ALL Metrics
-
Views
-
Downloads
Get PDF
Get XML
Cite
Export
Track
Research Article
Revised

The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment

[version 3; peer review: 2 approved]
PUBLISHED 16 Sep 2014
Author details Author details
OPEN PEER REVIEW
REVIEWER STATUS

Abstract

The structure of a protein provides insight into its physiological interactions with other components of the cellular soup. Methods that predict putative structures from sequences typically yield multiple, closely-ranked possibilities. A critical component in the process is the model quality assessing program (MQAP), which selects the best candidate from this pool of structures. Here, we present a novel MQAP based on the physical properties of sidechain atoms. We propose a method for assessing the quality of protein structures based on the electrostatic potential difference (EPD) of Cβ atoms in consecutive residues. We demonstrate that the EPDs of Cβ atoms on consecutive residues provide unique signatures of the amino acid types. The EPD of Cβ atoms are learnt from a set of 1000 non-homologous protein structures with a resolution cuto of 1.6 Å obtained from the PISCES database. Based on the Boltzmann hypothesis that lower energy conformations are proportionately sampled more, and on Annsen's thermodynamic hypothesis that the native structure of a protein is the minimum free energy state, we hypothesize that the deviation of observed EPD values from the mean values obtained in the learning phase is minimized in the native structure. We achieved an average specificity of 0.91, 0.94 and 0.93 on hg_structal, 4state_reduced and ig_structal decoy sets, respectively, taken from the Decoys `R' Us database. The source code and manual is made available at https://github.com/sanchak/mqap and permanently available on 10.5281/zenodo.7134.

Keywords

Computational biology ; protein structure prediction ; Model quality assessment programs ; Boltzmann distribution ; Decoys `R' Us ; Annsen's thermodynamic hypothesis ; Finite difference PoissonBoltzmann (FDPB) ; APBS ; statistical potentials ; protein sidechain ; decoy sets ; template based modeling ; ab initio protein structure prediction ;

Revised Amendments from Version 2

We have modified our discussion to reflect the point we had missed previously regarding the pKa values in accordance with Dr Kammerlin's suggestion.

See the authors' detailed response to the review by Patricia C Weber

Introduction

The challenge of deriving the native structure of a protein from its sequence has intrigued researchers for decades1. Methods that predict putative structures from sequences are based either on features from databases of known structures (template-based methods)24 or use first principles of atomic interactions (ab initio or de novo methods)57. Typically, these methods yield multiple, closely-ranked possibilities. Model quality assessment programs (MQAP) that validate accuracy of these predicted structures are used to select the best candidate from the set of predicted structures.

MQAPs can be classified as energy, consensus or knowledge based. Two major sources of errors in energy based methods used for refining or discriminating protein structures are inaccuracies in the force field due to the inherent approximations in equations that model multi-atomic configurations, and inadequate sampling of the conformational space812. Consensus based methods are based on the principle that structural features that are frequently observed in a population of structures are more likely to be present in the native structure1316. These clustering methods outperform other MQAP methods14 and are “very useful for structural meta-predictors17”. However, they are prone to be computationally intensive due structure-to-structure comparison of all models16, and are of limited use when the number of possible structures is small18. Knowledge based methods proceed by deriving an empirical potential (also known as statistical potential) from the frequency of residue contacts in the known structures of native proteins19,20. For a system in thermodynamic equilibrium, statistical physics hypothesizes that the accessible states are populated with a frequency which depends on the free energy of the state and is given by the Boltzmann distribution. The Boltzmann hypothesis states that if the database of known native protein structures is assumed to be a statistical system in thermodynamic equilibrium, specific structural features would be populated based on the free energy of the protein conformational state. Applying a converse logic, Sippl reasoned that the frequencies of occurrence of structural features such as interatomic distances in the database of known protein structures could be used to assign a free energy (potential of mean force) for a given protein conformation21,22. Furthermore, this statistical potential can be used to discriminate the native structure2327. The proper characterization of the reference state is a critical aspect in applying statistical potentials23. In spite of their popularity, the application of such empirical energy functions to predict and assess protein structures are vigorously debated28,29. Many MQAP programs perform better when multiple statistical metrics are combined3033. The paramount importance of obtaining high quality protein structures from sequences using in silico methods can be estimated by the effort invested by researchers every two years34 to evaluate both structure prediction tools35 and MQAPs17,34,36.

