Recycling Corner/Alpha Helix Generator

RIBOZOME - an Alpha Helix Generator script

Creates an alpha helix from a user input string.

Jmol script by Ron Mignery with help from Angel Herráez

Script for Jmol application

#   RIBOZOME - Jmol script by Ron Mignery
#   v1.5 beta    12/03/2013
#
#   RIBOZOME takes a string message encoding an amino acid (aa) sequence
#   and generates a corresponding alpha helix one aa at a time from the
#   N terminus to the C terminus rotating the emerging helix as it goes.
#
#   The message is a string entered by the user at a prompt.
#   It may be typed in or pasted in and be of any length
#   If the message is prepended with <C>: (where C is any single letter)
#   then the chain is so labeled and separated from existing chains
#   if different from the first chain. 
#
#   The IUPAC/IUBMB 1 letter code is used:
#   A=ALAnine B=GLutam?X* C=CYSteine D=ASPartate E=GLUtamate
#   F=PHEnylalanine G=GLYcine H=HIStidine I=IsoLEucine K=LYSine
#   L=LEUcine M=METhionine N=ASparagiNe O=PYrroLysine*** P=PROline
#   Q=GLutamiNe R=ARGinine S=SERine T=THReonine U=SElenoCysteine
#   V=VALine W=TRyPtophan X=UNKnown Y=TYRosine Z=ASpar?X**
#     *Either GLU or GLN: drawn as GLN with chi3 flipped 
#    **Either ASP or ASN: drawn as ASN with chi3 flipped
#   ***Not supported: drawn as ALA

# The following constant values determine the pitch of the alpha helix
gPHI = -57    # Dihedral angle of N-CA bond (nominally -57)
gPSI = -47    # Dihedral angle of CA-C bond (nominally -47)
gOMEGA = 180    # Dihedral angle of the peptide bond (nominally 180)
gPEPTIDE_ANGLE = 110    # C-N-CA angle (nominally 110)
gPRO_BUMP = -10 # Psi angle change increment to N-3psi when N is Pro
gCHAIN = 'A'    # The chain id

# Lookup 3 letter code from 1 letter code
g3from1 = {"A":"ALA", "B":"GLX","C":"CYS", "D":"ASP","E":"GLU", "F":"PHE",
    "G":"GLY", "H":"HIS","I":"ILE", "K":"LYS","L":"LEU", "M":"MET",
    "N":"GLN", "O":"PYL","P":"PRO", "Q":"GLN","R":"ARG", "S":"SER",
    "T":"THR", "U":"SEC","V":"VAL", "W":"TRP","X":"UNK", "Y":"TYR", "Z":"ASX"}

# Generate PDB atom record
function genAtom(e, aa, i, xyz) {
    gA =  format("ATOM  %5d %4s %3s ", gN, e, aa )          
    gA +=  format("%s%4d    %8.3f", gCHAIN, i, xyz[1] )          
    gA +=  format("%8.3f%8.3f\n", xyz[2], xyz[3] )
    gN++
    return gA
};

# Generate a PDB amino acid record set
function genAA(i, aa) {    # Writes globals gA and gN

    # From constructed AAs
    var N0 = [0.0, 0.0, 0.0]
    var CA = [ 0.200, 1.174, 0.911 ]
    var C  = [ -1.110, 1.668, 1.425 ]
    var O  = [ -1.320, 1.693, 2.62 ]
    var CB = [ 1.062, 2.1950, 0.230 ]
    
    var G1 = [ 2.359, 1.607, -0.344]
    var G2 = [ 1.363, 3.336, 1.157 ]
    var D1 = [ 3.222, 2.656, -1.048 ]
    var D2 = [ 3.143, 0.904, 0.725 ]
    var E1 = [ 3.645, 3.749, -0.167 ]
    var E2 = [ 2.491, 3.234, -2.249 ]
    var Z  = [ 4.474, 4.857, -0.565 ]
    var H1 = [ 4.090, 6.173, -0.166 ]
    var H2 = [ 5.565, 4.707, -1.229 ]
    
