Probability-based protein secondary structure identification using combined NMR chemical-shift data

Chemical-shift statistics

The averaged ¹H^N, ¹⁵N, ¹H^α, ¹³C^α, ¹³C^β, and ¹³C` chemical shifts, together with the standard deviations categorized according to three secondary structure types, are listed in Table 1. These statistical data are derived from a carefully prepared database containing >6100 amino acids. Since the late 1980s, several statistical studies on the chemical shifts of the 20 amino acids have been reported with the accumulation of NMR data (Wuthrich 1986; Wishart et al. 1991; Lukin et al. 1997; Schwarzinger et al. 2000). The results presented here expand upon the earlier studies in the following respects.

First, the most recently published chemical-shift assignments and structure data are included in the statistical analysis. All of the proteins selected in this study are large in size (>80 residues), double or triple isotope labeled, and their chemical-shifts are assigned by use of multidimensional NMR techniques. The larger chemical-shift and protein coordinate database allows us to specify and take into account other conditions such as chemical-shift reference, pH, and temperature to avoid their possible effects on chemical shift. Table 2 provides a detailed list of the proteins together with BMRB and PDB entries selected for this study. Although most of the BMRB files contain one or more corresponding PDB access numbers, of the 36 proteins used in this study, only 2 can be found in the list of BMRB entries manually matched to PDB NMR entries. Manually matching chemical-shift data (BMRB entry) with the known protein coordinates (PDB entry) is essential for this study. As shown in this table, sometimes sequence renumbering is necessary to obtain a correct match.

Second, an explicit and exact protocol is applied to define a protein's secondary structure from its 3D coordinates. Accurate assignment of secondary structures in proteins with known 3D structures is crucial for the determination of the relationship between protein secondary structure and the observed chemical shift. However, the correlation always remains subjected to some inaccuracy due to the differences in the concept of secondary structure, as well as errors and inconsistencies in experimental structural data. This was shown in the comparison (Colloch et al. 1993) of three methods for structure determination, DSSP (Kabsch and Sander 1983), DEFINE (Richards and Kundrot 1988), and P-curve (Sklenar et al. 1989) on a set of 154 proteins in which all 3 methods agree only 63% of the time. Another comparison (Cuff and Barton 1999) of DSSP, DEFINE, and STRIDE (Frishman and Argos 1995) on a set of 126 proteins showed an overall agreement of only 71%. Among these various protocols/programs, we tried to choose one by which the secondary structures defined could be in a better agreement with the observed chemical-shift data. For this purpose, three automatic programs, VADAR (Wishart et al. 1995a), DSSP, and STRIDE, were used to define the secondary structure during our statistical study. All three programs agree well with each other in defining both the location and the length of long (≥ 4 residues) and well-formed (in terms of dihedral angle, hydrogen bond, etc.) β-strand/α-helix, but not the short (< 4 residues) β-strand/α-helix and poorly-formed β-strand/α-helix. In most cases, a separated β-bridge (one residue) defined by DSSP/STRIDE is assigned as a three-residue β-strand by VADAR. A separated 3₁₀-helix (only three residues) defined by DSSP/STRIDE is normally assigned to random coil by VADAR. For these two situations, we found that the results from VADAR agree with the observed chemical-shift data. For a long β-strand/α-helix with poorly formed boundary, VADAR defines more β-strand/α-helix. Sometimes, modifications had to be made on one or two residues at the end of β-strand or α-helix defined by VADAR, taking into account the backbone dihedral angle, to which the chemical shift is sensitive (Williamson et al. 1992; Wishart and Nip 1997), as well as the results from DSSP and STRIDE.

Furthermore, the 3D coordinates, from which the secondary structures were extracted and used as reference, were carefully selected and priority was given to high-resolution X-ray structures, which have always been the gold standard for the determination of NMR parameters such as ³J_HNHα coupling constants, etc. When NMR structures were used, at least three individual structures were selected to generate a secondary structure reference.