Here, we propose a novel statistical potential to assess the quality of protein structures based on the electrostatic potential difference (EPD) of Cβ atoms in consecutive residues - EPD profile of sidechain atoms used in assessment of protein structures (ESCAPIST). Previously, we have established that the EPD is conserved in cognate pairs of active site residues in proteins with the same function3740. The ability of finite difference methods to quickly obtain consistent electrostatic properties from peptide structures provides an invaluable tool for investigating other innate properties of protein structures41. We plot the EPD profiles for different atom types (Cα atoms, Cβ atoms and the C-N bond) in consecutive residues from a set of non-homologous protein structures obtained from the PISCES database (http://dunbrack.fccc.edu/PISCES.php)42. We proceed to show that the EPD between Cβ atoms in consecutive residues can be used to generate a scoring function that assesses the quality of protein structures. This EPD scoring function is then applied to standard decoy sets from the Decoys ‘R’ Us database (http://dd.compbio.washington.edu) to establish the validity of our method43.

Results

Electrostatic potential difference (EPD) based discrimination

To extract feature values we chose a set of 1000 proteins from the PISCES database with percentage identity cutoff of 20%, resolution cutoff of 1.6 Å and a R-factor cutoff of 0.25 (SI Table 1).

Table 1. Electrostatic potential differences (EPD) for consecutive residue pairs for Cα atoms for residue pairs that include proline.

While these pairs have for a low standard deviation (SD) like all other pairs, the absolute value of their mean is different (higher) than any pair that does not include a proline. This also highlights the unique nature of proline in protein structures.

PairMean EPDSDNumber of
samples
AP-167.328.6328
CP-15330.345
DP-184.529.5290
EP-176.627.3346
FP-160.425.3173
GP-165.329.2339
HP-162.734.692
IP-161.927.2175
KP-156.629.6203
LP-165.228.3323
MP-161.329.570
NP-159.627.6168
PQ168.526.1131
PR156.231.5184
PS172.325.9269
PT170.827.6218
PV164.430.4299
PW158.529.770
PY155.529141

Invariance of the EPD in the C-N peptide bond and between Cα atoms of consecutive residues

Adaptive Poisson-Boltzmann Solve (APBS) writes out the electrostatic potential in dimensionless units of kT/e where k is Boltzmann’s constant, T is the temperature in K and e is the charge of an electron. The units of EPD are same as that of the electrostatic potential. The EPD of the C-N peptide bond has a Gaussian distribution with mean = 420 EPD units and SD = 55 EPD units (Figure 1). In the probability distribution for four pairs of amino acids the mean of all pairs of amino acids are the same (Figure 1a). Figure 1b shows the scatter plot for the mean and standard deviation (SD). Thus, the amino acids are indistinguishable using the profile of the EPD of the C-N peptide bond across all protein structures since they have identical mean values and a large variance (SD=~50).

d6df8bfa-2658-41d9-89c0-735490706b64_figure1.gif

Figure 1. Electrostatic potential differences (PD) for the C-N peptide bond.

AA: Alanine/Alanine, AC: Alanine/Cysteine, HS: Histidine/Serine and DF: Aspartic-acid/Phenylalanine. (a) Probability distribution for four pairs of amino acids. (b) Scatter plot for all pairs of amino acids. It can be seen that the mean and SD for all pairs of amino acids are the same. Further, the variance is large (SD=~50), indicating that this feature is not tightly constrained in peptide structures.

The probability distribution for four pairs of amino acids for the EPD between the Cα atoms of consecutive residues (Figure 2a) have means that are slightly more varied than those for the C-N bond (Figure 1a). In the scatter plot for the mean and SD of all pairs (Figure 2b) the outliers are pairs that include proline, which have a higher mean, although the magnitude of SD is the same (Table 1).

d6df8bfa-2658-41d9-89c0-735490706b64_figure2.gif

Figure 2. Electrostatic potential differences (PD) for consecutive residue pairs for Cα atoms.

A: Alanine/Alanine, AC: Alanine/Cysteine, HS: Histidine/Serine, DF: Aspartic-acid/Phenylalanine. (a) Probability distribution for four pairs of amino acids. (b) Scatter plot for all pairs of amino acids. It is seen that pairs of amino acids which include proline have a higher mean, although the magnitude of SD is the same.

