teaching and education
Logistic regression models to predict solvent accessible residues using sequence and homologybased qualitative and quantitative descriptors applied to a domaincomplete Xray structure learning set
^{a}Department of Chemistry, San Jose State University, San Jose, CA 951920101, USA, ^{b}Department of Mathematics and Statistics, San Jose State University, San Jose, CA 951920101, USA, ^{c}Department of Biomedical, Chemical and Materials Engineering, San Jose State University, San Jose, CA 951920101, USA, ^{d}Department of General Engineering, San Jose State University, San Jose, CA 951920101, USA, ^{e}Department of Chemistry and Biochemistry, Cal Poly San Luis Obispo, San Luis Obispo, CA 93407, USA, ^{f}Department of Bioengineering, University of California, San Diego, San Diego, CA 920930412, USA, and ^{g}College of Science and Mathematics, California State University San Marcos, San Marcos, CA 920960001, USA
^{*}Correspondence email: brooke.lustig@sjsu.edu
A working example of relative solvent accessibility (RSA) prediction for proteins is presented. Novel logistic regression models with various qualitative descriptors that include amino acid type and quantitative descriptors that include 20 and sixterm sequence
have been built and validated. A domaincomplete learning set of over 1300 proteins is used to fit initial models with various sequence homology descriptors as well as query residue qualitative descriptors. Homology descriptors are derived from BLASTp sequence alignments, whereas the RSA values are determined directly from the The logistic regression models are fitted using dichotomous responses indicating buried or accessible solvent, with binary classifications obtained from the RSA values. The fitted models determine binary predictions of residue solvent accessibility with accuracies comparable to other less computationally intensive methods using the standard RSA threshold criteria 20 and 25% as solvent accessible. When an additional nonhomology descriptor describing Lobanov–Galzitskaya residue disorder propensity is included, incremental improvements in accuracy are achieved with 25% threshold accuracies of 76.12 and 74.79% for the Manesh215 and CASP(8+9) test sets, respectively. Moreover, the described software and the accompanying learning and validation sets allow students and researchers to explore the utility of RSA prediction with simple, physically intuitive models in any number of related applications.1. Introduction
The characterization of solvent accessible surfaces is a key task, the results of which are useful in protein design, structural biology and proteomics, notably identifying certain protein–protein interactions. There has been significant effort in the largescale screening of sequences for characterization of function, including key interactions with ligands and other proteins (Watson et al., 2005; Tuncbag & Gursoy, 2009; Zhang et al., 2013). Possible approaches include the characterization of solvent accessible surfaces directly from sequence information, allowing for the identification of relevant clusters on the surface (Xue et al., 2011; Tygai et al., 2012). Other structural features may prove amenable to prediction from sequence, including specifically the identification of critical core hydrophobic residues (Berezofsky & Trifonov, 2001; Gromiha & Selvaraj, 2004). Such residues can describe important constraints in modeling protein folding and structure and may be useful when designing modifications for proteins.
Methods using protein sequence information, including firstgeneration machine learning approaches such as with neural networks, typically have shown a percent accuracy of the order of 70–75% (Rost & Sander, 1994; Richardson & Barlow, 1999; Ahmad et al., 2003). Subsequent methods including largescale linear regression, support vector regression, support vector machines, knearestneighbor analysis and random forest approaches have reported somewhat better results for certain proteins (Wagner et al., 2005; Wang et al., 2007; Joo et al., 2012; Pugalenthi et al., 2012). The advantage of regressionbased approaches is their relative simplicity in both implementation and interpretation. Most recently, a simple, computationally efficient machine learning approach utilizing a general neural network has also been implemented to determine accessible surface area values (Faraggi et al., 2014).
Linear and generalized linear models can include both quantitative and qualitative predictors, here referred to as `descriptors' (Kutner et al., 2004). Following our previous work (Rose et al., 2011; Nepal, 2013), we include a qualitative descriptor representing query residue type (AA) as well as four homology descriptors: 20term (E20) and sixterm (E6) sequence fraction of aligned residues that are strongly hydrophobic (FSHP), and fraction of small residue glycine or alanine (FSR). The AA descriptor alone has been shown to be a significant predictor (∼70%) of residue solvent accessibility.
