Protein structural fluctuation, measured by Debye-Waller factors or B-factors, is known to correlate to protein flexibility and function. A variety of methods has been developed for protein Debye-Waller factor prediction and related applications to domain separation, docking pose ranking, entropy calculation, hinge detection, stability analysis, etc. Nevertheless, none of the current methodologies are able to deliver an accuracy of 0.7 in terms of the Pearson correlation coefficients averaged over a large set of proteins. In this work, we introduce a paradigm-shifting geometric graph model, multiscale weighted colored graph (MWCG), to provide a new generation of computational algorithms to significantly change the current status of protein structural fluctuation analysis. Our MWCG model divides a protein graph into multiple subgraphs based on interaction types between graph nodes and represents the protein rigidity by generalized centralities of subgraphs. MWCGs not only predict the B-factors of protein residues but also accurately analyze the flexibility of all atoms in a protein. The MWCG model is validated over a number of protein test sets and compared with many standard methods. An extensive numerical study indicates that the proposed MWCG offers an accuracy of over 0.8 and thus provides perhaps the first reliable method for estimating protein flexibility and B-factors. It also simultaneously predicts all-atom flexibility in a molecule.
I. INTRODUCTION
The Debye-Waller factor is a measure of x-ray scattering model uncertainty caused by thermal motions. In proteins, one refers to this measure as the beta factor (B-factor) or temperature factor. The strength of thermal motions is proportional to the B-factor and is thus a meaningful metric in understanding the protein structure, flexibility, and function.1 Previous studies have shown that intrinsic structural flexibility is related to important protein conformational variations.2 That is, protein dynamics provides a link between the structure and function.
One of the first methods used for B-factor prediction is normal mode analysis (NMA).2–6 NMA takes a time-independent approach by adopting an interaction Hamiltonian from molecular mechanics (MM). In this model, bond lengths and angles are fixed. Normal mode analysis is computed via the diagonalization of the Hamiltonian on an energy minimized structure. The normal modes are the orthogonal resonant patterns of the MM system. The collective motion of the protein can then be described by a superposition of the normal modes. Low-frequency modes will involve highly cooperative motions which are meaningful in applications such as hinge detection. Previous studies have shown that the low-frequency modes of NMA have a strong correlation with the transition pathways of macromolecules.2 In particular, NMA efficiently characterizes the coarse-grained deformation motion of supramolecular complexes.
In 1996, the elastic network model (ENM)7 was proposed to simplify NMA. The anisotropic network model (ANM) was introduced as another elastic network model which describes a protein as a spring network using a simple spring potential between residues represented by Cα atoms.8 Using this simplified potential, its modes are then obtained from matrix diagonalization. In this method, all springs have the same force constant. The minimalist approach provided by ANM has been shown to provide good insight into the dynamics of a protein with lower computational cost than NMA.
Similar to ANM, the Gaussian network model (GNM)9,10 bypasses detailed force functions and parameters and represents protein Cα interactions by a Kirchoff matrix, which is a measure of the connectivity of the local environment of each atom. The diagonalization of the Kirchoff matrix gives rise to eigenmodes and eigenvalues for describing protein B-factors. Like ANM, GNM is a minimalist coarse-grained approximation of protein dynamics.9 GNM is known for its better accuracy and efficiency.11 Additionally, graph theory12 and the rotation translation block method13,14 have been proposed. In addition to their applications in protein fluctuation analysis, these methods are also devised for entropy estimation. These approaches have been improved to include crystal periodicity and cofactor corrections,15–17 and density-cluster rotational-translational blocking.14 Applications have been considered to stability18 and docking analysis.19 Many interesting case studies have been reported on hemoglobin,20 F1 ATPase,21,22 chaperonin GroEL,23,24 viral capsids,25,26 and ribosome27,28 as shown in review papers.2,11,29,30
Mathematically, the above-mentioned methods utilize ideas from algebraic graph theory which is the study of graphs by using algebraic methods such as the characteristic polynomial, eigenvalues, and eigenvectors of Laplacian or adjacency matrices associated with the graphs. Algebraic graph theory has also been widely applied to quantum chemistry.31,32 Due to the matrix-diagonalization procedure, the aforementioned methods have a computational complexity of , with N being the number of elements in the involved matrix. Additionally, these methods suffer from limited accuracy. It was reported that for small-sized, medium-sized, and large-sized protein structures, the average Pearson correlation coefficients (PCCs) of B-factor predictions from NMA and GNM are, respectively, below 0.5 and 0.6.33 In fact, both NMA and GNM even deliver negative correlation coefficients for many proteins.33 Therefore, there is a pressing need to develop accurate and reliable methods for protein flexibility analysis and entropy estimation.
In the past few years, an alternative mathematical method based on geometric graphs, called flexibility-rigidity index (FRI), was introduced to bypass matrix-diagonalization.34–36 FRI makes use of protein graph connectivity and centrality to analyze protein flexibility. It assumes that protein interactions, including those with its environment, fully determine its structure in a given environment. The protein structure and its environment, in turn, fully determine protein flexibility and function. As a consequence, one does not need to invoke a protein interaction Hamiltonian as in spectral graph theory to analyze protein flexibility when the accurate structure of the protein and its environment is known. Earlier FRI34 is of in computational complexity34 and the fast FRI (fFRI)35 is of . We have also developed anisotropic FRI (aFRI)35 and generalized FRI (gFRI).37 Multiscale FRI (mFRI) was introduced to capture multiscale interactions in macromolecules,38 leading to multiple graphs, i.e., graphs with parallel edges. Impressively, mFRI is about 20% more accurate than GNM on a set of 364 proteins,38 while fFRI is orders of magnitude faster than GNM on a set of 44 proteins.35 It is able to predict the B-factors of the HIV virus capsid (1E6J) with 313 236 residues in less than 30 seconds on a single-core laptop.35 FRI matrices have been used to construct generalized GNM (gGNM), generalized ANM (gANM), multiscale GNM (mGNM), and multiscale ANM (mANM) methods39 to significantly improve their accuracy in protein flexibility analysis. In fact, mathematically, GNM might be regarded as a spectral graph approximation of the geometric graph centrality. Nonetheless, it is still a challenge to accurately predict protein flexibility. The average PCC of B-factor predictions from the aforementioned methods is typically below 0.7, which is insufficient for a reliable protein flexibility analysis. Given the importance of flexibility analysis, this challenge calls for innovative strategies.
However, none of the aforementioned methods is able to accurately predict the B-factors of different types of atoms in a protein. This limitation is a consequence that previous graph theory based methods do not distinguish different chemical and biological attributions in a graph. This problem can be addressed by appropriate graph coloring and subgraph division.
The objective of this work is to introduce a multiscale weighted colored graph (MWCG) model for protein flexibility analysis. MWCG is a geometric graph model and offers the most accurate and reliable protein flexibility analysis and B-factor prediction. Our basic idea is to color a protein graph by interaction types between graph nodes and define subgraphs according to colors. Generalized centrality is defined on each subgraph via radial basis functions. In a multiscale setting, graphic rigidity at each node in each scale is approximated by the generalized centrality. The proposed MWCG method can be combined with various earlier FRI approaches, such as fFRI, mFRI, and aFRI etc., to further strengthen its power in protein flexibility analysis. Additionally, we show that MWCG works well not only for residues but also for all the atoms in a protein, i.e., non-Cα carbon, nitrogen, oxygen, and sulfur atoms. Hydrogen atoms can be treated similarly if they are available in the data set. In the following, we present a detailed description of our new method and algorithm in terms of weighted colored graph theory. The performance of our method is validated and compared with that of other methods over various protein data sets. We show that the proposed method is over 40% more accurate than GNM on a set of 364 proteins.
II. METHODS AND ALGORITHMS
A. Weighted colored graphs
We provide a description of weighted colored graphs. It is convenient to consider proteins as a network and describe FRI in terms of graph theory. A graph G(V, E) is defined by a set of nodes V, called vertices, and a set of edges of the graph, E, which relates pairs of vertices. A protein network is a graph whose nodes and edges have specific attributes. Specifically, individual atoms represent nodes and edges correspond to various distance-based correlation metrics. Many of existing methods in B-factor prediction use networks of three-dimensional (3D) spatial atomic coordinate data from the Protein Databank (PDB). This approach works because the distance between two atoms in a protein is generally proportional to their interaction strength.
The weighted colored graph (WCG) method converts 3D protein geometric information about atomic coordinates into protein connectivity. The original algorithm considers only Cα atoms in a given protein. In this work, we consider all N atoms in a protein given by a colored graph G(V, E). As such, the ith atom is labeled by its element type αj and position rj and thus , where {C, N, O, S } is a set containing element types in a protein. Hydrogen element is omitted due to its absence from most PDB files and can be added without affecting the present description. To describe the set of edges in a colored protein graph, it is convenient to define directed element-specific pairs (i.e., directed and colored graphs) {CC, CN, CO, CS, NC, NN, NO, NS, OC, ON, OO, OS, SC, SN, SO, SS}. For example, subset {CN} contains all directed CN pairs in the protein such that the first atom is a carbon and the second one is a nitrogen. Therefore, E is a set of weighted directed edges describing the potential interactions of various pairs of atoms,
where ||ri − rj|| is the Euclidean distance between the ith and jth atoms, ηij is a characteristic distance between the atoms, and (αiαj) is a directed pair of element types. Here Φk is a correlation function and is chosen to have the following properties:35
Our previous work35 has shown that generalized exponential functions,
and generalized Lorentz functions,
are good choices which satisfy the assumptions.
Centrality is an important concept in graph theory and has many applications.40 There are many centrality definitions. For example, normalized closeness centrality41 and Harmonic centrality42 of node ri in a connected graph are given as 1/∑j||ri − rj|| and ∑j1/||ri − rj||, respectively. In this context, we extend Harmonic centrality to subgraphs with weighted edges defined by generalized correlation functions,
where is a weight function related to the element type. The WCG centrality in Eq. (6) describes the atomic specific rigidity which measures the stiffness at the ith atom due to the kth set of contact atoms.
B. Weighted colored graph based flexibility analysis
A standard procedure for constructing flexibility index from its corresponding rigidity index is to take a reciprocal function. Therefore, we have a colored flexibility index on subgraphs,
Our recent work indicates that other forms of flexibility index work equally well.37 The flexibility index at each atom corresponds to temperature fluctuation so we can model the B-factor of the ith atom as
where represents the theoretically predicted B-factor of the ith atom. The coefficients ck and b are determined by minimizing the linear system,
where is the experimentally measured B-factor of the ith atom.
C. Multiscale weighted colored graph based flexibility analysis
Macromolecular interactions are of a short-range type, i.e., covalent bonds, medium-range type, such as hydrogen bonds, electrostatics, and van der Waals, and long-range type, namely, hydrophobicity. Consequently, protein flexibility is intrinsically associated with multiple characteristic length scales. To characterize protein multiscale interactions, we propose multiscale weighted colored graphs (MWCGs). The flexibility of the ith atom at the nth scale due to the kth set of interaction atoms is given by
where is an atomic type dependent parameter, a correlation kernel, and a scale parameter. Minimization takes the form
where are experimentally predicted B-factors. In this work, we construct three-scale correlation kernels using two generalized Lorentz kernels and a generalized exponential kernel. By choosing appropriate values for η, ν, and κ, our method is parameter free.
While sulfur atoms play an important role in proteins, they are so sparse that their kernels have a negligible effect on the current model. Therefore, it is convenient to consider a subset of in practical computations,
While we chose C, N, and O due to their high occurrence frequency and important biological relevance, the method can also be adapted to include any element the user prefers. Additionally, when we compute the B-factors of S atoms, we will consider all possible element pairs, SC, SN, SO, and SS in our WCG calculations.
The proposed method is distinct in its ability to consider the effects of Cα interactions in addition to nitrogen, oxygen, and other carbon atoms. The method creates the three aforementioned correlation kernels for all carbon-carbon (CC), carbon-nitrogen (CN), and carbon-oxygen (CO) interactions. Additionally, we consider three-scale interactions, which give rise to a total of 9 correlation kernels, making up the corresponding graph centralities and flexibilities. Our method is then fitted using those C elements from each of the correlation kernels. The element-specific correlation kernels of the proposed method use existing data about carbon, nitrogen, and oxygen interactions that other methods such as mFRI, GNM, and NMA fail to take into account.
By using NC, NN, NO or OC, ON, and OO kernel combinations, one can also use this method to predict the B-factors of these heavy elements in addition to carbon B-factor prediction.
D. Data sets
The study uses two data sets, one from Refs. 35 and 38 and the other from the work of Park, Jernigan, and Wu.33 The first contains 364 proteins35,38 and the second contains 3 subsets of small, medium, and large proteins.33 All sequences have a resolution of 3 Å or higher and an average resolution of 1.3 Å, and the sets include proteins that range from 4 to 3912 residues.33
III. RESULTS
A. Evaluation metric
We use the proposed method to predict the B-factor of Cα atoms for the given set of proteins. In addition to the Cα B-factor prediction, we also used the proposed method to predict the B-factors of nitrogen, oxygen, and sulfur and non-Cα carbon atoms.
To quantitatively assess our method for B-factor prediction, we use the Pearson correlation coefficient given by
where are predicted B-factors using the proposed method and experimental B-factors from the PDB file. The terms and represent the ith theoretical and experimental B-factors, respectively. Here and are averaged B-factors.
B. Parametrization
Using CC, CN, and CO element specific correlation kernels described in Eq. (10) provides a total of 9 unique correlation kernels for the present graph theory-based method. In this work, we set and in all computation.
We carried out a simplified parameter search using the 364 data set to determine near optimal parameters for Cα B-factor predictions. We choose three kernels, in which we set ν = 1 and 3 for Lorentz kernels and κ = 1 for the exponential kernel, respectively. Our earlier analysis indicates that when ν = 3 and κ = 1, one can obtain a fast FRI via the k-d tree scheme by choosing an optimal box size R of R = 4.6η.35 As an approximation, we fix R = 4.6η and when we try to determine a set of near-optimal ηn values.
