), which requires only a repeated subunit structure and its symmetric connectivity to neighboring subunits to simulate the entire system. In the case of chaperonin, only six subunits (i.e., three from each ring) were used out of the eight subunits comprising each ring. A smooth and symmetric pathway between the open and closed conformations was generated by elastic network interpolation (ENI). To support this result, we also performed a symmetry‐constrained normal mode analysis (NMA), which revealed the intrinsic vibration features of the given structures. The NMA and ENI results for the representative single subunit were duplicated according to the symmetry pattern to reconstruct the entire assembly. To test the feasibility of the symmetry model, its results were also compared with those obtained from the full model. This study allowed the folding mechanism of chaperonin Mm‐cpn to be elucidated by SCENM in a timely manner.     

Dynameomics: Data‐driven methods and models for utilizing large‐scale protein structure repositories for improving fragment‐based loop prediction

Protein function is intimately linked to protein structure and dynamics yet experimentally determined structures frequently omit regions within a protein due to indeterminate data, which is often due protein dynamics. We propose that atomistic molecular dynamics simulations provide a diverse sampling of biologically relevant structures for these missing segments (and beyond) to improve structural modeling and structure prediction. Here we make use of the Dynameomics data warehouse, which contains simulations of representatives of essentially all known protein folds. We developed novel computational methods to efficiently identify, rank and retrieve small peptide structures, or fragments, from this database. We also created a novel data model to analyze and compare large repositories of structural data, such as contained within the Protein Data Bank and the Dynameomics data warehouse. Our evaluation compares these structural repositories for improving loop predictions and analyzes the utility of our methods and models. Using a standard set of loop structures, containing 510 loops, 30 for each loop length from 4 to 20 residues, we find that the inclusion of Dynameomics structures in fragment‐based methods improves the quality of the loop predictions without being dependent on sequence homology. Depending on loop length, ～25–75% of the best predictions came from the Dynameomics set, resulting in lower main chain root‐mean‐square deviations for all fragment lengths using the combined fragment library. We also provide specific cases where Dynameomics fragments provide better predictions for NMR loop structures than fragments from crystal structures. Online access to these fragment libraries is available at http://www.dynameomics.org/fragments .     

All‐atom and coarse‐grained simulations of the forced unfolding pathways of the SNARE complex

The SNARE complex, consisting of three proteins (VAMP2, syntaxin, and SNAP‐25), is thought to drive membrane fusion by assembling into a four‐helix bundle through a zippering process. In support of the above zippering model, a recent single‐molecule optical tweezers experiment by Gao et al. revealed a sequential unzipping of SNARE along VAMP2 in the order of the linker domain → the C‐terminal domain → the N‐terminal domain. To offer detailed structural insights to this unzipping process, we have performed all‐atom and coarse‐grained steered molecular dynamics (sMD) simulations of the forced unfolding pathways of SNARE using different models and force fields. Our findings are summarized as follows: First, the sMD simulations based on either an all‐atom force field (with an implicit solvent model) or a coarse‐grained Go model were unable to capture the forced unfolding pathway of SNARE as observed by Gao et al., which may be attributed to insufficient simulation time and inaccurate force fields. Second, the sMD simulations based on a reparameterized coarse‐grained model (i.e., modified elastic network model) were able to predict a sequential unzipping of SNARE in good agreement with the findings by Gao et al. The key to this success is to reparameterize the intrahelix and interhelix nonbonded force constants against the pair‐wise residue–residue distance fluctuations collected from all‐atom MD simulations of SNARE. Therefore, our finding supports the importance of accurately describing the inherent dynamics/flexibility of SNARE (in the absence of force), in order to correctly simulate its unfolding behaviors under force. This study has established a useful computational framework for future studies of the zippering function of SNARE and its perturbations by point mutations with amino‐acid level of details, and more generally the forced unfolding pathways of other helix bundle proteins. Proteins 2014; 82:1376–1386. © 2014 Wiley Periodicals, Inc.     

Coarse‐ and fine‐grained models for proteins: Evaluation by decoy discrimination

Coarse‐grained models for protein structure are increasingly used in simulations and structural bioinformatics. In this study, we evaluated the effectiveness of three granularities of protein representation based on their ability to discriminate between correctly folded native structures and incorrectly folded decoy structures. The three levels of representation used one bead per amino acid (coarse), two beads per amino acid (medium), and all atoms (fine). Multiple structure features were compared at each representation level including two‐body interactions, three‐body interactions, solvent exposure, contact numbers, and angle bending. In most cases, the all‐atom level was most successful at discriminating decoys, but the two‐bead level provided a good compromise between the number of model parameters which must be estimated and the accuracy achieved. The most effective feature type appeared to be two‐body interactions. Considering three‐body interactions increased accuracy only marginally when all atoms were used and not at all in medium and coarse representations. Though two‐body interactions were most effective for the coarse representations, the accuracy loss for using only solvent exposure or contact number was proportionally less at these levels than in the all‐atom representation. We propose an optimization method capable of selecting bead types of different granularities to create a mixed representation of the protein. We illustrate its behavior on decoy discrimination and discuss implications for data‐driven protein model selection. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Assessment of ATR‐NIR and ATR‐MIR spectroscopy as an analytical tool for the quantification of the total polyphenols in Dendrobium huoshanense

