native like structures with a physico-chemical metric (pcSM) in protein folding

Biochimica et Biophysica Acta 1834 (2013) 1520–1531

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Biochimica et Biophysica Acta journal homepage: www.elsevier.com/locate/bbapap

Capturing native/native like structures with a physico-chemical metric (pcSM) in protein folding Avinash Mishra a, Satyanarayan Rao b, Aditya Mittal a, B. Jayaram a, b, c,⁎ a b c

Kusuma School of Biological Sciences, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Supercomputing Facility for Bioinformatics & Computational Biology, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India Department of Chemistry, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

a r t i c l e

i n f o

Article history: Received 15 February 2013 Received in revised form 12 April 2013 Accepted 15 April 2013 Available online 7 May 2013 Keywords: Protein folding Protein structure prediction Decoy Scoring function Native structure

a b s t r a c t Specification of the three dimensional structure of a protein from its amino acid sequence, also called a “Grand Challenge” problem, has eluded a solution for over six decades. A modestly successful strategy has evolved over the last couple of decades based on development of scoring functions (e.g. mimicking free energy) that can capture native or native-like structures from an ensemble of decoys generated as plausible candidates for the native structure. A scoring function must be fast enough in discriminating the native from unfolded/misfolded structures, and requires validation on a large data set(s) to generate sufficient confidence in the score. Here we develop a scoring function called pcSM that detects true native structure in the top 5 with 93% accuracy from an ensemble of candidate structures. If we eliminate the native from ensemble of decoys then pcSM is able to capture near native structure (RMSD b =5 Ǻ) in top 10 with 86% accuracy. The parameters considered in pcSM are a C-alpha Euclidean metric, secondary structural propensity, surface areas and an intramolecular energy function. pcSM has been tested on 415 systems consisting 142,698 decoys (public and CASP—largest reported hitherto in literature). The average rank for the native is 2.38, a significant improvement over that existing in literature. In-silico protein structure prediction requires robust scoring technique(s). Therefore, pcSM is easily amenable to integration into a successful protein structure prediction strategy. The tool is freely available at http://www.scfbio-iitd.res.in/software/pcsm.jsp. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Prediction of the tertiary structure of a protein from its amino acid sequence continues to be a grand challenge in biology [1–3]. Modern textbook knowledge on understanding protein structures is essentially reflective of a body of literature having well defined secondary structures [4–6] that can be formed by a continuous series of amino acids in a primary sequence (a.k.a. window size), with each amino acid having a defined ‘propensity’ to be a part of a particular secondary structure. Prediction of secondary structure component of protein can be classified into various phases based on the accuracy of an algorithm. Most of these algorithms employ machine learning approaches for prediction. Initial methods were based on physico-chemical properties [7–9] where the accuracy was reported as 56–60% [10,11]. As the data availability increased with time, accuracy of the machine learning approaches improved and went up to 70% [12–16]. Subsequently,

⁎ Corresponding author at: Department of Chemistry, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India. Tel.: +91 11 2659 1505, +91 11 2659 6786; fax: +91 11 2658 2037, +91 11 2659 7530. E-mail address: [email protected] (B. Jayaram). URL: http://www.scfbio-iitd.res.in (B. Jayaram). 1570-9639/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.bbapap.2013.04.023

due to improvements in sequence alignment, secondary structure prediction also advanced to 80% accuracy [17,18]. Modern protein tertiary structure prediction algorithms rely either on the concept of Anfinsen-inspired energy landscapes with native structures having the lowest free energies [19–33] or on the utilization of homology/template based models scored via statistical potentials [34–41] (for individual amino acids and occurrence of a variable series of peptide-bonded amino acids in primary sequences) developed from experimentally determined structures [42]. A thorough inspection of the literature on protein folding reveals the following broad classification of the algorithms developed for structure prediction—(a) homology/ template based [43–49], (b) fold recognition [50–56], (c) ab initio [57–61] and (d) hybrid methods [62] to compensate for and minimize the limitations of either of the methods. With a remarkable increase in the availability of computational resources in the last few years [63–80], coupled with an accessibility of growing high resolution crystal structure data through the Protein Data Bank, substantial progress has been made towards developing algorithms for predicting protein structures from primary sequences [81,82]. However, limitations of the existing algorithms are well appreciated, evidence for which is in the continued efforts to develop better algorithms [83]; number of CASP (Critical Assessment of protein Structure Prediction) participants since the first one as a function of the CASP iteration is shown