Distinctive EPD between Cβ atoms of consecutive residues for certain amino acid pairs

In contrast to the results described above, the EPD between the Cβ atoms in consecutive residues in the peptide structure can be used to discriminate different amino acid pairs in the protein structure. The mean EPD of all amino acid pairs are much more varied (Figure 3a). These pairs do not include glycine, which lacks a sidechain. In the scatter plot for the mean and SD, the outliers are pairs that include cysteine (Figure 3b), which have a much higher SD (=~90) as compared to other pairs (SD=~35) (Table 2), and thus cannot be used for discriminatory purposes.

d6df8bfa-2658-41d9-89c0-735490706b64_figure3.gif

Figure 3. Electrostatic potential differences (PD) for consecutive residue pairs for Cβ atoms.

AA: Alanine/Alanine, AD: Alanine/Aspartic-acid, AE: Alanine/Glutamic-acid, DF: Aspartic-acid/Phenylalanine, DY - Aspartic-acid/Tyrosine, HT: Histidine/Threonine, HS: Histidine/Serine. (a) Probability distribution for seven pairs of amino acids. (b) Scatter plot for all pairs of amino acids. The pairs which include cysteine have a high standard deviation. It is seen that the mean is much more varied than the electrostatic potential difference (EPD) for Cα and the C-N peptide bond.

Table 2. Electrostatic potential differences (EPD) for consecutive residue pairs for Cβ atoms for residue pairs that has one cysteine.

These pairs have a random values for the mean and a high standard deviation (SD), with the exception of the pair ‘CC’ (not the disulfide bond) which has a low mean value and SD. Consequently, these values can not discriminate between pairs of amino acids.

PairMean EPDSDNumber of
samples
AC-53.786.9178
CC-7.130.436
CD103.892.7154
CE96.894.7121
CF-21.484.285
CH-1293.397
CI32.880.9136
CK50.293.9131
CL42.890.6224
CM61.910039
CN63.796.1115
CP24.98845
CQ66.792.195
CR35.495.1144
CS106.398.1184
CT109.997.5173
CV54.990.7183
CW-0.285.943
CY8.591.596

These values are used as a discriminator when choosing the native structure from a set of possible candidates (Table 3). To establish the non-triviality of these values, we also show that the variance of the EPD between these pairs increases with increasing sequence distance. Thus, the EPD between the pairs ‘DF’ and ‘HS’ has lesser correlation as the sequence distance between them increases (sample size for each sequence distance is > 30) (Figure 4). The SD for distance 1 (i.e. consecutive residues) is 29.8 EPD units and 31.8 EPD units for ‘DF’ and ‘HS’, respectively - and rises to around 60 EPD units with increasing sequence distance.

Table 3. Electrostatic potential differences (EPD) in a sample of consecutive residue pairs of Cβ atoms.

These pairs are used for discriminating predicted structures in order to obtain the native structure. The complete set is available at https://github.com/sanchak/mqap.

PairMean EPDSDNumber of
samples
DF-108.929.5481
DY-107.430.7442
DH-105.233.5242
DW-104.127.7209
EH-98.528.5200
EY-96.528378
EW-94.229.8184
SY-93.527.5403
EF-93.127.6439
TY-9328.6384
TW-90.828.7144
SW-89.227.7169
FT89.226.8436
FS92.328.4453
HS93.731.8235
HT95.131.5235
d6df8bfa-2658-41d9-89c0-735490706b64_figure4.gif

Figure 4. Standard deviation (SD) of the electrostatic potential difference between Cβ atoms increases with increasing sequence distance for amino acid pairs.

Each sequence distance has at least 30 sample points. DF: Aspartic-acid/Phenylalanine, HS: Histidine/Serine. As expected, there is lesser correlation in the EPD values between the shown amino acid pairs ‘DF’ and ‘HS’ as the sequence distance between the residues increases. The SD for distance 1 (i.e. consecutive residues) is 29.8 EPD units and 31.8 EPD units for ‘DF’ and ‘HS’, respectively - and rises to around 60 EPD units with increasing sequence distance.

