1PO Box 2548, Sunnyvale, CA 94087-0548 and 3Department of Biomolecular Engineering, University of California at Santa Cruz, Santa Cruz, CA 95064. USA
2 To whom correspondence should be addressed. E-mail: ohur1688{at}alumni.ucsd.edu
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Abstract |
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Keywords: heavy atom distance/NMR/proton distance
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Introduction |
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The translation is done by plotting graphs to calibrate the relationships between the heavy atom distance restraints and the corresponding proton distance restraints from a dataset of 100 high-resolution crystal structure (1.71.0 Å) PDB files (Table I) (Word et al., 1999a) with all hydrogen atoms added and optimized by Reduce (Word et al., 1999b
). Two-dimensional scatter graphs and heat maps and three-dimensional histograms of the heavy atom distances versus their corresponding interproton distances are plotted. We also report here that based on the curve fitting, linear equations can yield fairly good approximations for translating proton distance restraints into the corresponding heavy atom distance restraints.
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Materials and methods |
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In our calculations, the distances involving diastereotropic protons or methyl protons are calculated as the average of all possible proton pairs because 1H NMR experimental data do not distinguish the three methyl protons. For example, the interproton distance between the HA of Gly and HA of Lys is calculated as the average of the two distances 1HA GlyHA Lys and 2HA GlyHA Lys. Diastereotropic -protons and ß-protons include HA of Gly and all HB except Ala, Gly, Ile, Thr and Val. Methyl protons include HB of Ala, HD1 and HG2 of Ile, HD1 and HD2 of Leu, HE of Met, HG2 of Thr, HG1 and HG2 of Val.
The data points are plotted according to their secondary structures, defined in the PDB files (Word et al., 1999a). The two-dimensional scatter graphs for heavy atom distances versus their corresponding interproton distances are plotted in red, green and blue representing
-helices, ß-sheets and loops, respectively. These graphs are also fitted with linear equations for the optimal fits, upper bounds and lower bounds (see Table V). The optimal fits are determined by linear regression while the upper bounds and lower bounds are obtained visually. Moreover, two-dimensional heat maps and three-dimensional histograms are created to determine the spots with the highest data point concentrations. The inverse distance weighting interpolation method (Equation 1) (Shepard, 1968
; McLain, 1976
) is used in the smoothing transformation to transform the scatter graphs into two-dimensional heat maps and three-dimensional histograms.
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Results and discussion |
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Part B of Figures 25 and part E of Figure 4 show the two-dimensional heat maps using inverse distance weighting interpolation (Equation 1) to represent the distribution density of the corresponding scatter plots of part A of Figures 2
5 and part D of Figure 4, respectively. Also, for clarity, the relationship between heavy atom distances and the corresponding interproton distances of HA(i)HN(i + j) are shown in two different two-dimensional heat maps for
-helices and ß-sheets in Figure 5D and E, respectively. In addition, part C of Figures 2
5 and part F of Figure 4 show part B of 25 and part E of Figure 4, respectively, in three-dimensional histograms. From these two-dimensional heat maps and three-dimensional histograms, the relative distributions of the data points from the original scatter plots (part A of 25 and part D of Figure 4) can be observed. Heavy concentrations of data points form clusters in the two-dimensional heat maps and three-dimensional histograms.
Figure 4G and H and Figure 5F and G are scatter graphs for various anti-parallel and parallel ß-sheet interactions. The distances between adjacent residues among amide protons, -protons and ß-protons are listed in Table II for
-helices and ß-sheets. The interproton distances between residues in adjacent strands in anti-parallel and parallel ß-sheets are listed in Tables III and IV, respectively.