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in Supplementary Table S1. Regardless of the variety of algorithms, over the years, some computational filters have emerged to create and/or screen ensembles of 3D structures, from primary sequences, towards obtaining/identifying native structures. These include degree of compactness [84,85] and constraints on variations of loops connecting different secondary structures [86–88] etc. However, structural variations within different native structures lead to (sometimes severe) limitations of these computational filters. In this work, in an attempt to overcome the limitations of existing algorithms in capturing the native-like conformation out of an ensemble of protein structures, we develop a robust metric that effectively combines the chemical, physical, geometrical and energetic constraints known to be important in protein folding. While none of the constraints is sufficient to capture the native individually all the time in its fold diversity, we design a combination metric that captures the native/native-like structure out of an ensemble of structures with 95% success. We test the metric for its ability to capture the native structure from the well established ensembles of protein structures in the literature. Further, we also mimic the real scenario of protein structure prediction where native is not present in ensemble and test the ability of pcSM to capture the under 5 Ǻ structure if there are any. We report that our algorithm performs better than any known existing algorithm for capturing native/native-like structures out of an ensemble of structures. Our results strongly highlight the need to combine chemical, physical, structural and energetic constraints in attempts to predict native structures. 2. Methods 2.1. Metric components Following are the parameters we have chosen for designing our scoring function: (a) Secondary Structure Penalty (P) = PH + PS Secondary structure of a sequence is predicted and the value of Xi (either 0 or 1) is assigned for each position and termed as reference array. Secondary structure of the Decoy is evaluated for a given decoy structure and value of Xi is assigned for decoy now XOR operator is applied on both these arrays (reference and decoy). We do this separately for helix and sheet, formula for helix case is given below. Similarly we do this for sheet and add PH and PS. i¼n n o X PH ¼ ½X1 ; X2 ; X3 …Xn Reference ⊕½X1 ; X2 ; X3 …Xn Decoy i¼1

Xi = 1 =0 ‘n’

Given a sequence of amino acids, the predicted secondary structure is treated as the reference. Mismatches between the secondary structural patterns of the decoy and the reference are treated as penalty 1 whereas matches are given a score of 0. Secondary structural elements can guide us in capturing the native from a pool of decoys. This parameter is quite efficient in filtering those conformations whose secondary structures are not properly formed in the complete tertiary form. The implementation is illustrated in Supplementary Text S1. This filter however, is limited by the accuracies of the secondary structure prediction which is currently placed at ~80%. (b) Euclidean distance (M)

M¼

n −1 X

n X

ð1Þ

CAij

i¼1 j¼iþ1

CA ‘n’

Euclidean distance between the Cα atoms of the ith and jth residues number of amino acids.

This parameter covers the globular compactness of the structures. There can be a total of 210 unique residue pairs with 20 amino acids. We calculate the mean of Euclidean distances of Cα atoms of all possible unique pairs [89–91]. All of them are then summed (Eq. (1)) to give a distance measure which we denote as M. A sample calculation on a peptide with six amino acids in two conformations is illustrated in Fig. 1. In this example, the extended structure (B), which is likely to be thermodynamically less stable, shows a higher value for M while a compact and folded structure (A) shows a smaller value. To illustrate the efficiency of this metric, we show its value for three decoys (D1, D2 and D3) with different conformations taken from the in-house decoy set for a protein with PDB ID: 1AT0 in Fig. 2, M value is calculated using Eq. (1) where D2 shows the least value which makes it a better decoy. (c) Surface areas (i) Fractional area of exposed nonpolar residues (A1) t X

A1 ¼

exAnp

i n X

HELIX

(presence of helix) (absence of helix) Number of amino acids. Here, ‘⊕’ refers to XOR operator, a logical binary operator which is TRUE if only one of the operands is TRUE.

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ð2Þ exAT

i

exAnp exAT t n

exposed area of nonpolar residue exposed area of a residue total number of nonpolar residues total number of residues.

Fig. 1. Illustration of Euclidean distance. MA represents a folded structure on a rectangle made of unit squares and MB represents an extended form.