Here we implement logistic regression methods to further elucidate the relationship between simple homology and query sequence descriptors with surface accessibility. We consider both estimation and validation tasks, fitting logistic regression models using learning sets and evaluating our fitted models on test data. Logistic models are one method that should be explored in the context of protein topology, easily incorporating the corresponding quantitative and qualitative descriptors. Logistic regression models have proven to be an adaptable choice for binary classification problems in fields such as economics, epidemiology and the social sciences and are now well established. Logistic approaches have the advantage of directly modeling the probability of success, restricting predicted probabilities to [0, 1] and providing for a natural interpretation in terms of the odds of success.
Our goal is to establish the utility of simple logistic models for the longestablished problem of the binary identification of solvent accessible residues. Notably, this is a first step in exploring the functionality of such methods in predicting protein–protein interfaces and interactions from sequence. Such exploration may be accelerated by these methods, given the associated computational complexity.
In addition to providing a working example of such prediction for residue solvent accessibility and applying it to problems associated with protein–protein interaction, we introduce students and researchers in structural biology, biophysical chemistry, bioinformatics and allied fields to an application of logistic regression that includes explicitly both qualitative and quantitative predictors.
Our software (https://www.iucr.org/education/resources ) and the accompanying learning and validation sets allow users to explore the utility of residue solvent accessibility (RSA) prediction with simple, physically intuitive models in any number of related applications. Moreover, the corresponding R and Python code can be implemented or otherwise modified to directly predict certain structural features (e.g. possible protein–protein interfaces), and new test sequences can be explored by simple implementation of NCBI BLASTp (https://blast.ncbi.nlm.nih.gov/Blast.cgi?PAGE=Proteins ) and the Protein Data Bank (https://www.rcsb.org/pdb/home/home.do ).
2. Methods
2.1. Sequence and other homologybased descriptors
As an alternative to the standard 20term (E20) sequence ) we calculated the sixterm (E6) sequence (Mirny & Shakhnovich, 1999). The terms are summed over six classes of amino acids (e.g. polar), where the sequence at the kth residue position is expressed as
(Gerstein & Altman, 1995Here the probability P_{jk} at amino acid sequence position k is derived from the frequency for an amino acid class j at sequence position k for N aligned residues. Including gaps as the 21st element in our original 20term sequence calculations was problematic (Liao et al., 2005). Thus, we treated the remaining sequence homology terms, fraction strongly hydrophobic (FSHP) and small residue (FSR), as just fractions of aligned residues. Note the strongly hydrophobic residues (i.e. V, L, I, F, Y, M, W), and the remaining 13 are the nonstrongly hydrophobic residues.
2.2. Data assembly
Our original learning set of 268 protein chains included query proteins with known threedimensional Xray crystallographic structure and was confirmed to be a diverse, representative set (Mishra, 2010). A more extensive learning set of 1363 protein chains (Nepal, 2013) was similarly selected with a resolution < 2.5 Å and an R value < 0.3 using PISCES (Wang & Dunbrack, 2003) from an exhaustive list involving some 6500 protein domains (Bondugula et al., 2011). Redundant and other problematic sequences were also culled for chains with percent identities greater than 25. To determine our sets of aligned protein sequences and their individual residue elements, we chose a straightforward and nonbiased standard application of BLASTp (Altschul et al., 1997) to a nonredundant database (GenBank; https://www.ncbi.nlm.nih.gov/genbank/ ), with BLOSUM62 (Henikoff & Henikoff, 1992) allowing for bit scores greater than or equal to 40% of the best score (see Fig. 1). Test sets are similarly treated. Corresponding homologybased calculations such as E20 using psiBLAST (Altschul et al., 1997) showed little added value in prediction accuracy. Alternative applications of multiple sequence alignment using MUSCLE (Edgar, 2004) indicated no significant differences in accuracy (E. Chung & B. Lustig, unpublished results).
We continue with simple approaches to parsing homology data, noting that requiring at least ten aligning BLASTp subject sequences given the 40% threshold relative to the highest bit score is a reasonable condition for fully reliable sequence entropies (Liao et al., 2005; Rose et al., 2011). We validate our models using two test sets, where one standard test set, Manesh215 (NaderiManesh et al., 2001), has been thoroughly evaluated with respect to many standard RSA approaches (Nguyen & Rajapske, 2006). Additionally, we evaluated the models on the more recent CASP(8+9), a comparably sized test set evaluated by more current methods (Joo et al., 2012). However, for the Manesh215 and CASP(8+9) test sets we are required to use a nonoptimum homology subset, given that the corresponding sequence and coordination data are listed externally. Fourteen such proteins are noted for the Manesh215 set, six proteins from the set of 102 Xray structures of CASP8 and 12 proteins from the set of 88 Xray structures of CASP9 (see Table 1).

