SphereCon-a method for precise estimation of residue relative solvent accessible area from limited structural information.

Bioinformatics, YYYY, 0–0 doi: 10.1093/bioinformatics/xxxxx Advance Access Publication Date: DD Month YYYY Manuscript Category Structural Bioinformatics SphereCon - A method for precise estimation of residue relative solvent accessible area from limited structural information. Alexander Gress1,2,* and Olga V. Kalinina1,3 1Helmholtz Institute for Pharmaceutical Research Saarland (HIPS), Helmholtz Centre for Infection Research (HZI), Campus E8.1, 66123 Saarbrücken, Germany 2Graduate School of Computer Science, Saarland University, 66123 Saarbrücken, Germany. 3Medical Faculty, Saarland University, 66421 Homburg, Germany. *To whom correspondence should be addressed. Associate Editor: XXXXXXX Received on XXXXX; revised on XXXXX; accepted on XXXXX Abstract Motivation: In proteins, solvent accessibility of individual residues is a factor contributing to their importance for protein function and stability. Hence one might wish to calculate solvent accessibility in order to predict the impact of mutations, their pathogenicity, and for other biomedical applications. A direct computation of solvent accessibility is only possible if all atoms of a protein threedimensional structure are reliably resolved. Results: We present SphereCon, a new precise measure that can estimate residue relative solvent accessibility (RSA) from limited data. The measure is based on calculating the volume of intersection of a sphere with a cone cut out in the direction opposite of the residue with surrounding atoms. We propose a method for estimating the position and volume of residue atoms in cases when they are not known from the structure, or when the structural data are unreliable or missing. We show that in cases of reliable input structures, SphereCon correlated almost perfectly with the directly computed RSA, and outperforms other previously suggested indirect method. Moreover, SphereCon is the only measure that yield accurate results when the identities of amino acids are unknown. A significant novel feature of SphereCon is that it can estimate RSA from inter-residue distance and contact matrices, without any information about the actual atom coordinates. Availability: https://github.com/kalininalab/spherecon Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online. 1 Introduction Protein function is intimately related to protein three-dimensional (3D) structure, which, in turn, is determined by proteins amino acid sequence. Protein 3D structures are more conserved than their sequences, meaning that distantly related proteins, for which homology is difficult to detect via sequence comparison, still can fold into very similar 3D structures (Illergård et al., 2009). Homology modelling approaches allow to computationally predict 3D structures for proteins with no experimentally resolved structures available using template 3D structures of proteins with as low as 30-35% sequence identity (Rost, 1999). However, in these models, the coordinates of amino acid residues can be reconstructed imprecisely, particularly for the residues at the protein surface (Eisenmenger et al., 1993). Amino acid residues located on protein surface and within its core play different functional roles (Aloy et al., 2001), and are under different evolutionary constraints (Bordo and Argos, 1990; Sasidharan and Chothia, 2007; Bloom et al., 2006). For example, mutations of residues A.Gress et al. in protein core can influence protein overall stability (Jackson et al., 1993; Brockwell et al., 2002; Lim et al., 1992; Bullock et al., 1997) and in extreme cases lead to protein misfolding and aggregation (Xu et al., 2011; van der Kamp and Daggett, 2010), whereas mutations of residues on the protein surface may influence the stability and specificity of protein interactions (Yi et al., 2017). If the mutated residue is not a part of an interaction interface or binding pocket, and the mutation does not introduce an unfavourable hydrophobic residue at the surface, it is likely to be of no consequence. In line with this, it has been reported that pathogenic mutations can have a destabilizing effect on protein structure, affect conformational dynamics or hydrogen bond networks (Kucukkal et al., 2015; Stefl et al., 2013) and are enriched in protein core and depleted from their surface (Wang and Moult, 2001; Gress et al., 2017). Thus the relative position of residues with respect to protein core are predictive of the functional importance of these residues and pathogenicity of mutating them. The solvent accessible area (SA) is a measure of the extent to which a residue lies on protein surface or in its core. For an experimentally resolved protein 3D structure, it