The first kernel is chosen to be a Lorentz function, and its optimal η1 was found to be η1 = 16 as shown in Fig. 1. Then, instead of a global search, we fixed η1 = 16 to search an optimal η2 for another Lorentz kernel and found that η2 = 2 offers the optimal prediction as shown in Fig. 1. Finally, we fixed η1 = 16 and η2 = 2 to search η3 for an exponential kernel. In this case, we run into a situation that the average Pearson correlation coefficient (PCC) does not decay even if η3 is as large as 40 as shown in Fig. 1. Nevertheless, this parameter behavior is quite reasonable. When only one kernel is used, a good approximation can be obtained by a mediate η value of the range of 12–17. The second η favors a small value to capture the small-scale interactions in proteins. The third η appears to pick up large-scale interactions. However, the larger the η value is, the more expensive the calculation becomes. We, therefore, choose η3 = 31 in our parameter-free MWCG method as listed in Table I. The exponential kernel is used to capture large-scale effects because it decays fast. In this work, as a good approximation, we use this set of parameters for all flexibility analysis.
The average Pearson correlation coefficient (PCC) as found by optimizing individual kernels in the range of ηn = 1, …, 40.
The average Pearson correlation coefficient (PCC) as found by optimizing individual kernels in the range of ηn = 1, …, 40.
C. Visualization of element-specific correlation maps
Visualization is an important part of methodological development. The monotonically decreasing radial basis functions used in the proposed method allow us to create various correlation maps of a given protein. Given that the current method considers carbon, nitrogen, and oxygen atoms, we can create correlation maps that show the relationship between not only carbon atoms but nitrogen and oxygen atoms as well. For each element pair, these maps were calculated using the average of the three kernels described in Sec. III A. The axes of each correlation map correspond to the carbon, nitrogen, or oxygen atoms. As presented in previous work, correlation maps provide a visual display of important structural features.35 Our work extends this concept to more general carbon-carbon, nitrogen-nitrogen, and oxygen-oxygen maps. As an example, we consider three proteins with PDB IDs 3TYS, 1AIE, and 3PSM. Correlation maps can be seen in Figs. 2–5.
(a) VMD representation of PBD ID 1AIE. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 1AIE. The thicker band along the main diagonal of (b) and (c) corresponds to the alpha helix secondary structure in 1AIE.
(a) VMD representation of PBD ID 1AIE. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 1AIE. The thicker band along the main diagonal of (b) and (c) corresponds to the alpha helix secondary structure in 1AIE.
(a) VMD representation of PBD ID 1KGM. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 1KGM. The bands perpendicular to the main diagonal of (b) and (c) correspond to the anti-parallel beta sheet present in 1KGM.
(a) VMD representation of PBD ID 1KGM. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 1KGM. The bands perpendicular to the main diagonal of (b) and (c) correspond to the anti-parallel beta sheet present in 1KGM.
(a) VMD representation of PBD ID 5IIV. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 5IIV. The presence of the two distinct thick bands along the main diagonal of (b) and (c) corresponds to the two alpha helices present in 5IIV. The off-diagonal bands correspond to the bonding interaction between alpha helices.
(a) VMD representation of PBD ID 5IIV. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 5IIV. The presence of the two distinct thick bands along the main diagonal of (b) and (c) corresponds to the two alpha helices present in 5IIV. The off-diagonal bands correspond to the bonding interaction between alpha helices.
(a) VMD representation of PBD ID 3PSM. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 3PSM. The thicker bands along the main diagonal of (b) and (c) correspond to the two alpha helices present in 3PSM while bands perpendicular to the main diagonal correspond to anti-parallel beta sheets.
(a) VMD representation of PBD ID 3PSM. (b) Correlation maps for nitrogen-nitrogen (NN) and (c) oxygen-oxygen (OO) interactions for protein 3PSM. The thicker bands along the main diagonal of (b) and (c) correspond to the two alpha helices present in 3PSM while bands perpendicular to the main diagonal correspond to anti-parallel beta sheets.
D. Validation and comparison
Table II displays the MWCG results for all 364 proteins in the data set. We compare the results of the proposed method with those from the optimal FRI (opFRI), parameter-free FRI (pFRI), and GNM. Tables III–V provide the same comparison for proteins of relatively small, medium, and large sizes.
Correlation coefficients for B-factor prediction obtained by optimal FRI (opFRI), parameter free FRI (pfFRI), and Gaussian normal mode (GNM) for a set of 364 proteins. GNM scores reported here are the result of our tests with a processed set of PDB files as described in Sec. III.
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . |
---|---|---|---|---|---|---|---|---|---|---|---|
1ABA | 87 | 0.855 | 0.727 | 0.698 | 0.613 | 1PEF | 18 | 0.989 | 0.888 | 0.826 | 0.808 |
1AHO | 64 | 0.768 | 0.698 | 0.625 | 0.562 | 1PEN | 16 | 0.957 | 0.516 | 0.465 | 0.27 |
1AIE | 31 | 0.969 | 0.588 | 0.416 | 0.155 | 1PMY | 123 | 0.701 | 0.671 | 0.654 | 0.685 |
1AKG | 16 | 0.945 | 0.373 | 0.35 | 0.185 | 1PZ4 | 114 | 0.921 | 0.828 | 0.781 | 0.843 |
1ATG | 231 | 0.843 | 0.613 | 0.578 | 0.497 | 1Q9B | 43 | 0.957 | 0.746 | 0.726 | 0.656 |
1BGF | 124 | 0.834 | 0.603 | 0.539 | 0.543 | 1QAU | 112 | 0.786 | 0.678 | 0.672 | 0.62 |
1BX7 | 51 | 0.896 | 0.726 | 0.623 | 0.706 | 1QKI | 3912 | 0.508 | 0.809 | 0.751 | 0.645 |
1BYI | 224 | 0.600 | 0.543 | 0.491 | 0.552 | 1QTO | 122 | 0.809 | 0.543 | 0.52 | 0.334 |
1CCR | 111 | 0.741 | 0.58 | 0.512 | 0.351 | 1R29 | 122 | 0.787 | 0.65 | 0.631 | 0.556 |
1CYO | 88 | 0.860 | 0.751 | 0.702 | 0.741 | 1R7J | 90 | 0.859 | 0.789 | 0.621 | 0.368 |
1DF4 | 57 | 0.941 | 0.912 | 0.889 | 0.832 | 1RJU | 36 | 0.805 | 0.517 | 0.447 | 0.431 |
1E5K | 188 | 0.848 | 0.746 | 0.732 | 0.859 | 1RRO | 112 | 0.748 | 0.435 | 0.372 | 0.529 |
1ES5 | 260 | 0.700 | 0.653 | 0.638 | 0.677 | 1SAU | 114 | 0.819 | 0.742 | 0.671 | 0.596 |
1ETL | 12 | 0.932 | 0.71 | 0.609 | 0.628 | 1TGR | 104 | 0.810 | 0.72 | 0.711 | 0.714 |
1ETM | 12 | 0.941 | 0.544 | 0.393 | 0.432 | 1TZV | 141 | 0.869 | 0.837 | 0.82 | 0.841 |
1ETN | 12 | 0.949 | 0.089 | 0.023 | −0.274 | 1U06 | 55 | 0.774 | 0.474 | 0.429 | 0.434 |
1EW4 | 106 | 0.804 | 0.65 | 0.644 | 0.547 | 1U7I | 267 | 0.885 | 0.778 | 0.762 | 0.691 |
1F8R | 1932 | 0.504 | 0.878 | 0.859 | 0.738 | 1U9C | 221 | 0.764 | 0.6 | 0.577 | 0.522 |
1FF4 | 65 | 0.933 | 0.718 | 0.613 | 0.674 | 1UHA | 83 | 0.838 | 0.726 | 0.665 | 0.638 |
1FK5 | 93 | 0.648 | 0.59 | 0.568 | 0.485 | 1UKU | 102 | 0.765 | 0.665 | 0.661 | 0.742 |
1GCO | 1044 | 0.839 | 0.766 | 0.693 | 0.646 | 1ULR | 87 | 0.718 | 0.639 | 0.594 | 0.495 |
1GK7 | 39 | 0.984 | 0.845 | 0.773 | 0.821 | 1UOY | 64 | 0.769 | 0.713 | 0.653 | 0.671 |
1GVD | 52 | 0.849 | 0.781 | 0.732 | 0.591 | 1USE | 40 | 0.960 | 0.438 | 0.146 | −0.142 |
1GXU | 88 | 0.901 | 0.748 | 0.634 | 0.421 | 1USM | 77 | 0.819 | 0.832 | 0.809 | 0.798 |
1H6V | 2927 | 0.133 | 0.488 | 0.429 | 0.306 | 1UTG | 70 | 0.745 | 0.691 | 0.61 | 0.538 |
1HJE | 13 | 0.931 | 0.811 | 0.686 | 0.616 | 1V05 | 96 | 0.841 | 0.629 | 0.599 | 0.632 |
1I71 | 83 | 0.798 | 0.549 | 0.516 | 0.549 | 1V70 | 105 | 0.854 | 0.622 | 0.492 | 0.162 |
1IDP | 441 | 0.827 | 0.735 | 0.715 | 0.69 | 1VRZ | 21 | 0.995 | 0.792 | 0.695 | 0.677 |
1IFR | 113 | 0.875 | 0.697 | 0.689 | 0.637 | 1W2L | 97 | 0.747 | 0.691 | 0.564 | 0.397 |
1K8U | 89 | 0.856 | 0.553 | 0.531 | 0.378 | 1WBE | 204 | 0.767 | 0.591 | 0.577 | 0.549 |
1KMM | 1499 | 0.740 | 0.749 | 0.744 | 0.558 | 1WHI | 122 | 0.804 | 0.601 | 0.539 | 0.27 |
1KNG | 144 | 0.810 | 0.547 | 0.536 | 0.512 | 1WLY | 322 | 0.728 | 0.695 | 0.679 | 0.666 |
1KR4 | 110 | 0.892 | 0.635 | 0.612 | 0.466 | 1WPA | 107 | 0.797 | 0.634 | 0.577 | 0.417 |
1KYC | 15 | 0.971 | 0.796 | 0.763 | 0.754 | 1X3O | 80 | 0.787 | 0.6 | 0.559 | 0.654 |
1LR7 | 73 | 0.929 | 0.679 | 0.657 | 0.62 | 1XY1 | 18 | 0.933 | 0.832 | 0.645 | 0.447 |