2.3. Nearest neighbors and propensity for disorder
One simple and physically intuitive approach to account for the effects of sequence neighbors is to utilize the Ising approach of Lobanov et al. (2012). Here the propensity for each residue being disordered, the Lobanov–Galzitskaya disorder probability (LGDP), is introduced as an additional quantitative descriptor (IsUnstruct; https://bioinfo.protres.ru/IsUnstruct/ ). Calculations of Lobanov–Galzitskaya propensities include a very limited number (<2%) of FASTA (https://www.ncbi.nlm.nih.gov/BLAST/blastcgihelp.shtml ) neighbors not included in the PDB coordinates. Undefined FASTA residues, typically less than 1% of our sequences, are assumed to be alanine for the purposes of adjacent neighbor analysis only. Also, specifically the two sequence adjacent residues, adjacent query neighbors (AQN), are defined by FASTA and can be treated as qualitative descriptors. All regression documented here is scalable on a single E5410 Intel Xeon 4P Linux box or comparable 64bit laptop. Lobanov–Galzitskaya Isingmodel calculations appear algorithmically straightforward and are not significantly intensive.
2.4. Surface accessibility
One gold standard for validation of solvent accessibility predictions is the RSA values determined from the query Xray structures using NACCESS (Lee & Richards, 1971; Hubbard & Thornton, 1993). Alternative calculations using DSSPbased (Kabsch & Sander, 1983; Ahmad et al., 2004) solvent accessibility data showed no significant differences in prediction accuracy (J. Spencer, B. Lustig & A. Gottlieb, unpublished results). Here we initially treated amino acids with less than 20% relative exposure to solvent (RSA) as buried (Carugo, 2000). An alternative threshold of 25% was subsequently explored. Model accuracies are estimated on the basis of the standard expression of Richardson & Barlow (1999), where the accuracy is
Solvent accessibility for interdomain (interface) regions between chains is directly evaluated from the relevant PDB (RCSB or PISAPDBe) coordinate files via NACCESS, consistent with Bahadur et al. (2004). The 1363protein learning set is considered diverse, robust and exhaustive (Nepal, 2013). Very conservative application of the biological unit as prescribed by PISAPDBe (https://www.ebi.ac.uk/pdbe/pisa/ ) has been implemented in the test sets to optimize the reliability of their evaluation for accuracy. Only unambiguously oligomeric protein structures [88 for Manesh215, 123 out of 200 for CASP(8+9) from PISAPDBe, with a biological unit different from the 66 and 80 for Manesh215 and CASP(8+9), respectively] are noted as such for analysis.
2.5. Logistic regression
Here we directly model the probability of accessibility utilizing the naturally dichotomous outcome variable, accessibility status. This approach avoids the common pitfalls of inappropriately applying multiple regression to percentage data, such as obtaining negative probabilities or probabilities that exceed 1. We assume the independence of all residues, although in reality there is some correlation between neighbors. A logistic regression model using residue solvent accessibility as a dichotomous response with Y = 0 for buried residues and Y = 1 for accessible residues was implemented.
Logistic models are a generalization of multiple linear regression in which a binary dependent variable is described as a function of both quantitative and qualitative variables (Kutner et al., 2004; Hosmer et al., 2013). We utilized four quantitative descriptors and 19 dummy variables corresponding to the descriptor AA, such that linear predictor is of the form
for j = 1,…, 19. Here X_{j} are the indicator variables associated with qualitative descriptor AA. We used treatment coding with Val as the baseline treatment via R 3.1.0, where the X_{j} values are either 0 or 1, with 1 corresponding to the given amino acid type.
Let p denote the probability that a particular residue is accessible and 1 − p the probability of a residue being buried. Under the logistic regression framework, the odds of success, p/(1 − p), are modeled as an exponentiated linear combination of the descriptors:
The probability that a particular residue is accessible can be expressed by rearranging the terms in equation (4), so that
Estimates for the model parameters are obtained using ). The probability distribution function associated with equation (5) is an Sshaped curve and a more realistic representation of probabilities associated with binary outcomes. The corresponding fitted values are probabilities, which then can be converted to classifications of either 1 or 0 using a 0.5 standard threshold. Shown in Fig. 2 are the logistic regression predictions superimposed on the leastsquares regression fit for the 18protein transientbinding set as identified by Pettit et al. (2007).
methods, determining parameters that optimize the likelihood of the observed data (consisting of zeros and ones) being described by the model (Long, 1997The expression in equation (5) is commonly referred to as the odds, where the difference between two log odds can be expressed as
As an example, we assume all other nonE6 terms are held constant such that the ratio of the odds of success corresponding to a increase of 1
so that E6* = E6 + 1, is given byTable 2 reports the results of a logistic regression fit using the 1363based learning set. Included are the parameter estimates, corresponding standard errors, and z and p values based on the Wald test (Ghosh & Sen, 1991). We find that all of the continuous descriptors and nearly all of the dummy variables associated with the categorical descriptor are significant at a 0.05 significance level.