Validating using decoy sets

We obtained the score (PDScore) of any given protein structure by comparing the electrostatics of the Cβ atoms based on Table 3. To benchmark model quality assessment programs, we used decoy sets from the Decoys ‘R’ Us database43. We detail our results from some of these decoy sets. Each set has several structures that are supposed to be ranked worse than the native structure.

The misfold decoy set has ~20 protein structures, each of which has a correct and an incorrect structure specified (three structures have two incorrect structures: we randomly chose the first)44. The PDScore of these proteins were computed (Table 4). Barring three structures (PDBids: 1CBH, 1FDX and 2SSI), the PDScore of the incorrect structure is higher than that of the correct structures.

Table 4. Misfold decoy set.

This decoy set has ~20 protein structures - each of which has a correct and an incorrect structure specified. The PDBs are sorted based on the number of residues in the structure (NRes). Three of the structures (1CBH, 1FDX and 2SSI) have a lower PDScore for the incorrect structure.

PDBNResCorrect
PDScore
Incorrect
PDScore
Specificity
1CBH3618.712.60
1PPT361833.51
1FDX543330.90
5RXN5425.1351
1SN36520.730.31
2CI26519.935.21
2CRO6526.743.41
1HIP8519.136.81
2B5C8522.134.31
2CDV10717.440.91
2SSI10722.6200
1BP21232144.11
2PAZ12319.327.31
1P2P12428.6291
1RN312420.728.81
1LH11531826.21
2I1B1531927.61
1REI21216.521.81
5PAD21218.8321
1RHD29323.231.91
2CYP29321.235.81
2TMN31627.232.21
2TS131721.328.21

The hg_structal set has about ~30 proteins. Each protein has 30 structures (including the native structure). Table 5A shows specificity obtained for structures in this decoy set. The average specificity obtained for this decoy set is 0.91 (Table 5A). The decoy set 4state_reduced has ~600 structures for each of the seven proteins. We obtain an average specificity of 0.94 for this decoy set (Table 5B). Similarly, for the ig_structal decoy set we obtain a specificity of 0.93 (Supplementary Table 1).

Table 5. hg_structal and 4state_reduced decoy sets.

The PDBs are sorted based on specificity. (A) The hg_structal decoy set has ~30 protein structures - each of which has 30 structures. The average specificity obtained for the set is 0.91. (B) The 4state_reduced decoy set has 7 protein structures - each of which has ~600 structures. The average specificity obtained for the set is 0.94. (C) The fisa set has 4 protein structures - each of which has 500 structures. The electrostatic discriminator has low specificities in this case. We have previously demnostrated that this decoy set can be discriminated by a distance based criterion. It consists of physically nonviable structures, thus rendering an electrostatic analysis meaningless. NRes = number of residues, NStructures = number of structures in the decoy set.

PDBNResNStructuresSpecificity
(A)
hg_structal
2PGHA141300.2
1MBS153300.5
2DHBA141300.6
1HDAB145300.9
1MYT146300.9
1HLM158300.9
1HSY153300.9
1MBA146300.9
1MYGA153300.9
1MYJA153300.9
1ASH147301
1BABB146301
1COLA197301
1CPCA162301
1ECD136301
1EMY153301
1FLP142301
1GDM153301
1HBG147301
1HBHA142301
1HBHB146301
1HDAA141301
1HLB157301
1ITHA141301
1LHT153301
2DHBB146301
2LHB149301
2PGHB146301
4SDHA145301
(B)
4state_reduced
2CRO656750.8
3ICB756540.9
4RXN546770.9
4PTI1186881
1CTF1316311
1R69976761
1SN3656611
(C)
fisa
4ICB765010
1FC2445010.4
1HDDC575010.1
2CRO655010.7

Discussion

The functional characterization of a protein from its sequence using in silico methods based on the ‘sequence to structure to function’ paradigm is contingent upon the availability of its 3D-structure. The rapidly developing field of next generation sequencing has exacerbated the bottleneck of obtaining structural data using crystallization techniques45. This ever-widening gap has been filled by methods that predict structures from sequences46, based either on features from databases of known structures24 or from first principles of atomic interactions5,6.

