improvement in accuracy of protein local structure determination from nmr data

ELSEVIER

THEO CHEM

Journal of Molecular Structure (Theochem) 368 (1996) 153-161

Improvement in accuracy of protein local structure determination from NMR data’

Simon Shermana**, Stanley Scloveb, Leonid Kimarsky”, Igor Tomchina, Oleg Shatsa

BEppky Institute for Research in Cancer and Allied Diseases, University of Nebraska Medical Center, 600 South 42nd St., Omaha, NE 68198-6805, USA

%formation and Decision Sciences Dept. M/C 294 University of Illinois at Chicago, 601 South Morgan St., Chicago, IL 60607-7124, USA

Received 1 November 1995; accepted 29 March 1996

Abstract

A method for determining the most probable conformations of amino acid residues from semiquantitatively estimated nuclear

Overhauser effects (NOEs) and coupling constants was developed and coded in the FiSiNOE-2 program. This program is a new version of the FiSiNOE program, utilizing NMR data with complementary knowledge-based information on protein structures. In FiSiNOE-2 this information is conformational clusters of the dihedral angles (4, +, x1) derived from the Protein Data Bank. The FiSiNOE-2 method determines mathematical expectations and standard deviations for the angles 4, $, and x1, and provides direct determination of the local structure of proteins from NMR data before building and refining their spatial structure. The

results of the FiSiNOE-2 program in combination with the results of the HABAS program may be used to provide stereospecific assignments of a pair of /3-methylene protons and to determine precisely allowed ranges of the 6, $, and x1 dihedral angles consistent with a given set of NMR data. To do this, a new procedure, COMBINE, was developed. Computational experiments with the NMR data simulated from X-ray coordinates of the BPTI showed that use of the COMBINE procedure, in comparison with results obtained when HABAS was used alone, increases by more than 30% the number of correct assignments for flCHz groups and reduces the total lengths of the combined angular intervals for $, I/J, and x1 angles to 1.9, 2.4, and 1.8 times, respectively. In contrast to the redundant dihedral angle constraints (REDAC) strategy, that derives REDAC from preliminary calculations of the complete structure, the COMBINE procedure reduces the length of the angular intervals before using the

variable target function algorithm to determine spatial structures of proteins. This feature of the COMBINE strategy may be especially beneficial in the cases when there is lack of long-range NOES.

Keywords: Protein; Structure; NMR

1. Introduction methods for studies of protein structure in solution

has been seen in the last 15 years. Information pro- Dramatic progress in implementation of NMR vided by NMR on chemical shifts, intensity of NOE

cross-peaks, coupling constants, amide groups parti-

* Corresponding author. cipating in the formation of intramolecular hydrogen ’ Presented at the Second Electronic Computational Chemistry

Conference, November 1995. This issue along with any supplimen- bonds, etc., is widely used for protein structure deter-

tary material can be accessed from the THEOCHEM HomePage at mination. The procedures for obtaining such experi-

URL:http://www.elsevier.nl/locate/theochem. mental information are well known [l-5].

0166-1280/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved PIZ SO166-1280(96)04650-7

154 S. Sherman et aLlJournal of Molecular Structure (Theochem) 368 (1996) 153-161

Different methods and approaches to define protein structures from NMR data (NOES and coupling constants) have been proposed. Two basic approaches are generally employed for three dimensional (3D) protein structure determination: (I) metric matrix distance geometry [6,71, and (ii) a variable target function algorithm [8]. The use of matrix distance geometry is usually followed by restrained molecular dynamics simulations [9]. This approach is fully implemented in the X-PLOR program [lo]. The use of a variable target function algorithm provides 3D protein structures of acceptable quality which may be further relined by energy mini- mizations. This approach is well-implemented in the DIANA P'OgKiIll [II].

