Nucleic Acids Research, Supplementary data
Conformation-dependent restraints for polynucleotides: I. Clustering of the geometry of the phosphodiester group Supplementary materials Marcin Kowiel 1,2 , Dariusz Brzezinski 3 Mariusz Jaskolski 1,4∗ 1 Center for Biocrystallographic Research, Institute of Bioorganic Chemistry, Polish Academy 2 Department of Organic Chemistry, Poznan University of Medical Sciences, Poznan, 60-780,
of Sciences, Poznan, 61-714, Poland, Poland, 3 Institute of Computing 4 Science, Poznan University of Technology, Poznan, 60-965, Poland, Department of Crystallography, Faculty of Chemistry, A. Mickiewicz University, Poznan, 61-614, Poland NOTATION τ3 , ζ τ5 , α φ12 φ13 φ15
C3'-O3'-P-O5' torsion angle C5'-O5'-P-O3' torsion angle O1-P-O2 angle O1-P-O3' angle O1-P-O5' angle
φ23 φ25 φ35 φ33 φ55
O2-P-O3' angle O2-P-O5' angle O3'-P-O5' angle P-O3'-C3' angle P-O5'-C5' angle
SUPPLEMENTARY FIGURES AND TABLES
R6(-sc/+sc) or R8(-c/+c)
R6(+sc/-sc) or R8(+c/-c)
R5(–sp/–sp), R7(–sc/–sc), or AS(–sc/–sc)
(a)
AA(–sc/ap)
R5(+sp/+sp), R7(+sc/+sc), or AS(+sc/+sc)
(b)
AA(+sc/ap)
AA(ap/+sc)
(c)
AA(ap/-sc)
Terminal
(d)
Figure S1. Atom labeling. Atom labeling schemes and schematic Fischer projections of the C-O-PO2 -O-C (a-c) and C-O-PO3 (d) moieties, illustrating the conformational groups defined in this work (see main text and Table 2). The categories of six- and eightmembered rings (R6, R8) (a); of five- and seven-membered rings (R5, R7) and the acyclic symmetric category (AS) (b); and the acyclic asymmetric category (AA) (c); as well as the terminal C-O-PO3 group (d) are shown in separate panels.
∗ Tel:
+48-61-829-1274; Fax: +48-61-829-1555; Email:
[email protected]
© 2016 Marcin Kowiel, Dariusz Brzezinski, and Mariusz Jaskolski This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nucleic Acids Research, Supplementary data 2
category
(a) Manual categorization
cluster
(b) Automatic clustering
Figure S2. CSD torsion-valence angle relationships. Scatter matrix of the torsion angles (y-axis, ◦ ) in relation to the valence angles (x-axis, ◦ ) from: (a) the CSD search, clustered manually into categories R5, R6, R7, R8, AS and AA; (b) the CSD search, clustered automatically by the AHC algorithm (with k = 4, merge=average) into clusters A, B, C and D.
Figure S3. NDB torsion-valence angle relationships. Scatter matrix of the torsion angles (y-axis, ◦ ) in relation to the valence angles (x-axis, ◦ ) from the NDB search, clustered manually into groups AS(+sc/+sc), AS(−sc/−sc), AA(−sc/ap), AA(+sc/ap) and AA(ap/−sc).
Nucleic Acids Research, Supplementary data 3
category
(a) Manual categorization
cluster
(b) Automatic clustering
Figure S4. CSD torsion angle-bond length relationships. Scatter matrix of the torsion angles (y-axis, ◦ ) in relation to the bond lengths ˚ from: (a) the CSD search, clustered manually into categories R5, R6, R7, R8, AS and AA; (b) the CSD search, clustered (x-axis, A) automatically by the AHC algorithm (with k=4, merge=average) into clusters A, B, C and D.
Figure S5. NDB torsion angle-bond length relationships. Scatter matrix of the torsion angles (y-axis, ◦ ) in relation to the bond lengths ˚ from the NDB search, clustered manually into groups AS(+sc/+sc), AS(−sc/−sc), AA(−sc/ap), AA(+sc/ap) and AA(ap/−sc). (x-axis, A)
Nucleic Acids Research, Supplementary data 4
Figure S6. CSD angle histograms. Histograms of the valence angles (◦ ) from the CSD search, divided into categories R5, R6, R7, R8, AS and AA.