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(ii) Fractional area of exposed nonpolar part of residues (A2)

A2 ¼

n X npA

i

totAi

i

npAi totAi n

ð3Þ

exposed area of nonpolar part of residue ‘i’ exposed area of a residue ‘i’ total number of residues.

n X

miAi

332  qi  qj D  rij

ij

ð4Þ

cij12 r12 ij

−

ij

rij = distance between pair of atoms i and j. 12

6

12

ij

6

M12 ¼ ε  R ; M6 ¼ 2  ε  R : Ai

ð5Þ

i

Ai n

ij

Here σ and ε are the sum of van der Waals radii and well depth respectively of the interacting pair of atoms i and j ij

A4 ¼

ð8Þ

C12 ¼ ε  σ ; C6 ¼ 2  ε  σ :

(iv) Total surface area (A4) n X

ð7Þ

r6ij

M12 M6 − 6 r12 rij ij

ij

molecular mass of residue ‘i’ exposed area of residue ‘i’ total number of residues.

ð6Þ

cij6

ij

ij

Ehyd ¼

1

mi Ai n

ij

Eelec ¼

EVdW ¼

(iii) Weighted exposed area (A3)

A3 ¼

(d) Empirical potential energy function (E)

Here, R is a distance variable and ε is set to 1.

exposed area of residue ‘i’ total number of residues.

Minimum accessible surface area of nonpolar residues is a widely recognized facet of native conformations. Varieties of hydrophobic scales were established [92,93] and so also procedures for calculating surface area-related parameters [94]. Hydrophobic collapse is better represented by a loss of SASA because of the observed strong correlation between atomic surface area and solvation energy [95]. Propensity of any amino acid to be found on the surface or in the core is dependent on the side chain of that particular residue [96–98]. This rule works fine in most cases except where mis-aggregated structures are present in the decoy set. For examining the strength and limitation of this metric, accessible surface area (ASA) [99] is calculated first for a given structure. This metric calculates the exposed area of each residue of protein and computes total exposed area by adding all the atomic values and this is termed as exAT. Nonpolar residues are then selected from the protein and total exposed area is calculated for them and this is termed as exAnp. A1, A2, A3 and A4 are calculated by using formulas given in Eqs. (2), (3), (4) and (5) respectively. Fig. 3 describes how the exposed surface area varies between two different conformations of a protein. Here the second conformation is characterized by lower values of A1, A2 and A3 parameters. Second conformation is indeed the native.

E¼

n−1 X

n X

i

j¼iþ1

ij

ij

ij

Eelec þ EVdW þ Ehyd n

ð9Þ

n above is the number of atoms in the system and summation is over all unique pairs of atoms. An empirical intramolecular interaction energy based scoring function was used to discriminate the native earlier by Narang et al. [100–103], where the native conformation was at first rank energywise with respect to the decoys in 67 out of 69 systems. The energy function used contained contributions from electrostatics, van der Waals and a desolvation term captured by a Gurney function. In this study, we have mapped the Gurney description of desolvation on to a continuous potential [20] viz. a “hydrophobic interaction potential” as shown in Eq. (8). Eq. (9) gives the total non-bonded energy per atom of the protein. Energy based scoring has been used in several studies to detect the native but unfortunately energy value is only meaningful when the given structure is energetically minimized. This minimization of energy is one of the compute intensive steps. Other limitation particularly with a large set of decoys is the degeneracy, i.e. structures with different RMSDs from the native having similar values for energy. Due to this

Fig. 2. Variation of Cα distances among 3 different decoys. Sum of pair wise Cα distances of three different decoys, illustrating the fact that compactness of structure leads to lower values of M (PDB ID: 1AT0).

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Fig. 3. Values of all area metric for 2 different decoys. A1, A2, A3 and A4 are different numerical representations of exposed area components of a protein (PDB ID: 1A6Q). The values of these parameters are expected to be at a minimum for native conformation.

degeneracy, multiple structures can possess same energy value. Therefore on the basis of energy alone, it would be difficult to pick the native or native-like structures. We remove primary atomic clashes by running short steepest descent (SD) and conjugate gradient (CG) energy minimizations. After calculating the all atom energy of the energy minimized molecule, we divide it with the number of atoms to obtain energy (in kcal) per atom to arrive at an energy-based parameter that is protein size independent (Eq. (9)). For further illustration of energy score, we show two decoys (D1and D2) for the same amino acid sequence (T0283 system of CASP7) and their corresponding energies per atom in Fig. 4. It may be noted that for this system, the minimum energy structure (D2) corresponds to the native.