The DIANA program and the supporting program, HABAS [12], are used to determine a family of structures that match the distance and angular constraints. HABAS utilizes the distance constraints and the spin- spin coupling constants to obtain stereospecific ‘H NMR assignments for a pair of /3-methylene protons and to determine allowed intervals for some dihedral angles [ 121. An improvement in efficiency of structure calculations may be achieved by the use of redundant dihedral angle constraints (REDAC) derived from preliminary structural calculations [13]. It was shown that increasing the number of stereospecific assignments of a pair of fl-methylene protons and reducing the intervals for 4, $, and x1 angles to be searched are beneficial for enhancing accuracy, precision, and efficiency of spatial structure determination of proteins [12,13].

At present, a workable situation with the determination of 3D structures of small globular proteins in solution by NMR data is achieved. However, the structure determination is still a very time-consuming process. Moreover, the uncertainties in experimental data and the limitations of the existing methods of NMR data interpretation are often obstacles to determine the 3D protein structure with high resolution. Any additional information on protein structures that is not contained directly in NMR data may be used to improve the situation.

Complementary knowledge-based information on protein structures can be derived from the Protein Data Bank (PDB) [ 141. In this article, we present results of upgrading the method [l&16] for the determination of the most probable local conformations of proteins based on the use of NMR data with information on

local structures extracted from PDB. The new method is coded in the FiSiNOE-2 program. The program has calculated mathematical expectations and standard deviations for the r$, rc/, and x1 angles from NMR data (semiquantitatively estimated NOES and coupling constants) prior to building and refining of spatial structure of the protein. Thus, to use FiSiNOE-2 any knowledge regarding the overall spatial structure is not required. With the use of FiSiNOE-2, a novel procedure, COMBINE, is developed to provide stereospecillc assignments of a pair of /3-methylene protons and to reduce the intervals for 4, J/, and x1 angles to be searched when 3D protein structure is built. This procedure utilizes results obtained by the combined use of the FiSiNOE-2 and HABAS programs.

Comprehensive computational experiments with the NMR data simulated from X-ray coordinates of the BPTI were performed to assess efficacy of the use of FiSiNOE-2 and COMBINE. It was shown, that in comparison with FiSiNOE (a previous version of the program), FiSiNOE-2 determines backbone conformation of proteins with higher accuracy. The possibility of defining x1 angles, matching a given set of NMR restrictions, is a new distinguishable feature of the FiSiNOE-2 program. The use of the COMBINE procedure, in comparison with results obtained when HABAS was used alone, allowed us to increase significantly the number of assignments for /3CHz groups and to reduce the total lengths of the combined angular intervals for 4, J/, and x1 angles. These improvements may be beneficial for enhancing accuracy, precision, and efficacy of spatial structure determination of proteins from NMR data.

2. Methods

2.1. Determination of local conformations

Fig. 1 shows a typical dipeptide fragment (contain- ing two sequential peptide groups and a side chain) of a polypeptide chain. Main chain conformation of the fragment is determined by two dihedral angles, 4 and $. The x1 angle gives a general orientation of the side chain relative to the backbone.

Previously [ 151, a method for determining the most probable (4, $) values on the basis of the presence or absence of sequential d connectivities (SDCs) (i.e.

S. Sherman et al.lJournal of Molecular Structure (Theochem) 368 (1996) 153-161 155

Fig. 1. Polypeptide chain segment.

dUN, dNN, and dsN comrectivities, see Fig. 2), in conjunction with additional empirical information derived from PDB, was proposed.

In the earlier method, the (4, $) conformational space was divided into regions with the distinct sets of the corresponding SDCs. The probabilities for the backbone of any amino acid residue to be in each of these regions were estimated using the atomic coordinates of the proteins from the PDB with a crystallographic resolution of better than 2.0 A. For every region, weighted means of 4 and $ angles and their standard deviations, a+ and a$, were calculated.

To implement this approach, the FiSiNOE program was developed [16]. The program estimates the most probable values of the 4 and + angles and the asso- ciated standard deviations for each amino acid residue in a sequence by a giving set of corresponding SDCs. The estimations are based on two general assumptions: (i) for SDCs, the upper limit for the $orresponding interproton distances is less than 3.3 A, and (ii) dihedral angles lie within sterically allowed regions of the (4, +) conformational space. Comprehensive statistical analysis of results obtained by FiSiNOE showed that, for most of the conformational states, a set of SDCs was sufficient to obtain the (4, $) values unambiguously and with satisfactory accuracy [16,17]. For glycine residues, all possible conformations determined have to

Fig. 2. Sequential d connectivities.