can be computed by rolling a probe sphere over the van der Waals surface of the protein (Sanner et al., 1996). The surface traced by the center of the probe sphere is then called the protein accessible surface. The whole accessible surface of a protein can be divided with respect to the contributions of each residue, and these contributions are called accessible surface of individual residues. To compute the area of a residue accessible surface (SA) directly, the coordinates of all heavy atoms must be known. SA alone gives limited information, since residues of different types vary in size considerably. The relative solvent accessible area (RSA) is the residue SA divided by a residue maximal SA, which is constant for all amino acid residues of the same type. RSA provides a reasonable way of comparing different residues with respect to their position relative to the protein surface. Given a full-atom structure of a protein, it can be deterministically computed by different tools (Kabsch and Sander, 1983). However, the computation fails if coordinates of some atoms are missing, e.g. in cases when the position of some residues has not been experimentally resolved. RSA can also be computed for homology models using the same tools, but this introduces another source of error: if coordinates of some residues have been reconstructed incorrectly, which can happen in particular for protein surface residues, the direct calculation of RSA can be incorrect. For such cases, other measures for estimating SA and RSA from limited information have been developed. When only the coordinates of the Cα atoms of the protein are known, which is often the case for structures of low resolution, and is also in an intermediate step of protein structure modeling pipelines (Fasnacht et al., 2007; Gadkari et al., 2009), specialized surface measures can be used. One of the first such measures was the coordination number (CN) (Simons et al., 1997) that is based on counting the number of Cα atoms in a sphere around the Cα atom of the residue in question. For residues on the protein surface, one expects a half of such a sphere to be less populated compared to residues lying in the protein core, thus CN negatively correlates with RSA. While measuring CN can satisfactorily differentiate between residues predominantly exposed to the solvent and residues completely buried in the protein core, it lacks the ability to recognize finer differences of the degree of solvent exposure among partially exposed residues. To mitigate this problem, the half-sphere exposure (HSE) method (Hamelryck, 2005) was developed. In this approach, the sphere used for determining the CN is cut into two half spheres by a plane orthogonal to the Cα-Cβ vector of the residue in question. This results in two new measures: the values of CN for the lower and upper half-spheres, where upper half-sphere corresponds to the direction towards the Cβ atom. Comparing the values of CN for the upper and bottom half-spheres for structures, for which RSA can be computed directly from the all-atom coordinates, proves that RSA can be inferred from the CN values corresponding to the upper half-sphere, whereas the CN values of the lower half-sphere are not correlated to it. Thus the CN value of the upper half-sphere, which is called the half-sphere exposure (HSE), can be used as a proxy of RSA. However, to compute it, one needs to know not only the coordinates of the Cα atoms, but also the coordinates of the Cβ atoms. These latter coordinates can be estimated using the positions of the Cα atoms of the neighboring residues. The correlation between HSE and the directly computed RSA from all-atom structures reaches 82%, which is enough to differentiate between buried residues and predominantly exposed residues. For partially exposed residues, HSE performs better than CN, but still is not perfect. In this study, we present a novel approach to assess the RSA from limited data that outperforms all other tools for the case when only the coordinates of Cα atoms are available. The typical use case for our measure is when the protein sequence is known, however, we also present a variant, where this information is also missing. Similarly to CN and HSE, we assume that the more space around a residue in question is occupied by other residues and the more evenly it is occupied by them, the less it is exposed to the solvent. The main novelty of our method is not to represent residues as points or spheres in the 3D space corresponding to the coordinates of their Cα atoms, but as space-filling bodies, which differ for different amino acid types. Each residue is represented by a sphere, the radius of which is amino acid type-specific. A search space is defined as a sphere with a cut-out cone placed around the