The various sources of error in protein structure prediction have been previously discussed in detail47. An incorrect model of a protein structure will result in an inaccurate analysis of its properties48. For example, continuum models49 that compute potential differences and pKa values from charge interactions in proteins50 are sensitive to the spatial arrangement of the atoms in the structure. It must be pointed out that other detailed methods using quantum mechanical/molecular mechanical (QM/MM) techniques and and doing extensive conformational sampling have been able to determine the side chain pKa values with high accuracy51. Accurate structural information is indispensable for in silico methods that extract the electrostatic profile of atoms in the peptide structure41,52, and for other methods widely used in pharmacology for drug discovery53. Model quality assessment programs (MQAP) that validate the accuracy of predicted structures are thus a critical aspect in the process of modeling a protein structure from its sequence. MQAPs can be classified as energy812, consensus1316 or knowledge based (statistical potential)2127. The state of the art methods for predicting structures35 and MQAPs17,34,36 are evaluated by researchers every two years.

Previously, we hypothesized and demonstrated that the electrostatic potential difference (EPD) in cognate pairs in the active site are conserved in proteins with the same functionality37,40,54, even when evolution has converged to the same catalytic from completely different sequences55. This similarity is observed in structures solved independently over many years and establishes the reliability of the APBS and PDB2PQR implementations41,56. We focused on unraveling other electrostatic features that are innate to protein structures. Here, we first demonstrate that the EPD between the C-N peptide bond and the Cα atoms of consecutive residues are independent of the amino acid type. This is expected, since the distance between these atoms are almost invariant across all structures. The EPD of the C-N bond has a high variance, implying that the backbone accommodates relatively large variations while seeking energetically minimized structures.

The true source of the chemical and structural diversity in protein structures is the side chain atoms. Every amino acid, except glycine, has a Cβ atom that hosts a unique moiety of atoms. Although the reactive groups are different for amino acids, we show that this difference is encapsulated in the backbone Cβ atoms. We first show that different pairs of amino acids have significantly different mean EPD values in side chain Cβ atoms (Figure 3), unlike the EPD of the C-N peptide bond (Figure 1) or the EPD between consecutive Cα atoms (Figure 2). Further, the variance is much less than in the EPD of the C-N bond. These facts suggested that the EPD between Cβ atoms of consecutive residues in the peptide structure might act as a discriminator. Our hypothesis is based on the insightful Boltzmann law that lower energy conformations are disproportionately sampled, on the thermodynamic hypothesis57 that the native structure has minimal energy, and the hypothesis that statistical derived features in known protein structures have a Gaussian distribution21. We apply our discriminator to standard decoy sets from the Decoys ‘R’ Us database to establish the validity of the method43.

Our work also highlights the unique properties of proline in the protein structure58. This is evident from the different magnitude of EPD in consecutive Cα atoms involving proline (Table 1). Another noteworthy aspect is the large variation in EPD in consecutive Cβ atoms involving cysteine (Table 2), demonstrating the unique role cysteine plays in providing flexibility to protein structures, a critical element in the evolution of complex organisms59. The discrimination of Cβ atoms also provides a uniform basis for methods that require a single-atom representation of a residue. Such methods depend on a correct parameterization of the reactive atoms37, a task further complicated by amino acids such as histidine which has two reactive atoms. For example, the EPD between the negatively charged E and D with respect to the aromatic phenylalanine is -108 and -93 EPD units, in spite of the difference in their reactive atom. Similarly, the EPD between alanine and the three aromatic amino acids (F, W and Y) are -67, -66 and -63 EPD units respectively.

We achieved an average specificity of 0.91, 0.94 and 0.93 on hg_structal, 4state_reduced and ig_structal decoy sets, respectively, taken from the Decoys ‘R’ Us database. We have previously demonstrated that the fisa decoy set can be discriminated by a distance based discriminator60. ESCAPIST does not discriminate the native structure in this decoy set (Table 5C). The physical implication of ESCAPIST results on the fisa decoy set, which has significant RMSD for backbone Cα atoms, needs further elaboration. The input to a finite difference Poisson-Boltzmann (FDPB) analysis is a charge distribution that might be unfeasible due to energy functions other than electrostatics. For example, van der Waals force or the elastic bond length force components might prevent two atoms from being in close proximity. However, if such a physically impossible configuration were presented to a FDPB-based analysis tool, such as APBS41, it would still generate an electrostatic potential landscape. Inferences based on this potential landscape would be incorrect due to its physical non-viability. Thus, before invoking the EPD constraints specified here, it is imperative that other spatial constraints that are rarely violated in structures are checked. Possibly for this same reason, MQAPs that combine many features in their scoring functions are superior. Moreover, it should be kept in mind that decoy sets, like most benchmarking sets, are prone to biases61 and possible errors31. In fact, the fisa decoy set has been shown to violate the van der Waals term61. To summarize, we present a novel discriminating feature in protein structures based on the electrostatic properties of the side chain atoms. We validated this discrimination in several decoy sets taken from the Decoys ‘R’ Us database, and achieved high specificities in most decoy sets.