Fig. 3. Intraresidue d connectivities.

be taken into account for further evaluation. In contrast to other existing methods which estimate only allowed ranges for local dihedral angles, this method determines the first two statistical moments: mathematical expectations, and standard deviations for the angles. Detailed information about this probabilistic approach and its performance in comparison to other methods has been reviewed in [17].

In the present work, we used semiquantitatively estimated NOES for sequential and intraresidue d-connectivities (see Fig. 2 and Fig. 3) and coupling constants, 3JaN and 3Ja~, in conjunction with the results of cluster analysis of conformational states of amino acid residues derived from PDB.

The cluster analysis of the (4, $, x1) points was performed for all types of amino acid residues from the joint probability density functions derived from the dataset of 60 high-resolution proteins. This dataset was taken from the set of nonredundant proteins listed

Fig. 4. Positioning of the clusters on the Fbrnachandran plot (1: x1 - -60; 2: x, = 180; 3: x1 - +60).

156 S. Sherman et aLlJournal of Molecular Structure (Theochem) 368 (19%) 1.53-161

Table 1 The 14 cluster means

Cluster Dihedral angles

4 ti

b-/3-structure bl -129 155 b2 -115 124 b3 -146 160

p-polyproline II-helix

Pl -93 141

P2 -73 131

P3 -90 157

r-righthand a-helix rl -65 -36 r2 -63 -44 r3 -70 -21

t--transition state (between b and I) t1 -95 -9 t2 -88 -38 t3 -114 7

I-lefthand a-helix I1 59 37 12 65 39

Xl

-61 180 64

-63 180 65

-68 178 67

-62 179 62

-62 190

in Fig, 2 in [ 181. The dataset of 60 proteins was chosen with a resolution of better than 2.0 A. This database was used to derive the joint probability density functions that were clustered into 14 sets (see Fig. 4 and Table 1). It should be noted that including (or exclud- ing from the database) the BPTI molecule, used as a “test protein”, did not influence noticeably the joint probability density functions or the results of the cluster analysis.

For every cluster, the mathematical expectations of the 4, $, and x1 angles and their standard deviations, u+, a$, and uXl, were estimated. These data were used in a new program, FiSiNOE-2.

2.2. The FiSitVOE-2 program

The program was developed on an IBM PC in Bor- land C++3.1 under Windows applications. FiSiNOE-2 implements the following functions: (i) editing the amino acid sequence; (ii) entering short-range NOES and coupling constants; and (iii) determining the first statistical moments for 4, $, and x1 angles. The program determines a corresponding cluster(s) by the

values of intraresidual and sequential cross-peak intensities, graded as strong, medium, and weak, and by the values of coupling constants, 3JuN and “Jab, graded as high, intermediate, low, and negligible. For this cluster, FiSiNOE-2 estimates values of mathematical expectation for 4, $, and x1 angles and their standard deviations. Thus, the FiSiNOE-2 approach gives the most probable intervals for the dihedral angles that are consistent with a given set of NMR data. For a given dihedral angle 0, having a mathematical expectation (@) and a standard deviation ae, the real value of the angle will be within the interval (0) 2 2~ in more than 95% of the cases.

2.3. The COMBINE procedure

This procedure, based on the combined use of the FiSiNOE-2 and HABAS programs, attempts to obtain stereospecific ‘H NMR assignments for a pair of @- methylene protons and to find the allowed intervals for r$, $, and x1 angles consistent with a given set of NMR data. Two approaches, FiSiNOE-2 and HABAS,

use the same input data (local NOE distance constraints and the spin-spin coupling constants) but are based on fundamentally different principles. FiSi- NOE-2 is a knowledge-based approach implemented to estimate mathematical expectations and standard deviations for 4, $, and x1 angles by combining a previously-known distribution function for these dihedral angles with a measured set of experimental data. In contrast, a major purpose of HABAS is to obtain stereospecific ‘H NMR assignments for a pair of /3- methylene protons. As a by-product of these assignments, HABAS also determines sterically allowed intervals for 4, $, and x1 angles consistent with a given set of NMR data. Of note, restrictions on the allowed ranges for the 4, $, and x1 angles may result even if no unambiguous stereospecific assignments can be derived from the available data.