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In this study, if a ß carbon has two ß-protons, the two diastereotropic ß-proton distances are averaged. In many cases where ß-protons are studied, distinct clusters can be observed for each of the rotamers. The most striking example is CB(i)N(j) vs HB(i)HN(j) (Figure 1). In Figure 1, the gray dots are for -helix residues where j = i + 1 and the black dots are for anti-parallel ß-sheets where the amide nitrogen and carbonyl oxygen of residue (i) form hydrogen bonds with carbonyl oxygen and amide nitrogen of residue j, respectively. In both interactions of the
-helices and anti-parallel ß-sheets, three distinct clusters are observed with the center one being the most prominent. In addition, the
-helix interactions of the heavy atom distances versus the corresponding interproton distances of HA(i)HB(i + 1) (data not shown), HA(i)HB(i + 2) (data not shown) and HN(i)HB(i + 1) (data not shown) also show three distinct clusters with the center one being the most intense.
At ß-carbons of most amino acids, three rotamers can form. The center prominent cluster is from the trans rotamer and the two smaller ones are from the two gauche rotamers. The trans rotamer is the most favorable configuration owing to its staggered geometry, so its cluster is also the strongest.
Interproton distances of side chains
Figure 2AC show the graphs for the methyl carbon distances between all methyl carbons versus their corresponding methyl protons (j > i). The distances from all three methyl protons are averaged for each methyl carbon because 1H NMR experimental data do not distinguish the three methyl protons. Figure 2AC show that the data points are concentrated in a narrower range around the optimal fit (solid line) than any other distance relationship (Figures 1 and 35), probably because the three interproton distances are averaged, removing most variations due to rotation of the methyl groups. Also, no single prominent cluster of data points is observed. Instead, the data points are spread evenly between the upper limit and lower limit in Figure 2B and C.
Another side chain proton pair, HB(i)HB(i + j), j 2 (Table V, graph not shown), also shows a narrow range between its lower and upper bounds. However, the area for the data points in HB(i)HB(i + j) is still wider than the region between the lower bound and upper bound in methyl proton(i)methyl proton(j) in Figure 2AC. In Figure 2AC for methyl carbon(i)methyl carbon(j) versus methyl proton(i)methyl proton(j), the absence of three rotamers at methyl carbons, due to three methyl protons, causes the data point region to be narrower than those side chain proton distances involved with rotamers, for example, the distance relationship of CB(i)CB(i + j) and HB(i)HB(i + j) (data not shown).
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Figure 3AC are the graphs for the heavy atom distances versus the corresponding interproton distances of HB(i)HA(i + 1). The upper and lower bounds are y = 5.00 and 4.20, respectively, that is, the heavy atom distances are independent of the proton distances (Table V). The range for interproton distance of HB(i)HA(i + 1) is wide, 4.06.0 Å, compared with the range of the corresponding heavy atom distance of CB(i)CA(i + 1),
4.25.0 Å. In addition, the distance relationships for interproton distances of HA(i)HB(i + 1) (data not shown), HB(i)HN(i + 1) (data not shown), HN(i)HN(i + 1) (data not shown), HN(i)HA(i + 1) (data not shown) and the distances of the corresponding heavy atoms also show that the upper and lower bounds have slopes of zero (Table V).
Second, the -helix interactions (red dots) are concentrated into a more compact region than the ß-sheet interactions (green dots) in Figure 3A. This can be explained by the fact that
-helices are more rigid structurally than ß-sheets. The hydrogen bonding pattern in ß-sheets allows strands to twist and bend. Hence clusters of
-helix interactions are more constrained than those of ß-sheets interactions.
Linear relationship for -helix interactions in the interproton distances of HN(i)HN(i ± j) when j
2
One major cluster and two minor clusters, mostly from -helix interactions (red dots in Figure 4A and D), are observed along the optimal fit line (solid black line in Figure 4A, B and E, Table V) for the distance relationship between heavy atoms and the corresponding HN(i)HN(i + j) when j
2. The solid black line in Figure 4A, B and E, y = 0.39 + 0.93x (Table V), is the optimal fit for the interactions from all secondary structures; whereas the solid green line in Figure 4D, y = x, is the optimal fit for the interactions only from
-helices. These two optimal fits are very similar to each other. In addition, the major cluster in the center gives a much higher intensity than the other two smaller clusters (Figure 4B, C, E and F). Data points from ß-sheet (green dots) and loop (blue dots) interactions are distributed over a wider area than
-helices (red dots) (Figure 4A).