residue, and the intersections between the search space and the spheres corresponding to the neighboring residues are calculated. In this way, neighboring residues influence the estimated RSA more than the distant ones. Additionally, we introduce differentiation between amino acid residues of different size. We demonstrate that these features make SphereCon more accurate than earlier approaches. Interestingly, even when the residue-specific radii are ignored, and all residues are represented by spheres of the same size and only the coordinates of Cα atom are used (which corresponds to the case when protein sequence is unknown), SphereCon still performs better than other tools, all of which use additional information. Perhaps the most interesting part of SphereCon is a novel simple method for estimating RSA from data on residue-residue contacts, without knowing their 3D coordinates. This makes our method potentially useful in novel de novo modelling schemes, where inter-residue contacts are predicted from multiple sequence alignment statistics (Wang et al., 2017; Seemayer et al., 2014; Zhang et al., 2016; Adhikari et al., 2018; Ovchinnikov et al.; Jones et al., 2015; Tegge et al., 2009; Eickholt and Cheng, 2012). Another tool in the field that can predict RSA from predicted residue contacts, SPOT-1D (Hanson et al., 2019), employs deep learning. We show that even with a simple geometric method using even this limited information, we are able to reconstruct the RSA values with a positive correlation. We apply our methods to the most recent CASP targets and show that even for this most challenging dataset we achieve reasonable results. 2 Methods We developed four alternative measures that use the same principle, but are designed for different types of input information. The key steps of the algorithm are the following: define a search space around a given residue using a sphere of a large diameter, possibly with a cut-out cone; SphereCon define intersecting volumes for each surrounding residue colliding with the search space; and calculate the unoccupied fraction of the search space, resulting in a value between 0 and 1. The search space (see Fig.1) is defined as a sphere of radius r (parameter of the optimization problem, see below) and a cone cut out from the sphere. The search sphere is centered at the centroid of all the side-chain atoms of a given residue. The apex of the cone coincides with the center of the sphere and the cone axis is collinear to the centroid-to-Cα vector C. In our main application scenario, we assume that the coordinates of the side-chain atoms are unknown, so we also developed a method for estimating the centroids coordinates (see below). The apex angle a regulates the volume cut out from the search sphere. The case when the apex angle is zero corresponds to the full sphere as the search space, the apex angle equal to 180° amounts to the same search space as in the HSE method. Figure 1: Schematic representation of the design of the search space. Thus the search space is defined by three parameters: the position of the sphere center; the radius of the search sphere; and the apex angle of the cone. We describe three scenarios based on different amount of structural information available. In the different scenarios we have to employ different techniques to estimate the parameters necessary to define the search space. 3.1 Scenario 1 (SC-S1): All atom coordinates available The first scenario corresponds to the case, when the coordinates of all atoms in a 3D structure of the protein are available, and hence the RSA can be calculated directly. The center of the search sphere is placed at the centroid of the coordinates of the side chain atoms of the residue in question. The search sphere radius and the cosine of the apex angle of the cut-out cone are residue-specific constants that yield the best correlation with RSA for a test dataset, determined by a grid search. The heavy atoms of all other residues are represented by their van der Waals spheres, and the intersection with the search space is calculated for them. The sum of all intersecting volumes is called total occupied volume. SphereCon is defined as the ratio of the volume of the search space and the total occupied volume. Since for this scenario the RSA can be directly calculated, SphereCon has here no practical use case, but the results for SphereCon in this scenario are import for evaluating the method. 