Nucleic Acids Research, Supplementary data 5
(a)
(b)
Figure S7. Error histograms. Histograms comparing the differences in angles (a) and bond lengths (b) between the NDB-derived mean values and restraint targets compiled by Gelbin et al. (3) (red) and proposed in this paper (blue).
Nucleic Acids Research, Supplementary data 6
Figure S8. NDB angle histograms. Histograms of the valence angles (◦ ) from the NDB search, divided into groups AS(+sc/+sc), AS(−sc/−sc), AA(−sc/ap), AA(+sc/ap) and AA(ap/−sc).
Table S1. Summary of database search criteria. N/A denotes no restriction used for this criterion. Purpose Restraints P-O3', O3'-C3', φ33 restraints P-O5', O5'-C5', φ55 restraints Terminal PO4 Validation
Query C-O-PO2 -O-C ribose/deoxyribose-C-O-PO2 -O-C (O3' substituted) ribose/deoxyribose-C-O-PO2 -O-C (O5' substituted) C-O-PO3 oligonucleotides
Source CSD CSD CSD CSD NDB+CSD
R-factor [%] ≤7.5 ≤7.5 ≤7.5 ≤7.5 ≤10.0
˚ Resolution [A] N/A N/A N/A N/A at least 1.0
Structures 204 57 12 62 36 (27+9)
Phosphates 238 62 16 77 126 (102+24)
Table S2. CSD-derived mean values and standard deviations (in parentheses, given in units of the last significant digit of the mean value) for the torsion and valence ˚ for the R5, R6, R7, R8, AS, AA categories, after the application of all allowed permutations angles (in ◦ ) and for the P-O1, P-O2, P-O3', P-O5' bond distances (in A) (Table 1). The values of the P-O3', O3'-C3', P-O5', O5'-C5' bond lengths can be found in Table 4. The proposed default values to be used for DNA and RNA structures are marked in bold. The τ3 and τ5 angles are not to be treated as restraints but as reference values for the categorization of actual cases. Permutation (id) (12)(35) -35 -12 (id) (12)(35) -35 -12 (id) (12)(35) -35 -12 (id) (12)(35) -35 -12 (id) (12)(35) -35 -12 (id) (12)(35) -35 -12
Group
τ3 (ζ)
τ5 (α)
φ12
φ13
φ15
φ23
φ25
φ35
φ33
φ55
P-O1
P-O2
P-O3'
P-O5'
-sp/-sp -sp/-sp +sp/+sp +sp/+sp −sc/+sc +sc/−sc −sc/+sc +sc/−sc −sc/−sc −sc/−sc +sc/+sc +sc/+sc -c/+c +c/-c -c/+c +c/-c −sc/−sc −sc/−sc +sc/+sc +sc/+sc −sc/ap ap/−sc ap/+sc +sc/ap
-2(19) -6(15) 6(15) 2(19) -51(4) 52(3) -52(3) 51(4) -44(5) -48(5) 48(5) 44(5) -94(2) 94(3) -94(3) 94(2) -70(10) -69(9) 69(9) 70(10) -67(8) 171(15) -171(15) 67(8)
-6(15) -2(19) 2(19) 6(15) 52(3) -51(4) 51(4) -52(3) -48(5) -44(5) 44(5) 48(5) 94(3) -94(2) 94(2) -94(3) -69(9) -70(10) 70(10) 69(9) 171(15) -67(8) 67(8) -171(15)
117.2(8) 117.2(8) 117.2(8) 117.2(8) 118.4(11) 118.4(11) 118.4(11) 118.4(11) 119.7(12) 119.7(12) 119.7(12) 119.7(12) 120.5(8) 120.5(8) 120.5(8) 120.5(8) 119.9(16) 119.9(16) 119.9(16) 119.9(16) 117.6(12) 117.6(12) 117.6(12) 117.6(12)