1MF7 | 194 | 0.757 | 0.687 | 0.681 | 0.7 | 1XY2 | 8 | 1.000 | 0.619 | 0.57 | 0.562 |
1N7E | 95 | 0.812 | 0.651 | 0.609 | 0.497 | 1Y6X | 87 | 0.838 | 0.596 | 0.524 | 0.366 |
1NKD | 59 | 0.911 | 0.75 | 0.703 | 0.631 | 1YJO | 6 | 1.000 | 0.375 | 0.333 | 0.434 |
1NKO | 122 | 0.831 | 0.619 | 0.535 | 0.368 | 1YZM | 46 | 0.970 | 0.842 | 0.834 | 0.901 |
1NLS | 238 | 0.799 | 0.669 | 0.53 | 0.523 | 1Z21 | 96 | 0.725 | 0.662 | 0.638 | 0.433 |
1NNX | 93 | 0.834 | 0.795 | 0.789 | 0.631 | 1ZCE | 146 | 0.898 | 0.808 | 0.757 | 0.77 |
1NOA | 113 | 0.808 | 0.622 | 0.604 | 0.615 | 1ZVA | 75 | 0.911 | 0.756 | 0.579 | 0.69 |
1NOT | 13 | 0.937 | 0.746 | 0.622 | 0.523 | 2A50 | 457 | 0.704 | 0.564 | 0.524 | 0.281 |
1O06 | 20 | 0.988 | 0.91 | 0.874 | 0.844 | 2AGK | 233 | 0.821 | 0.705 | 0.694 | 0.512 |
1O08 | 221 | 0.516 | 0.562 | 0.333 | 0.309 | 2AH1 | 939 | 0.462 | 0.684 | 0.593 | 0.521 |
1OB4 | 16 | 1.000 | 0.776 | 0.763 | 0.75 | 2B0A | 186 | 0.805 | 0.639 | 0.603 | 0.467 |
1OB7 | 16 | 1.000 | 0.737 | 0.545 | 0.652 | 2BCM | 413 | 0.695 | 0.555 | 0.551 | 0.477 |
1OPD | 85 | 0.607 | 0.555 | 0.409 | 0.398 | 2BF9 | 36 | 0.714 | 0.606 | 0.554 | 0.68 |
1P9I | 29 | 0.841 | 0.754 | 0.742 | 0.625 | 2BRF | 100 | 0.873 | 0.795 | 0.764 | 0.71 |
2CE0 | 99 | 0.824 | 0.706 | 0.598 | 0.529 | 2C71 | 205 | 0.773 | 0.658 | 0.649 | 0.56 |
2CG7 | 90 | 0.738 | 0.551 | 0.539 | 0.379 | 2OLX | 4 | 1.000 | 0.917 | 0.888 | 0.885 |
2COV | 534 | 0.895 | 0.846 | 0.823 | 0.812 | 2PKT | 93 | 0.762 | 0.162 | 0.003 | 0.193 |
2CWS | 227 | 0.756 | 0.647 | 0.64 | 0.696 | 2PLT | 99 | 0.635 | 0.508 | 0.484 | 0.509 |
2D5W | 1214 | 0.448 | 0.689 | 0.682 | 0.681 | 2PMR | 76 | 0.799 | 0.693 | 0.682 | 0.619 |
2DKO | 253 | 0.873 | 0.816 | 0.812 | 0.69 | 2POF | 440 | 0.743 | 0.682 | 0.651 | 0.589 |
2DPL | 565 | 0.721 | 0.596 | 0.538 | 0.658 | 2PPN | 107 | 0.673 | 0.677 | 0.638 | 0.668 |
2DSX | 52 | 0.704 | 0.337 | 0.333 | 0.127 | 2PSF | 608 | 0.641 | 0.526 | 0.5 | 0.565 |
2E10 | 439 | 0.808 | 0.798 | 0.796 | 0.692 | 2PTH | 193 | 0.901 | 0.822 | 0.784 | 0.767 |
2E3H | 81 | 0.794 | 0.692 | 0.682 | 0.605 | 2Q4N | 153 | 0.846 | 0.711 | 0.667 | 0.74 |
2EAQ | 89 | 0.817 | 0.753 | 0.69 | 0.695 | 2Q52 | 412 | 0.510 | 0.756 | 0.748 | 0.621 |
2EHP | 248 | 0.832 | 0.804 | 0.804 | 0.773 | 2QJL | 99 | 0.611 | 0.594 | 0.584 | 0.594 |
2EHS | 75 | 0.805 | 0.72 | 0.713 | 0.747 | 2R16 | 176 | 0.640 | 0.582 | 0.495 | 0.618 |
2ERW | 53 | 0.513 | 0.461 | 0.253 | 0.199 | 2R6Q | 138 | 0.915 | 0.603 | 0.54 | 0.529 |
2ETX | 389 | 0.854 | 0.58 | 0.556 | 0.632 | 2RB8 | 93 | 0.840 | 0.727 | 0.614 | 0.517 |
2FB6 | 116 | 0.850 | 0.791 | 0.786 | 0.74 | 2RE2 | 238 | 0.711 | 0.652 | 0.613 | 0.673 |
2FG1 | 157 | 0.719 | 0.62 | 0.617 | 0.584 | 2RFR | 154 | 0.826 | 0.693 | 0.671 | 0.753 |
2FN9 | 560 | 0.704 | 0.607 | 0.595 | 0.611 | 2V9V | 135 | 0.697 | 0.555 | 0.548 | 0.528 |
2FQ3 | 85 | 0.844 | 0.719 | 0.692 | 0.348 | 2VE8 | 515 | 0.698 | 0.744 | 0.643 | 0.616 |
2G69 | 99 | 0.850 | 0.622 | 0.59 | 0.436 | 2VH7 | 94 | 0.851 | 0.775 | 0.726 | 0.596 |
2G7O | 68 | 0.888 | 0.785 | 0.784 | 0.66 | 2VIM | 104 | 0.859 | 0.413 | 0.393 | 0.212 |
2G7S | 190 | 0.756 | 0.67 | 0.644 | 0.649 | 2VPA | 204 | 0.757 | 0.763 | 0.755 | 0.576 |
2GKG | 122 | 0.748 | 0.688 | 0.646 | 0.711 | 2VQ4 | 106 | 0.776 | 0.68 | 0.679 | 0.555 |
2GOM | 121 | 0.874 | 0.586 | 0.584 | 0.491 | 2VY8 | 149 | 0.759 | 0.77 | 0.724 | 0.533 |
2GXG | 140 | 0.901 | 0.847 | 0.78 | 0.52 | 2VYO | 210 | 0.777 | 0.675 | 0.648 | 0.729 |
2GZQ | 191 | 0.462 | 0.505 | 0.382 | 0.369 | 2W1V | 548 | 0.761 | 0.68 | 0.68 | 0.571 |
2HQK | 213 | 0.897 | 0.824 | 0.809 | 0.365 | 2W2A | 350 | 0.819 | 0.706 | 0.638 | 0.589 |
2HYK | 238 | 0.728 | 0.585 | 0.575 | 0.51 | 2W6A | 117 | 0.804 | 0.823 | 0.748 | 0.647 |
2I24 | 113 | 0.672 | 0.593 | 0.498 | 0.494 | 2WJ5 | 96 | 0.821 | 0.484 | 0.44 | 0.357 |
2I49 | 398 | 0.766 | 0.714 | 0.683 | 0.601 | 2WUJ | 100 | 0.919 | 0.739 | 0.598 | 0.598 |
2IBL | 108 | 0.919 | 0.629 | 0.625 | 0.352 | 2WW7 | 150 | 0.629 | 0.499 | 0.471 | 0.356 |
2IGD | 61 | 0.865 | 0.585 | 0.481 | 0.386 | 2WWE | 111 | 0.903 | 0.692 | 0.582 | 0.628 |
2IMF | 203 | 0.798 | 0.652 | 0.625 | 0.514 | 2X1Q | 240 | 0.505 | 0.534 | 0.478 | 0.443 |
2IP6 | 87 | 0.841 | 0.654 | 0.578 | 0.572 | 2X25 | 168 | 0.710 | 0.632 | 0.598 | 0.403 |
2IVY | 88 | 0.837 | 0.544 | 0.483 | 0.271 | 2X3M | 166 | 0.875 | 0.744 | 0.717 | 0.655 |
2J32 | 244 | 0.878 | 0.863 | 0.848 | 0.855 | 2X5Y | 171 | 0.799 | 0.718 | 0.705 | 0.694 |
2J9W | 200 | 0.741 | 0.716 | 0.705 | 0.662 | 2X9Z | 262 | 0.726 | 0.583 | 0.578 | 0.574 |
2JKU | 35 | 0.926 | 0.805 | 0.695 | 0.656 | 2XHF | 310 | 0.830 | 0.606 | 0.591 | 0.569 |
2JLI | 100 | 0.937 | 0.779 | 0.613 | 0.622 | 2Y0T | 101 | 0.834 | 0.778 | 0.774 | 0.798 |
2JLJ | 115 | 0.811 | 0.741 | 0.72 | 0.527 | 2Y72 | 170 | 0.926 | 0.78 | 0.754 | 0.766 |
2MCM | 113 | 0.867 | 0.789 | 0.713 | 0.639 | 2Y7L | 319 | 0.939 | 0.928 | 0.797 | 0.747 |
2NLS | 36 | 0.937 | 0.605 | 0.559 | 0.53 | 2Y9F | 149 | 0.769 | 0.771 | 0.762 | 0.664 |
2NR7 | 194 | 0.885 | 0.803 | 0.785 | 0.727 | 2YLB | 400 | 0.820 | 0.807 | 0.807 | 0.675 |
2NUH | 104 | 0.922 | 0.835 | 0.691 | 0.771 | 2YNY | 315 | 0.836 | 0.813 | 0.804 | 0.706 |
2O6X | 306 | 0.825 | 0.814 | 0.799 | 0.651 | 2ZCM | 357 | 0.723 | 0.458 | 0.422 | 0.42 |
2OA2 | 132 | 0.703 | 0.571 | 0.456 | 0.458 | 2ZU1 | 360 | 0.753 | 0.689 | 0.672 | 0.653 |
2OCT | 192 | 0.673 | 0.567 | 0.55 | 0.54 | 3A0M | 148 | 0.916 | 0.807 | 0.712 | 0.392 |
2OHW | 256 | 0.743 | 0.614 | 0.539 | 0.475 | 3A7L | 128 | 0.806 | 0.713 | 0.663 | 0.756 |
2OKT | 342 | 0.779 | 0.433 | 0.411 | 0.336 | 3AMC | 614 | 0.758 | 0.675 | 0.669 | 0.581 |
2OL9 | 6 | 1.000 | 0.909 | 0.904 | 0.689 | 3AUB | 116 | 0.650 | 0.614 | 0.608 | 0.637 |
3BA1 | 312 | 0.827 | 0.661 | 0.624 | 0.621 | 3B5O | 230 | 0.729 | 0.644 | 0.629 | 0.601 |
3BED | 261 | 0.874 | 0.845 | 0.82 | 0.684 | 3MD4 | 12 | 0.999 | 0.86 | 0.781 | 0.914 |
3BQX | 139 | 0.900 | 0.634 | 0.481 | 0.297 | 3MD5 | 12 | 0.998 | 0.649 | 0.413 | −0.218 |
3BZQ | 99 | 0.848 | 0.532 | 0.516 | 0.466 | 3MEA | 166 | 0.872 | 0.669 | 0.669 | 0.6 |
3BZZ | 100 | 0.783 | 0.485 | 0.45 | 0.6 | 3MGN | 348 | 0.742 | 0.205 | 0.119 | 0.193 |
3DRF | 547 | 0.781 | 0.559 | 0.549 | 0.488 | 3MRE | 383 | 0.675 | 0.661 | 0.641 | 0.567 |
3DWV | 325 | 0.754 | 0.707 | 0.661 | 0.547 | 3N11 | 325 | 0.736 | 0.614 | 0.583 | 0.517 |
3E5T | 228 | 0.731 | 0.502 | 0.489 | 0.296 | 3NE0 | 208 | 0.859 | 0.706 | 0.645 | 0.659 |
3E7R | 40 | 0.769 | 0.706 | 0.687 | 0.642 | 3NGG | 94 | 0.867 | 0.696 | 0.689 | 0.719 |
3EUR | 140 | 0.874 | 0.431 | 0.427 | 0.577 | 3NPV | 495 | 0.855 | 0.702 | 0.653 | 0.677 |
3F2Z | 149 | 0.877 | 0.824 | 0.792 | 0.74 | 3NVG | 6 | 1.000 | 0.721 | 0.617 | 0.597 |
3F7E | 254 | 0.847 | 0.812 | 0.803 | 0.811 | 3NZL | 73 | 0.713 | 0.627 | 0.583 | 0.506 |
3FCN | 158 | 0.741 | 0.64 | 0.606 | 0.632 | 3O0P | 194 | 0.898 | 0.727 | 0.706 | 0.734 |
3FE7 | 91 | 0.914 | 0.583 | 0.533 | 0.276 | 3O5P | 128 | 0.787 | 0.734 | 0.698 | 0.63 |
3FKE | 250 | 0.755 | 0.525 | 0.476 | 0.435 | 3OBQ | 150 | 0.877 | 0.649 | 0.645 | 0.655 |
3FMY | 66 | 0.857 | 0.701 | 0.655 | 0.556 | 3OQY | 234 | 0.807 | 0.698 | 0.686 | 0.637 |
3FOD | 48 | 0.725 | 0.532 | 0.44 | −0.126 | 3P6J | 125 | 0.689 | 0.774 | 0.767 | 0.81 |
3FSO | 221 | 0.906 | 0.831 | 0.817 | 0.793 | 3PD7 | 188 | 0.848 | 0.77 | 0.723 | 0.589 |
3FTD | 240 | 0.818 | 0.722 | 0.713 | 0.634 | 3PES | 165 | 0.861 | 0.697 | 0.642 | 0.683 |
3FVA | 6 | 1.000 | 0.835 | 0.825 | 0.789 | 3PID | 387 | 0.677 | 0.537 | 0.531 | 0.642 |
3G1S | 418 | 0.879 | 0.771 | 0.7 | 0.63 | 3PIW | 154 | 0.772 | 0.758 | 0.744 | 0.717 |
3GBW | 161 | 0.864 | 0.82 | 0.747 | 0.51 | 3PKV | 221 | 0.731 | 0.625 | 0.597 | 0.568 |
3GHJ | 116 | 0.864 | 0.732 | 0.511 | 0.196 | 3PSM | 94 | 0.914 | 0.876 | 0.79 | 0.745 |
3HFO | 197 | 0.825 | 0.691 | 0.67 | 0.518 | 3PTL | 289 | 0.611 | 0.543 | 0.541 | 0.468 |
3HHP | 1234 | 0.830 | 0.72 | 0.716 | 0.683 | 3PVE | 347 | 0.785 | 0.718 | 0.667 | 0.568 |
3HNY | 156 | 0.885 | 0.793 | 0.723 | 0.758 | 3PZ9 | 357 | 0.758 | 0.709 | 0.709 | 0.678 |
3HP4 | 183 | 0.690 | 0.534 | 0.5 | 0.573 | 3PZZ | 12 | 0.998 | 0.945 | 0.922 | 0.95 |
3HWU | 144 | 0.905 | 0.754 | 0.748 | 0.841 | 3Q2X | 6 | 1.000 | 0.922 | 0.904 | 0.866 |
3HYD | 7 | 1.000 | 0.966 | 0.95 | 0.867 | 3Q6L | 131 | 0.723 | 0.622 | 0.577 | 0.605 |
3HZ8 | 192 | 0.857 | 0.617 | 0.502 | 0.475 | 3QDS | 284 | 0.782 | 0.78 | 0.745 | 0.568 |
3I2V | 124 | 0.879 | 0.486 | 0.441 | 0.301 | 3QPA | 197 | 0.616 | 0.587 | 0.442 | 0.503 |
