Structural flexibility in proteins: impact of the crystal environment

MOTIVATION: In the study of the structural flexibility of proteins, crystallographic Debye-Waller factors are the most important experimental information used in the calibration and validation of computational models, such as the very successful elastic network models (ENMs). However, these models are applied to single protein molecules, whereas the experiments are performed on crystals. Moreover, the energy scale in standard ENMs is undefined and must be obtained by fitting to the same data that the ENM is trying to predict, reducing the predictive power of the model. RESULTS: We develop an elastic network model for the whole protein crystal in order to study the influence of crystal packing and lattice vibrations on the thermal fluctuations of the atom positions. We use experimental values for the compressibility of the crystal to establish the energy scale of our model. We predict the elastic constants of the crystal and compare with experimental data. Our main findings are (1) crystal packing modifies the atomic fluctuations considerably and (2) thermal fluctuations are not the dominant contribution to crystallographic Debye-Waller factors. AVAILABILITY: The programs developed for this work are available as supplementary material at Bioinformatics Online.     

Validating and improving elastic network models with molecular dynamics simulations

Elastic network models (ENMs) are a class of simple models intended to represent the collective motions of proteins. In contrast to all‐atom molecular dynamics simulations, the low computational investment required to use an ENM makes them ideal for speculative hypothesis‐testing situations. Historically, ENMs have been validated via comparison to crystallographic B‐factors, but this comparison is relatively low‐resolution and only tests the predictions of relative flexibility. In this work, we systematically validate and optimize a number of ENM‐type models by quantitatively comparing their predictions to microsecond‐scale all‐atom simulations of three different G protein coupled receptors. We show that, despite their apparent simplicity, well‐optimized ENMs perform remarkably well, reproducing the protein fluctuations with an accuracy comparable to what one would expect from all‐atom simulations run for several hundred nanoseconds. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

All-Atom Contact Model for Understanding Protein Dynamics from Crystallographic B-Factors

An all-atom local contact model is described that can be used to predict protein motions underlying isotropic crystallographic B-factors. It uses a mean-field approximation to represent the motion of an atom in a harmonic potential generated by the surrounding atoms resting at their equilibrium positions. Based on a 400-ns molecular dynamics simulation of ubiquitin in explicit water, it is found that each surrounding atom stiffens the spring constant by a term that on average scales exponentially with the interatomic distance. This model combines features of the local density model by Halle and the local contact model by Zhang and Brüschweiler. When applied to a nonredundant set of 98 ultra-high resolution protein structures, an average correlation coefficient of 0.75 is obtained for all atoms. The systematic inclusion of crystal contact contributions and fraying effects is found to enhance the performance substantially. Because the computational cost of the local contact model scales linearly with the number of protein atoms, it is applicable to proteins of any size for the prediction of B-factors of both backbone and side-chain atoms. The model performs as well as or better than several other models tested, such as rigid-body motional models, the local density model, and various forms of the elastic network model. It is concluded that at the currently achievable level of accuracy, collective intramolecular motions are not essential for the interpretation of B-factors.     

vGNM: a better model for understanding the dynamics of proteins in crystals

The dynamics of proteins are important for understanding their functions. In recent years, the simple coarse-grained Gaussian Network Model (GNM) has been fairly successful in interpreting crystallographic B-factors. However, the model clearly ignores the contribution of the rigid body motions and the effect of crystal packing. The model cannot explain the fact that the same protein may have significantly different B-factors under different crystal packing conditions. In this work, we propose a new GNM, called vGNM, which takes into account both the contribution of the rigid body motions and the effect of crystal packing, by allowing the amplitude of the internal modes to be variables. It hypothesizes that the effect of crystal packing should cause some modes to be amplified and others to become less important. In doing so, vGNM is able to resolve the apparent discrepancy in experimental B-factors among structures of the same protein but with different crystal packing conditions, which GNM cannot explain. With a small number of parameters, vGNM is able to reproduce experimental B-factors for a large set of proteins with significantly better correlations (having a mean value of 0.81 as compared to 0.59 by GNM). The results of applying vGNM also show that the rigid body motions account for nearly 60% of the total fluctuations, in good agreement with previous findings.     