2.2. Cumulative parameter score (CS) Cumulative score (CS) is comprised of seven different parameters with each having its own individual native discriminating potential. To avoid sophisticated empirical formalisms, CS is designed as a linear combination of these seven parameters in such a way that native/ native like structures show minimum values and thus can be captured in top 10. Range of numerical values of these parameters differs significantly since each of the parameters has a different “arbitrary unit”. Thus a simple linear combination without any coefficient could result in a biased CS towards parameters with higher magnitudes. Therefore we decided to assign coefficients to each parameter

to bring contributions of each of the parameters on a comparable/ similar scale. As a result the linear summation of the product of individual coefficients with the respective parameters allowed similar weightage to each parameter in CS as shown in Eq. (10) below: CS ¼ cA1 A1 þ cA2 A2 þ cA3 A3 þ cA4 A4 þ cP max ðPH ; PS Þ þ cM1 M1

ð10Þ

where, A1, A2, A3, A4, M1, PH and PS are the parameters and “c” followed by parameter names are respective coefficients. The following steps were taken to optimize and fix the values of coefficients in this work: 1. Four different systems from public and CASP decoys were randomly selected as test set—these were 1ctf, 4rxn, 4pti and CASP9_T0546. 2. All these four systems gave rise to 2199 decoys, including 4 distinct natives. 3. A1, A2, A3, A4, M1, PH and PS were calculated for these 2199 decoys. 4. Average values of each of the parameters calculated for the 2199 decoys were found to be A1 = 0.332, A2 = 51.89, A3 = 721,364.25, A4 = 5383.75, M1 = 4089.65, PH = 27.88, and, PS = 13.32. 5. For simplicity, and inspired by first principles of linear programming, we multiplied the above average values with coefficients such that the resulting product would fall in a numerical range of 1 to 10. Thus A1 was multiplied with 10 resulting in 3.32 as the

Fig. 4. Energy value for 2 different conformations of same protein. Energy (in kcal) per atom for two different decoys taken from CASP7 (T0283) data set is calculated where structure with minimum energy corresponds to the native.

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contribution of A1 in CS. Similarly, A2, A3, A4 and M1 were multiplied with 0.1, 0.00001, 0.001 and .001 respectively resulting in 5.18, 7.21, 5.38 and 4.089 as their respective contributions in CS. This approach, while arbitrary, is straightforward and adequately addresses the possibility of any bias that may arise due to individual parameters in CS. 6. Since the secondary structure penalty parameters, PH and PS are statistical in nature compared to the purely physico-chemical nature of A1, A2, A3, A4 and M1, coefficients for these two parameters were fixed using an iterative strategy. First, values of PH and PS were multiplied with random coefficient values between 0 and 0.3 so that the resulting contributions of these parameters to CS were between 1 and 10. Then 10 random generation cycles each for PH and PS, i.e. total 100 cycles, were performed to calculate CS while keeping the other parameters fixed. It was found that a coefficient of 0.15 for PH and a coefficient of 0.21 for PS provided the best discriminating potential for the native in CS. Therefore, the final values adopted for the coefficients were fixed as: cA1 = 10; cA2 = 0.1; cA3 = 0.00001; cA4 = 0.001; cM1 = .001; Cp = 0.15(PH) and 0.21(PS). The implementation of pcSM is shown in Fig. 5 in the form of a flow chart. For any given decoy set, pcSM needs predicted secondary structure of the amino acid sequence in order to evaluate parameter P. Other parameters such as A1, A2, A3, A4, M and E are calculated from the tertiary structure simultaneously. Short energy minimization is performed to remove atomic clashes. Afterwards, five structures from each, P and A4 are chosen based on minimum scores and kept in the bin FINAL-RUN which contains structures on which the complete energy minimization (the last step of pcSM) has to be run.