3.2 Scenario 2 (SC-S2): Coordinates of Cα atoms are available and protein sequence is known In the second scenario for each residue only the coordinates of the Cα atom and the amino acid type are known. Since the coordinates of the side chain atoms are not available now, the centroid has to be predicted. As in SC-S1, the radius of the search sphere and the cone apex angle are determined based on a grid search. The atom-specific spheres corresponding to the atom van der Waals radii from SC-S1 are replaced by larger residue specific spheres centered at their predicted centroids. The radius is chosen, such that the volume of the sphere is equal to the sum of the van der Waals sphere volumes of the heavy atoms of the specific amino acid. The radii of the intersecting residue spheres range from 2.57 Å for glycine to 4.02 Å for tryptophan (Supplementary Table S1). 3.3 Scenario 3 (SC-S3): Only coordinates of Cα atoms are available The least amount of information, for which the RSA estimation by SphereCon is possible, are the 3D coordinates of the protein Cα atoms without the information on what amino acid residues they correspond to. Similarly to SC-S2, we have to predict the centroids for all residues. The search sphere radii cannot be residue specific anymore, since the type of amino acid at each position is not known. Again, a grid search is used to find the search sphere radius and the cosine of the apex angle of the cutting cone with the best performance in a residue-oblivious manner, i.e. the same value set for all positions. The intersecting volumes are spheres centered around all other predicted centroids with radius 3.23 Å (a radius that corresponds to the average volume of the twenty natural amino acids weighted by their frequency in our training set, see below). 3.4 Scenario 4 (SC-S4): Only prediction of a distance matrix or contact matrix is available In this scenario we depart completely from 3D coordinates of any atoms and use the output of sequence-based residue-residue contact prediction methods as input. In particular, we use pairwise contacts or distances predicted by RaptorX (Wang et al., 2016) or a similar tool. The information on the identity of amino acids in protein sequence is retained, and thus the different radii of the search spheres can be optimized by the grid search procedure. Since the coordinates of the backbone are not known, prediction of the centroid coordinates (orientation of the side chain) is not possible and the direction of the cutting cone cannot be estimated. Instead we use spheres in this scenario. Since the distances to other residues as well as identity of those residues are assumed to be known in this scenario, we can tell, which residues are within the search sphere or intersect with it, and calculate the intersection of the search sphere with residue-specific spheres corresponding to these residues. After these intersection volumes are calculated, SphereCon can be calculated as in other scenarios. For contact matrices, we just consider all residues predicted to be in contact to lie at a distance of 8 Å, and all other residues so far away that they do not intersect with the search sphere. As, the predicted distance matrices used as input may be sparse and contain errors, we calculate the sparsity of the input matrix and use a set of parameters (sphere radii) optimized for this particular sparsity. 3.5 Training datasets We created a gold standard set of protein 3D structures by choosing a representative structure from each SCOP (Murzin et al., 1995) family (only SCOP classes a, b, c and d) with all the heavy atoms resolved (Supplementary Table S2). For testing, we performed a four-fold cross validation, where we selected one SCOP class as the test set and used the A.Gress et al. other three for training (Supplementary Table S2). This cross-validation scenario is the most stringent in the sense that training and testing are performed for proteins with dramatically different topological properties. For optimizing parameters in SC-S4, we used distance matrices calculated from the 3D structures and removed all distances between the residues that are separated by less than three residues in the sequence, as these pairs are typically not considered by contact prediction tools. Then we increasingly removed random distances from the matrix in 10% bins. Beside the described above cross-validation, to test out method in SCS4, we used distance matrices predicted for the sequences of 13 targets from CASP13 (Kryshtafovych et al., 2019), for which a 3D structure was available in the PDB for the time of this writing, using the RaptorX (Wang et al., 2016) webserver. 