Predicting the order in which contacts are broken during single molecule protein stretching experiments

We combine two methods to enable the prediction of the order in which contacts are broken under external stretching forces in single molecule experiments. These two methods are Gō-like models and elastic network models. The Gō-like models have shown remarkable success in representing many aspects of protein behavior, including the reproduction of experimental data obtained from atomic force microscopy. The simple elastic network models are often used successfully to predict the fluctuations of residues around their mean positions, comparing favorably with the experimentally measured crystallographic B-factors. The behavior of biomolecules under external forces has been demonstrated to depend principally on their elastic properties and the overall shape of their structure. We have studied in detail the muscle protein titin and green fluorescent protein and tested for ten other proteins. First, we stretch the proteins computationally by performing stochastic dynamics simulations with the Gō-like model. We obtain the force-displacement curves and unfolding scenarios of possible mechanical unfolding. We then use the elastic network model to calculate temperature factors (B-factors) and compare the slowest modes of motion for the stretched proteins and compare them with the predicted order of breaking contacts between residues in the Gō-like model. Our results show that a simple Gaussian network model is able to predict contacts that break in the next time stage of stretching. Additionally, we have found that the contact disruption is strictly correlated with the highest force exerted by the backbone on these residues. Our prediction of bond-breaking agrees well with the unfolding scenario obtained with the Gō-like model. We anticipate that this method will be a useful new tool for interpreting stretching experiments.     

Constraints imposed by the membrane selectively guide the alternating access dynamics of the glutamate transporter GltPh

Substrate transport in sodium-coupled amino acid symporters involves a large-scale conformational change that shifts the access to the substrate-binding site from one side of the membrane to the other. The structural change is particularly substantial and entails a unique piston-like quaternary rearrangement in glutamate transporters, as evidenced by the difference between the outward-facing and inward-facing structures resolved for the archaeal aspartate transporter Glt(Ph). These structural changes occur over time and length scales that extend beyond the reach of current fully atomic models, but are regularly explored with the use of elastic network models (ENMs). Despite their success with other membrane proteins, ENM-based approaches for exploring the collective dynamics of Glt(Ph) have fallen short of providing a plausible mechanism. This deficiency is attributed here to the anisotropic constraints imposed by the membrane, which are not incorporated into conventional ENMs. Here we employ two novel (to our knowledge) ENMs to demonstrate that one can largely capture the experimentally observed structural change using only the few lowest-energy modes of motion that are intrinsically accessible to the transporter, provided that the surrounding lipid molecules are incorporated into the ENM. The presence of the membrane reduces the overall energy of the transition compared with conventional models, showing that the membrane not only guides the selected mechanism but also acts as a facilitator. Finally, we show that the dynamics of Glt(Ph) is biased toward transitions of individual subunits of the trimer rather than cooperative transitions of all three subunits simultaneously, suggesting a mechanism of transport that exploits the intrinsic dynamics of individual subunits. Our software is available online at http://www.membranm.csb.pitt.edu.     

Models with energy penalty on interresidue rotation address insufficiencies of conventional elastic network models

In this study, I present a new elastic network model, to our knowledge, that addresses insufficiencies of two conventional models—the Gaussian network model (GNM) and the anisotropic network model (ANM). It has been shown previously that the GNM is not rotation-invariant due to its energy, which penalizes rigid-body rotation (external rotation). As a result, GNM models are found contaminated with rigid-body rotation, especially in the most collective ones. A new model (EPIRM) is proposed to remove such external component in modes. The extracted internal motions result from a potential that penalizes interresidue stretching and rotation in a protein. The new model is shown to pertinently describe crystallographic temperature factors (B-factors) and protein open↔closed transitions. Also, the capability of separating internal and external motions in GNM slow modes permits reexamining important mechanochemical properties in enzyme active sites. The results suggest that catalytic residues stay closer to rigid-body rotation axes than their immediate backbone neighbors. I show that the cumulative density of states for EPIRM and ANM follow different power laws as functions of low-mode frequencies. When using a cutoff distance of 7.5 Å, The cumulative density of states of EPIRM scales faster than that of all-atom normal mode analysis and slower than that of simple lattices.     

