conformation
Class Dssp

java.lang.Object
  conformation.Dssp

public class Dssp

extends java.lang.Object

DSSP: Determine Secondary Structure of Proteins.

See: W. Kabsch and C. Sander, Biopolymers, 22, pp. 2577-2637 (1983).

The basic concept is as follows:

• find (per-residue) backbone "hydrogen bonds" H_b(i);
• make non-unique assignment of H_b(i) to basic secondary structure elements S_b(i) (turns and bridges);
• make non-unique assignment of S_b(i) to compound secondary structure elements S_c(i) (turns→helices, bridges→ladders→sheets);
• make unique secondary structure assignment using ad hoc priority rules.

From the abstract:

Cooperative seccondary structure is recognized as repeats of the elementary hydrogen-bonding patterns "turn" and "bridge". Repeating turns are "helices", repeating bridges are "ladders", connected ladders are "sheets".

One residue may be of more more than different secondary-structure elements. In order to avoid duplicates in the output, (ad hoc) priority rules are applied. Additionally, each secondary structure element has a one-character label.

From the article:

Structural overlaps are eliminated [...] by giving priority to H, B, E, G, I, T, S in this order, i.e., when several symbols coincide, the first one in this list is written.

So a bridge (B) is given priority over a ladder (E), which is clearly nonsense, since each ladder is made up of bridges. In the present program, the priorities of B and E are therefore inverted (see table below).

The following secondary structure elements are recognized (sorted by priority used in this program):

Element Name	Element Description	DSSP code	Priority (paper)	Priority (here)
α-helix	a.k.a. 4-helix	H	0	0
Extended Ladder	β-ladder of length > 1 ("extended"), both parallel and antiparallel.	E	2	1
Bridge	β-ladder of length 1, both parallel and antiparallel.	B	1	2
3,10-helix	a.k.a. 3-helix	G	3	3
π-helix	a.k.a. 5-helix	I	4	4
Turns	Non-helix turns or pieces of 3,10- or π-helix with less than minimal length.	T	5	5
Bend	A "bent" piece of backbone (see below).	S	6	6
unstructured	An "unstructured" piece of backbone (see below).		7	7

In short, the priority rules are as follows:

α-helix/4-helix > β-sheet/bridge > 3,10-helix/3-helix > π-helix/5-helix > H-bonded turn > bend

Author:

Vincent Kraeutler, Mika Kastenholz, Ulf Boerjesson

Field Summary

protected static int	acceptor
static int	alphaHelixT secondary structure codes substructure types (beta, helix, bend) must be contiguous and sorted by their respective priorities (see priority table).
static int	antiBetaBridgeT
static int	antiBetaSheetT
(package private) Particles	atoms
(package private) int[][]	bbAN the backbone atom numbers
static int	bendT
protected static int	C backbone atom indices
protected static int	CA
protected static int	donor hydrogen bond indices
static double	energyCutoff kabsch & sander hydrogen bond energy parameters
static double	f kabsch & sander hydrogen bond energy parameters
protected static int	H
(package private) int[]	Helix
protected static int	N
protected static int	O
static int	parallelBetaBridgeT
static int	parallelBetaSheetT
static int	piHelixT
static double	q1 kabsch & sander hydrogen bond energy parameters
static double	q1q2f
static double	q2 kabsch & sander hydrogen bond energy parameters
static int	threeTenHelixT
(package private) int[]	Turn
static int	turnT
static int	unstructeredT

Constructor Summary

Dssp(Particles atoms)

Method Summary

static int[]	assignUniqueSecondaryStructure(int[] helix4Res, int[] betaRes, int[] helix3Res, int[] helix5Res, int[] turnRes, int[] bendRes) every residue may have just one secondary structure type.
(package private) static void	fill(int[] stuff, int start, int end, int value) fill a part of vector stuff with value.
static int[][]	findBackBoneAtoms(Particles atoms) Find indices of the protein backbone atoms.
static int[]	findBends(double[][] cAlphaPos) Check if a residue is part of a bend.
static int[][]	findBridges(boolean[][] hbondMatrix) find bridges in the hydrogen bonding pattern.
static boolean[][]	findHbonds(int[][] bbaNum, double[][][] bbaPos, int[] rnum, int numRes) Rather than directly inspecting structural characteristics, the dssp algorithm looks at the "energy" of a hydrogen bond to determine if it's there.
static int[]	findHelices(int[] turns, int offset, int helixType) Turns may be parts of helices.
static int[]	findLaddersAndSheets(int[][] betaBridges) Find β-ladders and -sheets.
static int[]	findTurns(boolean[][] hbondMatrix, int offset) find turns in the hydrogen bonding pattern.
static double[][][]	getBackboneCoords(double[][] pos, int[][] bban) get the coords of the backbone atoms.
static double	hbEnergy(int ar, int dr, double[][][] bbap) The Kabsch-Sander "energy" of a hydrogen bond.
int[]	kabschSander() kabschSander, the non-static version
static int[]	kabschSander(int[][] backboneAtomNumbers, double[][][] backbonePositions, int[] residueNumbers, int numRes) this is the main dssp routine.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