The averaged chemical shifts in this study are compared with the earlier reported values and those showing significant discrepancies are indicated in bold in Table 1. More specifically, ¹H^N and ¹H^α were compared with Wishart's result (Wishart et al. 1991); ¹⁵N, ¹³C^α, ¹³C^β, and ¹³C` with that of Lukin's (Lukin et al. 1997). The statistics of the chemical-shift difference, Δδ (averaged chemical-shift value in this study minus previously reported value), are also listed in Table 3. As shown in Tables 1 and 3, despite significant differences for certain amino acids, on average, the <sup>1</sup>H<sup>N</sup>, <sup>1</sup>H<sup>α</sup>, and <sup>13</sup>C<sup>α</sup> chemical shifts reported in this study are in good agreement with the earlier results, whereas for <sup>15</sup>N, <sup>13</sup>C<sup>β</sup>, and <sup>13</sup>C` chemical shifts, the discrepancies are relatively larger for both the overall averaged chemical shift and certain individual amino acids. Because the random coil chemical shift is usually used as a reference in the identification of secondary structure, a number of random coil data sets have been published. A comparison of the random coil chemical shift obtained in this study with those most recently obtained by Schwarzinger et al. (2000) on Ac-GGXGG-NH2 hexapeptides in pH 2.3, 8 M urea is listed in Table 4. As shown in Table 4, despite the difference in the methods applied, on average, the random coil chemical shifts of ¹H^N, ¹H^α, ¹³C^β, and ¹³C^α reported in this study are in good agreement with those of Schwarzinger et al. (2000). However, as is apparent from this table, systematic deviation of nearly 1.0 ppm is observed between the two sets of data for ¹³C` for most of the amino acids except Asp and Cys. As the data of Schwarzinger et al. (2000) were obtained at very low pH (2.3), the CO may be partly protonated and, hence, affect the observed the chemical shifts. It is of great interest to find that significant deviations also exist for ¹³C^β chemical shift on Asp and Cys. One possible reason for this could be the formation of an intra-residue hydrogen bond, OH-CO for Asp and SH-CO for Cys. The other few significant deviations could be attributed to the different method used.

Most important is that the standard deviation of the chemical-shift distribution, which is ignored in earlier reports, is reported for each individual amino acid in this study. As we show later, the standard deviation plays an important role in evaluating the reliability of the identification. As shown in Table 1, the value of standard deviation varies greatly with the amino acid as well as the secondary structure type. In earlier studies, the standard deviation value was either not considered (Wishart et al. 1992; Wishart and Sykes 1994) or used as an averaged value (Lukin et al. 1997). As shown in Figure 1 ▶, the chemical-shift distribution varies from one amino acid to another. Using the standard deviation data specified for each of the individual amino acid and secondary structure type certainly increases the accuracy of the secondary structure identification. The statistics of the chemical-shift data in Table 1, we believe, will have other potential applications, such as automatic chemical-shift assignment.

Reliability of identification

When using observed chemical shifts to identify secondary structure, we would like to know the reliability of the result. In this study, the reliability of using an observed chemical shift to identify secondary structure is investigated. This is accomplished by evaluating R, the resolution of the chemical-shift distribution between the three secondary structure types. The calculated R_{strand vs. coil} and R_{helix vs. coil} values (see Materials and Methods for definitions) for the 20 amino acids are listed in Table 5. The higher the R_{strand vs. coil} or R_{helix vs. coil} value, the higher the reliability of distinguishing a β-strand or an α-helix from a random-coil. A High-Low-Average chart of R_{strand vs. coil} and R_{helix vs. coil} is shown in Figure 2 ▶. Both R_{strand vs. coil} and R_{helix vs. coil} vary greatly with the nucleus and the amino acid. On the basis of the calculated values of R_{strand vs. coil} and R_{helix vs. coil}, on average, the reliability is in the order of: ¹³C^α>¹³C`><sup>1</sup>H<sup>α</sup>><sup>13</sup>C<sup>β</sup>><sup>15</sup>N><sup>1</sup>H<sup>N</sup> to distinguish an α-helix from a random coil; and <sup>1</sup>H<sup>α</sup>><sup>13</sup>C<sup>β</sup> ><sup>1</sup>H<sup>N</sup> ∼<sup>13</sup>C<sup>α</sup>∼<sup>13</sup>C`∼¹⁵N to distinguish a β-strand from a random coil. In this study, we also found that the amide ¹⁵N and ¹H^N chemical shifts, which were generally excluded in prior work, have almost the same ability/resolution as those of ¹³C^α and ¹³C` to distinguish a β-strand from random coil. It is of interest that the R_{strand vs. coil} values of amide ¹H^N are relatively higher for amino acids Cys, Phe, Ile, Val, Trp, Tyr, and His. Most of these amino acids are of high β-strand propensity (Kim and Berg 1993).

Probability-based secondary structure identification

In this study, the secondary structure is identified by comparing the joint probabilities derived from the observed ¹³C^α, ¹³C`, ¹H^α, ¹³C^β, ¹⁵N, and ¹H^N chemical shifts. After the secondary structure type of each residue is assigned, empirical pattern filters/functions are used to smooth poorly defined secondary structure fragments. Testing this probability-based method on a set of 30 proteins gave an accuracy (on a residue per residue basis) of 89% for β-strand, 84% for random-coil, and 89% for α-helix. For all of the residues (>6100), the global accuracy Q3 (see Materials and Methods for definition) is 88%. Testing on the same set of proteins, the current CSI methods (Wishart et al. 1992; Wishart and Sykes 1994) gave a global accuracy of 81%. This improvement in accuracy, we believe, is due to the oversimplified protocol used by the CSI method, which assigns the secondary structure type to each residue by simply comparing the observed chemical-shift with the random coil value. More specifically, if the measured chemical-shift value is within the range of the random coil (± 0.1 ppm for ¹H, ± 0.5 ∼0.7 ppm for ¹³C), then the residue is assigned as random coil, otherwise, it is assigned as either β-strand or α-helical. The over-simplified procedure used in CSI methods certainly causes a loss of accuracy. In addition, formerly ignored amide ¹⁵N and ¹H^N chemical shifts are included in this study, and they improve the accuracy and the confidence of identification.