Elastic network models capture the motions apparent within ensembles of RNA structures

The role of structure and dynamics in mechanisms for RNA becomes increasingly important. Computational approaches using simple dynamics models have been successful at predicting the motions of proteins and are often applied to ribonucleo-protein complexes but have not been thoroughly tested for well-packed nucleic acid structures. In order to characterize a true set of motions, we investigate the apparent motions from 16 ensembles of experimentally determined RNA structures. These indicate a relatively limited set of motions that are captured by a small set of principal components (PCs). These limited motions closely resemble the motions computed from low frequency normal modes from elastic network models (ENMs), either at atomic or coarse-grained resolution. Various ENM model types, parameters, and structure representations are tested here against the experimental RNA structural ensembles, exposing differences between models for proteins and for folded RNAs. Differences in performance are seen, depending on the structure alignment algorithm used to generate PCs, modulating the apparent utility of ENMs but not significantly impacting their ability to generate functional motions. The loss of dynamical information upon coarse-graining is somewhat larger for RNAs than for globular proteins, indicating, perhaps, the lower cooperativity of the less densely packed RNA. However, the RNA structures show less sensitivity to the elastic network model parameters than do proteins. These findings further demonstrate the utility of ENMs and the appropriateness of their application to well-packed RNA-only structures, justifying their use for studying the dynamics of ribonucleo-proteins, such as the ribosome and regulatory RNAs.     

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.     

Global Motions of the Nuclear Pore Complex: Insights from Elastic Network Models

The nuclear pore complex (NPC) is the gate to the nucleus. Recent determination of the configuration of proteins in the yeast NPC at ∼5 nm resolution permits us to study the NPC global dynamics using coarse-grained structural models. We investigate these large-scale motions by using an extended elastic network model (ENM) formalism applied to several coarse-grained representations of the NPC. Two types of collective motions (global modes) are predicted by the ENMs to be intrinsically favored by the NPC architecture: global bending and extension/contraction from circular to elliptical shapes. These motions are shown to be robust against tested variations in the representation of the NPC, and are largely captured by a simple model of a toroid with axially varying mass density. We demonstrate that spoke multiplicity significantly affects the accessible number of symmetric low-energy modes of motion; the NPC-like toroidal structures composed of 8 spokes have access to highly cooperative symmetric motions that are inaccessible to toroids composed of 7 or 9 spokes. The analysis reveals modes of motion that may facilitate macromolecular transport through the NPC, consistent with previous experimental observations.     

生态位模型在流行病学中的应用

随着新冠肺炎(COVID-19)疫情在全球逐渐开始蔓延, 对其传播范围以及强度的风险评估工作越来越受到人们的重视。作为生态学和生物地理学中常用的研究手段, 生态位模型也被应用到该项工作中来。虽然预测流行病的传播热点和趋势是生态位模型的应用方向之一, 但由于新冠病毒(SARS-CoV-2)自身特点, 生态位模型并非预测其潜在传播范围的有力工具。本文回顾了近些年来生态位模型在各种流行病学研究中的应用, 比较了疫病传播中常用生态位建模方法的优势与不足, 分析了适用生态位建模的疫病案例以及不适用于生态位建模的疫病特点, 明确指出, 生态位模型只能用于分析流行病在传播过程中受自然环境干扰的部分, 如中间宿主的潜在分布等。而对于包括COVID-19在内的主要通过人传人的流行病, 生态位模型尚无有效的手段进行预测。尽管生态位模型可用于分析流行病的传播范围, 但在使用时需要根据疾病特点有针对性地选择合适的建模方法与建模对象。为了量化疫病传播风险, 还需要考虑其他干扰因素, 以便准确测试和评估生态位模型。若不加选择地滥用生态位模型的工具, 反而会误导决策者的判断。总之, 在应用生态位模型进行研究工作, 特别是预测流行病的传播范围时, 首先要考虑建模对象是否满足生态学假设。     

Coupling between Normal Modes Drives Protein Conformational Dynamics: Illustrations Using Allosteric Transitions in Myosin II

Structure-based elastic network models (ENMs) have been remarkably successful in describing conformational transitions in a variety of biological systems. Low-frequency normal modes are usually calculated from the ENM that characterizes elastic interactions between residues in contact in a given protein structure with a uniform force constant. To explore the dynamical effects of nonuniform elastic interactions, we calculate the robustness and coupling of the low-frequency modes in the presence of nonuniform variations in the ENM force constant. The variations in the elastic interactions, approximated here by Gaussian noise, approximately account for perturbation effects of heterogeneous residue-residue interactions or evolutionary sequence changes within a protein family. First-order perturbation theory provides an efficient and qualitatively correct estimate of the mode robustness and mode coupling for finite perturbations to the ENM force constant. The mode coupling analysis and the mode robustness analysis identify groups of strongly coupled modes that encode for protein functional motions. We illustrate the new concepts using myosin II motor protein as an example. The biological implications of mode coupling in tuning the allosteric couplings among the actin-binding site, the nucleotide-binding site, and the force-generating converter and lever arm in myosin isoforms are discussed. We evaluate the robustness of the correlation functions that quantify the allosteric couplings among these three key structural motifs.     