In this study, the potentiality of applying attenuated total reflectance near‐infrared (ATR‐NIR) and attenuated total reflectance mid‐infrared (ATR‐MIR) techniques combined with a partial least squares (PLS) regression technology to quantify the total polyphenols (TPs) in Dendrobium huoshanense (DHS) was investigated and compared. The real TP contents in the DHS samples were analysed using methods of reference. The capability of the two IR spectroscopic techniques to quantify the TPs in DHS was assessed by the root‐mean‐square error of calibration (RMSEC) and determination coefficients (R²). The results showed that both NIR and MIR might be used as a fast and simple tool to replace traditional chemical assays for the determination of the TP contents in DHS, and the best NIR model showed slightly better prediction performance [root‐mean‐square error of prediction (RMSEP): 0.307, R²: 0.9122, ratio performance deviation (RPD): 4.43] than the best MIR model (RMSEP: 0.440, R²: 0.9069, RPD: 3.09). Results from this study indicated that both the NIR and MIR models could be used to quantify the TP in DHS, and ATR‐NIR appeared to be the more predominant and more robust technique for the quantification of the TP in DHS.     

REMO: A new protocol to refine full atomic protein models from C‐alpha traces by optimizing hydrogen‐bonding networks

Protein structure prediction approaches usually perform modeling simulations based on reduced representation of protein structures. For biological utilizations, it is an important step to construct full atomic models from the reduced structure decoys. Most of the current full atomic model reconstruction procedures have defects which either could not completely remove the steric clashes among backbone atoms or generate final atomic models with worse topology similarity relative to the native structures than the reduced models. In this work, we develop a new protocol, called REMO, to generate full atomic protein models by optimizing the hydrogen‐bonding network with basic fragments matched from a newly constructed backbone isomer library of solved protein structures. The algorithm is benchmarked on 230 nonhomologous proteins with reduced structure decoys generated by I‐TASSER simulations. The results show that REMO has a significant ability to remove steric clashes, and meanwhile retains good topology of the reduced model. The hydrogen‐bonding network of the final models is dramatically improved during the procedure. The REMO algorithm has been exploited in the recent CASP8 experiment which demonstrated significant improvements of the I‐TASSER models in both atomic‐level structural refinement and hydrogen‐bonding network construction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Selective refinement and selection of near‐native models in protein structure prediction

In recent years in silico protein structure prediction reached a level where fully automated servers can generate large pools of near‐native structures. However, the identification and further refinement of the best structures from the pool of models remain problematic. To address these issues, we have developed (i) a target‐specific selective refinement (SR) protocol; and (ii) molecular dynamics (MD) simulation based ranking (SMDR) method. In SR the all‐atom refinement of structures is accomplished via the Rosetta Relax protocol, subject to specific constraints determined by the size and complexity of the target. The best‐refined models are selected with SMDR by testing their relative stability against gradual heating through all‐atom MD simulations. Through extensive testing we have found that Mufold‐MD, our fully automated protein structure prediction server updated with the SR and SMDR modules consistently outperformed its previous versions. Proteins 2015; 83:1823–1835. © 2015 Wiley Periodicals, Inc.     

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the C_α-only elastic network models, which assume elastic interactions between pairs of residues whose C_α atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between C_α atoms or heavy atoms derived from a large set of protein crystal structures.     

Bivariate random‐effects meta‐analysis models for diagnostic test accuracy studies using arcsine‐based transformations

Diagnostic or screening tests are widely used in medical fields to classify patients according to their disease status. Several statistical models for meta‐analysis of diagnostic test accuracy studies have been developed to synthesize test sensitivity and specificity of a diagnostic test of interest. Because of the correlation between test sensitivity and specificity, modeling the two measures using a bivariate model is recommended. In this paper, we extend the current standard bivariate linear mixed model (LMM) by proposing two variance‐stabilizing transformations: the arcsine square root and the Freeman–Tukey double arcsine transformation. We compared the performance of the proposed methods with the standard method through simulations using several performance measures. The simulation results showed that our proposed methods performed better than the standard LMM in terms of bias, root mean square error, and coverage probability in most of the scenarios, even when data were generated assuming the standard LMM. We also illustrated the methods using two real data sets.     

Cross‐scale predictive modeling of CHO cell culture growth and metabolites using Raman spectroscopy and multivariate analysis

Multi‐component, multi‐scale Raman spectroscopy modeling results from a monoclonal antibody producing CHO cell culture process including data from two development scales (3 L, 200 L) and a clinical manufacturing scale environment (2,000 L) are presented. Multivariate analysis principles are a critical component to partial least squares (PLS) modeling but can quickly turn into an overly iterative process, thus a simplified protocol is proposed for addressing necessary steps including spectral preprocessing, spectral region selection, and outlier removal to create models exclusively from cell culture process data without the inclusion of spectral data from chemically defined nutrient solutions or targeted component spiking studies. An array of single‐scale and combination‐scale modeling iterations were generated to evaluate technology capabilities and model scalability. Analysis of prediction errors across models suggests that glucose, lactate, and osmolality are well modeled. Model strength was confirmed via predictive validation and by examining performance similarity across single‐scale and combination‐scale models. Additionally, accurate predictive models were attained in most cases for viable cell density and total cell density; however, these components exhibited some scale‐dependencies that hindered model quality in cross‐scale predictions where only development data was used in calibration. Glutamate and ammonium models were also able to achieve accurate predictions in most cases. However, there are differences in the absolute concentration ranges of these components across the datasets of individual bioreactor scales. Thus, glutamate and ammonium PLS models were forced to extrapolate in cases where models were derived from small scale data only but used in cross‐scale applications predicting against manufacturing scale batches. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:566–577, 2015