The COMBINE procedure determines intervals for 4, $, and x1 angles as intersections of the corresponding intervals determined by the FiSiNOE-2 and HABAS programs. To do this, for every dihedral angle 0, an interval (19) + 2~ is taken as the probabilistic interval determined by FiSiNOE-2. COMBINE determines an intersection of the corresponding probabilistic and steric intervals for every 4, $, and x1 angle in a given amino acid sequence, and introduces these

S. Sherman et al./Journal of Molecular Structure (Theochem) 368 (1996) 153-161 157

inteIVdS as rfXEWd angUlarreStriCtiOnSfOr HABAS. By these renewal angular restrictions, HABAS reestimates stereospecific ‘H NMR assignments for a pair of /3- methylene protons.

2.4. Data and software used

Artificial NMR-type data were simulated from X- ray coordinates of the protein basic pancreatic trypsin inhibitor (BPTI). The SYBYL software package [19] was used to add hydrogens to the BPTI heavy atoms, to calculate interproton distances, and to estimate the values of the r$, II/, and x1 angles based on X-ray atomic coordinates taken from the PDB file, 4pti.pdb [14,20]. All interresidual and zequential proton-proton distances shorter that 4.0 A were consid- ered. In order to mimic a typical NMR input for a structure calculation, these precise distances were substituted by corresponding upper limits on the distances: for the intraresidual constraints and for constraints between protons in sequentially adjacent residues, upper limits of 2.5, 3.0, 2.5, and 4.0 A were used, where the limit0 < 2.5 A applies t! all distances shorter than 2.5 A, the limit < 3.0 A, to all distances within the interval from 2.5 to 3.0 A, etc., [12]. Values of coupling constants 3JmN and 3Jus were estimated using the Karplus-type relations [21]; these constants were taken to define the center of an interval of half-width 2.0 Hz, to mimic the precision of a typical NMR experiment [12].

Intraresidual and sequential NOE distance constraints and the 3JaN and 3JoLB coupling constants were used as input data for the FiSiNOE-2 and HABAS programs. In the use of FiSiNOE-2, it was assumed that the upper limits of 2.5, 3.0, and 3.5 A correspond to strong, medium, and weak cross-peaks, and values of coupling constants, 3JaN and 3Jols, were graded as high ( > 9 Hz), intermediate (in the interval, 6-9 Hz), low (in the interval 2-6 Hz), and negligible ( < 2 Hz).

The BPTI local conformations determined from artificial NMR data by both the FiSiNOE and FiSi- NOE-2 programs were compared with the crystallographic local structure of the BPTI to estimate their comparable capabilities. In these comparisons, the crystallographic conformation was used as a target (“true” value or “gold standard”), and criteria based on the evaluation of the angular RMS

deviations (ARMSDs) between the dihedral angles defined from NMR data and the corresponding angles in the target structure were employed. Analysis of variance, ANOVA (two-factor without replications), incorporated in Microsoft’s EXCEL 4.0 was used to evaluate the statistical significance of the differences among three data sets: X-ray conformation, and two sets of conformations determined by FiSiNOE and FiSiNOE-2.

3. Results and discussion

To evaluate efficiency of the FiSiNOE-2 program, in comparison with the FiSiNOE program, and the COMBINE approach, in comparison with when the HABAS program was used alone, computational experiments were carried out. Artificial NMR data for the BPTI molecule were processed by both programs, FiSiNOE and FiSiNOE-2. For each amino acid residue in the BPTI sequence, FiSiNOE defined a set of most probable main chain conformations, $I and $ angles, matching the given set of SDCs connectivities, while FiSiNOE-2 provided the most probable values of 4, $, and x1 angles, satisfying both the given set of intraresidue and sequential cross-peak intensities, and the values of coupling constants, 3JuN and 3JLyB, In addition, FiSiNOE-2 determined all other possible sets of 4, $, and x1 angles (with lower probabilities) matching the given NMR constraints.