    var D1dn = [ 2.955, 2.229, -1.250 ]
    var D2dn = [ 2.859, 0.552, 0.102 ]
    
    var E1eq = [ 3.821, 3.528, -0.382 ]
    var E2eq = [ 3.337, 2.634, -2.293 ]
    
    var Gp = [ 2.008, 1.24, -0.46 ]
    var Dp = [ 1.022, 0.213, -1.031 ]
    
    var Gfy  = [ 2.368, 1.471, -0.0152 ]
    var D1fy = [ 3.346, 1.524, 0.921 ]
    var D2fy = [ 2.493, 0.516, -1.151 ]
    var E1fy = [ 4.513, 0.615, 0.8244 ]
    var E2fy = [ 3.528, -0.336, -1.206 ]
    var Zfy  = [ 4.588, -0.285, -0.168 ]
    var Hfy = [ 5.738, -1.245, -0.233 ]
    
    var Ghw  = [ 2.406, 1.626, -0.134 ]
    var D1hw = [3.498, 1.936, 0.675]
    var D2hw = [ 2.713, 0.901, -1.211 ]
    var E1hw = [ 4.160, 0.518, -1.178 ]
    var E2hw = [ 4.622, 1.160, 0.0816 ]
    var E3hw = [ 3.789, 2.523, 1.944 ]
    var Z2hw = [ 5.973, 1.177, 0.689 ]
    var Z3hw = [ 5.014, 2.550, 2.503 ]
    var H2hw = [ 6.153, 1.846, 1.844 ]
    
    #N1 = [ 2.069, -2.122, -0.554]
    
    # Build PDB atom records common to all AAs
    var a3 = g3from1[aa]
    if (a3 = "") {
        a3 = "UNK"
    }
    print format("+ %s%d/%d", a3, i, gSeq.count + gResno)
    gA = genAtom(" N  ", a3, i, N0)
    gA += genAtom(" CA ", a3, i, CA)
    gA += genAtom(" C  ", a3, i, C)
    gA += genAtom(" O  ", a3, i, O)
    if ((aa != 'G') && (aa != 'X')) {
        gA += genAtom(" CB ", a3, i, CB)
    }