Methods

Our proposed method has two phases. In the learning phase, we process multiple structures to extract the feature values - mean values of electrostatic potential difference (EPD) for each amino acid pair. These feature values are applied on query proteins to obtain a score (PDscore) that indicates the deviation of the feature values in the given structure from the ‘ideal’ values. Thus, a lower PDscore indicates a better candidate.

Learning phase

Algorithm 1 shows the procedure LearnFeatures() that extracts the feature values from a set of proteins ΦLearningPhaseproteins (Equation 1). We ignore the first x=IgnoreNTerm and last y=IgnoreCTerm pairs of residues in the protein structure to exclude the terminals. For every consecutive pair of residues in the structure, we calculate the EPD (see below for method) between two specified atoms (atomP and atomQ). Both atomP and atomQ are set to Cβ to obtain EPD values for Cβ atoms, while we set atomP to ‘C’ and atomQ to ‘N’ in order to obtain the C-N peptide bond EPD values. The mean (Mean learnt value - MLV) and standard deviation (SD) are computed for each amino acid type pair (AAType) in protein (Equation 2), and the mean computed for the globals set of proteins (MLV(AATypex, AATypey)) for each pair of amino acid types (Equation 3). Pairs whose EPD have a SD greater than a threshold value (sdThresh, 50 by default) are ignored. Means for all significant pairs (ϕpairMean) are noted to a file, which is the input to the quality assessment phase. The EPD between a pair of amino acid is order-independent - for example, the EPD statistics for the pair ‘AC’ (alanine-cysteine) includes the EPD of both ‘AC’ and ‘CA’ (with the sign reversed).

ΦproteinsLearning Phase={P1, P2PM}     (1)

MLV(AATypeResn,AATypeResn+1)Pi=n=1+xNy1(EPD(Resn(atomP),Resn+1(atomQ)))(Nyx2)     (2)

MLV(AATypex,AATypey)=[i=1M,and AATypexand AATypey](n=1M(MLV(AATypex,AATypey)Pi)M     (3)

Quality assessment phase

Algorithm 2 shows the function AssessEPDQuality() that generates the PDscore for a given protein from the template file generated by the learning phase. The set of proteins ΦproteinsAssessment Phase consists of the native structure P1 and N-1 decoys structures (Equation 4). Once again, barring x=IgnoreNTerm and y=IgnoreCTerm number of residues from the N and C terminals, the pairwise EPD for consecutive residues are computed. The absolute value of the difference of these values from their corresponding means, if they exist, in the template file is added to generate the absolute score (Equation 5). This score is normalized with the number of residues that have been compared to obtain the final PDscore. In summary, the PDscore encapsulates the average distance of the EPD for the given atom pairs (it may be Cβ, Cα or the C-N bond) of consecutive residues from their mean values. We hypothesize that in the native or a near native structure, the PDscore will be minimized for the EPD of Cβ atoms of consecutive residues, i.e. given a set of proteins Φproteins consists of the native structure P1 and N-1 decoys structures, P1 will have the minimum PDscore (Equation 6).

ΦproteinsAssessment Phase={P1, P2PN}     (4)

PDscorePi=n=1+xNy1Abs(EPD(Resn(atomP),Resn+1(atomQ))MLV(AATypeResn,AATypeResn+1))(Nyx2)     (5)

[i=2N](PDscoreP1<PDscorePi)     (6)

The top level procedure ESCAPIST() is shown in Algorithm 3. It invokes the function LearnFeatures() once, and applies the learnt values to assess the quality of structures based on the feature values obtained.