For proteins with well-defined secondary structure and sufficient ¹H, ¹³C, and ¹⁵N chemical-shift assignments, PSSI can give an accuracy of identification as high as 95% (i.e., HTLV-I Capsid Protein). We notice that almost all of the misidentifications occur between β-strand/random coil or α-helix/random coil. Among the misidentifications, those between β-strand/α-helix are <1%. Amide ¹⁵N and ¹H^N chemical shifts, which were easily obtained but excluded from application, were found actually useful, specifically for distinguishing β-strand from random coil. Including these two nuclei into the calculation allows a 1.6% increase of Q3 value for the proteins we tested.

If a residue is in a well-defined secondary fragment, in most cases it has a probability of that secondary structure type above 0.9 (the sum of the probabilities of all the secondary structure types are normalized to 1) and is readily distinguished from the other two types. Plotted in Figure 3 ▶, are the normalized joint probabilities calculated from ¹H, ¹⁵N, and ¹³C chemical-shifts for a fragment of pathogenesis-related protein P14a as well as the secondary structures extracted from its 3D coordinates. The probability distributions shown in this figure provide high-confidence identification of the β-strand, random coil, and α-helix. Those with a poorly defined secondary structure type, for example, the isolated short β-bridge and 3₁₀-helix, are clearly indicated by the ambiguity of the probability between the three secondary structure types.

A JAVA user interface graphic program, PSSI, has been developed to make the process automatic. The chemical-shift data can be read from a file in the NMR-str format (essential for the deposition of the chemical-shift data in the BioMagResBank) or input by the user directly. Its output includes: (1) The normalized joint probability of each secondary structure type, the basis of which the secondary structure is automatically assigned. As we discussed earlier, in this study, empirical filters/functions are used to smooth the poorly defined secondary structure fragments. However, users can also make judgements by themselves on the basis of the probabilities provided by PSSI. (2) The secondary structure, which is editable, derived from chemical-shift data. (3) A graphic output displaying the identified secondary structure. A graphic output from PSSI showing the secondary structure derived from NMR chemical-shift data is shown in Figure 4 ▶. Because chemical-shift references, other than DSS, could be used, a function to calibrate the chemical-shift reference is also provided. The whole package is available at http://ccsr3150-p3.stanford.edu.

Secondary structure identification

Two steps were used to identify the secondary structure elements from the observed NMR chemical-shift data.

Step l: Joint probability

Given a { δ_n} (n = δ_N, δ_CA, δ_CO, δ_CB, δ_HA, δ_HN) are the observed chemical shifts for amino acid i; the secondary structure type of this amino acid is adjudged by comparing the joint probability of the three secondary structure types, Ps,i.

F_s,i represents the probability for amino acid i at the secondary structure type s (s = β-strand, random coil, or α-helix); G_s,i is the Gaussian distribution.

During the calculation, G_s,i(δ_n) is set to 1 if δ_n is not available. G of three secondary structure types is normalized so that its sum is equal to 1.0, as is the joint probability, Ps, for each residue. The secondary structure type is initially assigned to B, C, or H (representing β-strand, random coil, and α-helix, respectively) based on joint probability of each type, that is, B if P_β,i>P_c,i and P_β,i>P_α,i.

Step 2: Smoothing/filtering

This step is optional. Users can make their own adjustments on the basis of the calculated probabilities. The result from step 1 can be further smoothed/filtered by use of empirical patterns and smoothing functions. For example, (1) if a local density of either B or C exceeds one-half for a five-residue window, its secondary structure type is adjusted on the basis of Ps values, that is, a BBCBC segment will be adjusted to BBBBB (if P_β of the last residue is >0.35) or BBBBC (if P_β of the last residue = <0.35); (2) if a C-type residue is not covered by the smoothing/filtering in (1) and is located either at the end or in the middle of B or H segment, its Ps is recalculated and its secondary structure type is readjudged accordingly. For example, for a CHHH segment, the P_s,i of the first residue is recalculated as P _s,i = 0.5*P_s,1 + 0.3*P _s,2 + 0.2*P_s,3 for the second N-terminal residue; (3) separated short (less than two residues) B or H segments are smoothed to C.

The global accuracy of identification Q3 (Schulz and Schimer 1979) is defined as:

in which P_s is the number of residues identified in the s (β-strand, random coil, and α-helix) state, effectively observed in the s state; T is the total number of residues.

The JAVA user interface program (PSSI), which makes the entire procedure fully automated, was developed by one of the authors (Y.J. Wang)