After removal of atomic clashes, top 50 structures are chosen for the next step. Best five structures from each E, P, A1 and A2 from the above 50 structures are chosen based on their minimum scores and added to FINAL-RUN bin. Cumulative score (CS) is calculated for all 50 structures and their respective energies (E) are also added and termed as ‘S’, thereafter based on minimum S score top 10 structures are selected and added to FINAL-RUN bin. The redundancy in FINAL-RUN bin is removed to get unique structures for complete energy minimization. After the complete energy minimization, top 10 as well as top 5 structures are selected based on minimum energy score (E) which is expected to capture the native or native-like structures. 2.3. Case study Fig. 6 further illustrates the working of the combination metric pcSM on a sample case (PDB ID: 1EH2) belonging to public decoys Semfold. As to how the screening is done at different levels of the protocol based on various metrics is depicted here. Also please see the flow chart in Fig. 5. The total number of decoys in the data set is 11,441. Rank of the native is given on individual metrics at each level in parenthesis. ‘A1’ performs best while ‘P’ does not do well at the initial level. The individual rankings at initial level and at different subsequent stages can differ in other cases. At next level, top 50 decoys are selected on energy basis after short minimization. Here rank of the native on individual metrics has improved due to a reduction in the number of decoys. In cumulative score (CS) rank of the native is 1 on top 50 decoys which indicates the dominance of ‘P’ and ‘A1’ scores in the value of CS. Native remains at top after adding energy, as energy also picks the native at first position in the top 50 decoys. In the final stage, native is captured at rank 1.

Fig. 5. Flow chart for pcSM.

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Fig. 6. A case study of decoy set. A Semfold public decoy was considered with PBD ID: 1EH2, containing 11,441 decoys. Number in parenthesis refers to rank of native on given parameter. Short minimization: SD(35) CG(15), complete minimization: SD(75) CG(125).

3. Data selection Primarily, two types of data set are chosen: (i) Public decoys from Decoys ‘R’ Us (http://dd.compbio.washington.edu/) and, (ii) Server predictions of CASP experiments CASP5 to CASP9 (http://predictioncenter. org/download_area/). Table 1 describes the data sets and the number of systems therein. Overall, we have considered 415 systems comprising 142,698 decoys. Decoy generation methods discussed below have been taken from documentation of the corresponding decoy set. (i) Public decoys (a) 4state_reduced (b) Fisa (c) Fisa_casp3 (c) Lattice_ssfit (c) Lmds (d) ROSETTA (e) rosetta_decoys_62 (f) CASP5. The public decoys considered in this study (http://www.scfbio-iitd. res.in/software/pcsm/dataset/public-decoys) comprise 137 systems and contain 92,329 decoys (Supplementary Table S3). (ii) CASP decoys (a) CASP5 (b) CASP6 (c) CASP7 (d) CASP8 (e) CASP8.

Table 1 Description of data set taken to evaluate the robustness of the scoring function (pcSM). Decoy set CASP

Public decoys

Total

Number of decoys 92,329

50,369

142,698

Decoys

Systems

CASP5 CASP6 CASP7 CASP8 CASP9 4state_reduced casp5 (public decoys) Fisa fisa_casp3 John-2002 Lattice_ssfit Lmds Rosetta Rosetta 62 Semfold

37 37 51 75 78 7 3 4 5 20 8 10 21 57 2 415

In all, the CASP decoy set considered in this study (http://www. scfbio-iitd.res.in/software/pcsm/dataset/CASP-decoys) comprises 278 systems and contains 50,369 decoys/modeled structures generated by different servers (Supplementary Table S4). 4. Results Table 2 shows the performance of the scoring function on the complete data set obtained from public and CASP decoys. Here the last column shows the performance of the pcSM in capturing the native. Out of the 137 public decoy sets, pcSM is able to capture the native in top 5 in 126 cases. In 5 systems, Ranknative lies between 6 and 10 and in 3 systems natives are above rank 10. There are 3 more systems where native is not ranked by pcSM as it has not passed through the initial filters namely 2(a), 2(b) and 3(a) steps in the flow chart of pcSM (Fig. 5). Out of the 278 CASP decoy sets, pcSM is able to capture the native in top 5 in 223 cases. In 27 systems Ranknative lies between 6 and 10 and in 17 systems above rank 10. There are 11 more systems in which native is not ranked by pcSM as it has not passed through the initial filters namely 2(a), 2(b) and 3(a) steps in the flow chart of pcSM (Fig. 5). 4.1. A comparative analysis of pcSM A few comparative studies of various scoring functions have been reported previously. One such study by Fiser's Group shows the average rank of native on CASP5 to CASP8 decoys with top 20 scoring