3.6 Centroid prediction For all structures in the gold standard dataset, we compute the Cαcentroid vector for each residue. Then for each amino acid type we calculate the average orientation of these vectors to the plane spanned by the C-alpha coordinates of the residue and its two neighbor residues. These amino acid type specific average Cα-centroid vectors can now be used to predict the centroid of residues with missing coordinates by placing them on the respective planes. For scenario 3, one average vector for all amino acid types in the gold standard dataset was used. 3.7 Optimization The goal of the optimization step is to define the optimal parameters in order to maximize the Pearson's correlation between SphereCon and RSA. In order to find the optimal search space parameters, i.e. the radius of the search sphere and the apex angle of the cone, we describe the following optimization problem: ❑❑❑❑❑❑ ( ( () ) ) , where r is search sphere radius, a is the cosine of the apex angle, corr is the Pearson’s correlation. Then r*, a* are the optimal search space parameters. We performed a two-dimensional grid search in the space of the radii values in the interval [4 Å, 20 Å] with the steps of 0.5 Å and the cosine of the apex angle in the interval [0.5, 1] with the steps of 0.05. For each residue for all structures in the training dataset, the RSA and the SphereCon for all combinations of the two parameters were computed, separately for each scenario. 3 Results 3.1 Optimization The optimal parameters for all scenarios were found in the grid search (Supplementary Table S3). The radii of the search spheres correlate with the size of the amino acid, ranging from 6.5 Å to 8.0 Å for SC-S1 and from 6.75 Å to 9.0 Å for SC-S2. In SC-S1 sharp cutting cone angles were preferred for most of the residues, while for SC-S2 half of the residues the preference is using no cutting cone (cos(a*) = 1.0). There is a trend that larger residues favor wider angles, in particular tryptophan corresponds to an apex angle with a cosine of -0.6. In SC-S4 only one parameter is subject of the optimization, yielding r* = 7.5 Å. A portion of the corresponding heatmap that represents the correlation for all structures in the test set can be seen in Supplementary Figure S1. The maximum correlation that could be achieved is 0.893. The change of the correlation value is small between the neighboring parameter values, and thus that our optimization landscape is smooth and well-defined. 3.2 Cross-validation When comparing the optimal search parameters learned from the cross validation setup to the optimal parameters learned on the whole dataset (Supplementary Table S3), we notice only slight differences, which evidences the stability of the learned parameters. Performance of SphereCon is very little influenced by the exact training and testing setup (Table 1). When compared to the overall performance of SphereCon listed in Table 2, one notes that they are identical and hence there are no signs of any overtraining effects. Table 1: Each cell contains the Pearson’s correlation between SphereCon and RSA for the different scenarios and different test set setups. SCOP class A SCOP class B SCOP class C SCOP class D SC-S1 0.95 0.94 0.95 0.95 SC-S2 0.91 0.92 0.91 0.91 SC-S3 0.89 0.89 0.89 0.89 SC-S4 0.87 0.87 0.87 0.88 3.3 Benchmark We benchmarked SphereCon against CN (Simons et al., 1997) and HSE (Hamelryck, 2005), which we re-implemented with the original parameters (Table 2). We were able to reproduce the same values of Pearson's correlation between the CN, HSE and RSA measures as reported in (Hamelryck, 2005) in spite of the fact that we use a dataset different from the one in the original publication. This indicates that these measures are robust with respect to the test dataset. SphereCon correlates well with both CN and HSE in all three scenarios. As expected, the more input information is used, the better is the correlation with the RSA. Even in the worst-case scenario, when the sequence of residues in the backbone is unknown, we achieve a clear improvement over HSE, which uses information not only on the position of Cα but also on the position of the residue’s Cβ atoms. Table 2: Pearson's correlation coefficients between all tested measures for the full dataset. RSA CN HSE SC-S4 SC-S3 SC-S2 SC-S1 RSA n/a -0.770 -0.823 0.878 0.890 0.916 0.945 CN n/a 0.817 -0.795 -0.866 -0.830 -0.778 HSE n/a -0.819 -0.882 -0.860 -0.835 SC-S4 n/a 0.899 0.949 0.903 SphereCon SC-S3 n/a 0.949 0.907 SC-S2 n/a 0.944 SC-S1 n/a Another quality criterion of a measure for estimating the RSA is how well can it be used in order to distinguish between surface and core residues. We classified each residue in the dataset as surface or core based on an RSA threshold of 16% (Rost, 1997), using CN, HSE and SphereCon as predictors (Figure 2). With an AUC of 0.943, HSE was already an excellent surface/core prediction measure, but SphereCon performed even better, achieving the AUC of 0.963 even in the most difficult scenario SC-S3, in which much less information is used as in HSE. The balance point yields the threshold of 0.27, which results in only 23041 mis-classifications over the total of 211539 residues (Figure 3). Figure 2: ROC curves of all measures based on the binary class assignment (surface/core) done by RSA. Figure 3: Scatterplots of different measures against RSA, red lines indicate the classification threshold and the balance point for different methods. Further, we analyzed how stable SphereCon is in regards to different secondary structure elements (assigned with DSSP (Kabsch and Sander, 1983), Supplementary Table 4). Interestingly, in all scenarios the performance was better for α-helices and coiled regions compared to βsheets. 