109.3(7) 109.9(5) 111.1(10) 110.8(6) 107.0(7) 109.9(9) 108.0(5) 109.5(7) 104.9(9) 106.3(5) 110.8(6) 111.9(6) 105.1(6) 109.4(6) 105.7(4) 109.8(5) 104.5(9) 105.2(8) 110.3(8) 111.5(11) 106.2(11) 109.3(9) 110.2(13) 112.2(10)
111.1(10) 110.8(6) 109.3(7) 109.9(5) 108.0(5) 109.5(7) 107.0(7) 109.9(9) 110.8(6) 111.9(6) 104.9(9) 106.3(5) 105.7(4) 109.8(5) 105.1(6) 109.4(6) 110.3(8) 111.5(11) 104.5(9) 105.2(8) 110.2(13) 112.2(10) 106.2(11) 109.3(9)
110.8(6) 111.1(10) 109.9(5) 109.3(7) 109.5(7) 108.0(5) 109.9(9) 107.0(7) 111.9(6) 110.8(6) 106.3(5) 104.9(9) 109.8(5) 105.7(4) 109.4(6) 105.1(6) 111.5(11) 110.3(8) 105.2(8) 104.5(9) 112.2(10) 110.2(13) 109.3(9) 106.2(11)
109.9(5) 109.3(7) 110.8(6) 111.1(10) 109.9(9) 107.0(7) 109.5(7) 108.0(5) 106.3(5) 104.9(9) 111.9(6) 110.8(6) 109.4(6) 105.1(6) 109.8(5) 105.7(4) 105.2(8) 104.5(9) 111.5(11) 110.3(8) 109.3(9) 106.2(11) 112.2(10) 110.2(13)
96.6(4) 96.6(4) 96.6(4) 96.6(4) 102.9(9) 102.9(9) 102.9(9) 102.9(9) 101.9(9) 101.9(9) 101.9(9) 101.9(9) 105.2(5) 105.2(5) 105.2(5) 105.2(5) 104.2(15) 104.2(15) 104.2(15) 104.2(15) 99.9(7) 99.9(7) 99.9(7) 99.9(7)
111.3(18) 111.9(6) 111.9(6) 111.3(18) 115.8(25) 116.2(27) 116.2(27) 115.8(25) 119.0(21) 117.7(17) 117.7(17) 119.0(21) 122.7(14) 122.4(15) 122.4(15) 122.7(14) 121.5(30) 121.6(28) 121.6(28) 121.5(30) 120.8(11) 120.3(19) 120.3(19) 120.8(11)
111.9(6) 111.3(18) 111.3(18) 111.9(6) 116.2(27) 115.8(25) 115.8(25) 116.2(27) 117.7(17) 119.0(21) 119.0(21) 117.7(17) 122.4(15) 122.7(14) 122.7(14) 122.4(15) 121.6(28) 121.5(30) 121.5(30) 121.6(28) 120.3(19) 120.8(11) 120.8(11) 120.3(19)
1.483(4) 1.480(4) 1.483(4) 1.480(4) 1.483(9) 1.488(7) 1.483(9) 1.488(7) 1.482(7) 1.472(9) 1.482(7) 1.472(9) 1.472(8) 1.477(6) 1.472(8) 1.477(6) 1.484(12) 1.478(10) 1.484(12) 1.478(10) 1.487(10) 1.483(10) 1.487(10) 1.483(10)
1.480(4) 1.483(4) 1.480(4) 1.483(4) 1.488(7) 1.483(9) 1.488(7) 1.483(9) 1.472(9) 1.482(7) 1.472(9) 1.482(7) 1.477(6) 1.472(8) 1.477(6) 1.472(8) 1.478(10) 1.484(12) 1.478(10) 1.484(12) 1.483(10) 1.487(10) 1.483(10) 1.487(10)
1.613(8) 1.607(3) 1.607(3) 1.613(8) 1.604(10) 1.600(8) 1.600(8) 1.604(10) 1.616(12) 1.616(8) 1.616(8) 1.616(12) 1.605(7) 1.607(7) 1.607(7) 1.605(7) 1.599(16) 1.601(16) 1.601(16) 1.599(16) 1.580(10) 1.603(11) 1.603(11) 1.580(10)
1.607(3) 1.613(8) 1.613(8) 1.607(3) 1.600(8) 1.604(10) 1.604(10) 1.600(8) 1.616(8) 1.616(12) 1.616(12) 1.616(8) 1.607(7) 1.605(7) 1.605(7) 1.607(7) 1.601(16) 1.599(16) 1.599(16) 1.601(16) 1.603(11) 1.580(10) 1.580(10) 1.603(11)
