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.     

Association of putative concave protein-binding sites with the fluctuation behavior of residues

Here, we propose a binding site prediction method based on the high frequency end of the spectrum in the native state of the protein structural dynamics. The spectrum is obtained using an elastic network model (GNM). High frequency vibrating (HFV) residues are determined from the fastest modes dynamics. HFV residue clusters and the associated surface patch residues are tested for their likelihood to locate at the binding interfaces using two different data sets, the Benchmark Set of mainly enzymes and antigen/antibodies and the Cluster Set of more diverse structures. The binding interface is identified to be within 7.5 A of the HFV residue clusters in the Benchmark Set and Cluster Set, for 77% and 70% of the structures, respectively. The success rate increases to 88% and 84%, respectively, by using the surface patches. The results suggest that concave binding interfaces, typically those of enzyme-binding sites, are enriched by the HFV residues. Thus, we expect that the association of HFV residues with the interfaces is mostly for enzymes. If, however, a binding region has invaginations and cavities, as in some of the antigen/antibodies and in cases in the Cluster data set, we expect it would be detected there too. This implies that binding sites possess several (inter-related) properties such as cavities, high packing density, conservation, and disposition for hotspots at binding surfaces. It further suggests that the high frequency vibrating residue-based approach is a potential tool for identification of regions likely to serve as protein-binding sites. The software is available at http://www.prc.boun.edu.tr/PRC/software.html.     

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.     

淀粉蔗糖酶AcAS的工作机理与去折叠性质研究

淀粉蔗糖酶(amylosucrase, AS)是一种葡萄糖基转移酶(E.C. 2.4.1.4),隶属于糖苷水解酶13家族．当体系中存在葡聚糖时,AS可以蔗糖为唯一底物催化合成直链葡聚糖．与AS相比,其他拥有合成直链淀粉样多糖的酶都需要利用昂贵的核苷酸激活糖来进行合成．这使得AS成为一种具有工业应用潜力的工业酶．尽管具有较大应用潜力,但是较弱的稳定性严重影响其在工业上的应用．本工作中,以NpAS和DgAS的晶体结构为模板,对氯酚节杆菌(Arthrobacter chlorophenolicus)中发现的一种新型AS(AcAS)结构进行了模建．通过对AcAS与其他AS结构进行详细的比较,推断出AcAS的工作机理．随后,利用高斯网络模型(GNM)对其功能型运动进行了分析．根据GNM的结果,发现AcAS可分为两个运动方向相异的部分．最后,利用迭代高斯网络对AcAS的去折叠性质进行了研究．这些结果对随后的淀粉蔗糖酶的工业开发有一定帮助．     

Deriving correlated motions in proteins from X-ray structure refinement by using TLS parameters

Dynamic information in proteins may provide valuable information for understanding allosteric regulation of protein complexes or long-range effects of the mutations on enzyme activity. Experimental data such as X-ray B-factors or NMR order parameters provide a convenient estimate of atomic fluctuations (or atomic auto-correlated motions) in proteins. However, it is not as straightforward to obtain atomic cross-correlated motions in proteins — one usually resorts to more sophisticated computational methods such as Molecular Dynamics, normal mode analysis or atomic network models. In this report, we show that atomic cross-correlations can be reliably obtained directly from protein structure using X-ray refinement data. We have derived an analytic form of atomic correlated motions in terms of the original TLS parameters used to refine the B-factors of X-ray structures. The correlated maps computed using this equation are well correlated with those of the method based on a mechanical model (the correlation coefficient is 0.75) for a non-homologous dataset comprising 100 structures. We have developed an approach to compute atomic cross-correlations directly from X-ray protein structure. Being in analytic form, it is fast and provides a feasible way to compute correlated motions in proteins in a high throughput way. In addition, avoiding sophisticated computational operations; it provides a quick, reliable way, especially for non-computational biologists, to obtain dynamics information directly from protein structure relevant to its function.     

Topological thermal instability and length of proteins

We present an analysis of the effects of global topology on the structural stability of folded proteins in thermal equilibrium with a heat bath. For a large class of single domain proteins, we computed the harmonic spectrum within the Gaussian Network Model (GNM) and determined their spectral dimension, a parameter describing the low frequency behavior of the density of modes. We found a surprisingly strong correlation between the spectral dimension and the number of amino acids in the protein. Considering that larger spectral dimension values relate to more topologically compact folded states, our results indicate that, for a given temperature and length of protein, the folded structure corresponds to a less compact folding, one compatible with thermodynamic stability.     