Table 2 Native capturing efficiency of pcSM on all the systems taken from public and CASP decoys. Decoy set

Number of systems

Number of decoys

Average RankNative

Public decoys CASP decoys Total

137 278 415

92,329 50,369 142,698

1.85 (3 NFa) 2.91 (11 NFa) 2.38

a

NF: Native not crossed the first filter so there is no ranking of native.

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Table 3 Comparison of top 20 scoring functions considered by Fiser et al. with pcSM in CASP5– 8 decoys set in the presence of native. Scoring function

Avg. Ranknative

pcSM RF_HA_SRS Shortle2006 VSCORE-pair QMEANall_atom QMEAN6 RF_CB_SRS RF_CB_SRS_OD RF_CB_OD VSCORE combined Liang_geometric OPUS_PSP RF_CB RF_HA QMEAN-torsion NAMD Shortle2005 QMEAN-pairwise DOPE PROSA-pair

1.30 1.66 2.54 2.81 2.9 3.26 3.46 3.6 3.65 3.79 3.94 4.11 4.31 4.37 4.66 4.96 5.19 5.86 5.97 6.02

To gauze the relative performance of pcSM on public decoys, we have adapted the comparison format of Tian et al. [117] in which 7 different scoring functions [118–122] were considered. This data set includes 32 different proteins from public decoys containing all the decoys of corresponding systems. Results are shown in Table 4. Rank of the native is given under the name of each scoring function. Average rank of the native calculated by pcSM is 3.3 which asserts its better performance over other scoring functions given in Table 4. Samudrala and coworkers while introducing LoCo recently compared 30 scoring functions [123–140]. Table 5 shows a comparison of pcSM with respect to 77 public decoy sets. Details of the decoy sets in this study are provided in Supplementary Table S5. pcSM gives an average rank of 4.04 for the native which is better than the rank obtained by all other scoring functions mentioned. Over all, results in Tables 2 to 5 indicate that the pcSM scoring function shows a very high efficiency in bracketing the native. 4.2. Detection of near native structure

functions as shown in Table 3. Varieties of scoring functions [104–116] are considered in this comparative study. The performance evaluation of pcSM has been done on the same data set consisting of 143 systems having 2628 decoys. The best average rank of the native reported earlier was 1.66 by RF_HA_SRS. pcSM showed a better performance compared to all other scoring functions with average rank of the native at 1.30 as shown in the second column of Table 3.

We also evaluated the potential of pcSM on capturing near native structures from the ensemble, here we eliminate true native from the pool of decoys and mimic the real scenario of protein structure prediction. We consider a structure of RMSD less than 5 Ǻ as near native. After eliminating native we tested that whether pcSM is able to pick any near native structure in top 5 or not. In this case we considered only those decoy set where there is at least one structure which is falling in near native criteria (b=5 Ǻ RMSD), thus we have 100 such decoy set in CASP whereas 106 in public decoy set. Out of these 206 systems we are able to pick near native structure in 177 systems with 86% of accuracy in top 10.

Table 4 Comparison of pcSM with other scoring functions on data from Decoys ‘R’ Us. Decoy set

4state_reduced

Fisa

fisa_casp3

Lmds

lattice_ssffit

Total Average of Native

System name

1ctf 1r69 1sn3 2cro 3icb 4pti 4rxn 1fc2 1hdd-C 2cro 4icb 1bg8-A 1bl0 1jwe 1b0n-B 1bba 1ctf 1dtk 1fc2 1igd 1shf-A 2cro 2ovo 4pti 1beo 1ctf 1dkt-A 1fca 1nkl 1pgb 1trl-A 4icb

Avg. Ranknative Sequence length

RAPDF

Atomic KBP

DFIRE-A

DFIRE-B

PC2CA

DFMAC

NCACO

pcSM

68 63 65 65 75 58 54 43 57 65 76 76 99 114 31 36 68 57 43 61 59 65 56 58 98 68 72 55 78 56 62 76