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.     

Characterizing and predicting species distributions across environments and scales: Argentine ant occurrences in the eye of the beholder

Aim Species distribution models (SDMs) or, more specifically, ecological niche models (ENMs) are a useful and rapidly proliferating tool in ecology and global change biology. ENMs attempt to capture associations between a species and its environment and are often used to draw biological inferences, to predict potential occurrences in unoccupied regions and to forecast future distributions under environmental change. The accuracy of ENMs, however, hinges critically on the quality of occurrence data. ENMs often use haphazardly collected data rather than data collected across the full spectrum of existing environmental conditions. Moreover, it remains unclear how processes affecting ENM predictions operate at different spatial scales. The scale (i.e. grain size) of analysis may be dictated more by the sampling regime than by biologically meaningful processes. The aim of our study is to jointly quantify how issues relating to region and scale affect ENM predictions using an economically important and ecologically damaging invasive species, the Argentine ant (Linepithema humile). Location California, USA. Methods We analysed the relationship between sampling sufficiency, regional differences in environmental parameter space and cell size of analysis and resampling environmental layers using two independently collected sets of presence/absence data. Differences in variable importance were determined using model averaging and logistic regression. Model accuracy was measured with area under the curve (AUC) and Cohen's kappa. Results We first demonstrate that insufficient sampling of environmental parameter space can cause large errors in predicted distributions and biological interpretation. Models performed best when they were parametrized with data that sufficiently sampled environmental parameter space. Second, we show that altering the spatial grain of analysis changes the relative importance of different environmental variables. These changes apparently result from how environmental constraints and the sampling distributions of environmental variables change with spatial grain. Conclusions These findings have clear relevance for biological inference. Taken together, our results illustrate potentially general limitations for ENMs, especially when such models are used to predict species occurrences in novel environments. We offer basic methodological and conceptual guidelines for appropriate sampling and scale matching.     

Population dynamics can be more important than physiological limits for determining range shifts under climate change

Evidence is accumulating that species' responses to climate changes are best predicted by modelling the interaction of physiological limits, biotic processes and the effects of dispersal‐limitation. Using commercially harvested blacklip (Haliotis rubra) and greenlip abalone (Haliotis laevigata) as case studies, we determine the relative importance of accounting for interactions among physiology, metapopulation dynamics and exploitation in predictions of range (geographical occupancy) and abundance (spatially explicit density) under various climate change scenarios. Traditional correlative ecological niche models (ENM) predict that climate change will benefit the commercial exploitation of abalone by promoting increased abundances without any reduction in range size. However, models that account simultaneously for demographic processes and physiological responses to climate‐related factors result in future (and present) estimates of area of occupancy (AOO) and abundance that differ from those generated by ENMs alone. Range expansion and population growth are unlikely for blacklip abalone because of important interactions between climate‐dependent mortality and metapopulation processes; in contrast, greenlip abalone should increase in abundance despite a contraction in AOO. The strongly non‐linear relationship between abalone population size and AOO has important ramifications for the use of ENM predictions that rely on metrics describing change in habitat area as proxies for extinction risk. These results show that predicting species' responses to climate change often require physiological information to understand climatic range determinants, and a metapopulation model that can make full use of this data to more realistically account for processes such as local extirpation, demographic rescue, source‐sink dynamics and dispersal‐limitation.     

A-site residues move independently from P-site residues in all-atom molecular dynamics simulations of the 70S bacterial ribosome

The ribosome is a large macromolecular machine, and correlated motion between residues is necessary for coordinating function across multiple protein and RNA chains. We ran two all-atom, explicit solvent molecular dynamics simulations of the bacterial ribosome and calculated correlated motion between residue pairs by using mutual information. Because of the short timescales of our simulation (ns), we expect that dynamics are largely local fluctuations around the crystal structure. We hypothesize that residues that show coupled dynamics are functionally related, even on longer timescales. We validate our model by showing that crystallographic B-factors correlate well with the entropy calculated as part of our mutual information calculations. We reveal that A-site residues move relatively independently from P-site residues, effectively insulating A-site functions from P-site functions during translation.     