2.6. Learning and test sets
As a first example, included for pedagogical purposes, we fit a logistic model with a qualitative descriptor describing all 20 amino acid types (AA) and a quantitative predictor E6 with the results shown in Fig. 2. The learning set corresponds to all 18 available transientbinding proteins from our original 268 learning set (Mishra, 2010; Rose et al., 2011) and current 1363based learning set. These transientbinding proteins were originally characterized as such by Pettit et al. (2007). Included in this figure is the leastsquares fit with slope of 10.56 for each amino acid type and varying intercepts (Val and Asp samples are shown in Fig. 2). The logistic fit generates probabilities, which allows for binary classification of all residues as buried versus solvent accessible. We then analysed the accuracies for 13 transientbinding proteins similarly identified from the standard Manesh215 test set.
Our next step is to build various models based on the domaincomplete 1363protein learning set and validate them on the complete standard Manesh215 test set and the more recent CASP(8+9). We were initially interested in evaluating our models on relevant subsets of the test sets, in particular, transientbinding proteins. However, defining transientbinding proteins is not currently a consensus exercise (AcunerOzbabacan et al., 2011). Here, we make a more conventional delineation between oligomers and nonoligomers that is effectively universal in its application. A more complete examination of oligomers and the remaining nonoligomers is warranted.
2.7. Specific strategies for optimum homology versus nonoptimum homology proteins
As shown in the flowchart (see Fig. 1) there is a key branch point involving test sets being partitioned into an optimum homology (i.e. ten or more aligned sequences) subset and a remaining nonoptimum homology subset (see Table 1 for complete list). The reason is that homologybased descriptors are not reliable predictors for nonoptimum homology proteins, where we only validate those models with exclusively nonhomology descriptors. The resulting strategy is to use models with exclusively nonhomology descriptors for the nonoptimum proteins. Therefore, we report a weighted average for all proteins based on the accuracies of two components: (1) predictions for optimum homology proteins from models that include both homologybased descriptors (e.g. E6) and nonhomology ones (e.g. LGDP); (2) predictions for nonoptimum homology proteins from models including exclusively nonhomology descriptors.
3. Results and discussion
3.1. General
We have evaluated various models with different subsets of the descriptors. Table 2 reports an initial regression for the saturated E20+E6+FSR+FSHP+AA model (referred to here as the classic model). Note that for this logistic regression E20 and E6 were shown in the corresponding correlation matrix output to be 83% correlated. Models showing at least 70% accuracy indicate comparable standard errors and p values based on the Wald test to the saturated model illustrated in Table 2. However, it is clear that descriptors FSR and FSHP are somewhat unique in their pattern of being primarily 1 or 0 in value (Mishra, 2010). So, most recently Box–Tidwell power transformations were applied to test/optimize loglinearity. The resulting relative order and sign of the β regression coefficients, compared to those originally determined for Table 2, remain unchanged and no significant increases in resulting classification accuracy are indicated.
Table 3 reports the accuracies for a family of models for the optimum homology subsets for the Manesh215 and CASP(8+9) test sets, and Table 4 reports the accuracies of models also evaluated on oligomer and nonoligomer subsets. The classic model of Table 2 remains the best homologybased model in terms of prediction accuracy. However, we note the high correlation (0.83) between E6 and E20, unlike other quantitative predictors. Also, even the simpler E6+AA model performs nearly as well for both the 20% and the alternative 25% RSA threshold. In both the multiple linear regression (Rose et al., 2011; Nepal, 2013) and logistic models, E6 appears to be the more reliable predictor of residue solvent accessibility as opposed to E20 (see Table 3). This is consistent with the notion that E6 is the more sensitive measure of residue packing (Mirny & Shakhnovich, 2001).