Fig. 5 and Fig. 6 show differences between the backbone conformations in the X-ray structure and the corresponding r$ and $J angles defined by the FiSiNOE and FiSiNOE-2 programs. Since FiSiNOE-2 resulted in a set of all possible conformations for each residue, the most probable conformations were taken into account. The problem of determining glycine conformations was previously discussed [15,22]. All Gly residues were excluded from the statistics.

The statistical significance of the differences among the three data sets (the X-ray conformation and the conformations defined by FiSiNOE and FiSiNOE-2) was evaluated by two-factor analysis of variance, ANOVA. The first factor was the set of residues, and the second consisted of the three data sets from X-ray, FiSiNOE, and FiSiNOE-2.

158 S. Sherman et al.lJoumal of Molecular Structure (Theochem) 368 (1996) 153-161

RESIDUE NUMBER

Fig. 5. Differences between 4 angles in the X-ray structure and the corresponding angles defined by the FMNOE (triangles) and RSINOE-2 (squares) programs.

The F-statistics that deals with all three data sets simultaneously, as well as the ARMSDs between X- ray and FiSiNOE (X/FiSiNOE) and between X-ray and FiSiNOE-2 (X/FiSiNOE-2), were calculated for the C$ and $ angles separately. The results are shown in Table 2.

Taking as the null hypothesis that these three data sets are statistically indistinguishable, with

0.05 as the significance level of the critical values for the F-statistics, one can conclude that in all cases, except $ angle for ar-helices, this hypothesis cannot be rejected. This means that all three data sets are quantitatively close. However, the ARMSDs for 4 angles were significantly improved for all types of structure, indicating a better quality of the r$ angles’ determination by using FiSiNOE-2, while

RESIDUE NUMBER

Fig. 6. Differences between $ angles in the X-ray structure and the corresponding angles defined by the FISINOE (triangles) and FISINOE-2

(squares) programs.

S. Sherman et al./Journal of Molecular Structure (Theochem) 368 (1996) 153-161 159

Table 2 Statistical comparison of the conformations

Structural fragment ARMSD (deg.)d

Angle F” d.f.* PC XIFISINOE X/FlSINOE-2

cx-helices (3-6,48-55)

z 0.50 6.84 2, 2, 11 11 0.61 0.005 11.3 17.5 10.2 9.9

&strands (18-24, 29-35) 4 1.31 2, 13 0.29 21.3 13.4 $ 0.81 2, 13 0.45 14.6 11.8

Irregular (1, 2, 7-17,25-27, 38-47) 6 0.45 2, 24 0.64 25.5 16.7 4 0.85 2, 24 0.43 24.5 26.8

All residues (except Gly: 12, 28, 36, 37, 56, 57)

z 0.35 2.81 2, 2, 49 49 0.71 0.07 22.7 19.2 14.4 19.7

’ F: value of F-statistics. b d.f.: degrees of freedom. ’ P: probability computed under the assumption that the null hypothesis is true. d The angular root-mean-square deviations (ARMSDs) between X-ray structure and the structures derived from simulated NMR data by

FiSiNOE and FiSiNOE-2, respectively. For X/FiSiNOE-2, ARMSDs are calculated with the most probable conformation for each amino acid residue.

$ angles were determined with the equal quality as by FiSiNOE. The observed statistically meaningful differences in determination of cr-helical fragments by FiSiNOE occurred due to a small systematic error in evaluation of the distorted a-helix (residues 3-6). It is remarkable that FiSiNOE-2 has assigned conformations of these residues much more precisely than was done by FiSiNOE (see Fig. 6).

The possibility of defining x1 angles, matching a given set of NMR restrictions, is a new distinguishable feature of the FiSiNOE-2 program. From 42 amino acid residues with side chains, FiSiNOE-2 correctly determined the most probable x1 conformers for 39 residues. In one case, Tyr-10, the correct confor- mer was assigned as possible but with lower probability. In only two cases, Phe-22 and Asn-44, the program failed to correctly find the x1 conformers. ARMSD for correctly assigned x1 conformers was about 10”.