3I2Z | 138 | 0.732 | 0.613 | 0.599 | 0.317 | 3R6D | 221 | 0.854 | 0.688 | 0.669 | 0.495 |
3I4O | 135 | 0.767 | 0.735 | 0.714 | 0.738 | 3R87 | 132 | 0.861 | 0.452 | 0.419 | 0.286 |
3I7M | 134 | 0.604 | 0.667 | 0.635 | 0.695 | 3RQ9 | 162 | 0.711 | 0.51 | 0.403 | 0.242 |
3IHS | 169 | 0.807 | 0.586 | 0.565 | 0.409 | 3RY0 | 128 | 0.790 | 0.616 | 0.606 | 0.47 |
3IVV | 149 | 0.866 | 0.817 | 0.797 | 0.693 | 3RZY | 139 | 0.867 | 0.8 | 0.784 | 0.849 |
3K6Y | 227 | 0.817 | 0.586 | 0.535 | 0.301 | 3S0A | 119 | 0.713 | 0.562 | 0.524 | 0.526 |
3KBE | 140 | 0.743 | 0.705 | 0.704 | 0.611 | 3SD2 | 86 | 0.842 | 0.523 | 0.421 | 0.237 |
3KGK | 190 | 0.798 | 0.784 | 0.775 | 0.68 | 3SEB | 238 | 0.879 | 0.801 | 0.712 | 0.826 |
3KZD | 85 | 0.789 | 0.647 | 0.611 | 0.475 | 3SED | 124 | 0.870 | 0.709 | 0.658 | 0.712 |
3L41 | 220 | 0.776 | 0.718 | 0.716 | 0.669 | 3SO6 | 150 | 0.747 | 0.675 | 0.666 | 0.63 |
3LAA | 169 | 0.880 | 0.827 | 0.647 | 0.659 | 3SR3 | 637 | 0.633 | 0.619 | 0.611 | 0.624 |
3LAX | 106 | 0.924 | 0.734 | 0.73 | 0.584 | 3SUK | 248 | 0.721 | 0.644 | 0.633 | 0.567 |
3LG3 | 833 | 0.701 | 0.658 | 0.614 | 0.589 | 3SZH | 697 | 0.860 | 0.817 | 0.815 | 0.697 |
3LJI | 272 | 0.720 | 0.612 | 0.608 | 0.551 | 3T0H | 208 | 0.897 | 0.808 | 0.775 | 0.694 |
3M3P | 249 | 0.697 | 0.584 | 0.554 | 0.338 | 3T3K | 122 | 0.803 | 0.796 | 0.748 | 0.735 |
3M8J | 178 | 0.813 | 0.73 | 0.728 | 0.628 | 3T47 | 141 | 0.759 | 0.592 | 0.527 | 0.447 |
3M9J | 210 | 0.867 | 0.639 | 0.574 | 0.296 | 3TDN | 357 | 0.668 | 0.458 | 0.419 | 0.24 |
3M9Q | 176 | 0.851 | 0.591 | 0.51 | 0.471 | 3TOW | 152 | 0.722 | 0.578 | 0.556 | 0.571 |
3MAB | 173 | 0.770 | 0.664 | 0.591 | 0.451 | 3TUA | 210 | 0.696 | 0.665 | 0.658 | 0.588 |
3U6G | 248 | 0.808 | 0.635 | 0.632 | 0.526 | 3TYS | 75 | 0.918 | 0.853 | 0.8 | 0.791 |
3U97 | 77 | 0.819 | 0.753 | 0.736 | 0.712 | 4DT4 | 160 | 0.784 | 0.776 | 0.738 | 0.716 |
3UCI | 72 | 0.689 | 0.589 | 0.526 | 0.495 | 4EK3 | 287 | 0.830 | 0.68 | 0.68 | 0.674 |
3UR8 | 637 | 0.832 | 0.666 | 0.652 | 0.597 | 4ERY | 318 | 0.801 | 0.74 | 0.701 | 0.688 |
3US6 | 148 | 0.668 | 0.698 | 0.586 | 0.553 | 4ES1 | 95 | 0.820 | 0.648 | 0.625 | 0.551 |
3V1A | 48 | 0.811 | 0.531 | 0.487 | 0.583 | 4EUG | 225 | 0.592 | 0.57 | 0.529 | 0.405 |
3V75 | 285 | 0.674 | 0.604 | 0.596 | 0.491 | 4F01 | 448 | 0.883 | 0.633 | 0.372 | 0.688 |
3VN0 | 193 | 0.889 | 0.84 | 0.837 | 0.812 | 4F3J | 143 | 0.879 | 0.617 | 0.598 | 0.551 |
3VOR | 182 | 0.686 | 0.602 | 0.557 | 0.484 | 4FR9 | 141 | 0.806 | 0.671 | 0.655 | 0.501 |
3VUB | 101 | 0.852 | 0.625 | 0.61 | 0.607 | 4G14 | 15 | 1.000 | 0.467 | 0.323 | 0.356 |
3VVV | 108 | 0.951 | 0.833 | 0.741 | 0.753 | 4G2E | 151 | 0.835 | 0.76 | 0.755 | 0.758 |
3VZ9 | 163 | 0.887 | 0.785 | 0.749 | 0.695 | 4G5X | 550 | 0.822 | 0.786 | 0.754 | 0.743 |
3W4Q | 773 | 0.798 | 0.737 | 0.725 | 0.649 | 4G6C | 658 | 0.834 | 0.591 | 0.59 | 0.528 |
3ZBD | 213 | 0.891 | 0.651 | 0.516 | 0.632 | 4G7X | 194 | 0.840 | 0.688 | 0.587 | 0.624 |
3ZIT | 152 | 0.641 | 0.43 | 0.404 | 0.392 | 4GA2 | 144 | 0.782 | 0.528 | 0.485 | 0.406 |
3ZRX | 221 | 0.639 | 0.59 | 0.562 | 0.391 | 4GMQ | 92 | 0.794 | 0.678 | 0.628 | 0.55 |
3ZSL | 138 | 0.903 | 0.691 | 0.687 | 0.526 | 4GS3 | 90 | 0.698 | 0.544 | 0.522 | 0.547 |
3ZZP | 74 | 0.692 | 0.524 | 0.46 | 0.448 | 4H4J | 236 | 0.866 | 0.81 | 0.806 | 0.689 |
3ZZY | 226 | 0.804 | 0.746 | 0.709 | 0.728 | 4H89 | 168 | 0.624 | 0.682 | 0.588 | 0.596 |
4A02 | 166 | 0.730 | 0.618 | 0.516 | 0.303 | 4HDE | 168 | 0.783 | 0.745 | 0.728 | 0.615 |
4ACJ | 167 | 0.827 | 0.748 | 0.746 | 0.759 | 4HJP | 281 | 0.730 | 0.703 | 0.649 | 0.51 |
4AE7 | 186 | 0.862 | 0.724 | 0.717 | 0.717 | 4HWM | 117 | 0.807 | 0.638 | 0.622 | 0.499 |
4AM1 | 345 | 0.796 | 0.674 | 0.619 | 0.46 | 4IL7 | 85 | 0.719 | 0.446 | 0.404 | 0.316 |
4ANN | 176 | 0.562 | 0.551 | 0.536 | 0.47 | 4J11 | 357 | 0.726 | 0.62 | 0.562 | 0.401 |
4AVR | 188 | 0.759 | 0.68 | 0.605 | 0.65 | 4J5O | 220 | 0.817 | 0.793 | 0.757 | 0.777 |
4AXY | 54 | 0.973 | 0.7 | 0.623 | 0.72 | 4J5Q | 146 | 0.851 | 0.742 | 0.742 | 0.689 |
4B6G | 558 | 0.804 | 0.765 | 0.756 | 0.669 | 4J78 | 305 | 0.729 | 0.658 | 0.648 | 0.608 |
4B9G | 292 | 0.855 | 0.844 | 0.816 | 0.763 | 4JG2 | 185 | 0.889 | 0.746 | 0.736 | 0.543 |
4DD5 | 387 | 0.850 | 0.615 | 0.596 | 0.351 | 4JVU | 207 | 0.800 | 0.723 | 0.697 | 0.553 |
4DKN | 423 | 0.786 | 0.781 | 0.761 | 0.539 | 4JYP | 534 | 0.800 | 0.688 | 0.682 | 0.538 |
4DND | 95 | 0.829 | 0.763 | 0.75 | 0.582 | 4KEF | 133 | 0.704 | 0.58 | 0.53 | 0.324 |
4DPZ | 109 | 0.837 | 0.73 | 0.726 | 0.651 | 5CYT | 103 | 0.548 | 0.441 | 0.421 | 0.331 |
4DQ7 | 328 | 0.776 | 0.69 | 0.683 | 0.376 | 6RXN | 45 | 0.583 | 0.614 | 0.574 | 0.594 |
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . |
---|---|---|---|---|---|---|---|---|---|---|---|
1ABA | 87 | 0.855 | 0.727 | 0.698 | 0.613 | 1PEF | 18 | 0.989 | 0.888 | 0.826 | 0.808 |
1AHO | 64 | 0.768 | 0.698 | 0.625 | 0.562 | 1PEN | 16 | 0.957 | 0.516 | 0.465 | 0.27 |
1AIE | 31 | 0.969 | 0.588 | 0.416 | 0.155 | 1PMY | 123 | 0.701 | 0.671 | 0.654 | 0.685 |
1AKG | 16 | 0.945 | 0.373 | 0.35 | 0.185 | 1PZ4 | 114 | 0.921 | 0.828 | 0.781 | 0.843 |
1ATG | 231 | 0.843 | 0.613 | 0.578 | 0.497 | 1Q9B | 43 | 0.957 | 0.746 | 0.726 | 0.656 |
1BGF | 124 | 0.834 | 0.603 | 0.539 | 0.543 | 1QAU | 112 | 0.786 | 0.678 | 0.672 | 0.62 |
1BX7 | 51 | 0.896 | 0.726 | 0.623 | 0.706 | 1QKI | 3912 | 0.508 | 0.809 | 0.751 | 0.645 |
1BYI | 224 | 0.600 | 0.543 | 0.491 | 0.552 | 1QTO | 122 | 0.809 | 0.543 | 0.52 | 0.334 |
1CCR | 111 | 0.741 | 0.58 | 0.512 | 0.351 | 1R29 | 122 | 0.787 | 0.65 | 0.631 | 0.556 |
1CYO | 88 | 0.860 | 0.751 | 0.702 | 0.741 | 1R7J | 90 | 0.859 | 0.789 | 0.621 | 0.368 |
1DF4 | 57 | 0.941 | 0.912 | 0.889 | 0.832 | 1RJU | 36 | 0.805 | 0.517 | 0.447 | 0.431 |
1E5K | 188 | 0.848 | 0.746 | 0.732 | 0.859 | 1RRO | 112 | 0.748 | 0.435 | 0.372 | 0.529 |
1ES5 | 260 | 0.700 | 0.653 | 0.638 | 0.677 | 1SAU | 114 | 0.819 | 0.742 | 0.671 | 0.596 |
1ETL | 12 | 0.932 | 0.71 | 0.609 | 0.628 | 1TGR | 104 | 0.810 | 0.72 | 0.711 | 0.714 |
1ETM | 12 | 0.941 | 0.544 | 0.393 | 0.432 | 1TZV | 141 | 0.869 | 0.837 | 0.82 | 0.841 |
1ETN | 12 | 0.949 | 0.089 | 0.023 | −0.274 | 1U06 | 55 | 0.774 | 0.474 | 0.429 | 0.434 |
1EW4 | 106 | 0.804 | 0.65 | 0.644 | 0.547 | 1U7I | 267 | 0.885 | 0.778 | 0.762 | 0.691 |
1F8R | 1932 | 0.504 | 0.878 | 0.859 | 0.738 | 1U9C | 221 | 0.764 | 0.6 | 0.577 | 0.522 |
1FF4 | 65 | 0.933 | 0.718 | 0.613 | 0.674 | 1UHA | 83 | 0.838 | 0.726 | 0.665 | 0.638 |
1FK5 | 93 | 0.648 | 0.59 | 0.568 | 0.485 | 1UKU | 102 | 0.765 | 0.665 | 0.661 | 0.742 |
1GCO | 1044 | 0.839 | 0.766 | 0.693 | 0.646 | 1ULR | 87 | 0.718 | 0.639 | 0.594 | 0.495 |
1GK7 | 39 | 0.984 | 0.845 | 0.773 | 0.821 | 1UOY | 64 | 0.769 | 0.713 | 0.653 | 0.671 |
1GVD | 52 | 0.849 | 0.781 | 0.732 | 0.591 | 1USE | 40 | 0.960 | 0.438 | 0.146 | −0.142 |
1GXU | 88 | 0.901 | 0.748 | 0.634 | 0.421 | 1USM | 77 | 0.819 | 0.832 | 0.809 | 0.798 |
1H6V | 2927 | 0.133 | 0.488 | 0.429 | 0.306 | 1UTG | 70 | 0.745 | 0.691 | 0.61 | 0.538 |
1HJE | 13 | 0.931 | 0.811 | 0.686 | 0.616 | 1V05 | 96 | 0.841 | 0.629 | 0.599 | 0.632 |
1I71 | 83 | 0.798 | 0.549 | 0.516 | 0.549 | 1V70 | 105 | 0.854 | 0.622 | 0.492 | 0.162 |
1IDP | 441 | 0.827 | 0.735 | 0.715 | 0.69 | 1VRZ | 21 | 0.995 | 0.792 | 0.695 | 0.677 |
1IFR | 113 | 0.875 | 0.697 | 0.689 | 0.637 | 1W2L | 97 | 0.747 | 0.691 | 0.564 | 0.397 |
1K8U | 89 | 0.856 | 0.553 | 0.531 | 0.378 | 1WBE | 204 | 0.767 | 0.591 | 0.577 | 0.549 |
1KMM | 1499 | 0.740 | 0.749 | 0.744 | 0.558 | 1WHI | 122 | 0.804 | 0.601 | 0.539 | 0.27 |
1KNG | 144 | 0.810 | 0.547 | 0.536 | 0.512 | 1WLY | 322 | 0.728 | 0.695 | 0.679 | 0.666 |
1KR4 | 110 | 0.892 | 0.635 | 0.612 | 0.466 | 1WPA | 107 | 0.797 | 0.634 | 0.577 | 0.417 |
1KYC | 15 | 0.971 | 0.796 | 0.763 | 0.754 | 1X3O | 80 | 0.787 | 0.6 | 0.559 | 0.654 |
1LR7 | 73 | 0.929 | 0.679 | 0.657 | 0.62 | 1XY1 | 18 | 0.933 | 0.832 | 0.645 | 0.447 |
1MF7 | 194 | 0.757 | 0.687 | 0.681 | 0.7 | 1XY2 | 8 | 1.000 | 0.619 | 0.57 | 0.562 |
1N7E | 95 | 0.812 | 0.651 | 0.609 | 0.497 | 1Y6X | 87 | 0.838 | 0.596 | 0.524 | 0.366 |
1NKD | 59 | 0.911 | 0.75 | 0.703 | 0.631 | 1YJO | 6 | 1.000 | 0.375 | 0.333 | 0.434 |
1NKO | 122 | 0.831 | 0.619 | 0.535 | 0.368 | 1YZM | 46 | 0.970 | 0.842 | 0.834 | 0.901 |
1NLS | 238 | 0.799 | 0.669 | 0.53 | 0.523 | 1Z21 | 96 | 0.725 | 0.662 | 0.638 | 0.433 |
1NNX | 93 | 0.834 | 0.795 | 0.789 | 0.631 | 1ZCE | 146 | 0.898 | 0.808 | 0.757 | 0.77 |