‡Optimum homology CASP(8+9) subset (41 967 residues). § Nonoptimum homology Manesh215 subset (3113 residues). ¶ Nonoptimum homology CASP(8+9) subset (2832 residues). ††Note the other two models with AA and a single quantitative descriptor, E20+AA and FSHP+AA, are not reported as they have less predictive accuracy than E6+AA. ‡‡As shown in Table 2, E20+E6+FSR+FSHP+AA saturated model. 
‡Optimum homology CASP(8+9) subset for oligomers (24 176 residues; 18 573 residues noninterfacial) and nonoligomers (17 791 residues). §Nonhomology descriptor model evaluated on nonoptimum homology Manesh215, gives percent accuracies of 73.12 (25% threshold) and 71.49 (20% threshold), for oligomers (919 residues; 787 residues noninterfacial); 70.95 (25% threshold) and 71.75 (20% threshold) for nonoligomers (2194 residues). ¶Nonhomology descriptor model that, when evaluated on nonoptimum homology CASP(8+9), gives percent accuracies of 72.26 (25% threshold) and 71.83 (20% threshold) for oligomers (2080 residues; 1393 residues noninterfacial); 69.55 (25% threshold) and 70.88 (20% threshold) for nonoligomers (752 residues). ††E6+FSR+FSHP+AA+LGDP+AQN model. ‡‡Residue weighted accuracies, comprehensive model for optimum homology proteins and nonhomology descriptors for nonoptimum homology proteins. 
We augmented our set of descriptors with several query sequencebased variables. Inclusion of the LGDP quantitative descriptor and two AQN qualitative descriptors describing the amino acid type for the two sequenceadjacent amino acids generated incremental associated gains in accuracy (Table 4). A comprehensive model consisting of sequence homologybased descriptors (E6, FSR, FSHP) and sequencebased descriptors (AA, LGDP, AQN) was found to produce the highest accuracies for both Manesh215 and CASP(8+9) optimum homology subsets. Note that the total allproteins accuracies are, for the respective 25 and 20% thresholds, 76.11 and 76.00 for Manesh215, and 74.79 and 74.55% for CASP(8+9).
Moreover, nonoligomers are often associated with higher accuracy than the oligomers (see Table 4). This is especially true when looking at models with a significant homologybased descriptor component. More importantly, the removal of likely interfacial residues resulted in slightly better accuracies. Here such a set comprising about onefifth of the total oligomer residues was determined from residues showing measurable increases in singlechain NACCESS values when compared to the corresponding oligomer ones. As a typical example the likely interfacial residues for the allproteins model show a reduced accuracy with a 25% threshold of 71.66 and 70.35 for Manesh215 and CASP(8+9), respectively.
3.2. Implementation of simple logistic models
In this study, the initial focus has been the examination of sequence and homologybased descriptors in logistic regression models for protein residue accessibility. Here, a logistic model including only the E6 descriptor sequence et al., 2003; Read et al., 2011). Though computationally intensive, it is a onetime event and does not interfere with the model simplicity.
for a particular sequence position in conjunction with AA, the amino acid type, offers nearly the same degree of prediction accuracy as the classic model that also includes E20 and the fraction of aligned residues that are strongly hydrophobic (FSHP) as well as being small (FSR). But E6 and E20 are highly correlated, so we preferred the former descriptor because of its generally better prediction capabilities. We have demonstrated that the inclusion of an additional quantitative descriptor, the LGDP, gives associated gains in prediction accuracy of the order of 1%, while the adjacent neighbor descriptors give somewhat less associated gain in prediction accuracy. Certainly, further model building including other simple descriptors is a reasonable next step. One could even consider further of the coordinate data sets themselves based on established structure validation criteria (ReddyEven the most computationally intensive machinelearning methods involving optimal threshold RSA criteria show binary prediction limits at or below 80% in accuracy (Joo et al., 2012). Indeed, our logistic regression models with homologybased and qualitative query sequence descriptors compare favorably with existing singlestage methods and other approaches that preclude an extensive machinelearning task (Gianese et al., 2003). Simple models have great utility, including computational simplicity and efficiency. Prioritization of parsimony in model selection is consistent with the Pareto principle, suggesting that any model for which some 80% of outcomes can be described by 20% of the causes is preferable (Pareto, 1971). This prioritization may be required for the greater challenges associated with very large scale calculations involving the applications of these and related models to exhaustive searches of the proteome, including the search for possible protein–protein interactions.