    # Now add AA specific atom records
    switch (aa) {
    case 'A' :
        break;
    case 'B' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" CD ", a3, i, D1)
        gA += genAtom(" OE1", a3, i, E2eq)    # GLN with Es switched
        gA += genAtom(" NE2", a3, i, E1eq)
        break;
    case 'C' :
        gA += genAtom(" SG ", a3, i, G2)
        break;
    case 'D' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" OD1", a3, i, D1dn)
        gA += genAtom(" OD2", a3, i, D2dn)
        break;
    case 'E' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" CD ", a3, i, D1)
        gA += genAtom(" OE1", a3, i, E1eq)
        gA += genAtom(" OE2", a3, i, E2eq)
        break;
    case 'F' :
        gA += genAtom(" CG ", a3, i, Gfy)
        gA += genAtom(" CD1", a3, i, D1fy)
        gA += genAtom(" CD2", a3, i, D2fy)
        gA += genAtom(" CE1", a3, i, E1fy)
        gA += genAtom(" CE2", a3, i, E2fy)
        gA += genAtom(" CZ ", a3, i, Zfy)
        break;
    case 'G' :
        break;
    case 'H' :
        gA += genAtom(" CG ", a3, i, Ghw)
        gA += genAtom(" ND1", a3, i, D1hw)
        gA += genAtom(" CD2", a3, i, D2hw)
        gA += genAtom(" CE1", a3, i, E2hw)
        gA += genAtom(" NE2", a3, i, E1hw)
        break;
    case 'I' :
        gA += genAtom(" CG1", a3, i, G1)
        gA += genAtom(" CG2", a3, i, G2)
        gA += genAtom(" CD1", a3, i, D1)
        break;
    case 'K' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" CD ", a3, i, D1)
        gA += genAtom(" CE ", a3, i, E1)
        gA += genAtom(" NZ ", a3, i, Z)
        break;
    case 'L' :
        gA += genAtom(" CG1", a3, i, G1)
        gA += genAtom(" CD1", a3, i, D1)
        gA += genAtom(" CD2", a3, i, D2)
        break;
    case 'M' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" SD ", a3, i, D1)
        gA += genAtom(" CE ", a3, i, E1)
        break;
    case 'N' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" OD1", a3, i, D1dn)
        gA += genAtom(" ND2", a3, i, D2dn)
        break;
    case 'P' :
        gA += genAtom(" CG ", a3, i, GP)
        gA += genAtom(" CD ", a3, i, DP)
        break;
    case 'Q' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" CD ", a3, i, D1)
        gA += genAtom(" OE1", a3, i, E1eq)
        gA += genAtom(" NE2", a3, i, E2eq)
        break;
    case 'R' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" CD ", a3, i, D1)
        gA += genAtom(" NE ", a3, i, E1)
        gA += genAtom(" CZ ", a3, i, Z)
        gA += genAtom(" NH1", a3, i, H1)
        gA += genAtom(" NH2", a3, i, H2)
        break;
    case 'S' :
        gA += genAtom(" OG ", a3, i, G1)
        break;
    case 'T' :
        gA += genAtom(" OG1", a3, i, G1)
        gA += genAtom(" CG2", a3, i, G2)
        break;
    case 'U' :
        gA += genAtom("SeG ", a3, i, G1)
        break;
    case 'V' :
        gA += genAtom(" CG1", a3, i, G1)
        gA += genAtom(" CG2", a3, i, G2)
        break;
    case 'W' :
        gA += genAtom(" CG ", a3, i, Ghw)
        gA += genAtom(" CD1", a3, i, D1hw)
        gA += genAtom(" CD2", a3, i, D2hw)
        gA += genAtom(" CE2", a3, i, E2hw)
        gA += genAtom(" NE1", a3, i, E1hw)
        gA += genAtom(" CE3", a3, i, E3hw)
        gA += genAtom(" CZ2", a3, i, Z2hw)
        gA += genAtom(" CZ3", a3, i, Z3hw)
        gA += genAtom(" CH2", a3, i, H2hw)
        break;
    case 'X' :
        gA += genAtom(" Xx ", a3, i, CB)
        break;
    case 'Y' :
        gA += genAtom(" CG ", a3, i, Gfy)
        gA += genAtom(" CD1", a3, i, D1fy)
        gA += genAtom(" CD2", a3, i, D2fy)
        gA += genAtom(" CE1", a3, i, E1fy)
        gA += genAtom(" CE2", a3, i, E2fy)
        gA += genAtom(" CZ ", a3, i, Zfy)
        gA += genAtom(" OH ", a3, i, Hfy)
        break;
    case 'Z' :
        gA += genAtom(" CG ", a3, i, G1)
        gA += genAtom(" OD1", a3, i, D2dn)    # ASN with Ds switched
        gA += genAtom(" ND2", a3, i, D1dn)
        break;
    default :
        break;
    }

    return gA
};

# Generate an alpha helix
function plicoGenAlpha(gSeq) {
    
    gSeq = gSeq%9999%0
    if (gSeq[2] == ':') {
        gCHAIN = gSeq[1]
        gSeq[1] = ' '
        gSeq[2] = ' '
        gSeq = gSeq%0
    }

    gN = all.count + 1 # global new N atom index

    # Find last linkable N if any
    gResno = 0    # global pre-existing AA count
    var pn = 1    # previous gN
    for (var i = all.count-1; i  > 0; i--) {
    
        # If found
        if (distance({atomno=i}, {0,0,0})  < 0.1) {
            pn = i
            
            # Delete O
            delete {atomIndex=@{all.atomIndex.max}}
            
            # If new chain, separate from existing chain
            if ({atomno=i}.chain != gCHAIN) {
                select all
                translateselected {2.069, -2.122, -0.554 } #N1
            }
            else {
                gResno = {atomno=i}.resno
            }
            break;
        }
    }