Spatial perspectives enhance modeling of nanomaterial risks

Novel engineered nanomaterials (ENMs) are increasingly being manufactured and integrated into renewable energy generation and storage technologies. Past research estimated the potential impact of this increased demand on environmental systems, due to both the life cycle impact of ENM production and the potential for their direct release into ecosystems. However, many models treat ENM production and use as spatially implicit, without considering the specific geographic location of potential emissions. By not considering geographical context, ENM accumulation or impact may be underestimated. Here, we introduce an integrated predictive model that forecasts likely ENM manufacturing locations and potential emissions to the environment, with a focus on critical environmental areas and freshwater ecosystems. Spatially explicit ENM concentrations are estimated for four case study ENMs that have promising application in lithium‐ion battery production. Results demonstrate that potential ENM exposure from manufacturing locations within buffer zones of sensitive ecosystems would accumulate to levels associated with measured ecotoxicity risk under high release scenarios, underscoring the importance of adding a spatial and temporal perspective to life cycle toxicity impact assessment. This predictive integrated modeling approach is novel to the nanomaterial literature and can be adapted to other regions and material case studies to proactively inform life cycle tradeoffs and decision‐making.     

Field validation supports novel niche modeling strategies in a cryptic endangered amphibian

Many studies employ ecological niche models (ENMs) to predict species’ occurrences in undersampled regions, generally without field confirmation. Here, we use field surveys to test the relative utility of four potential refinements to the standard ENM approach: 1) altering model complexity based on AIC_c, 2) selecting background points from a biologically informed region, 3) using target‐group background to account for sampling bias in existing localities, and 4) using many rangewide localities (global model) versus fewer proximal localities (local model) to construct geographically restricted range predictions. We used Maxent to predict new localities for the California tiger salamander Ambystoma californiense, an endangered species that often goes undocumented due to its cryptic lifestyle. We followed this with a field survey of 260 previously unsampled potential breeding sites in Solano County, CA and used the resulting presence/absence data to compare all factorial combinations of the four model refinements using a new application of the Kruskal–Wallis test for ENM outputs. Our field surveys led to the discovery of 81 previously undocumented breeding localities for the California tiger salamander and demonstrated that ENMs could be significantly improved by utilizing target‐group background to account for spatial sampling bias and local models to focus model output on the subregion of the range being surveyed. Our results clearly demonstrate the potential for local models to outperform global models, and we recommend supplementing traditional Maxent global models that utilize all known localities with local models, particularly when species occupy geographically structured, heterogeneous habitat types. We also recommend using target‐group background since the improvement we observed when including it in our models was significant and very similar to that documented by previous studies. Most importantly, we emphasize the importance of field verification to enable rigorous statistical comparisons among models.     

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse‐grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass‐weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well‐known proteins of which both closed and open conformations are available as well as three α‐helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.     

Atomic resolution structure of prokaryotic phospholipase A2: analysis of internal motion and implication for a catalytic mechanism

We have found a secreted phospholipase A(2) (PLA(2), EC 3.1.1.4) from Streptomyces violaceoruber A-2688, which is the first PLA(2) identified in prokaryote, and determined its tertiary structure by NMR and X-ray analyses. In this study, we collected the X-ray diffraction data of the bacterial PLA(2) at room temperature (297 K) using conventional MoK(alpha) radiation and refined the structure at a 1.05 A resolution. The atomic resolution analysis led us to introduce disordered conformations and hydrogen atoms into a full anisotropic model. The molecular motion, which is expressed as the sum of rigid-body motion and internal motion of protein, is roughly estimated as the thermal motion when the X-ray diffraction data are collected at room temperature. In this study, we applied a TLS (rigid-body motion in terms of translation, libration, and screw motions) model to analyze the rigid-body motion of the bacterial PLA(2) and calculated the internal motion by subtracting the estimate of the rigid-body motion from the observed anisotropic temperature factor. We also subjected the TLS model to estimate the internal motion of the bovine pancreatic PLA(2) using the anisotropic temperature factor deposited in the Protein Data Bank. Both results indicate that the localization of regions exhibiting larger internal motion in the bacterial PLA(2) is almost the same as that in the bovine pancreatic PLA(2), suggesting that although the tertiary structure of the bacterial PLA(2) is strikingly different from that of the bovine pancreatic PLA(2), the internal motion, which is associated with the calcium(II) ion-binding, phospholipid-binding, and allosteric interfacial activation, is commonly observed in both PLA(2)s.