Table S3. CSD-derived mean values and standard deviations (in parentheses, given in units of the last significant digit of the mean value) for the torsion and valence ˚ for terminal C-O-PO3 groups. Allowed permutation are presented in Table S4. Note that the angles (in ◦ ) and for the P-O1, P-O2, P-O3, P-O5' bond distances (in A) O5'/C5' labels are used merely as placeholders, and could be, for example, O3'/C3'. N is the number of cases [number of cases before outlier rejection in square brackets]. Category Terminal
N 60 [77]
O1-P-O2 111.7(10)
O1-P-O3 114.0(7)
O1-P-O5' 107.5(7)
O2-P-O3 112.8(10)
O2-P-O5' 107.2(8)
O3-P-O5' 102.8(12)
P-O5'-C5' 119.0(22)
P-O1 1.514(9)
P-O2 1.520(9)
P-O3 1.514(10)
P-O5' 1.622(9)
Nucleic Acids Research, Supplementary data 7
Category R5 R5 R5 R5 R6 R6 R6 R6 R7 R7 R7 R7 R8 R8 R8 R8 AS AS AS AS AA AA AA AA
Table S4. Allowed permutations of terminal C-O-PO3 atom labeling. ❵ ❵❵ ❵❵ Initial O1 O2 O3 O5' O1-P-O2 O1-P-O3 Permutation ❵❵❵ (12) (13) (123) (23) (132)
O2 O3 O2 O1 O3
O1 O2 O3 O3 O1
O3 O1 O1 O2 O2
O5' O5' O5' O5' O5'
O1-P-O2 O2-P-O3 O2-P-O3 O1-P-O3 O1-P-O3
O2-P-O3 O1-P-O3 O1-P-O2 O1-P-O2 O2-P-O3
O1-P-O5'
O2-P-O3
O2-P-O5'
O3-P-O5'
P-O5'-C5'
P-O1
P-O2
P-O3
P-O5'
O5'-C5'
O2-P-O5' O3-P-O5' O2-P-O5' O1-P-O5' O3-P-O5'
O1-P-O3 O1-P-O2 O1-P-O3 O2-P-O3 O1-P-O2
O1-P-O5' O2-P-O5' O3-P-O5' O3-P-O5' O1-P-O5'
O3-P-O5' O1-P-O5' O1-P-O5' O2-P-O5' O2-P-O5'
P-O5'-C5' P-O5'-C5' P-O5'-C5' P-O5'-C5' P-O5'-C5'
P-O2 P-O3 P-O2 P-O1 P-O3
P-O1 P-O2 P-O3 P-O3 P-O1
P-O3 P-O1 P-O1 P-O2 P-O2
P-O5' P-O5' P-O5' P-O5' P-O5'
O5'-C5' O5'-C5' O5'-C5' O5'-C5' O5'-C5'
Table S5. NDB-derived mean values and standard deviations (in parentheses, given in units of the last significant digit of the mean value) for the AS(−sc/−sc), ˚ and had to pass the outlier AS(+sc/+sc), AA(−sc/ap), AA(+sc/ap) and AA(ap/−sc) groups. The accepted crystal structures had R < 10% and resolution higher than 1 A, ˚ filtering procedure (see text). N is the number of cases [number of cases before outlier rejection in square brackets]. All angles are in ◦ , distances in A. Group AS(−sc/−sc) AS(+sc/+sc) AA(−sc/ap) AA(+sc/ap) AA(ap/−sc)
N 49 [58] 26 [38] 10 [13] 2 [6] 6 [11]
τ3 (ζ) τ5 (α) -73(10) -69(8) 74(7) 69(7) -70(9) -156(28) 64(2) 168(1) -166(47) -73(9)
φ12 119.9(9) 119.2(13) 117.9(10) 118.2(5) 118.1(11)
φ13 105.2(13) 111.1(9) 106.0(6) 111.6(2) 108.2(16)
φ15 110.4(11) 105.5(8) 110.0(9) 110.3(3) 110.5(8)
φ23 110.1(11) 104.7(8) 110.5(7) 105.2(4) 110.8(11)
φ25 105.5(12) 110.4(8) 110.4(7) 110.0(1) 106.6(19)
φ35 104.7(10) 105.2(7) 100.6(8) 100.1(1) 101.3(28)
φ33 121.2(13) 121.5(17) 121.1(12) 122.5(4) 122.0(23)