3.4 Sparse distance and contact matrices in SC-S4 Since the use case for SC-S4 is fundamentally different from other scenarios, , we modified the cross-validation setup. For the test set structures, we calculated the distance matrices and randomly removed entries for non-neighboring residues creating a sparse distance matrix. In these sparse matrices, between 50% and 100% of all contacts were retained. In this way, we simulate the potential missing values in the contact of distance matrices derived from correlations in the multiple sequence alignments. As expected, the performance drops with the increase of sparsity (Table 3), but even with a distance matrix containing only 70% of all true entries, SphereCon performs as well as HSE with full information. Table 3: Pearson’s correlation of SphereCon and RSA for SC-S4. Sparsity (% of distances removed) Test set (training set consists of the other three SCOP classes) SCOP class A SCOP class B SCOP class C SCOP class D 10% 0.83 0.83 0.83 0.83 20% 0.82 0.82 0.82 0.83 30% 0.80 0.80 0.80 0.81 40% 0.75 0.76 0.74 0.76 50% 0.77 0.77 0.76 0.78 60% 0.73 0.74 0.72 0.74 70% 0.75 0.75 0.73 0.75 80% 0.72 0.73 0.71 0.73 90% 0.71 0.71 0.70 0.72 HSE (full coordinate information) -0.82 -0.81 -0.82 -0.81 Although the community now is experiencing an advent of methods that are capable of predicting inter-residue contacts from sequence data (Xu and Wang, 2019), methods that only predict contacts, defined as two residues separated by a distance below a certain threshold (typically 8 Å) are still more common (Marks et al., 2011; Jones et al., 2015; Seemayer et al., 2014). Hence we modified SC-S4 to use this kind of data. In this, we converted the distance matrices in contact matrices by dropping all distance larger than 8 Å and setting the rest to 5 Å. Then we modified the resulting contact matrices by random removing or adding up to 50% of spurious contacts to mimic the errors that the predictions might entail. A.Gress et al. The correlation with the true computed RSA is still remarkably high (Supplementary Table S4), and drops slowly as more random contacts are added or removed. For 10% random contacts, the quality of our prediction is still better than that of CN, which has the full atomic coordinates. In a similar approach SPOT-1D (Hanson et al., 2019) deep learning is used to predict RSA from predicted contact maps, outperforming SphereCon (the reported correlation of SPOT-1D to true RSA values is between 0.79 and 0.82 depending on the test set). Comparing Tables 3 and 4, one can see that the performance of SphereCon can be much improved by using specific distance values instead of contacts, which may be also the case for SPOT-1D. 3.5 Testing SphereCon on predicted distance matrices Finally, we have applied SphereCon to distance matrices predicted by RaptorX (Wang et al., 2016) for the target sequences from the last CASP round, which represent probably a dataset most challenging one can imagine. The sparsity of the predicted matrices varies considerably, because for a protein of length L the distance matrix has a size L×L, and only L, L/5, or L/10 top-quality distances are usually reported. So for longer sequences the distance matrices are sparser. We compared the predicted SphereCon values to the actual RSA from the experimentally resolved structures (Table 4). The correlation between SphereCon and RSA varies between 0.404 and 0.771, whereas the sparsity of the distance matrices ranges between 60% and over 90%. Thus, the correlation is typically lower than in our benchmark and, unlike the benchmark, there is no apparent correlation between the matrix sparsity and the SphereCon prediction quality. Table 4: Pearson’s correlation of SphereCon and RSA for CASP targets. Target PDB ID Sequence length Sparsity Pearson’s correlation to RSA 6EK4 chain A 342 92.3% 0.600 6F45 chain A 68 70.5% 0.484 5W9F chain A 72 58.8% 0.460 6CP8 chain A 157 78.8% 0.740 6BTC chain A 84 67.1% 0.771 6CP9 chain A 116 73.2% 0.742 6CP9 chain B 114 75.1% 0.706 6CCI chain A 354 93.2% 0.631 6G57 chain A 97 66.0% 0.404 6GNX chain A 98 72.3% 0.729 6D7Y chain A 89 69.2% 0.620 6Q64 chain A 319 90.6% 0.552 6MSP chain A 80 59.7% 0.719 Thus with SphereCon we can offer an alternative tool for predicting RSA from predicted contact/distance