    # For each aa
    set appendnew false
    var nn = gN    # new N
    for (var i = 1; i <= gSeq.count; i++) {

        # Move polypeptide C to bond distance from new AA N
        select all
        fix none
        translateselected {2.069, -2.122, -0.554 } #N1

        # Gen AA
        gA = "data \"append aa\"\n"    # global PDB atom record
        gA += genAA(i + gResno, gSeq[i]);    # gN is updated in subroutine
        gA += "end \"append aa\""
        script inline @{gA}

        # If PRO ahead
        var pb = 0
        if ((gSeq.count - i) >= 2) {
            if (gSeq[i + 2] == 'P') {
                pb = gPRO_BUMP
            }
        }	

        # If not first AA
        if (nn > 1) {

            # Gen axis on new N perpendicular to the plane
            # containing atoms nn, pn+2 and nn+1
            var v1={atomno = @{pn+2}}.xyz - {atomno = nn}.xyz
            var v2={atomno = @{nn+1}}.xyz - {atomno = nn}.xyz
            var axis = cross(v1, v2)
            
            # Center on atom previous C
            axis += {atomno = @{pn+2}}.xyz

            # Rotate the polypeptide N on the new AA C to tetrahedral (nominally 110)
            select atomno < nn
            fix atomno >= nn
            rotateselected @axis {atomno = nn} @{gPEPTIDE_ANGLE - 69.3}
            
            # Make omega dihedral = gOMEGA (nominally 180)
            rotateselected {atomno=@{pn+2}} {atomno=nn} @{gOMEGA - 147.4}

            # Make the new phi dihedral = gPHI (nominally -57)
            rotateselected {atomno = nn} {atomno = @{nn+1}} @{gPHI - 8.7}

            # Make the old psi dihedral = gPSI (nominally -47)
            select atomno < @{pn+2} && atomno != @{pn+3}
            rotateselected {atomno=@{pn+1}} {atomno=@{pn+2}} @{gPSI + 33.4 + pb}
        }
        
        # Step new and previous N
        pn = nn
        nn = gN

        # Make the peptide bond
        connect
    }
    
    # Add terminal O
    gA = "data \"append aa\"\n"    # global PDB atom record
    gA += genAtom(" OXT", g3from1[gSeq[gResno+gSeq.count]],
        gResno+gSeq.count, [ -2.142, 2.057, 0.574])
    gA += "end \"append aa\""
    script inline @{gA}
    connect
    
    # Clean up
    connect ([UNK].CA) ([UNK].Xx and within(group, _1))
    select all
    fix none
    print format("%d atoms generated", gN-1)
}


function plicoGenPP {
    echo Generating Alpha Helix
    gPHI = -57
    gPSI = -47
    gOMEGA = 180
    gPEPTIDE_ANGLE = 110
    gPRO_BUMP = -10
    gCHAIN = 'A'
    g3from1 = {"A":"ALA", "B":"GLX","C":"CYS", "D":"ASP","E":"GLU", "F":"PHE",
        "G":"GLY", "H":"HIS","I":"ILE", "K":"LYS","L":"LEU", "M":"MET",
        "N":"GLN", "O":"PYL","P":"PRO", "Q":"GLN","R":"ARG", "S":"SER",
        "T":"THR", "U":"SEC","V":"VAL", "W":"TRP","X":"UNK", "Y":"TYR", "Z":"ASX"}
    
    # Get the sequence from the user
    gSeq = prompt("Enter AA sequence (1 char coded)", "")%9999%0
    if (gSeq.count > 0) {
        print format ("Sequence=%s  phi=%d  psi=%d", gSeq, gPHI, gPSI)
        plicoGenAlpha(gSeq)
    }
}

In a webpage

The main script is a small adaptation of the one above. Sequence input has been moved to the webpage. In addition, the helix parameters (which are fixed in the original script) may be changed in the page by a user. The model is generated and displayed in a Jmol object in the page (JmolApplet or JSmol HTML5 object).

The JSmol variant is not working yet. We need debugging the script, something in it fails to run properly in JSmol and no good helix is formed.

See it in action

Contributors

Remig, AngelHerraez