The first statistical moments for the 9, J/, and x1 angles obtained by FiSiNOE-2 were used to increase the number of stereospecific assignments for PCHz groups determined by the HABAS program. To do this, the intersections of allowed angular intervals obtained by HABAS, with corresponding probabilistic

intervals estimated from results of FiSiNOE-2, were determined by the COMBINE procedure. These angular intervals were used as renewal angular restrictions for HABAS to WStitIWk stereospecific ‘H NMR assignments for fi-methylene protons. It should be noted that initially HABAS could assign 21 PCHz groups from a total of 36 KHz groups in the BPTI molecule (i.e. 58%) and could determine allowed intervals for 138 dihedral angles (from total of 156 angles). By the use of the COMBINE procedure, unambiguous assignments for 32 /3CH2 groups were obtained and angular restrictions for all 4, J/, and x1 angles of BPTI were determined. The use of the COMBINE procedure, in comparison with results obtained when HABAS was used alone, allowed us to increase the number of correct assignments for &Hz groups by more than 30% (89% by COMBINE vs. 58% by HABAS alone) and to decrease the total lengths of the combined angular intervals for 4, $, and x1 angles to 1.9, 2.4, and 1.8 times, correspondingly. (Note, Gly and Pro residues that are not treated by HABAS were excluded from these comparisons of the total length.) Comparisons of the ranges for 4 and J/ angle constraints for the HABAS and COMBINE data sets are shown in Fig. 7 and Fig. 8.

160 S. Sherman et aLlJournal of Molecular Structure (Theochem) 368 (1996) 1.53-161

240

ACP 180

RESIDUE NUMBER

Fig. 7. Comparisons of the ranges for $I angle constraints (in degrees) determined by the HABAS (points) and COMBINE (bars) procedures.

4. Conclusion

Computational experiments with the simulated NMR data showed that FiSiNOE-2 enables the user to determine the main chain local structure with a high precision and accuracy; no systematic errors were observed for any types of structure. FiSiNOE-2 correctly assigned most of the x1 conformers. In comparison with the estimations made when the HABAS

360 -

/

300 --

240 --

A* 180 --

120 --

program was used alone, utilization of the COMBINE procedure significantly increases the number of stereospecific ‘H NMR assignments for a pair of /3- methylene protons. The use of the COMBINE procedure also reduces the total lengths of the angular intervals for 4, $, and x1 angles to be searched when spatial structures of proteins are built.

Two different strategies, REDAC and COMBINE,

which reduce the angular intervals and thus increase

15 25 35 45 55

RESIDUE NUMBER

Fig. 8. Comparisons of the ranges for 4 angle constraints (in degrees) determined by the HABAS (points) and COMBINE (bars) procedures.

S. Sherman et al.JJound of Molecular Structure (Theochem) 368 (1996) 153-161 161

efficiency of 3D structure determination from NMR data, are complementary. REDAC derives redundant dihedral angle constraints from preliminary calculations of a set of conformers that are consistent with a whole set of available NMR constraints. The success of the REDAC strategy is primarily due to the feedback of useful information about the local structure of a given protein derived from preliminary determined complete structures. In contrast to the wm4c strategy, the COMBINE procedure reduces the length of the 6, $, and x1 angular intervals before 3D structure determi- nations. The success of the FiSiNOE-2 calculations and the COMBINE strategy is provided by the utilization of additional structural information extracted from PDB that is not contained directly in NMR data. Note, that the use of the COMBINE strategy does not require any knowledge regarding the overall spatial structure. This feature of the COMBINE strategy may be especially beneficial in cases when there is lack of long-range NOES. Thus, the complementary use of the COMBINE and REDAC strategies may provide additional improvements in protein structure determi- nations from NMR data.

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The Molecular Modeling Core Facility of the UNMC/Eppley Cancer Center was used in these studies.

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improvement in accuracy of protein local structure determination from nmr data

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