Calculate structure

Basis of Secondary Structure Determination

Calculate structure is based on Defined Secondary Structure of Protein (DSSP), a program written in Pascal.^[2] The secondary structure recognition algorithms used in DSSP are based mainly on hydrogen-bonding patterns along with some geometric structures , such as bends. There are two different hydrogen-bonding patterns which are recognized. The one determines the value of n in the expression i + n (i is a residue that forms a hydrogen bond with a residue n residues removed from residue i.) where n = 3, 4 or 5. These values define three types of turns. A peptide segment that has repeating turns of the same type are called 3₁₀-helix, α-helix, or п-helix, respectively. If the turn is isolate, it is simply called an n-turn. The other recognized pattern is a hydrogen bond which is between residues which are not close together in sequence. This type of hydrogen bond is called a bridge. Kabsch & Sanders define a ladder as a "set of one or more consecutive bridges of identical type" and a sheet as a "set of one or more ladders connected by shared residues"^[2]. Bends are peptide segments with high curvature, and the determination of curvature involves angles of the C^α. Bends can overlap with helices and turns.

After its completion the results of calculate structure computation are printed in the upper box of the console. One part of that output is a summary of the different types of secondary structure with each type having a one letter identifier. (The summary for myohemerytherin (2mhr) is given below with a key for the one letter identifier.) It is possible for a residue or a segment of residues to be assigned more than one structural type, and for this reason the key for the identifiers is rank ordered in decreasing priority of assignment. With bend having the lowest priority in assignment a structure is identified as a bend only if it is not assigned any other structural type. The helices and sheets which are identified on the summary can easily be associated with the corresponding structures in the applet, but the turns need some additional explanation.

Relationship to β and γ Turns

The DSSP determination of helices and β-sheets is in agreement with the generally accepted view of these two structures, but the DSSP determination of turns is not as specific as the generally accepted definition of turns. As described above DSSP identifies turns that have 3, 4, or 5 residues with a backbone hbond being present between the first and the last residues. The presence of the hbond is a requirement to be classified as a turn. Phi and psi torsional angles of the C^α are not used by the DSSP procedure, but the generally accepted definitions of β and γ turns involve these angles.

β-turns contain four residues and therefore are 4-turns found by DSSP. The classes of β-turns are defined by the range of psi and phi values for the second and third residues.^[3] β-turns often have a hbond between residues one and four (i + 3) of β-turns, but there is not an absolute requirement for one. In three classes (VIa1, VIa2, VIb) a Pro in the third position has the cis configuration which does not permit the formation of a hbond (View display of structure.). The turns in these three classes are not detected by DSSP since they do not contain a hbond.

γ-turns contain three residues having a hbond between residues i and i + 1 and are included with the 3-turns found by DSSP. The classic γ-turns have phi and psi values at residue i + 1 of +75.0 and -64, respectively, and the inverse γ-turns have phi and psi values at residue i + 1 of -79 and +69, respectively.^[4]

Problems encountered when identifying β and γ-turns

See below for more details and illustrations of these problems.
β-turns

• DSSP does not report classes VIa1, VIa2, and VIb because of the lack of a hbond. If a segment is not colored blue but appears that it may be a β-turns, check for a cis-Pro at i + 2. Also, the values for phi and psi angles at i + 1 and i + 2 can be determined.
• Segments labeled with T and contain one residue may not be a 3-turn, but a β-turn (4-turn) that partially overlaps a structure that has a higher priority, and only the non-overlapping residue is reported as a turn. DSSP is described as only identifying a turn as a n-turn if the turn is isolated, but in practice this does not always happen. If a turn segment in the Summary is only one residue long and that segment is displayed as a blue trace short than four residues, it is still a β-turn if there is a hbond between i + 3.
• A β-turn can be nested in a 5-turn, and in the Summary this turn will show as a three residue segment. A β-turn nested in a 5-turn contains two hbonds. One located between i and i + 3, and the other one is between i and i + 4.

γ-turns

• In the SUMMARY for Domain 2 of Chain A Glycogen Phosphorylase there are six T labeled segments which contain one residue and are 3-turns because they all have a hbond between i and i + 2. The phi values for residue i + 1 are negative, but the psi values are also negative. These six 3-turns could be inverse γ-turns, if the range for psi values given by Miner-White, et. al. is extended to negative values.^[4] Miner-White, et. al. seem to allow for this by stating in the legend of Table 1, "To qualify for a classic γ-turn, the value of the mainchain dihedral angle φ of residue i + 1 has to be greater than 0°; for an inverse γ-turn it has to be less than 0°." The values that they report for psi are the means of the values that they found in the 54 proteins that they investigated.
• Calculate structure did not find classic γ-turns in many of the proteins in which Miner-White, et. al. had found the classic turns. This occurred because the DSSP identified those residues as the end of a helix.

In the SUMMARY for Myohemerytherin given below observe that all the segments that are labeled T (Turn) are composed of one, two, or three residues. One might suspect that the segments that have one residue, two residues, and three residues are the interior residues of 3-turns, 4-turn and 5-turns, respectively, and that the 3-turns are γ-turns and the 4-turns are β-turns. This is often the case, but in many cases it is not this simple. As illustrated below only one out of the five turns identified by DSSP in myohemerytherin have a two residue segment in the summary, but all five are β-turns. One reason for this is that the turns may partially overlap structures that have higher priority (In myohemerytherin they are helices.), so that a one residue segment in the summary represents a 4-turn. DSSP is described as only identifying a turn as a n-turn if the turn is isolated, but in practice this does not always happen. Another possibility could be that one turn is nested in a second one. This occurs with the three residue segment in the myohemerytherin summary. In order to identify which type of turn is actually present from these different possibilities, one needs to determine between which two residues the hbond occurs and thereby determine which type of n-turn is present.