Computing electrostatic potentials

Adaptive Poisson-Boltzmann Solver41 (APBS) and the PDB2PQR package56 package was used to calculate the potential difference between the reactive atoms of the corresponding proteins. The APBS parameters are set as follows - solute dielectric: 2, solvent dielectric: 78, solvent probe radius: 1.4 Å, Temperature: 298 K and 0 ionic strength. APBS writes out the electrostatic potential in dimensionless units of kT/e where k is Boltzmann’s constant, T is the temperature in K and e is the charge of an electron.

Algorithm 1: LearnFeatures(): extract electrostatic potential difference (EPD) values from a given pair of amino acids

Input: ϕproteins = {P1 ··· PM} : M Proteins in the learning set

Input: IgnoreNTerm: Ignore this number of residues in the N Terminal

Input: IgnoreCTerm: Ignore this number of residues in the C Terminal

Input: atomP: Atom type in first residue

Input: atomQ: Atom type in second residue

Input: sdThresh: Threshfold for standard deviation of the EPD

Output: ϕpairMean = {meanPDC1 ··· meanPDCK}: Mean values of EPD between specified atoms

               of successive residues, there being K such significant pairs

begin

      /*K pairs of amino acid type (sorted: AC and CA are equivalent)*/

      /*Each set is initialize to be the null set*/

      ϕpair = {ϕ1PDC ··· ϕKPDC} :

      foreach Pi in ϕproteins do

           N = NumberOfResidues(Pi);

           for p ← IgnoreNTerm to (N − IgnoreCTerm) do

               q = p + 1 ;

               /* Amino acid pairs are order independent */

               ResiduePairTypeString = ResidueTypeString(p) + ResidueTypeString(q);

               ResiduePairTypeStringSorted = Sort(ResiduePairTypeString;

               /* Reverse sign of potential difference accordingly */

               multfactor = 1 ;

               if (ResiduePairTypeStringSorted != ResiduePairTypeString) then

                  multfactor = -1 ;

               end

               PD = PotentialDifference(p, q, atomP, atomQ) * multfactor ;

               /* Let the amino acid pair be the kth in the set ϕpair */

               InsertInSet(PD, ϕkPDC);

         end

      end

      /* Compute Mean and SD of each set - ignore pairs with SD greater than sdThresh*/

      ϕpairMean = ∅;

      foreach ϕipair in ϕpair do

           (Meani, SDi) = MeanAndSD(ϕipair);

           if (SDi > sdThresh) then

              Add(Meani, ϕpairMean);

           end

      end

      return (ϕpairMean);

end

Algorithm 2: AssessEPDQuality()

Input: P1 : Protein under consideration

Input: IgnoreNTerm: Ignore this number of residues in the N Terminal

Input: IgnoreCTerm: Ignore this number of residues in the C Terminal

Input: atomP: Atom type in first residue

Input: atomQ: Atom type in second residue

Input: ϕpairMean = {meanPDC1 ··· meanPDCM}: Mean values of EPD between specified atoms of

           successive residues

Output: PDscore: Score indicating the normalized distance of the observed values from the (mean)

             learnt values from native structures

begin

      PDscore = 0 ; NumberCompared = 0 ; N = NumberOfResidues(P1);

      for p ← IgnoreNTerm to (N − IgnoreCT erm) do

          q = p + 1 ;

          /* Amino acid pairs are order independent */

          ResiduePairTypeString = ResidueTypeString(p) + ResidueTypeString(q);

          ResiduePairTypeStringSorted = Sort(ResiduePairTypeString;

          /* Reverse sign of potential difference accordingly */

         multfactor = 1;

          if (ResiduePairTypeStringSorted != ResiduePairTypeString) then

             multfactor = -1 ;

          end

          /* Let the amino acid pair be the kth in the set ϕpair */

          PD = PotentialDifference(p, q, atomP, atomQ) * multfactor ;

          if (meanPDCk) then

             NumberCompared = NumberCompared + 1 ;

             diff = absolute(PD − meanPDCk);

             PDscore = PDscore + diff;

           end

      end

      /* Normalize */

      PDscore = PDscore/NumberCompared;

      return (PDscore);

end

Algorithm 3: ESCAPIST(): Top level function

Input: ϕproteins: Learning set

Input: P1: Protein to be scored

Input: IgnoreNTerm: Ignore this number of residues in the N Terminal

Input: IgnoreCTerm: Ignore this number of residues in the C Terminal

Input: atomP: Atom type in first residue

Input: atomQ: Atom type in second residue

Input: sdThresh: Threshfold for standard deviation of the EPD

Output: PDscore: Score indicating the normalized distance of the observed values from the (mean)

             learnt values from native structures

begin

      /* This is invoked once*/ ϕpairMean =

      LearnFeatures(ϕproteins, IgnoreNTerm, IgnoreCTerm, atomP, atomQ, sdT hresh);;