atoms

Particles atoms

q1

public static final double q1

kabsch & sander hydrogen bond energy parameters

See Also:

Constant Field Values

q2

public static final double q2

kabsch & sander hydrogen bond energy parameters

See Also:

Constant Field Values

f

public static final double f

kabsch & sander hydrogen bond energy parameters

See Also:

Constant Field Values

energyCutoff

public static final double energyCutoff

kabsch & sander hydrogen bond energy parameters

See Also:

Constant Field Values

q1q2f

public static final double q1q2f

See Also:

Constant Field Values

C

protected static final int C

backbone atom indices

See Also:

Constant Field Values

CA

protected static final int CA

See Also:

Constant Field Values

H

protected static final int H

See Also:

Constant Field Values

N

protected static final int N

See Also:

Constant Field Values

O

protected static final int O

See Also:

Constant Field Values

donor

protected static final int donor

hydrogen bond indices

See Also:

Constant Field Values

acceptor

protected static final int acceptor

See Also:

Constant Field Values

alphaHelixT

public static final int alphaHelixT

secondary structure codes substructure types (beta, helix, bend) must be contiguous and sorted by their respective priorities (see priority table).

See Also:

Constant Field Values

parallelBetaBridgeT

public static final int parallelBetaBridgeT

See Also:

Constant Field Values

antiBetaBridgeT

public static final int antiBetaBridgeT

See Also:

Constant Field Values

parallelBetaSheetT

public static final int parallelBetaSheetT

See Also:

Constant Field Values

antiBetaSheetT

public static final int antiBetaSheetT

See Also:

Constant Field Values

threeTenHelixT

public static final int threeTenHelixT

See Also:

Constant Field Values

piHelixT

public static final int piHelixT

See Also:

Constant Field Values

turnT

public static final int turnT

See Also:

Constant Field Values

bendT

public static final int bendT

See Also:

Constant Field Values

unstructeredT

public static final int unstructeredT

See Also:

Constant Field Values

bbAN

int[][] bbAN

the backbone atom numbers

Turn

int[] Turn

Helix

int[] Helix

Constructor Detail

Dssp

public Dssp(Particles atoms)

Method Detail

kabschSander

public static int[] kabschSander(int[][] backboneAtomNumbers,
                                 double[][][] backbonePositions,
                                 int[] residueNumbers,
                                 int numRes)

this is the main dssp routine.

Parameters:

backboneAtomNumbers - the matrix of atom numbers of the C, CA, H, N, O atoms

backbonePositions - the corresponding positions

residueNumbers - the residue number of each atom (in the system, this is a bit confusing)

Returns:

the secondary structure of each residue

kabschSander

public int[] kabschSander()

kabschSander, the non-static version

Returns:

the secondary structure of each residue

See Also:

Dssp#kabschSander(int[][], double[][][], int[])

findBackBoneAtoms

public static int[][] findBackBoneAtoms(Particles atoms)

Find indices of the protein backbone atoms.

Backbone atoms are defined as having atom names ∈ {C, CA, N, O, H}. Only one atom type per residue is allowed. There are, however, amino acids where one of the atoms may be missing (i.e. proline does not have an "H"). In this case, a -1 is inserted for the atom number.

Parameters:

atoms - a particles instance

Returns:

the backbone atom numbers. return[C] contains the atom number of the C-atoms etc.

getBackboneCoords

public static double[][][] getBackboneCoords(double[][] pos,
                                             int[][] bban)

get the coords of the backbone atoms.

Parameters:

pos - the positions of all atoms

bban - the backbone atom numbers. bban[C] contains the indices of all C-atoms, etc.