1NOA | 113 | 0.808 | 0.622 | 0.604 | 0.615 | 1ZVA | 75 | 0.911 | 0.756 | 0.579 | 0.69 |
1NOT | 13 | 0.937 | 0.746 | 0.622 | 0.523 | 2A50 | 457 | 0.704 | 0.564 | 0.524 | 0.281 |
1O06 | 20 | 0.988 | 0.91 | 0.874 | 0.844 | 2AGK | 233 | 0.821 | 0.705 | 0.694 | 0.512 |
1O08 | 221 | 0.516 | 0.562 | 0.333 | 0.309 | 2AH1 | 939 | 0.462 | 0.684 | 0.593 | 0.521 |
1OB4 | 16 | 1.000 | 0.776 | 0.763 | 0.75 | 2B0A | 186 | 0.805 | 0.639 | 0.603 | 0.467 |
1OB7 | 16 | 1.000 | 0.737 | 0.545 | 0.652 | 2BCM | 413 | 0.695 | 0.555 | 0.551 | 0.477 |
1OPD | 85 | 0.607 | 0.555 | 0.409 | 0.398 | 2BF9 | 36 | 0.714 | 0.606 | 0.554 | 0.68 |
1P9I | 29 | 0.841 | 0.754 | 0.742 | 0.625 | 2BRF | 100 | 0.873 | 0.795 | 0.764 | 0.71 |
2CE0 | 99 | 0.824 | 0.706 | 0.598 | 0.529 | 2C71 | 205 | 0.773 | 0.658 | 0.649 | 0.56 |
2CG7 | 90 | 0.738 | 0.551 | 0.539 | 0.379 | 2OLX | 4 | 1.000 | 0.917 | 0.888 | 0.885 |
2COV | 534 | 0.895 | 0.846 | 0.823 | 0.812 | 2PKT | 93 | 0.762 | 0.162 | 0.003 | 0.193 |
2CWS | 227 | 0.756 | 0.647 | 0.64 | 0.696 | 2PLT | 99 | 0.635 | 0.508 | 0.484 | 0.509 |
2D5W | 1214 | 0.448 | 0.689 | 0.682 | 0.681 | 2PMR | 76 | 0.799 | 0.693 | 0.682 | 0.619 |
2DKO | 253 | 0.873 | 0.816 | 0.812 | 0.69 | 2POF | 440 | 0.743 | 0.682 | 0.651 | 0.589 |
2DPL | 565 | 0.721 | 0.596 | 0.538 | 0.658 | 2PPN | 107 | 0.673 | 0.677 | 0.638 | 0.668 |
2DSX | 52 | 0.704 | 0.337 | 0.333 | 0.127 | 2PSF | 608 | 0.641 | 0.526 | 0.5 | 0.565 |
2E10 | 439 | 0.808 | 0.798 | 0.796 | 0.692 | 2PTH | 193 | 0.901 | 0.822 | 0.784 | 0.767 |
2E3H | 81 | 0.794 | 0.692 | 0.682 | 0.605 | 2Q4N | 153 | 0.846 | 0.711 | 0.667 | 0.74 |
2EAQ | 89 | 0.817 | 0.753 | 0.69 | 0.695 | 2Q52 | 412 | 0.510 | 0.756 | 0.748 | 0.621 |
2EHP | 248 | 0.832 | 0.804 | 0.804 | 0.773 | 2QJL | 99 | 0.611 | 0.594 | 0.584 | 0.594 |
2EHS | 75 | 0.805 | 0.72 | 0.713 | 0.747 | 2R16 | 176 | 0.640 | 0.582 | 0.495 | 0.618 |
2ERW | 53 | 0.513 | 0.461 | 0.253 | 0.199 | 2R6Q | 138 | 0.915 | 0.603 | 0.54 | 0.529 |
2ETX | 389 | 0.854 | 0.58 | 0.556 | 0.632 | 2RB8 | 93 | 0.840 | 0.727 | 0.614 | 0.517 |
2FB6 | 116 | 0.850 | 0.791 | 0.786 | 0.74 | 2RE2 | 238 | 0.711 | 0.652 | 0.613 | 0.673 |
2FG1 | 157 | 0.719 | 0.62 | 0.617 | 0.584 | 2RFR | 154 | 0.826 | 0.693 | 0.671 | 0.753 |
2FN9 | 560 | 0.704 | 0.607 | 0.595 | 0.611 | 2V9V | 135 | 0.697 | 0.555 | 0.548 | 0.528 |
2FQ3 | 85 | 0.844 | 0.719 | 0.692 | 0.348 | 2VE8 | 515 | 0.698 | 0.744 | 0.643 | 0.616 |
2G69 | 99 | 0.850 | 0.622 | 0.59 | 0.436 | 2VH7 | 94 | 0.851 | 0.775 | 0.726 | 0.596 |
2G7O | 68 | 0.888 | 0.785 | 0.784 | 0.66 | 2VIM | 104 | 0.859 | 0.413 | 0.393 | 0.212 |
2G7S | 190 | 0.756 | 0.67 | 0.644 | 0.649 | 2VPA | 204 | 0.757 | 0.763 | 0.755 | 0.576 |
2GKG | 122 | 0.748 | 0.688 | 0.646 | 0.711 | 2VQ4 | 106 | 0.776 | 0.68 | 0.679 | 0.555 |
2GOM | 121 | 0.874 | 0.586 | 0.584 | 0.491 | 2VY8 | 149 | 0.759 | 0.77 | 0.724 | 0.533 |
2GXG | 140 | 0.901 | 0.847 | 0.78 | 0.52 | 2VYO | 210 | 0.777 | 0.675 | 0.648 | 0.729 |
2GZQ | 191 | 0.462 | 0.505 | 0.382 | 0.369 | 2W1V | 548 | 0.761 | 0.68 | 0.68 | 0.571 |
2HQK | 213 | 0.897 | 0.824 | 0.809 | 0.365 | 2W2A | 350 | 0.819 | 0.706 | 0.638 | 0.589 |
2HYK | 238 | 0.728 | 0.585 | 0.575 | 0.51 | 2W6A | 117 | 0.804 | 0.823 | 0.748 | 0.647 |
2I24 | 113 | 0.672 | 0.593 | 0.498 | 0.494 | 2WJ5 | 96 | 0.821 | 0.484 | 0.44 | 0.357 |
2I49 | 398 | 0.766 | 0.714 | 0.683 | 0.601 | 2WUJ | 100 | 0.919 | 0.739 | 0.598 | 0.598 |
2IBL | 108 | 0.919 | 0.629 | 0.625 | 0.352 | 2WW7 | 150 | 0.629 | 0.499 | 0.471 | 0.356 |
2IGD | 61 | 0.865 | 0.585 | 0.481 | 0.386 | 2WWE | 111 | 0.903 | 0.692 | 0.582 | 0.628 |
2IMF | 203 | 0.798 | 0.652 | 0.625 | 0.514 | 2X1Q | 240 | 0.505 | 0.534 | 0.478 | 0.443 |
2IP6 | 87 | 0.841 | 0.654 | 0.578 | 0.572 | 2X25 | 168 | 0.710 | 0.632 | 0.598 | 0.403 |
2IVY | 88 | 0.837 | 0.544 | 0.483 | 0.271 | 2X3M | 166 | 0.875 | 0.744 | 0.717 | 0.655 |
2J32 | 244 | 0.878 | 0.863 | 0.848 | 0.855 | 2X5Y | 171 | 0.799 | 0.718 | 0.705 | 0.694 |
2J9W | 200 | 0.741 | 0.716 | 0.705 | 0.662 | 2X9Z | 262 | 0.726 | 0.583 | 0.578 | 0.574 |
2JKU | 35 | 0.926 | 0.805 | 0.695 | 0.656 | 2XHF | 310 | 0.830 | 0.606 | 0.591 | 0.569 |
2JLI | 100 | 0.937 | 0.779 | 0.613 | 0.622 | 2Y0T | 101 | 0.834 | 0.778 | 0.774 | 0.798 |
2JLJ | 115 | 0.811 | 0.741 | 0.72 | 0.527 | 2Y72 | 170 | 0.926 | 0.78 | 0.754 | 0.766 |
2MCM | 113 | 0.867 | 0.789 | 0.713 | 0.639 | 2Y7L | 319 | 0.939 | 0.928 | 0.797 | 0.747 |
2NLS | 36 | 0.937 | 0.605 | 0.559 | 0.53 | 2Y9F | 149 | 0.769 | 0.771 | 0.762 | 0.664 |
2NR7 | 194 | 0.885 | 0.803 | 0.785 | 0.727 | 2YLB | 400 | 0.820 | 0.807 | 0.807 | 0.675 |
2NUH | 104 | 0.922 | 0.835 | 0.691 | 0.771 | 2YNY | 315 | 0.836 | 0.813 | 0.804 | 0.706 |
2O6X | 306 | 0.825 | 0.814 | 0.799 | 0.651 | 2ZCM | 357 | 0.723 | 0.458 | 0.422 | 0.42 |
2OA2 | 132 | 0.703 | 0.571 | 0.456 | 0.458 | 2ZU1 | 360 | 0.753 | 0.689 | 0.672 | 0.653 |
2OCT | 192 | 0.673 | 0.567 | 0.55 | 0.54 | 3A0M | 148 | 0.916 | 0.807 | 0.712 | 0.392 |
2OHW | 256 | 0.743 | 0.614 | 0.539 | 0.475 | 3A7L | 128 | 0.806 | 0.713 | 0.663 | 0.756 |
2OKT | 342 | 0.779 | 0.433 | 0.411 | 0.336 | 3AMC | 614 | 0.758 | 0.675 | 0.669 | 0.581 |
2OL9 | 6 | 1.000 | 0.909 | 0.904 | 0.689 | 3AUB | 116 | 0.650 | 0.614 | 0.608 | 0.637 |
3BA1 | 312 | 0.827 | 0.661 | 0.624 | 0.621 | 3B5O | 230 | 0.729 | 0.644 | 0.629 | 0.601 |
3BED | 261 | 0.874 | 0.845 | 0.82 | 0.684 | 3MD4 | 12 | 0.999 | 0.86 | 0.781 | 0.914 |
3BQX | 139 | 0.900 | 0.634 | 0.481 | 0.297 | 3MD5 | 12 | 0.998 | 0.649 | 0.413 | −0.218 |
3BZQ | 99 | 0.848 | 0.532 | 0.516 | 0.466 | 3MEA | 166 | 0.872 | 0.669 | 0.669 | 0.6 |
3BZZ | 100 | 0.783 | 0.485 | 0.45 | 0.6 | 3MGN | 348 | 0.742 | 0.205 | 0.119 | 0.193 |
3DRF | 547 | 0.781 | 0.559 | 0.549 | 0.488 | 3MRE | 383 | 0.675 | 0.661 | 0.641 | 0.567 |
3DWV | 325 | 0.754 | 0.707 | 0.661 | 0.547 | 3N11 | 325 | 0.736 | 0.614 | 0.583 | 0.517 |
3E5T | 228 | 0.731 | 0.502 | 0.489 | 0.296 | 3NE0 | 208 | 0.859 | 0.706 | 0.645 | 0.659 |
3E7R | 40 | 0.769 | 0.706 | 0.687 | 0.642 | 3NGG | 94 | 0.867 | 0.696 | 0.689 | 0.719 |
3EUR | 140 | 0.874 | 0.431 | 0.427 | 0.577 | 3NPV | 495 | 0.855 | 0.702 | 0.653 | 0.677 |
3F2Z | 149 | 0.877 | 0.824 | 0.792 | 0.74 | 3NVG | 6 | 1.000 | 0.721 | 0.617 | 0.597 |
3F7E | 254 | 0.847 | 0.812 | 0.803 | 0.811 | 3NZL | 73 | 0.713 | 0.627 | 0.583 | 0.506 |
3FCN | 158 | 0.741 | 0.64 | 0.606 | 0.632 | 3O0P | 194 | 0.898 | 0.727 | 0.706 | 0.734 |
3FE7 | 91 | 0.914 | 0.583 | 0.533 | 0.276 | 3O5P | 128 | 0.787 | 0.734 | 0.698 | 0.63 |
3FKE | 250 | 0.755 | 0.525 | 0.476 | 0.435 | 3OBQ | 150 | 0.877 | 0.649 | 0.645 | 0.655 |
3FMY | 66 | 0.857 | 0.701 | 0.655 | 0.556 | 3OQY | 234 | 0.807 | 0.698 | 0.686 | 0.637 |
3FOD | 48 | 0.725 | 0.532 | 0.44 | −0.126 | 3P6J | 125 | 0.689 | 0.774 | 0.767 | 0.81 |
3FSO | 221 | 0.906 | 0.831 | 0.817 | 0.793 | 3PD7 | 188 | 0.848 | 0.77 | 0.723 | 0.589 |
3FTD | 240 | 0.818 | 0.722 | 0.713 | 0.634 | 3PES | 165 | 0.861 | 0.697 | 0.642 | 0.683 |
3FVA | 6 | 1.000 | 0.835 | 0.825 | 0.789 | 3PID | 387 | 0.677 | 0.537 | 0.531 | 0.642 |
3G1S | 418 | 0.879 | 0.771 | 0.7 | 0.63 | 3PIW | 154 | 0.772 | 0.758 | 0.744 | 0.717 |
3GBW | 161 | 0.864 | 0.82 | 0.747 | 0.51 | 3PKV | 221 | 0.731 | 0.625 | 0.597 | 0.568 |
3GHJ | 116 | 0.864 | 0.732 | 0.511 | 0.196 | 3PSM | 94 | 0.914 | 0.876 | 0.79 | 0.745 |
3HFO | 197 | 0.825 | 0.691 | 0.67 | 0.518 | 3PTL | 289 | 0.611 | 0.543 | 0.541 | 0.468 |
3HHP | 1234 | 0.830 | 0.72 | 0.716 | 0.683 | 3PVE | 347 | 0.785 | 0.718 | 0.667 | 0.568 |
3HNY | 156 | 0.885 | 0.793 | 0.723 | 0.758 | 3PZ9 | 357 | 0.758 | 0.709 | 0.709 | 0.678 |
3HP4 | 183 | 0.690 | 0.534 | 0.5 | 0.573 | 3PZZ | 12 | 0.998 | 0.945 | 0.922 | 0.95 |
3HWU | 144 | 0.905 | 0.754 | 0.748 | 0.841 | 3Q2X | 6 | 1.000 | 0.922 | 0.904 | 0.866 |
3HYD | 7 | 1.000 | 0.966 | 0.95 | 0.867 | 3Q6L | 131 | 0.723 | 0.622 | 0.577 | 0.605 |
3HZ8 | 192 | 0.857 | 0.617 | 0.502 | 0.475 | 3QDS | 284 | 0.782 | 0.78 | 0.745 | 0.568 |
3I2V | 124 | 0.879 | 0.486 | 0.441 | 0.301 | 3QPA | 197 | 0.616 | 0.587 | 0.442 | 0.503 |
3I2Z | 138 | 0.732 | 0.613 | 0.599 | 0.317 | 3R6D | 221 | 0.854 | 0.688 | 0.669 | 0.495 |
3I4O | 135 | 0.767 | 0.735 | 0.714 | 0.738 | 3R87 | 132 | 0.861 | 0.452 | 0.419 | 0.286 |
3I7M | 134 | 0.604 | 0.667 | 0.635 | 0.695 | 3RQ9 | 162 | 0.711 | 0.51 | 0.403 | 0.242 |
3IHS | 169 | 0.807 | 0.586 | 0.565 | 0.409 | 3RY0 | 128 | 0.790 | 0.616 | 0.606 | 0.47 |
3IVV | 149 | 0.866 | 0.817 | 0.797 | 0.693 | 3RZY | 139 | 0.867 | 0.8 | 0.784 | 0.849 |
3K6Y | 227 | 0.817 | 0.586 | 0.535 | 0.301 | 3S0A | 119 | 0.713 | 0.562 | 0.524 | 0.526 |