3.3. Intrinsic limitations and future opportunities
3.3.1. General
There appears to be a fundamental limitation for prediction accuracy for surface accessible residues, which probably involves the coupled nature of surface residue accessibility with interchain interactions. This constraint is similar to the intrinsic limitation of secondary structure prediction (Rost, 2001), which involves the coupling of secondary with (Kihara, 2005). Specifically, chain residue accessibility prediction is complicated by hydrophobic residues being found not only in core positions but also on surfaces involving interactions with other protein chains (Yan et al., 2008). Prediction of solvent accessibility is further obfuscated by the still largely uncharacterized nature of transient and related protein interactions. It is clear, however, that at least for oligomers, when likely interface residues are removed, small but measurable increases in accuracy are indicated. This unique character for such residues is consistent with previously detected residue conservation signals for oligomeric interface regions (Elcock & McCammon, 2001; Valdar & Thornton, 2001; Guharoy & Chakrabarti, 2005). Interestingly, the 1363based learning set partitioned into oligomers and nonoligomers showed significantly less accuracy for their respective application to the oligomers and nonoligomers.
Some 5% of PDB residues are identified as missing and possibly disordered and are a nontrivial component of the actual protein chains (Brandt et al., 2008; Lobanov et al., 2010). These generally correspond to residues not identified in an Xray structure. We note, at least for the aligned portions of FASTA and PDB sequences, a comparable number of such unaccounted residues exist. Of course, no gold standard such as the simple application of NACCESS is available for these types of residues. However, in the future as we continue to build models predicting protein–protein interfaces, the inclusion of such disordered residues is of likely advantage (Mészáros et al., 2009). Our successful incorporation of an intrinsic residue disorder propensity as a descriptor suggests the suitability of this sort of approach in related problems, notably the prediction of protein interfaces with respect to other proteins, and small ligands.
Largescale exploration of sequence space, generated off a set of structural ensembles for threedimensional protein structures, has shown clustering of sequence et al., 2002). In a similar fashion, Shannon entropies for protein sequence have been shown to correlate with configurational entropies calculated from local physical parameters, including backbone geometry (Koehl & Levitt, 2002). Our earlier calculations indicated a correlation between sequence and inverse packing density (a measure of local flexibility) as well as query hydrophobicity (Liao et al., 2005; Mishra, 2010). Here we can reasonably assume that there are a cohort of very buried residues that are both well packed and not likely to have any portion of their surface area accessible to solvent.
values corresponding to a particular fold (Larson3.3.2. Exploring additional features of protein structure in the classroom with logistic regression
For MAML1 and other proteins, the propensity of residue disorder as a possible indicator of local environments was explored as part of a graduate course seed project (Nedunuri, 2013). A broader exploration of proteins involving the 18 learning set and 13 test set transientbinding proteins (noted in Fig. 2) was made in the next such course offering, integrating the related LGDP descriptor into prediction and further classification of solvent accessible residues (Kadiyala, 2015). Logistic regression outputs such as those indicated by Table 2 can be considered tools for exploration. Note, for instance, the very large and negative β regression coefficient of −1.543 for Cys, which is unique among the AA qualitative descriptors. Such a value is consistent with Cys forming a tertiary contact (Dosztányi et al., 1997) and the fact that residues most likely to form tertiary contacts are significantly less likely to have side chains accessible to solvent (Kim & Park, 2004).
4. Conclusion
Homology and sequencebased descriptors can be used to build classifiers of residue accessibility. We establish their utility as both quantitative and qualitative descriptors in logistic regression models, demonstrating competitive accuracy using as few as two descriptors. Removal of likely oligomeric interfacial residues typically increases prediction accuracies, suggesting specific homologybased and other signals for such interfaces. In predicting solvent accessible residues, E6 sequence
is a very useful descriptor, consistent with the notion that to a first approximation highly conserved residues are typically found in the interior of the protein. Moreover, such conserved residues probably involve hydrophobic residues given their tendency to be buried. But also some conserved residues can be partitioned on the surface, accessible to solvent, and this includes some that are hydrophobic. Our methods are well suited for simple integration of homology variables with a variety of potential sequence and other sequence neighbor descriptors, allowing for application of a variety of models, including new ones, to even more challenging computational problems involving the characterization of protein interfaces and protein–protein interactions.Acknowledgements
This work was supported in part by a CSU California State University General Research Grant. The authors would like to thank Dr Shannon Bros and Megha Chandrashekhar and Anneli Hardy for their respective work in statistical analysis and database assembly and preliminary modeling. Thanks also to Saira Montermoso, Gerald Omictin and Jonathan Oribello for additional calculations, documentation and graphics.
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