1 1 1 1 1 1 1 497 17 14 1 1 1 1 359 501 1 116 501 1 1 416 4 157 1 1 1 1 1 1 1 1 81.37

1 1 1 1 1 1 1 413 25 24 6 2 215 4 74 500 1 31 501 1 2 175 1 13 1 1 1 1 1 1 1 1 62.59

1 1 1 1 4 1 1 254 1 1 1 1 1 1 430 501 1 1 501 1 1 1 1 1 1 1 1 1 1 1 1 1 53.65

1 1 1 2 24 1 19 1 1 1 1 1 3 1 261 501 1 5 441 1 1 1 27 1 1 1 1 1 1 1 1 1 40.8

1 1 1 1 1 1 667 1 1 1 1 1 1 1 1 501 1 2 53 1 1 1 1 1 1 1 1 1 1 1 1 1 39.09

1 1 1 1 1 1 1 399 1 1 1 14 8 1 1 501 1 70 501 1 1 1 1 3 1 1 1 1 1 1 1 1 47.53

1 1 1 1 1 1 1 461 21 3 1 44 3 6 1 497 1 8 113 1 1 1 1 1 1 1 1 1 1 1 1 1 36.8

1 1 1 1 3 1 1 18 1 1 1 1 1 1 5 26 1 1 28 1 1 1 1 1 1 1 1 1 2 1 1 1 3.3

In addition to the data referred to by Fiser's group [100], we also evaluated pcSM on a much larger data set of CASP5 to CASP9 consisting of 278 systems comprising 50,369 decoys (see Table 2).

A. Mishra et al. / Biochimica et Biophysica Acta 1834 (2013) 1520–1531

the chance of missing the native in the final bracket. Although the decoys considered in this study were generated by different protocols, the pcSM showed a good potential to pick the native/native like (93.3% in top 5). Interestingly, the ability of pcSM to discriminate the native structures from the ensembles of structures is independent of the type, number, conformation and size of proteins. Supplementary Table S3 shows the efficiency of pcSM on public decoys. Here 1fc2 and 1bba systems are a couple of exceptions in which rank of the native is above 5. The reason for this is not completely understood. There are 6 cases shown in Table 4 where pcSM failed to capture the native at top most rank. In these cases some other structures got captured in place of native therefore we calculated their RMSD shown in Supplementary Table S6, which essentially conveys that where native is not ranked at first position but a structure within 5 Å RMSD is captured in top 5 by pcSM. pcSM consists of six parameters, all of them are effective when they are implemented synergistically to detect the native. Supplementary Table S7 shows the rank of the native calculated on each parameter individually. It can be seen that all the parameters complement each other in several cases. Behavior of discriminating native from decoys switches from one parameter to another very often. This conveys that each one of them is important for discriminating the native in general. There are some cases when individual performance of each parameter is poor but the cumulative score (CS) is able to pick the native. All the six parameters considered in the cumulative score, result in 21 unique pairs. The pair correlations are shown in Supplementary Table S8. The values of correlation have been categorized into four classes: (1) weak (2) average (3) good and (4) high. It may be seen from the table; most of the pairs (18 out of 21) are weakly correlated indicating very low redundancy in choice of parameters. In three of the 21 pairs viz. A3–A4, A3–M and A4–M, a large number of systems fall in high correlation band which suggest to exclude some of parameter from scoring function because of high correlation. But read together with data in Supplementary Table S7. A3, A4 and M assign different rank to native despite of their high correlation. Therefore high correlation between a pair of parameters does not necessarily imply similar native discrimination capability. So it is better to include all parameters in pcSM. Fig. 5 illustrates that pcSM consists of three pathways to reach to FINAL-RUN and detection of native for a given decoy set requires all the three. These are: path I (1 → 2.a → 3.a), path II (1 → 2.a → 3.b → 4) and path III (1 → 2.b). Each pathway does not necessarily include all parameters. We assess the importance of each parameter by using “leave one out” method where one parameter is excluded from pcSM and rank of the native is calculated for each

Table 5 A comparative analysis of 30 scoring functions on 77 public decoy sets. Public decoys (77 systems) Scoring function