3KBE | 140 | 0.743 | 0.705 | 0.704 | 0.611 | 3SD2 | 86 | 0.842 | 0.523 | 0.421 | 0.237 |
3KGK | 190 | 0.798 | 0.784 | 0.775 | 0.68 | 3SEB | 238 | 0.879 | 0.801 | 0.712 | 0.826 |
3KZD | 85 | 0.789 | 0.647 | 0.611 | 0.475 | 3SED | 124 | 0.870 | 0.709 | 0.658 | 0.712 |
3L41 | 220 | 0.776 | 0.718 | 0.716 | 0.669 | 3SO6 | 150 | 0.747 | 0.675 | 0.666 | 0.63 |
3LAA | 169 | 0.880 | 0.827 | 0.647 | 0.659 | 3SR3 | 637 | 0.633 | 0.619 | 0.611 | 0.624 |
3LAX | 106 | 0.924 | 0.734 | 0.73 | 0.584 | 3SUK | 248 | 0.721 | 0.644 | 0.633 | 0.567 |
3LG3 | 833 | 0.701 | 0.658 | 0.614 | 0.589 | 3SZH | 697 | 0.860 | 0.817 | 0.815 | 0.697 |
3LJI | 272 | 0.720 | 0.612 | 0.608 | 0.551 | 3T0H | 208 | 0.897 | 0.808 | 0.775 | 0.694 |
3M3P | 249 | 0.697 | 0.584 | 0.554 | 0.338 | 3T3K | 122 | 0.803 | 0.796 | 0.748 | 0.735 |
3M8J | 178 | 0.813 | 0.73 | 0.728 | 0.628 | 3T47 | 141 | 0.759 | 0.592 | 0.527 | 0.447 |
3M9J | 210 | 0.867 | 0.639 | 0.574 | 0.296 | 3TDN | 357 | 0.668 | 0.458 | 0.419 | 0.24 |
3M9Q | 176 | 0.851 | 0.591 | 0.51 | 0.471 | 3TOW | 152 | 0.722 | 0.578 | 0.556 | 0.571 |
3MAB | 173 | 0.770 | 0.664 | 0.591 | 0.451 | 3TUA | 210 | 0.696 | 0.665 | 0.658 | 0.588 |
3U6G | 248 | 0.808 | 0.635 | 0.632 | 0.526 | 3TYS | 75 | 0.918 | 0.853 | 0.8 | 0.791 |
3U97 | 77 | 0.819 | 0.753 | 0.736 | 0.712 | 4DT4 | 160 | 0.784 | 0.776 | 0.738 | 0.716 |
3UCI | 72 | 0.689 | 0.589 | 0.526 | 0.495 | 4EK3 | 287 | 0.830 | 0.68 | 0.68 | 0.674 |
3UR8 | 637 | 0.832 | 0.666 | 0.652 | 0.597 | 4ERY | 318 | 0.801 | 0.74 | 0.701 | 0.688 |
3US6 | 148 | 0.668 | 0.698 | 0.586 | 0.553 | 4ES1 | 95 | 0.820 | 0.648 | 0.625 | 0.551 |
3V1A | 48 | 0.811 | 0.531 | 0.487 | 0.583 | 4EUG | 225 | 0.592 | 0.57 | 0.529 | 0.405 |
3V75 | 285 | 0.674 | 0.604 | 0.596 | 0.491 | 4F01 | 448 | 0.883 | 0.633 | 0.372 | 0.688 |
3VN0 | 193 | 0.889 | 0.84 | 0.837 | 0.812 | 4F3J | 143 | 0.879 | 0.617 | 0.598 | 0.551 |
3VOR | 182 | 0.686 | 0.602 | 0.557 | 0.484 | 4FR9 | 141 | 0.806 | 0.671 | 0.655 | 0.501 |
3VUB | 101 | 0.852 | 0.625 | 0.61 | 0.607 | 4G14 | 15 | 1.000 | 0.467 | 0.323 | 0.356 |
3VVV | 108 | 0.951 | 0.833 | 0.741 | 0.753 | 4G2E | 151 | 0.835 | 0.76 | 0.755 | 0.758 |
3VZ9 | 163 | 0.887 | 0.785 | 0.749 | 0.695 | 4G5X | 550 | 0.822 | 0.786 | 0.754 | 0.743 |
3W4Q | 773 | 0.798 | 0.737 | 0.725 | 0.649 | 4G6C | 658 | 0.834 | 0.591 | 0.59 | 0.528 |
3ZBD | 213 | 0.891 | 0.651 | 0.516 | 0.632 | 4G7X | 194 | 0.840 | 0.688 | 0.587 | 0.624 |
3ZIT | 152 | 0.641 | 0.43 | 0.404 | 0.392 | 4GA2 | 144 | 0.782 | 0.528 | 0.485 | 0.406 |
3ZRX | 221 | 0.639 | 0.59 | 0.562 | 0.391 | 4GMQ | 92 | 0.794 | 0.678 | 0.628 | 0.55 |
3ZSL | 138 | 0.903 | 0.691 | 0.687 | 0.526 | 4GS3 | 90 | 0.698 | 0.544 | 0.522 | 0.547 |
3ZZP | 74 | 0.692 | 0.524 | 0.46 | 0.448 | 4H4J | 236 | 0.866 | 0.81 | 0.806 | 0.689 |
3ZZY | 226 | 0.804 | 0.746 | 0.709 | 0.728 | 4H89 | 168 | 0.624 | 0.682 | 0.588 | 0.596 |
4A02 | 166 | 0.730 | 0.618 | 0.516 | 0.303 | 4HDE | 168 | 0.783 | 0.745 | 0.728 | 0.615 |
4ACJ | 167 | 0.827 | 0.748 | 0.746 | 0.759 | 4HJP | 281 | 0.730 | 0.703 | 0.649 | 0.51 |
4AE7 | 186 | 0.862 | 0.724 | 0.717 | 0.717 | 4HWM | 117 | 0.807 | 0.638 | 0.622 | 0.499 |
4AM1 | 345 | 0.796 | 0.674 | 0.619 | 0.46 | 4IL7 | 85 | 0.719 | 0.446 | 0.404 | 0.316 |
4ANN | 176 | 0.562 | 0.551 | 0.536 | 0.47 | 4J11 | 357 | 0.726 | 0.62 | 0.562 | 0.401 |
4AVR | 188 | 0.759 | 0.68 | 0.605 | 0.65 | 4J5O | 220 | 0.817 | 0.793 | 0.757 | 0.777 |
4AXY | 54 | 0.973 | 0.7 | 0.623 | 0.72 | 4J5Q | 146 | 0.851 | 0.742 | 0.742 | 0.689 |
4B6G | 558 | 0.804 | 0.765 | 0.756 | 0.669 | 4J78 | 305 | 0.729 | 0.658 | 0.648 | 0.608 |
4B9G | 292 | 0.855 | 0.844 | 0.816 | 0.763 | 4JG2 | 185 | 0.889 | 0.746 | 0.736 | 0.543 |
4DD5 | 387 | 0.850 | 0.615 | 0.596 | 0.351 | 4JVU | 207 | 0.800 | 0.723 | 0.697 | 0.553 |
4DKN | 423 | 0.786 | 0.781 | 0.761 | 0.539 | 4JYP | 534 | 0.800 | 0.688 | 0.682 | 0.538 |
4DND | 95 | 0.829 | 0.763 | 0.75 | 0.582 | 4KEF | 133 | 0.704 | 0.58 | 0.53 | 0.324 |
4DPZ | 109 | 0.837 | 0.73 | 0.726 | 0.651 | 5CYT | 103 | 0.548 | 0.441 | 0.421 | 0.331 |
4DQ7 | 328 | 0.776 | 0.69 | 0.683 | 0.376 | 6RXN | 45 | 0.583 | 0.614 | 0.574 | 0.594 |
Correlation coefficients for B-factor prediction obtained by optimal FRI (opFRI), parameter-free FRI (pfFRI), and Gaussian normal mode (GNM) for small-size structures. Results for opFRI and pfFRI are taken from Opron et al.35 GNM and NMA values are taken from the coarse-grained (Cα) results reported in Park et al.33 MWCG results are parameter free and use all C, N, and O to predict Cα.
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1AIE | 31 | 0.969 | 0.588 | 0.416 | 0.155 | 0.712 |
1AKG | 16 | 0.945 | 0.373 | 0.35 | 0.185 | −0.229 |
1BX7 | 51 | 0.896 | 0.726 | 0.623 | 0.706 | 0.868 |
1ETL | 12 | 0.932 | 0.71 | 0.609 | 0.628 | 0.355 |
1ETM | 12 | 0.941 | 0.544 | 0.393 | 0.432 | 0.027 |
1ETN | 12 | 0.949 | 0.089 | 0.023 | −0.274 | −0.573 |
1FF4 | 65 | 0.933 | 0.718 | 0.613 | 0.674 | 0.555 |
1GK7 | 39 | 0.984 | 0.845 | 0.773 | 0.821 | 0.822 |
1GVD | 52 | 0.849 | 0.781 | 0.732 | 0.591 | 0.570 |
1HJE | 13 | 0.931 | 0.811 | 0.686 | 0.616 | 0.562 |
1KYC | 15 | 0.971 | 0.796 | 0.763 | 0.754 | 0.784 |
1NOT | 13 | 0.937 | 0.746 | 0.622 | 0.523 | 0.567 |
1O06 | 20 | 0.988 | 0.91 | 0.874 | 0.844 | 0.900 |
1OB4 | 16 | 1.000 | 0.776 | 0.763 | 0.750 | 0.930 |
1OB7 | 16 | 1.000 | 0.737 | 0.545 | 0.652 | 0.952 |
1P9I | 29 | 0.841 | 0.754 | 0.742 | 0.625 | 0.603 |
1PEF | 18 | 0.989 | 0.888 | 0.826 | 0.808 | 0.888 |
1PEN | 16 | 0.957 | 0.516 | 0.465 | 0.270 | 0.056 |
1Q9B | 43 | 0.957 | 0.746 | 0.726 | 0.656 | 0.646 |
1RJU | 36 | 0.805 | 0.517 | 0.447 | 0.431 | 0.235 |
1U06 | 55 | 0.774 | 0.474 | 0.429 | 0.434 | 0.377 |
1UOY | 64 | 0.769 | 0.713 | 0.653 | 0.671 | 0.628 |
1USE | 40 | 0.960 | 0.438 | 0.146 | −0.142 | −0.399 |
1VRZ | 21 | 0.995 | 0.792 | 0.695 | 0.677 | −0.203 |
1XY2 | 8 | 1.000 | 0.619 | 0.57 | 0.562 | 0.458 |
1YJO | 6 | 1.000 | 0.375 | 0.333 | 0.434 | 0.445 |
1YZM | 46 | 0.970 | 0.842 | 0.834 | 0.901 | 0.939 |
2DSX | 52 | 0.704 | 0.337 | 0.333 | 0.127 | 0.433 |
2JKU | 35 | 0.926 | 0.805 | 0.695 | 0.656 | 0.850 |
2NLS | 36 | 0.937 | 0.605 | 0.559 | 0.530 | 0.088 |
2OL9 | 6 | 1.000 | 0.909 | 0.904 | 0.689 | 0.886 |
2OLX | 4 | 1.000 | 0.917 | 0.888 | 0.885 | 0.776 |
6RXN | 45 | 0.583 | 0.614 | 0.574 | 0.594 | 0.304 |
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1AIE | 31 | 0.969 | 0.588 | 0.416 | 0.155 | 0.712 |
1AKG | 16 | 0.945 | 0.373 | 0.35 | 0.185 | −0.229 |
1BX7 | 51 | 0.896 | 0.726 | 0.623 | 0.706 | 0.868 |
1ETL | 12 | 0.932 | 0.71 | 0.609 | 0.628 | 0.355 |
1ETM | 12 | 0.941 | 0.544 | 0.393 | 0.432 | 0.027 |
1ETN | 12 | 0.949 | 0.089 | 0.023 | −0.274 | −0.573 |
1FF4 | 65 | 0.933 | 0.718 | 0.613 | 0.674 | 0.555 |
1GK7 | 39 | 0.984 | 0.845 | 0.773 | 0.821 | 0.822 |
1GVD | 52 | 0.849 | 0.781 | 0.732 | 0.591 | 0.570 |
1HJE | 13 | 0.931 | 0.811 | 0.686 | 0.616 | 0.562 |
1KYC | 15 | 0.971 | 0.796 | 0.763 | 0.754 | 0.784 |
1NOT | 13 | 0.937 | 0.746 | 0.622 | 0.523 | 0.567 |
1O06 | 20 | 0.988 | 0.91 | 0.874 | 0.844 | 0.900 |
1OB4 | 16 | 1.000 | 0.776 | 0.763 | 0.750 | 0.930 |
1OB7 | 16 | 1.000 | 0.737 | 0.545 | 0.652 | 0.952 |
1P9I | 29 | 0.841 | 0.754 | 0.742 | 0.625 | 0.603 |
1PEF | 18 | 0.989 | 0.888 | 0.826 | 0.808 | 0.888 |
1PEN | 16 | 0.957 | 0.516 | 0.465 | 0.270 | 0.056 |
1Q9B | 43 | 0.957 | 0.746 | 0.726 | 0.656 | 0.646 |
1RJU | 36 | 0.805 | 0.517 | 0.447 | 0.431 | 0.235 |
1U06 | 55 | 0.774 | 0.474 | 0.429 | 0.434 | 0.377 |
1UOY | 64 | 0.769 | 0.713 | 0.653 | 0.671 | 0.628 |
1USE | 40 | 0.960 | 0.438 | 0.146 | −0.142 | −0.399 |
1VRZ | 21 | 0.995 | 0.792 | 0.695 | 0.677 | −0.203 |
1XY2 | 8 | 1.000 | 0.619 | 0.57 | 0.562 | 0.458 |
1YJO | 6 | 1.000 | 0.375 | 0.333 | 0.434 | 0.445 |
1YZM | 46 | 0.970 | 0.842 | 0.834 | 0.901 | 0.939 |
2DSX | 52 | 0.704 | 0.337 | 0.333 | 0.127 | 0.433 |
2JKU | 35 | 0.926 | 0.805 | 0.695 | 0.656 | 0.850 |
2NLS | 36 | 0.937 | 0.605 | 0.559 | 0.530 | 0.088 |
2OL9 | 6 | 1.000 | 0.909 | 0.904 | 0.689 | 0.886 |
2OLX | 4 | 1.000 | 0.917 | 0.888 | 0.885 | 0.776 |
6RXN | 45 | 0.583 | 0.614 | 0.574 | 0.594 | 0.304 |
Correlation coefficients for tB-factor prediction obtained by optimal FRI (opFRI), parameter-free FRI (pfFRI), and Gaussian normal mode (GNM) for medium-size structures. Results for opFRI and pfFRI are taken from Opron et al.35 GNM and NMA values are taken from the coarse-grained (Cα) results reported in Park et al.33 MWCG results are parameter free and use all C, N, and O to predict Cα.