φ55 120.1(15) 120.0(15) 122.2(13) 118.0(1) 120.8(27)
P-O1 1.481(13) 1.494(11) 1.489(6) 1.479(5) 1.487(9)
P-O2 1.481(13) 1.493(10) 1.484(11) 1.493(1) 1.482(5)
P-O3' 1.598(14) 1.601(9) 1.589(11) 1.594(5) 1.604(7)
P-O5' 1.586(10) 1.590(12) 1.588(14) 1.601(0) 1.593(7)
O3'-C3' 1.426(18) 1.433(14) 1.431(12) 1.431(5) 1.423(6)
O5'-C5' 1.432(18) 1.440(17) 1.431(10) 1.433(0) 1.435(11)
Table S6. The torsion angles (τ3 , τ5 ), valence angles (φ12 , φ13 , φ15 , φ23 , φ25 , φ35 ) and bond distances (P-O1, P-O2, P-O3', P-O5', O3'-C3', O5'-C5') for the PDB structure 3P4J (phosphate groups P2...P6 and P8...P12) with the reference geometry group from the present study based on the τ3 /τ5 torsion angles assigned in the ˚ and the least-squares-derived estimated standard uncertainties are given in parentheses. second column. All angles are in ◦ , distances in A, Assigned group
τ3 (ζ)
τ5 (α)
φ12
φ13
φ15
φ23
φ25
φ35
φ33
φ55
P-O1
P-O2
P-O3'
P-O5'
O3'-C3'
O5'-C5'
AS(+sc/+sc) AS(+sc/+sc) AS(+sc/+sc) AS(+sc/+sc) AS(+sc/+sc) AS(+sc/+sc) AA(−sc/ap) AA(−sc/ap) AA(−sc/ap) AA(+sc/ap)
78.0(1) 71.8(2) 73.5(1) 73.5(1) 74.0(1) 67.3(2) -68.9(2) -77.5(2) -69.2(2) 65.6(1)
60.2(2) 68.7(2) 75.2(1) 61.1(1) 65.2(1) 78.5(2) -148.1(2) -142.6(1) -148.9(2) 167.9(1)
118.7(1) 120.2(2) 119.3(1) 118.2(1) 118.7(1) 119.6(1) 117.6(2) 117.1(1) 117.7(1) 118.5(1)
112.2(1) 111.3(1) 110.6(1) 112.0(1) 110.9(1) 110.5(1) 106.0(2) 105.9(1) 107.2(1) 111.7(1)
104.7(1) 104.3(1) 105.2(1) 105.7(1) 105.5(1) 105.4(1) 110.7(1) 111.0(1) 109.7(1) 110.2(1)
104.5(1) 104.3(1) 104.2(1) 105.0(1) 104.2(1) 104.2(1) 110.9(1) 110.9(1) 110.5(1) 104.9(1)
110.5(1) 110.1(1) 111.0(1) 110.2(1) 111.0(1) 110.8(1) 110.2(2) 109.5(1) 109.8(1) 110.0(1)
105.6(1) 105.9(1) 105.9(1) 105.2(1) 105.9(1) 105.6(1) 100.0(1) 101.2(1) 100.5(1) 100.0(1)
121.6(1) 122.3(1) 120.9(1) 122.5(1) 121.8(1) 120.3(1) 121.2(1) 121.9(1) 121.1(1) 122.2(1)
119.9(1) 118.3(1) 120.9(1) 118.5(1) 117.7(1) 120.0(1) 120.8(1) 122.5(1) 121.1(1) 117.9(1)
1.494(2) 1.484(2) 1.495(2) 1.498(2) 1.488(2) 1.492(3) 1.494(2) 1.492(2) 1.488(2) 1.482(2)
1.497(2) 1.498(3) 1.498(2) 1.497(2) 1.500(2) 1.496(2) 1.472(2) 1.493(2) 1.497(2) 1.494(2)
1.599(2) 1.586(2) 1.601(2) 1.594(2) 1.590(2) 1.603(2) 1.583(2) 1.588(2) 1.585(2) 1.597(2)
1.593(2) 1.605(2) 1.589(2) 1.597(2) 1.600(2) 1.582(2) 1.607(2) 1.594(2) 1.594(2) 1.601(2)
1.433(2) 1.436(3) 1.440(2) 1.447(2) 1.440(2) 1.438(3) 1.444(3) 1.428(2) 1.436(2) 1.433(2)
1.437(2) 1.440(3) 1.440(2) 1.446(2) 1.443(2) 1.438(3) 1.440(2) 1.434(2) 1.432(2) 1.433(2)
Nucleic Acids Research, Supplementary data 8
Residue P2 P4 P6 P8 P 10 P 12 P3 P9 P 11 P5