Returns:

the positions of the backbone atoms. return[C] contains the positions of all C-atoms etc.

hbEnergy

public static double hbEnergy(int ar,
                              int dr,
                              double[][][] bbap)

The Kabsch-Sander "energy" of a hydrogen bond.

Parameters:

ar - the acceptor residue number

dr - the donor residue number

bbap - the backbone atom positions

Returns:

the energy

See Also:

Dssp#calcHbonds(int[][], double[][][], int[])

fill

static void fill(int[] stuff,
                 int start,
                 int end,
                 int value)

fill a part of vector stuff with value.

Parameters:

stuff -

start -

end -

value -

findHbonds

public static boolean[][] findHbonds(int[][] bbaNum,
                                     double[][][] bbaPos,
                                     int[] rnum,
                                     int numRes)

Rather than directly inspecting structural characteristics, the dssp algorithm looks at the "energy" of a hydrogen bond to determine if it's there.

Parameters:

bbaNum - the backbone atom numbers

bbaPos - the backbone atom positions

rnum - the residue numbers

Returns:

a list of [donors, acceptors]

See Also:

hbEnergy(int, int, double[][][])

findTurns

public static int[] findTurns(boolean[][] hbondMatrix,
                              int offset)

find turns in the hydrogen bonding pattern. turns are directed, i.e. they can only go from i to i+n, not from i to i-n, i and n positive.

findBridges

public static int[][] findBridges(boolean[][] hbondMatrix)

find bridges in the hydrogen bonding pattern.

parallel and anti-parallel bridges are assumed to be mutually exclusive, so we can do this in one go.

Parameters:

hbondMatrix -

Returns:

the bridging matrix

findHelices

public static int[] findHelices(int[] turns,
                                int offset,
                                int helixType)

Turns may be parts of helices.

From the paper:

A minimal [n]-helix is defined by two consecutive n-turns. For example, a 4-helix, of minimal length 4 from residues i to i+3, requires 4-turns at residues i-1 and i.

[...]

Note that nothing is required about the H-bond state of residues i+1 and i+2.

A helix consisting of n-turns is called a n-helix, with the following identifications:

• 3-helix: 3,10-helix
• 4-helix: α-helix
• 5-helix: π-helix

Notes:

• in the paper, 3-helices go from i to i+2, 4-helices go from i to i+3, but 5-helices go from i to i+5, which is not internally consistent and also not consistent with their tables. That last one is therefore interpreted as a typo, and we redefine 5-helices as going from i to i+4.
• we don't treat turn boundaries explicitly, so in order to identify a helix properly, rather than just asserting that i and i-1 are in the same kind of turn, we have to add the condition that i+n is also in that kind of turn, to avoid identifying a center of a turn as the beginning of a helix.

Parameters:

turns - the turns

Returns:

the helices

findLaddersAndSheets

public static int[] findLaddersAndSheets(int[][] betaBridges)

Find β-ladders and -sheets.

We do not differentiate between ladders (linked bridges) and sheets (linked ladders). So whenever we encounter β-bridges of the same type (parallel or antiparallel), this is identified as a ladder/sheet of that type.

Again, it is assumed that parallel and antiparallel β-bridges are mutually exclusive, so the order of assignment should not matter.

Parameters:

betaBridges -

Returns:

findBends

public static int[] findBends(double[][] cAlphaPos)

Check if a residue is part of a bend.

A bend is defined by the angle enclosed by three C_α-atoms:

γ(i) = γ(C_α(i - 2), C_α(i), C_α(i + 2))

Parameters:

cAlphaPos - the positions of the C_α-atoms

Returns:

the element of the returned array is unstructuredT if it's not in a bend, otherwise bendT

assignUniqueSecondaryStructure

public static int[] assignUniqueSecondaryStructure(int[] helix4Res,
                                                   int[] betaRes,
                                                   int[] helix3Res,
                                                   int[] helix5Res,
                                                   int[] turnRes,
                                                   int[] bendRes)

every residue may have just one secondary structure type.

This is enforced by first assigning each residue with the corresponding highest-priority secondary structure type, and then "scrubbing" the resulting assignment, i.e.

• single-bridge ladders are re-typed as bridges;
• helices shorter than the respective minimal lengths are re-typed as the corresponding turns.

Parameters:

helix4Res -

betaRes -

helix3Res -

helix5Res -

turnRes -

bendRes -

Returns:

an array containing the secondary structure code of each residue