Avg. Ranknative

pcSM DFMAC LoCo RF_CB_SRS_OD GKS Qp SKOb HLPL Qm SKOa SKJG Qa [119] BT TD MJ3 MJ3h MS MSBM TEs BFKV General-four-body MJPL TS VD Tel Four-body Short-range MJ2h MJ1 RO ProSa 2003

4.04 6.7 13.4 19.3 28.5 28.8 30.3 31.4 31.6 33.1 34.1 37.4 45.8 47.7 50.6 52.1 54 54.2 54.2 54.5 56.3 57.8 66.1 73.7 80 81.8 87.5 101.3 124.5 248.3 44

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5. Discussion A variety of scoring functions have been used in the past to detect the native but due to the size and structural diversity of the natives, there is always a probability that some natives slip out of the selection box. In this study, a scoring function (pcSM) based on physicochemical properties has been introduced and its efficiency in capturing the native structure is evaluated in diverse decoy sets comprising 415 different systems with 142,698 decoys and representing a vast sample space of protein conformations. The pcSM has four surface area descriptors along with pair wise Cα distance metric, secondary structure penalty and all atom non-bonded energy. Appropriate combination of all the above properties in the scoring function minimized

Table 6 Importance of parameters in pcSM pathways. a) Path I

Capturing native

Number of systems affected

Excluding ‘E’

Excluding ‘P’

Excluding ‘A1’

excluding ‘A2’

27

21

2

9

b). Path II

Excluding ‘A1’

Excluding ‘A2’

Excluding ‘A3’

Excluding ‘A4’

Excluding ‘M’

Excluding ‘P’

Number of systems affected

18

94

12

16

3

80

c). Path III

Number of systems affected Number of system affected means, system where native is missed out.

Capturing native Excluding ‘A4’

Excluding ‘P’

75

67

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Fig. 7. Overall strength of pcSM. The figure shows the discriminating strength of native or near native structures by pcSM in top 5 (0 Å RMSD structure corresponds to native). X-axis: RMSD (Å), Y-axis: percentage coverage for given RMSD.

of the path in Table 6 summarizing the result. It is seen that exclusion of any parameter diminishes the strength of pcSM. Thus if we exclude any parameter from any path then there is a chance of missing the native in top 10. Descriptors based on accessible surface areas do not fit well for proteins of small sequence length which may assume non-globular conformations. Other filters such as P, M and E are able to capture the native in such cases. Secondary structure filter (P) has a limitation in cases where decoys are generated following secondary structure prediction methods. In this case all decoys exhibit same secondary structure but other filters such as area (A1, A2, A3, A4), Euclidean distance (M) perform well to penalize non-native structures and bracketing the best structure. Energy (E) filter works quite efficiently in those cases where native is not in compact form or the nonpolar residues are not minimally exposed but their arrangements of atoms are energetically favorable. Overall strength of pcSM for 415 systems for capturing the native/ native structures in top 5 is shown in Fig. 7. It is clear that native (0 Å RMSD) is captured in 84.1% of the cases and a structure within 5 Å of RMSD from the native is captured 93.3% of the cases by pcSM. To further analyze the efficacy of pcSM protocol, we have run a one tailed p-value test using Ranknative as sample data set (Fig. 8). Rank of the

native is extracted from Supplementary Tables S3 and S4 and distributed in different bins and plotted against number of systems. Fig. 8 shows that in 304 cases Ranknative is below 1.36, in 45 cases Ranknative lies between 1.36 and 5.0 and in 27 systems Ranknative lies between 5 and 10 while in 25 cases rank of the native is greater than 10. Size of each bin in the distribution is 0.3SD (SD = standard deviation). The test validates pcSM with rank of native below 5 to 99% confidence level. Protein structure prediction demands a robust scoring function to discriminate correctly folded structures from a large pool of decoys. pcSM, developed in this work, is clearly a solid step in this direction. Here, it is important to note that while the current application of pcSM involves linear coefficients in the scoring function, values for which are determined and fixed based on a relatively straightforward linear programming approach, there is scope for even better performance by tuning these coefficients further by developing more advanced approaches. 6. Usage pcSM program is available on http://www.scfbio-iitd.res.in/software/ pcsm.jsp in user friendly form where the user can upload either a single

Fig. 8. Ranknative distribution for 401 systems.

A. Mishra et al. / Biochimica et Biophysica Acta 1834 (2013) 1520–1531

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