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1ABA | 87 | 0.855 | 0.727 | 0.698 | 0.613 | 0.057 |
1CYO | 88 | 0.860 | 0.751 | 0.702 | 0.741 | 0.774 |
1FK5 | 93 | 0.648 | 0.590 | 0.568 | 0.485 | 0.362 |
1GXU | 88 | 0.901 | 0.748 | 0.634 | 0.421 | 0.581 |
1I71 | 83 | 0.798 | 0.549 | 0.516 | 0.549 | 0.380 |
1LR7 | 73 | 0.929 | 0.679 | 0.657 | 0.620 | 0.795 |
1N7E | 95 | 0.812 | 0.651 | 0.609 | 0.497 | 0.385 |
1NNX | 93 | 0.834 | 0.795 | 0.789 | 0.631 | 0.517 |
1NOA | 113 | 0.808 | 0.622 | 0.604 | 0.615 | 0.485 |
1OPD | 85 | 0.607 | 0.555 | 0.409 | 0.398 | 0.796 |
1QAU | 112 | 0.786 | 0.678 | 0.672 | 0.620 | 0.533 |
1R7J | 90 | 0.859 | 0.789 | 0.621 | 0.368 | 0.078 |
1UHA | 83 | 0.838 | 0.726 | 0.665 | 0.638 | 0.308 |
1ULR | 87 | 0.718 | 0.639 | 0.594 | 0.495 | 0.223 |
1USM | 77 | 0.819 | 0.832 | 0.809 | 0.798 | 0.780 |
1V05 | 96 | 0.841 | 0.629 | 0.599 | 0.632 | 0.389 |
1W2L | 97 | 0.747 | 0.691 | 0.564 | 0.397 | 0.432 |
1X3O | 80 | 0.787 | 0.600 | 0.559 | 0.654 | 0.453 |
1Z21 | 96 | 0.725 | 0.662 | 0.638 | 0.433 | 0.289 |
1ZVA | 75 | 0.911 | 0.756 | 0.579 | 0.690 | 0.579 |
2BF9 | 36 | 0.714 | 0.606 | 0.554 | 0.680 | 0.521 |
2BRF | 100 | 0.873 | 0.795 | 0.764 | 0.710 | 0.535 |
2CE0 | 99 | 0.824 | 0.706 | 0.598 | 0.529 | 0.628 |
2E3H | 81 | 0.794 | 0.692 | 0.682 | 0.605 | 0.632 |
2EAQ | 89 | 0.817 | 0.753 | 0.690 | 0.695 | 0.688 |
2EHS | 75 | 0.805 | 0.720 | 0.713 | 0.747 | 0.565 |
2FQ3 | 85 | 0.844 | 0.719 | 0.692 | 0.348 | 0.508 |
2IP6 | 87 | 0.841 | 0.654 | 0.578 | 0.572 | 0.826 |
2MCM | 113 | 0.867 | 0.789 | 0.713 | 0.639 | 0.643 |
2NUH | 104 | 0.922 | 0.835 | 0.691 | 0.771 | 0.685 |
2PKT | 93 | 0.762 | 0.162 | 0.003 | −0.193 | −0.165 |
2PLT | 99 | 0.635 | 0.508 | 0.484 | 0.509 | 0.187 |
2QJL | 99 | 0.611 | 0.594 | 0.584 | 0.594 | 0.497 |
2RB8 | 93 | 0.840 | 0.727 | 0.614 | 0.517 | 0.485 |
3BZQ | 99 | 0.848 | 0.532 | 0.516 | 0.466 | 0.351 |
5CYT | 103 | 0.548 | 0.441 | 0.421 | 0.331 | 0.102 |
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1ABA | 87 | 0.855 | 0.727 | 0.698 | 0.613 | 0.057 |
1CYO | 88 | 0.860 | 0.751 | 0.702 | 0.741 | 0.774 |
1FK5 | 93 | 0.648 | 0.590 | 0.568 | 0.485 | 0.362 |
1GXU | 88 | 0.901 | 0.748 | 0.634 | 0.421 | 0.581 |
1I71 | 83 | 0.798 | 0.549 | 0.516 | 0.549 | 0.380 |
1LR7 | 73 | 0.929 | 0.679 | 0.657 | 0.620 | 0.795 |
1N7E | 95 | 0.812 | 0.651 | 0.609 | 0.497 | 0.385 |
1NNX | 93 | 0.834 | 0.795 | 0.789 | 0.631 | 0.517 |
1NOA | 113 | 0.808 | 0.622 | 0.604 | 0.615 | 0.485 |
1OPD | 85 | 0.607 | 0.555 | 0.409 | 0.398 | 0.796 |
1QAU | 112 | 0.786 | 0.678 | 0.672 | 0.620 | 0.533 |
1R7J | 90 | 0.859 | 0.789 | 0.621 | 0.368 | 0.078 |
1UHA | 83 | 0.838 | 0.726 | 0.665 | 0.638 | 0.308 |
1ULR | 87 | 0.718 | 0.639 | 0.594 | 0.495 | 0.223 |
1USM | 77 | 0.819 | 0.832 | 0.809 | 0.798 | 0.780 |
1V05 | 96 | 0.841 | 0.629 | 0.599 | 0.632 | 0.389 |
1W2L | 97 | 0.747 | 0.691 | 0.564 | 0.397 | 0.432 |
1X3O | 80 | 0.787 | 0.600 | 0.559 | 0.654 | 0.453 |
1Z21 | 96 | 0.725 | 0.662 | 0.638 | 0.433 | 0.289 |
1ZVA | 75 | 0.911 | 0.756 | 0.579 | 0.690 | 0.579 |
2BF9 | 36 | 0.714 | 0.606 | 0.554 | 0.680 | 0.521 |
2BRF | 100 | 0.873 | 0.795 | 0.764 | 0.710 | 0.535 |
2CE0 | 99 | 0.824 | 0.706 | 0.598 | 0.529 | 0.628 |
2E3H | 81 | 0.794 | 0.692 | 0.682 | 0.605 | 0.632 |
2EAQ | 89 | 0.817 | 0.753 | 0.690 | 0.695 | 0.688 |
2EHS | 75 | 0.805 | 0.720 | 0.713 | 0.747 | 0.565 |
2FQ3 | 85 | 0.844 | 0.719 | 0.692 | 0.348 | 0.508 |
2IP6 | 87 | 0.841 | 0.654 | 0.578 | 0.572 | 0.826 |
2MCM | 113 | 0.867 | 0.789 | 0.713 | 0.639 | 0.643 |
2NUH | 104 | 0.922 | 0.835 | 0.691 | 0.771 | 0.685 |
2PKT | 93 | 0.762 | 0.162 | 0.003 | −0.193 | −0.165 |
2PLT | 99 | 0.635 | 0.508 | 0.484 | 0.509 | 0.187 |
2QJL | 99 | 0.611 | 0.594 | 0.584 | 0.594 | 0.497 |
2RB8 | 93 | 0.840 | 0.727 | 0.614 | 0.517 | 0.485 |
3BZQ | 99 | 0.848 | 0.532 | 0.516 | 0.466 | 0.351 |
5CYT | 103 | 0.548 | 0.441 | 0.421 | 0.331 | 0.102 |
Correlation coefficients for the B-factor prediction obtained by optimal FRI (opFRI), parameter-free FRI (pfFRI), and Gaussian normal mode (GNM) for large-size structures. Results for opFRI and pfFRI are taken from Opron et al.35 GNM and NMA values are taken from the coarse-grained (Cα) results reported in Park et al.33 MWCG results are parameter free and use all C, N, and O to predict Cα.
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1AHO | 64 | 0.768 | 0.698 | 0.625 | 0.562 | 0.339 |
1ATG | 231 | 0.843 | 0.613 | 0.578 | 0.497 | 0.154 |
1BYI | 224 | 0.600 | 0.543 | 0.491 | 0.552 | 0.133 |
1CCR | 111 | 0.741 | 0.580 | 0.512 | 0.351 | 0.530 |
1E5K | 188 | 0.848 | 0.746 | 0.732 | 0.859 | 0.620 |
1EW4 | 106 | 0.804 | 0.650 | 0.644 | 0.547 | 0.447 |
1IFR | 113 | 0.875 | 0.697 | 0.689 | 0.637 | 0.330 |
1NKO | 122 | 0.831 | 0.619 | 0.535 | 0.368 | 0.322 |
1NLS | 238 | 0.799 | 0.669 | 0.530 | 0.523 | 0.385 |
1O08 | 221 | 0.516 | 0.562 | 0.333 | 0.309 | 0.616 |
1PMY | 123 | 0.701 | 0.671 | 0.654 | 0.685 | 0.702 |
1PZ4 | 114 | 0.921 | 0.828 | 0.781 | 0.843 | 0.844 |
1QTO | 122 | 0.809 | 0.543 | 0.520 | 0.334 | 0.725 |
1RRO | 112 | 0.748 | 0.435 | 0.372 | 0.529 | 0.546 |
1UKU | 102 | 0.765 | 0.665 | 0.661 | 0.742 | 0.720 |
1V70 | 105 | 0.854 | 0.622 | 0.492 | 0.162 | 0.285 |
1WBE | 204 | 0.767 | 0.591 | 0.577 | 0.549 | 0.574 |
1WHI | 122 | 0.804 | 0.601 | 0.539 | 0.270 | 0.414 |
1WPA | 107 | 0.797 | 0.634 | 0.577 | 0.417 | 0.380 |
2AGK | 233 | 0.821 | 0.705 | 0.694 | 0.512 | 0.514 |
2C71 | 205 | 0.773 | 0.658 | 0.649 | 0.560 | 0.584 |
2CG7 | 90 | 0.738 | 0.551 | 0.539 | 0.379 | 0.308 |
2CWS | 227 | 0.756 | 0.647 | 0.640 | 0.696 | 0.524 |
2HQK | 213 | 0.897 | 0.824 | 0.809 | 0.365 | 0.743 |
2HYK | 238 | 0.728 | 0.585 | 0.575 | 0.510 | 0.593 |
2I24 | 113 | 0.672 | 0.593 | 0.498 | 0.494 | 0.441 |
2IMF | 203 | 0.798 | 0.652 | 0.625 | 0.514 | 0.401 |
2PPN | 107 | 0.673 | 0.677 | 0.638 | 0.668 | 0.468 |
2R16 | 176 | 0.640 | 0.582 | 0.495 | 0.618 | 0.411 |
2V9V | 135 | 0.697 | 0.555 | 0.548 | 0.528 | 0.594 |
2VIM | 104 | 0.859 | 0.413 | 0.393 | 0.212 | 0.221 |
2VPA | 204 | 0.757 | 0.763 | 0.755 | 0.576 | 0.594 |
2VYO | 210 | 0.777 | 0.675 | 0.648 | 0.729 | 0.739 |
3SEB | 238 | 0.879 | 0.801 | 0.712 | 0.826 | 0.720 |
3VUB | 101 | 0.852 | 0.625 | 0.610 | 0.607 | 0.365 |
PDB ID . | N . | MWCG . | opFRI . | pfFRI . | GNM . | NMA . |
---|---|---|---|---|---|---|
1AHO | 64 | 0.768 | 0.698 | 0.625 | 0.562 | 0.339 |
1ATG | 231 | 0.843 | 0.613 | 0.578 | 0.497 | 0.154 |
1BYI | 224 | 0.600 | 0.543 | 0.491 | 0.552 | 0.133 |
1CCR | 111 | 0.741 | 0.580 | 0.512 | 0.351 | 0.530 |
1E5K | 188 | 0.848 | 0.746 | 0.732 | 0.859 | 0.620 |
1EW4 | 106 | 0.804 | 0.650 | 0.644 | 0.547 | 0.447 |
1IFR | 113 | 0.875 | 0.697 | 0.689 | 0.637 | 0.330 |
1NKO | 122 | 0.831 | 0.619 | 0.535 | 0.368 | 0.322 |
1NLS | 238 | 0.799 | 0.669 | 0.530 | 0.523 | 0.385 |
1O08 | 221 | 0.516 | 0.562 | 0.333 | 0.309 | 0.616 |
1PMY | 123 | 0.701 | 0.671 | 0.654 | 0.685 | 0.702 |
1PZ4 | 114 | 0.921 | 0.828 | 0.781 | 0.843 | 0.844 |
1QTO | 122 | 0.809 | 0.543 | 0.520 | 0.334 | 0.725 |
1RRO | 112 | 0.748 | 0.435 | 0.372 | 0.529 | 0.546 |
1UKU | 102 | 0.765 | 0.665 | 0.661 | 0.742 | 0.720 |
1V70 | 105 | 0.854 | 0.622 | 0.492 | 0.162 | 0.285 |
1WBE | 204 | 0.767 | 0.591 | 0.577 | 0.549 | 0.574 |
1WHI | 122 | 0.804 | 0.601 | 0.539 | 0.270 | 0.414 |
1WPA | 107 | 0.797 | 0.634 | 0.577 | 0.417 | 0.380 |
2AGK | 233 | 0.821 | 0.705 | 0.694 | 0.512 | 0.514 |
2C71 | 205 | 0.773 | 0.658 | 0.649 | 0.560 | 0.584 |
2CG7 | 90 | 0.738 | 0.551 | 0.539 | 0.379 | 0.308 |
2CWS | 227 | 0.756 | 0.647 | 0.640 | 0.696 | 0.524 |
2HQK | 213 | 0.897 | 0.824 | 0.809 | 0.365 | 0.743 |
2HYK | 238 | 0.728 | 0.585 | 0.575 | 0.510 | 0.593 |
2I24 | 113 | 0.672 | 0.593 | 0.498 | 0.494 | 0.441 |
2IMF | 203 | 0.798 | 0.652 | 0.625 | 0.514 | 0.401 |
2PPN | 107 | 0.673 | 0.677 | 0.638 | 0.668 | 0.468 |
2R16 | 176 | 0.640 | 0.582 | 0.495 | 0.618 | 0.411 |
2V9V | 135 | 0.697 | 0.555 | 0.548 | 0.528 | 0.594 |
2VIM | 104 | 0.859 | 0.413 | 0.393 | 0.212 | 0.221 |
2VPA | 204 | 0.757 | 0.763 | 0.755 | 0.576 | 0.594 |
2VYO | 210 | 0.777 | 0.675 | 0.648 | 0.729 | 0.739 |
3SEB | 238 | 0.879 | 0.801 | 0.712 | 0.826 | 0.720 |
3VUB | 101 | 0.852 | 0.625 | 0.610 | 0.607 | 0.365 |
A comparison of the average correlation coefficients for small, medium, and large proteins, as well as the protein superset, is provided in Table VI. It is seen that GNM is more accurate than NMA, as analyzed by Park el al.33 opFRI and pfFRI are more accurate than GNM. The proposed MWCG is about 28% more accurate than pfFRI and 42% more accurate than GNM.