The most prominent cluster is from the interactions of -helix residue pairs of HN(i)HN(i + 3) and anti-parallel and parallel ß-sheets interactions (Figure 4B and C). Moreover, Figure 4D and F show that the concentration for
-helix data points of HN(i)HN(i + 3) is much more dense than the concentrations of data points for HN(i)HN(i + 2) or HN(i)HN(i + 4) from the same secondary structure. This pattern suggests that the alignments of HN(i)HN(i + 3) and N(i)N(i + 3) is more rigid than others because N(i) and N(i + 3) are on the same plane. In
-helices, O(i 1) and N(i + 3) form a hydrogen bond. Moreover, the peptide bond between O(i 1) and N(i) cannot be freely rotated.
The three clusters for -helices, HN(i)HN(i + 2), HN(i)HN(i + 3) and HN(i)HN(i + 4), are on the optimal fit line for
-helices, y = x (green solid line in Figure 4D). This indicates that, at least for
-helices, the distances between amide proton pairs and between the corresponding amide nitrogen pairs are essentially the same when they are two, three or four residues apart. This linear relationship is due to the sp2 hybridization-like nature of amide nitrogen. The sp2 hybridization-like nature forces amide nitrogen to be trigonal planar with its lone pair interacting with electron deficient carbonyl carbon in the resonance form. All amide protons in
-helices point in the same direction. No other interaction shows this kind of linear relationship in our study.
Non-linear relationship for -helix interactions in the interproton distances of HA(i)HN(i ± j) when j
2
Figure 5A shows the scatter plot for the heavy atom distances versus their corresponding interproton distances of HA(i)HN(i + j) when j 2. In Figure 5B and C, five clusters of data points are observed. Two clusters, HA(i)HN(i + 3) and HA(i)HN(i + 4), which are formed mostly by the interactions from
-helices (Figure 5D, red dots in Figure 5A), are found along the optimal fit, y = 1.80 + 0.81x (solid line in Figure 5A, B, D and E, Table V). Another cluster in Figure 5BD, HA(i)HN(i + 2), located around the intersection of the two lower bound limits (dash line), is also from interactions in
-helices (red dots in Figure 5A).
In contrast to N(i)N(i + j) versus HN(i)HN(i + j) in Figure 4AE, the three data clusters from -helix interactions are not aligned linearly in Figure 5D. The positions of the clusters show that the interproton distance and the corresponding heavy atom distance for
-helices are not the same. We believe that this difference is due to the different hybridizations in amide nitrogen and
-carbon. The hybridization in
-carbon is sp3 with tetrahedral geometry. This tetrahedral geometry forces the
-carbon to protrude out of the
-helical face and the
-protons to point outwards in different directions. In addition, the distance relationship between heavy atom pairs and their corresponding proton pairs of HA(i)HA(i + j) when j
2 (data not shown) also show this non-linear relationship.
Conclusion
First, in many examples involving distances from ß-protons, distinct rotamers can be observed in -helices and ß-sheets. For example, in the relationship between the distances between heavy atoms and between the corresponding ß-protons and amide protons, three distinct clusters, representing each rotamer at the ß-carbon, can be observed. The largest cluster is from the trans rotamer and the two smaller clusters are from the two gauche rotamers.
Second, we found that in short-range interproton distances of HB(i)HA(i + 1), HA(i)HB(i + 1), HB(i)HN(i + 1), HN(i)HN(i + 1) and HN(i)HA(i + 1), the lower and upper bounds for the translation have slopes of zero. This suggests that the range allowed for heavy atom distances from the translation of their interproton distances is very small. We conclude that interproton distances that are less than six heavy atoms away are independent of their corresponding heavy atom distances.