Illustrations

The user is urged to use the above directions to open Jmol version 12 and to run the calculate structure and the accompanying commands so that the resulting display can be compared with the summary below. Without displaying the images generated by calculate structure and calculate hbonds structure the activities and comparisons described below can not be performed.

Myohemerytherin ()

• Locate any β-turns that are not being displayed by blue trace because there is not a hbond between the first and the last residues of the turn. Remember that you can confirm the presence of this type of β-turn by showing the presence of a Pro at position three. (Hover the cursor over the trace to display the name and number of the residues.) There are two such residues in myohemerytherin.
• The second T in the myohemerytherin summary is identified as segment A:68_A:69. serves to illustrate that most often 4-turns are identified in the summary by their two central residues. Most of the β-turns in myohemerythrin are exceptions to this generalization, but in glycogen phosphorylase (below) it does hold in the majority of cases. (Since calculate hbonds structure does not function in the green links of Proteopedia using Jmol 11.8, the calculate hbonds structure command must run in the console to display the hbonds after clicking a green link.) One can see that the hbond is between residues 67 and 70 making it a 4-turn, and the values for the phi and psi angles of residues 2 and 3 make it a class I β-turn. Notice, however, that part of residues 67 and 68 are colored white rather than blue.

The turn may overlap or partially overlap with a structure that has higher priority, so that a one residue segment in the summary could represent a 4-turn. Another possibility could be that one turn is nested in a second one. In order to clarify the specific nature of the turn one needs to determine between which two residues the hbond occurs and thereby which type of n-turn is present. Looking closely at a blue colored trace find the dashed line representing a hbond, and hovering over the trace where the dashed line meets the trace reveals the number of the residue that is hydrogen bonded. Go to the other end of the dashed line and determine the residue number at that end. The two numbers should be i and i + n. More detail on myohemerytherin's turns and their hbonds are given below with green links and description. Measuring the values of the torsional angles (Directions to display these angles) of the interior residues of the turn is another way of revealing the nature of the turns, because these values can be used to classify the turn as a β-turn or γ-turn. The description below identifies the β-turn class of each of the turns.

The first T is identified by a two residue segment, but the two residues, A:65_A:66, are the last two in the . Displaying the hbond shows that it is between residues A:63-A:66 which qualifies it for a 4-turn and the torsional angles classify it as type I β-turn. As shown by their coloration the first two residues also qualify as α-helix and are displayed as such since a helix has priority over a turn. The last T identifies a three residue segment indicating a . Calculate hbonds structure shows hbonds between 114 and 117 (4-turn and type II β-turn) and between 114 and 118 (5-turn). A β-turn is nested in a 5-turn. Residue 114 is part of the 310-helix so it is not colored blue.

The two remaining T's have one residue segments, and these could possibly be a 3-turn, but displaying with hbonds reveals that they are 4-turn with some of the other residues also being part of a helix which has priority over a turn. Both of these turns are class I β-turn.

There are two β-turns that are not detected by DSSP, and they are both class IVB which do not have a hbond. They are located at . Run calculate hbonds structure to confirm that there are no hbonds in these turns.

SUMMARY for Myohemerytherin:

G : A:12_A:14
H : A:19_A:37
H : A:41_A:64
T : A:65_A:66    
T : A:68_A:69     ; run the command calculate hbonds structure in the console to see the hbonds
H : A:70_A:85
T : A:86_A:86    
H : A:93_A:109
T : A:110_A:110    
G : A:111_A:114
T : A:115_A:117    
Key - H: α-helix; B: β-bridge; E: β-strand; G: 3₁₀-helix; I: π-helix; T: 3-, 4-, 5-turn; S: bend.

Show structure of

SUMMARY for Domain 2 of Chain A Glycogen Phosphorylase:
B : A:486_A:486
T : A:488_A:488
I : A:489_A:494
T : A:495_A:495
H : A:497_A:507
G : A:510_A:513
G : A:515_A:524
T : A:525_A:526
H : A:528_A:551
E : A:562_A:567
G : A:572_A:574
H : A:576_A:592
T : A:594_A:595
E : A:601_A:606
T : A:611_A:612
H : A:614_A:632
T : A:635_A:638
E : A:640_A:644
H : A:650_A:659
E : A:662_A:665
T : A:669_A:670
T : A:676_A:677
H : A:678_A:682
T : A:683_A:685
E : A:687_A:691
T : A:694_A:695
H : A:696_A:703
G : A:705_A:707
E : A:709_A:711
H : A:715_A:724
T : A:728_A:728
H : A:729_A:734
H : A:736_A:746
T : A:747_A:750
T : A:752_A:753
G : A:755_A:758
H : A:759_A:768
T : A:773_A:773
G : A:774_A:776
T : A:777_A:777
H : A:778_A:791
H : A:794_A:806
T : A:807_A:807
G : A:808_A:811
B : A:812_A:812
H : A:813_A:821
T : A:822_A:825