Average correlation coefficients for Cα B-factor prediction with FRI, GNM, and NMA for three structure sets from the work of Park et al.33 and a superset of 364 structures. Results for opFRI and pfFRI are taken from Opron et al.35 GNM and NMA values are taken from the coarse-grained (Cα) results reported in Park et al.33 MWCG results are parameter free and use all C, N, and O to predict Cα.
PDB set . | MWCG . | opFRI35 . | pfFRI35 . | GNM . | NMA33 . |
---|---|---|---|---|---|
Small | 0.921 | 0.667 | 0.594 | 0.54133 | 0.480 |
Medium | 0.795 | 0.664 | 0.605 | 0.55033 | 0.482 |
Large | 0.775 | 0.636 | 0.591 | 0.52933 | 0.494 |
Superset | 0.803 | 0.673 | 0.626 | 0.56535 | NA |
Lastly, Table VII displays the average correlation coefficient using MWCG to predict the B-factors of Cα, non-Cα carbon, nitrogen, oxygen, and sulfur atoms. Note that these predictions were not available for earlier GNM and FRI methods.
Correlation coefficients for Cα, non-Cα carbon, nitrogen, oxygen, and sulfur using parameter-free MWCG. Only 215 of the 364 proteins contain sulfur atoms.
Subset . | Cα . | Non-Cα carbon . | Nitrogen . | Oxygen . | Sulfur . |
---|---|---|---|---|---|
Average | 0.803 | 0.744 | 0.812 | 0.789 | 0.903 |
No. of proteins | 364 | 364 | 364 | 364 | 215 |
Subset . | Cα . | Non-Cα carbon . | Nitrogen . | Oxygen . | Sulfur . |
---|---|---|---|---|---|
Average | 0.803 | 0.744 | 0.812 | 0.789 | 0.903 |
No. of proteins | 364 | 364 | 364 | 364 | 215 |
E. Hinge detection
Protein hinge regions play an important role in enzymatic catalysis due to their flexibility. A flexible active site will more likely to accommodate binding ligands or partners. Protein hinges are also important in protein domain separation. As such, the characterization of protein hinges is a valuable application of flexibility methodologies. Our method can be applied as a protein hinge detection tool. We consider calmodulin, a good example of a hinge that affects both the structure and function. We compared the experimental B-factors and predicted B-factors of Cα residues of the three proteins: 1CLL, 1WHI, and 2HQK. Experimental observations are compared with predictions from WCG and GNM. To illustrate the utility of the element specific feature of MWCG, we use only one scale so that the method does not take advantage of the multiscale ability of MWCG. For PDB ID 1CLL, we include MWCG as a comparison. The results are generated with the MWCG CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å. The results are displayed in Figs. 6–8.
Top: from left to right, the structure of calmodulin (PDB ID: 1CLL) visualized in Visual Molecular Dynamics (VMD) 18 and colored by experimental B-factors, MWCG-predicted B-factors, WCG-predicted B-factors, and GNM-predicted B-factors with red representing the most flexible regions. Bottom: the experimental (Exp) and predicted B-factor values plotted per residue for PDB ID 1CLL. The GNM is the GNM method with a cutoff distance of 7 Å. We see that GNM clearly misses the flexible hinge region. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å. MWCG represents B-factor predictions determined from the MWCG method using the fixed parameters listed in Table I.
Top: from left to right, the structure of calmodulin (PDB ID: 1CLL) visualized in Visual Molecular Dynamics (VMD) 18 and colored by experimental B-factors, MWCG-predicted B-factors, WCG-predicted B-factors, and GNM-predicted B-factors with red representing the most flexible regions. Bottom: the experimental (Exp) and predicted B-factor values plotted per residue for PDB ID 1CLL. The GNM is the GNM method with a cutoff distance of 7 Å. We see that GNM clearly misses the flexible hinge region. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å. MWCG represents B-factor predictions determined from the MWCG method using the fixed parameters listed in Table I.
Top: a visual comparison of experimental B-factors (left), WCG-predicted B-factors (middle), and GNM-predicted B-factors (right) for the ribosomal protein L14 (PDB ID: 1WHI). Bottom: the experimental and predicted B-factor values plotted per residue. GNM represents predicted B-factors using GNM with a cutoff distance of 7 Å. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å.
Top: a visual comparison of experimental B-factors (left), WCG-predicted B-factors (middle), and GNM-predicted B-factors (right) for the ribosomal protein L14 (PDB ID: 1WHI). Bottom: the experimental and predicted B-factor values plotted per residue. GNM represents predicted B-factors using GNM with a cutoff distance of 7 Å. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å.
Top: a visual comparison of experimental B-factors (left), WCG-predicted B-factors (middle), and GNM-predicted B-factors (right) for the engineered cyan fluorescent protein, mTFP1 (PDB ID: 2HQK). Bottom: the experimental (Exp) and predicted B-factor values plotted per residue for PDB ID 2HQK. The GNM is the GNM method with a cutoff distance of 7 Å. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å.
Top: a visual comparison of experimental B-factors (left), WCG-predicted B-factors (middle), and GNM-predicted B-factors (right) for the engineered cyan fluorescent protein, mTFP1 (PDB ID: 2HQK). Bottom: the experimental (Exp) and predicted B-factor values plotted per residue for PDB ID 2HQK. The GNM is the GNM method with a cutoff distance of 7 Å. WCG is parametrized using CC, CN, and CO kernels of the exponential type with fixed parameters κ = 1 and η = 3 Å.
IV. DISCUSSION
When compared to opFRI, pfFRI, GNM, and NMA, the proposed MWCG method provides a significantly better Pearson correlation coefficient. For most proteins in the data set, MWCG improves upon opFRI. MWCG is about 28% and 42% more accurate than pfFRI and GNM on a set of 364 proteins. However, the parameters of the current MWCG method were not fully optimized. A grid search of MWCG parameters would undoubtedly provide even better results. Mathematically, GNM can be regarded as an algebraic graph theory approximation to the graph centrality of geometric graph theory, namely, FRI, as far as the B-factor prediction is concerned. In fact, it is a computationally more expensive approximation. Consequently, FRI methods are more accurate and efficient than GNM. Using multiscale analysis, graph coloring, and subgraph division, MWCG is able to significantly outperform all the earlier GNM and FRI methods.
Unlike the earlier methods, the MWCG method is not limited to B-factor prediction of Cα atoms. Due to graph coloring and subgraph division techniques, MWCG can also be used to accurately predict the B-factor of other heavy atoms as well. The results in Table VII show that the method also reliably predicts the B-factors of non-Cα carbon, nitrogen, oxygen, and sulfur atoms.
The correlation maps generated in this study provide evidence that using MWCG, one can recognize tertiary structures from a contact map not only using Cα atoms but also using nearby double bonded carbonyl oxygen and amine nitrogen atoms as well. In this study, we construct nitrogen- and oxygen-based protein correlation maps using the amine nitrogen and the double bonded carbonyl oxygen from each amino acid. In particular, an alpha helix can be clearly observed in the correlation maps along the diagonal as a thicker band as seen in Figs. 2, 4, and 5. The parallel bands in the correlation maps for 5IIV seen in Fig. 4 indicate the interaction between the left and right alpha helices. In Figs. 3 and 5, the bands perpendicular to the diagonal represent the interaction between the anti-parallel beta sheets for proteins 1KGM and 3PSM.
Ribosomal protein L14 (PDB ID: 1WHI) is an important component of the 60S ribosomal subunit. Structurally the protein is diverse, containing an alpha helix, a beta-barrel, a parallel beta strands, and a beta-hairpin motif. Due to the hard cutoff used in GNM, GNM underpredicts B-factors in stiff areas and overpredicts B-factors in flexible regions. This result is typical of GNM as the hard cutoff required in the Kirchoff matrix (i.e., Laplacian matrix) of GNM leads to an overemphasis of the importance of the bond importance near the cutoff. This behavior is seen in Figs. 6–8. Figure 6 depicts the B-factor prediction comparison for calcium-bound calmodulin. We see that GNM fails to predict the hinge region near the 75th residue. The single kernel weighted colored graph does show a peak in this region though it underestimates the magnitude of the flexibility found in this region. We see the multiscale property of MWCG does an even better job capturing the hinge in this region. Figure 7 shows the predicted Cα B-factors of the cyan fluorescent protein. Here the GNM prediction contains a large error near the 60th residue. Different GNM cutoffs can slightly improve this error, but it still exists regardless of the chosen cutoff. This region corresponds to a small alpha-helical region within a beta-barrel. In this region, there are at least two important interaction scales and GNM fails to take both into account. We can see from the figure that the single kernel weighted colored graph is able to capture these interactions accurately indicating that the element specificity is capturing at least some of the multiscale interaction.
The work presented here demonstrates the efficacy of modifying the FRI method to include element specific interactions between other heavy atoms. Compared to the optimized FRI method, the MWCG method provides an 18% increase in the average Pearson correlation coefficient. Moreover, even the single kernel element specific FRI provides encouraging results as seen in Figs. 7, 6, and 8. The new oxygen- and nitrogen-based correlation maps provide a fresh insight into protein topology and may be useful for future work. To the authors’ knowledge, no other method outperforms the current algorithm for Cα B-factor prediction.
Any regression method is prone to overfitting. We can see from Table VI that for small proteins, the MWCG method has a particularly high Pearson correlation coefficient, while the medium and large sets are more consistent with one another. This discrepancy is likely due to overfitting and could be addressed by using fewer correlation kernels. A similar problem exists with the sulfur atom B-factor prediction as demonstrated by the large Pearson correlation coefficient in Table VII. Future work will address this issue by combining machine learning and cross-validation techniques to provide a method robust against overfitting. Unlike the FRI methods discussed here, the machine learning approach has the added advantage of blind B-factor prediction.
V. CONCLUSION
Despite much effort, protein flexibility analysis remains a challenge due to low accuracy in B-factor prediction. For a large set of proteins, none of the current methods deliver an average Pearson correlation coefficient as high as 0.7 for protein B-factor prediction, which is unreliable for practical applications to hinge detection, domain separation, docking analysis, and entropy calculations. Additionally, earlier methods cannot simultaneously predict the flexibility of different types of atoms in a molecule. This work introduces a geometric graph model, multiscale weighted colored graph (MWCG), to address the aforementioned difficulties and significantly improve the current state-of-the-art approaches in protein flexibility analysis. The weighted colored graph theory describes pairwise interactions near an atom in the protein network. These interactions are organized according to their element types, which leads to subgraphs. The rigidity of each node at a given scale is represented by subgraph centralities from various scales. The present method is validated by a few standard data sets, including relatively small, medium, and large proteins. An extensive comparison is given to a number of standard methods, such as GNM, NMA, and various FRI models. We show that the present MWCG used in our study is over 40% more accurate than GNM and delivers an average Pearson correlation coefficient as high as 0.8 in protein B-factor prediction of 364 proteins, which offers a reliable method for protein flexibility analysis and various applications. MWCG also offers accurate predictions of all atoms in a protein data set. The proposed method can be used to improve the algebraic graph theory analysis of biomolecular algebraic connectivity. A drawback of the present minimization schedule is that it is subject to overfitting in predicting the B-factors of small molecules. This problem can be addressed by using advanced machine learning algorithms.
ACKNOWLEDGMENTS
This work was supported in part by NSF Grant Nos. DMS-1721024 and IIS-1302285 and the MSU Center for Mathematical Molecular Biosciences Initiative.