Coupling of structural fluctuations to deamidation reaction in triosephosphate isomerase by Gaussian network model

We study the structural fluctuations of triosephosphate isomerase (TIM) by an elastic model, namely, the Gaussian network model (GNM), to identify a network of coupled motions in the allosteric communication between its deamidation and catalytic sites, and the promoting motions for the deamidation activity. For this, three TIM structures have been studied: one crystal structure and two model structures designed to describe different putative models for the deamidation reaction taking place at the subunit interface. The structural fluctuations have been mapped on the functional properties; then the differences in the fluctuations between the two models in relation to the deamidation reaction have been considered. The results demonstrate that the qualitative picture of the mean-square fluctuations and the correlations between the fluctuations are similar in both, but the differences may affect the observed barrier height of the deamidation reaction. The higher packing density at regions close to deamidation sites, reflected by the high-frequency fluctuating residues in the respective regions, the stronger positive correlation between the fluctuations of the deamidation sites, and enhanced positive correlation of the primary deamidation site with the extended vicinity of the catalytic region on the juxtaposed unit promote the probability of the deamidation reaction. The results in general emphasize the importance of structural fluctuations in enzyme reactions, as well as proposing the present methodology as a plausible approach for studies on the network of coupled promoting motions in protein functions.     

Analyzing the flexibility of RNA structures by constraint counting

RNA requires conformational dynamics to undergo its diverse functional roles. Here, a new topological network representation of RNA structures is presented that allows analyzing RNA flexibility/rigidity based on constraint counting. The method extends the FIRST approach, which identifies flexible and rigid regions in atomic detail in a single, static, three-dimensional molecular framework. Initially, the network rigidity of a canonical A-form RNA is analyzed by counting on constraints of network elements of increasing size. These considerations demonstrate that it is the inclusion of hydrophobic contacts into the RNA topological network that is crucial for an accurate flexibility prediction. The counting also explains why a protein-based parameterization results in overly rigid RNA structures. The new network representation is then validated on a tRNA^ASP structure and all NMR-derived ensembles of RNA structures currently available in the Protein Data Bank (with chain length ≥40). The flexibility predictions demonstrate good agreement with experimental mobility data, and the results are superior compared to predictions based on two previously used network representations. Encouragingly, this holds for flexibility predictions as well as mobility predictions obtained by constrained geometric simulations on these networks. Potential applications of the approach to analyzing the flexibility of DNA and RNA/protein complexes are discussed.     

ATP binding enables broad antibiotic selectivity of aminoglycoside phosphotransferase(3')-IIIa: an elastic network analysis

The bacterial enzyme aminoglycoside phosphotransferase(3′)-IIIa (APH) confers resistance against a wide range of aminoglycoside antibiotics. In this study, we use the Gaussian network model to investigate how the binding of nucleotides and antibiotics influences the dynamics and thereby the ligand binding properties of APH. Interestingly, in NMR experiments, the dynamics differ significantly in various APH complexes, although crystallographic studies indicate that no larger conformational changes occur upon ligand binding. Isothermal titration calorimetry also shows different thermodynamic contributions to ligand binding. Formation of aminoglycoside-APH complexes is enthalpically driven, while the enthalpic change upon aminoglycoside binding to the nucleotide-APH complex is much smaller. The differential effects of nucleotide binding and antibiotic binding to APH can be explained theoretically by single-residue fluctuations and correlated motions of the enzyme. The surprising destabilization of β-sheet residues upon nucleotide binding, as seen in hydrogen/deuterium exchange experiments, shows that the number of closest neighbors does not fully explain residue flexibility. Additionally, we must consider correlated motions of dynamic protein domains, which show that not only connectivity but also the overall protein architecture is important for protein dynamics.     

Propagation of dynamic changes in barnase upon binding of barstar: an NMR and computational study

NMR spectroscopy and computer simulations were used to examine changes in chemical shifts and in dynamics of the ribonuclease barnase that result upon binding to its natural inhibitor barstar. Although the spatial structures of free and bound barnase are very similar, binding results in changes of the dynamics of both fast side-chains, as revealed by (2)H relaxation measurements, and NMR chemical shifts in an extended beta-sheet that is located far from the binding interface. Both side-chain dynamics and chemical shifts are sensitive to variations in the ensemble populations of the inter-converting molecular states, which can escape direct structural observation. Molecular dynamics simulations of free barnase and barnase in complex with barstar, as well as a normal mode analysis of barnase using a Gaussian network model, reveal relatively rigid domains that are separated by the extended beta-sheet mentioned above. The observed changes in NMR parameters upon ligation can thus be rationalized in terms of changes in inter-domain dynamics and in populations of exchanging states, without measurable structural changes. This provides an alternative model for the propagation of a molecular response to ligand binding across a protein that is based exclusively on changes in dynamics.