matrices, that can be used, for example, in the pipelines for protein 3D structure prediction that are based on evolutionary coupling data. 4 Discussion In this study, we present SphereCon, a new and more precise method for estimating residue relative solvent accessibility. We offer different usage scenarios, based on how much information about the structure of the protein of interest is available, from known coordinates of all atoms (SCS1) to only predicted contacts and no coordinate information (SC-S4). SC-S1 has not much practical use, since RSA can be computed directly from th atom coordinates, but it serves for comparison and shows that SphereCon correlates with the true RSA values better than other tools in the field (correlation coefficient 0.945). The balance point (0.15) for the binary classification in SC-S1 is also nearly identical to the threshold (0.16) commonly used to distinguish between surface and buried residues (Rost, 1996). Additionally, SphereCon is much less computationally expensive, since there is no need to run costly procedure of probe rolling over the whole protein surface, and can be recommended when only RSA of one or few residues is of interest. This might not be of importance when a few proteins are analyzed, but may become an issue for large-scale studies. The amount of information available in SC-S2 and SC-S3 is comparable to HSE, and thus potentially they share the use cases in practice with this measure. HSE estimates are mostly used as feature in various predictions methods (Jamroz et al., 2012; Wang et al., 2012; Zheng et al., 2012; Magnan and Baldi, 2014; Liu et al., 2018; Sanchez-Garcia et al., 2019; Sharma et al., 2019). Here, substituting HSE with SphereCon could result in improvemed performance, when SphereCon estimates are closer to the true RSA values. For example, in the 3D structure of the phosphoribosyl-AMP cyclohydrolase (PDB id 1ZPS), Gly105 is completely buried (RSA = 0), and still HSE is equal 5 (Figure 4). On the other hand, the SphereCon estimate for it is below 0. In this case, HSE might have got disoriented by the position of the amino acid in a bulge on the protein surface, close to it, but not exactly exposed to the solvent. Generally, SphereCon is likely to better treat the complex case of glycine, which lacks the Cβ residue, since HSE relies on its position for computation. SphereCon Figure 4: Glycine 105 (magenta) of Chain B (green) in the structure with the PDB-Id 1ZPS; the surface accessible area in transparent grey. Using an approximate measure can be a better choice than direct computation of RSA also on the case when the coordinates of side chain atoms are poorly resolved or modeled with a risk of introducing errors. In SC-S3, no information on the type of amino acid at each position is assumed. This can be useful if experimentally available structures have very poor resolution, or when the structure was modeled using templates with low sequence identity or de novo. HSE as well offers a possibility to compute the Cα-Cβ vector in a residue-oblivious manner, but the reported correlation for it is lower than for the implementation that is aware of amino acid types (Hamelryck, 2005). SphereCon in SC-S3, on the other hand, performs better than amino acid type-aware HSE implementation. A novel feature of SphereCon is the ability to predict RSA from residue distance or contact maps, that is, without any coordinate information at all. Such maps are routinely generated these days in the pipelines that attempt to predict protein 3D structure de novo using data on evolutionary couplings (Wang et al., 2017; Ovchinnikov et al., 2015; Marks et al., 2011). Another ingredient of these pipelines is prediction of RSA, often using deep or shallow neural networks (Magnan and Baldi, 2014; Faraggi et al., 2012; Rost, 1996; Wang et al., 2016). The accuracy of contact/distance prediction in these approaches is limited (Wang et al., 2016). Using SphereCon allows to reconstruct RSA with high accuracy, comparable to those of structure-based tools, even for noisy data where up to half of true contacts are missing or up to third of predicted contacts are spurious. Thus SphereCon can naturally fit in the pipelines predicting three-dimensional structure from sequence and potentially provide yet another bit of performance improvement for them. Conflict of Interest: none declared. Acknowledgments We want to offer our thanks for fruitful discussions and critical reading of the manuscript to Sebastian Keller, Sanjay kumar Srikakulam and Fawaz Dabbaghie. References Adhikari,B. et al. (2018) DNCON2: improved protein contact prediction using twolevel deep convolutional neural networks. Bioinformatics, 34, 1466–1472. Aloy,P. et al. 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