      PDscore = AssessEPDQuality(P1, IgnoreNTerm, IgnoreCTerm, atomP, atomQ, ϕpairMean);

      return (PDscore);

end

Comments on this article Comments (0)

Version 3
VERSION 3 PUBLISHED 13 Nov 2013
Comment
Author details Author details
Competing interests
Grant information
Copyright
Download
 
Export To
metrics
Views Downloads
F1000Research - -
PubMed Central
Data from PMC are received and updated monthly.
- -
Citations
CITE
how to cite this article
Chakraborty S, Venkatramani R, Rao BJ et al. The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment [version 3; peer review: 2 approved]. F1000Research 2014, 2:243 (https://doi.org/10.12688/f1000research.2-243.v3)
NOTE: If applicable, it is important to ensure the information in square brackets after the title is included in all citations of this article.
track
receive updates on this article
Track an article to receive email alerts on any updates to this article.

Open Peer Review

Current Reviewer Status: ?
Key to Reviewer Statuses VIEW
ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions
Version 2
VERSION 2
PUBLISHED 15 Nov 2013
Revised
Views
25
Cite
Reviewer Report 18 Jul 2014
Patricia C Weber, Imiplex LLC, Bristol, PA, USA 
Approved
VIEWS 25
The quality of protein structure models is assessed by the geometry of adjacent C beta atoms. The approach successfully distinguishes properly folded proteins in most cases. It adds a new way to assess protein models and could be included in ... Continue reading
CITE
CITE
HOW TO CITE THIS REPORT
Weber PC. Reviewer Report For: The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment [version 3; peer review: 2 approved]. F1000Research 2014, 2:243 (https://doi.org/10.5256/f1000research.3039.r5376)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • Author Response 15 Sep 2014
    Sandeep Chakraborty, Department of Biological Sciences, Tata Institute of Fundamental Research, Mumbai, 400 005, India
    15 Sep 2014
    Author Response
    We would like to thank you for taking the time and reviewing our paper, and deeply appreciate your positive comments. We do not have the expertise to comment on the ... Continue reading
COMMENTS ON THIS REPORT
  • Author Response 15 Sep 2014
    Sandeep Chakraborty, Department of Biological Sciences, Tata Institute of Fundamental Research, Mumbai, 400 005, India
    15 Sep 2014
    Author Response
    We would like to thank you for taking the time and reviewing our paper, and deeply appreciate your positive comments. We do not have the expertise to comment on the ... Continue reading
Views
34
Cite
Reviewer Report 12 Mar 2014
Shina Caroline Lynn Kamerlin, Computational and Systems Biology, Department of Cell and Molecular Biology, Uppsala University, Uppsala, Sweden 
Approved
VIEWS 34
This is an interesting idea that uses the physical (electrostatic) properties of amino acid side chains in order to predict secondary structure from sequence, and thus assess (and rank) the quality of protein structures. The manuscript is well-written, and the ... Continue reading
CITE
CITE
HOW TO CITE THIS REPORT
Kamerlin SCL. Reviewer Report For: The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment [version 3; peer review: 2 approved]. F1000Research 2014, 2:243 (https://doi.org/10.5256/f1000research.3039.r4062)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.

Comments on this article Comments (0)

Version 3
VERSION 3 PUBLISHED 13 Nov 2013
Comment
Alongside their report, reviewers assign a status to the article:
Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested
Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.
Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions
Sign In
If you've forgotten your password, please enter your email address below and we'll send you instructions on how to reset your password.

The email address should be the one you originally registered with F1000.

Email address not valid, please try again

You registered with F1000 via Google, so we cannot reset your password.

To sign in, please click here.

If you still need help with your Google account password, please click here.

You registered with F1000 via Facebook, so we cannot reset your password.

To sign in, please click here.

If you still need help with your Facebook account password, please click here.

Code not correct, please try again
Email us for further assistance.
Server error, please try again.