Finally, in the distance relationship of N(i)N(i + j) and HN(i)HN(i + j), all three (j = 2, 3 or 4) -helix data clusters are aligned linearly along the line of y = x. The linear relationship indicates that the distances of both N(i)N(i + j) and HN(i)HN(i + j) are essentially the same, if they are part of an
-helix. In contrast, the distance relationship of CA(i)N(i + j) and HA(i)HN(i + j) shows the three
-helix clusters aligned non-linearly and the distances CA(i)N(i + j) and HA(i)HN(i + j) are not the same. This difference can be attributed to the different hybridizations on amide nitrogen (sp2-like trigonal planar geometry) and on
-carbon (sp3 tetrahedral geometry). In
-helix secondary structure, all amide protons point in the same direction towards the N-terminus. In contrast,
-protons of
-helices point outwards, away from
-helices.
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References |
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Bowers,P.M., Strauss,C.E.M. and Baker,D. (2000) J. Biomol. NMR, 18, 311318.[CrossRef][ISI][Medline]
Brünger,A.T. (1992) X-PLOR Version 3.1: a System for X-ray Crystallography and NMR. Yale University Press, New Haven, CT.
Clore,G.M. and Gronenborn,A.M. (1998) Proc. Natl Acad. Sci. USA, 95, 58915898.
Güntert,P., Braun,W. and Wüthrich,K. (1991) J. Mol. Biol., 217, 517530.[CrossRef][ISI][Medline]
Güntert,P., Mumenthaler,C. and Wüthrich,K. (1997) J. Mol. Biol., 273, 283298.[CrossRef][ISI][Medline]
Hung,L.H. and Samudrala,R. (2003) Nucleic Acids Res., 31, 32963299.
Karplus,K., Karchin,R., Draper,J., Casper,J., Mandel-Gutfreund,Y., Diekhans,M and Hughey,R. (2003) Proteins: Struct. Funct. Genet., 53, Suppl 6, 491496.[CrossRef][ISI][Medline]
Li,W., Zhang,Y. and Skolnick,L. (2004) Biophys. J., 87, 12411248.
Markley,J.L., Bax,A., Arata,Y., Hilbers,C.W., Kaptein,R., Sykes,B.D., Wright,P.E. and Wüthrich,K. (1998) J. Mol. Biol., 280, 933952.[CrossRef][ISI][Medline]
McLain,D.H. (1976) Comput. J., 19, 178181.[ISI]
Meiler,J. and Baker,D. (2003) Proc. Natl Acad. Sci. USA, 100, 1540415409.
Nilges,M., Clore,G.M. and Gronenborn,A.M. (1988) FEBS Lett., 229, 317324.[CrossRef][ISI][Medline]
Ramachandran,G.N., Ramakrishnan,C. and Sasisekharan,V. (1963) J. Mol. Biol., 7, 9599.[ISI][Medline]
Schwieters,C.D., Kuszewski,J.J., Tjandra,N. and Clore,G.M. (2003) J. Magn. Reson., 160, 6674.
Shepard,D. (1968) In Proceedings of 23rd ACM National Conference, pp. 517524.
Word,J.M., Lovell,S.C., La Bean,T.H., Taylor,H.C., Zalis,M.E., Presley,B.K., Richardson,J.S. and Richardson,D.C. (1999a) J. Mol. Biol., 285, 17111733.[CrossRef][ISI][Medline]
Word,J.M., Lovell,S.C., Richardson,J.S. and Richardson,D.C. (1999b) J. Mol. Biol., 285, 17351747.[CrossRef][ISI][Medline]
Zheng,W. and Doniach,S. (2002) J. Mol. Biol., 316, 173187.
Received August 17, 2005; accepted September 8, 2005.
Edited by Marius Clore
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