def rotateSugar(antiSugarCoords, atoms, newChi = "syn"):
"""Given a sugar in anti configuration, rotate it to a new configuration (such as syn or high-anti).
ARGUMENTS:
antiSugarCoords - a dictionary containing a sugar in anti configuration in the format atomName: [x, y, z]
typically, this dictionary is generated by a BuildInitSugar object
atoms - a dictionary containing base coordinates in the format atomName: [x, y, z]
OPTIONAL ARGUMENTS:
newChi - the chi value to rotate the sugar to
may be "syn", "high-anti", or a number (in degrees)
defaults to "syn"
RETURNS:
synSugarCoords - a dictionary containing a sugar in syn configuration in the format atomName: [x, y, z]
"""
if newChi == "syn":
newChi = SYN_CHI
elif newChi == "high-anti":
newChi = HIGH_ANTI_CHI
#translate the sugar coordinates to the origin
synSugarCoords = dict([(atom, minus(coords, atoms["C1'"])) for (atom, coords) in antiSugarCoords.iteritems()])
#rotate the sugar
if atoms.has_key("N9"):
baseN = "N9"
else:
baseN = "N1"
axis = minus(atoms[baseN], atoms["C1'"])
synSugarCoords = rotateAtoms(synSugarCoords, axis, newChi - STARTING_CHI, atoms["C1'"])
return synSugarCoords
def buildSugar(self, baseAtoms, pucker):
"""Build a sugar of the specified pucker onto a base
ARGUMENTS:
baseAtoms - a dictionary of base atoms in the form atomName:[x, y, z]
Note that this dictionary MUST contain the C1' atom
pucker - the pucker of the sugar to be built (passed as an integer, either 2 or 3)
RETURNS:
coordinates for a sugar of the specified pucker in anti configuration with the base
"""
#fetch the appropriate sugar structure
if pucker == 3:
sugarAtoms = self.__c3pAtoms
elif pucker == 2:
sugarAtoms = self.__c2pAtoms
else:
raise "BuildInitSugar called with unrecognized pucker: " + str(pucker)
#I don't have to worry about accidentally modifying the original atom dictionaries, since
#rotateAtoms effectively makes a deep copy
#figure out which base atoms to use for alignment
if baseAtoms.has_key("N9"):
Natom = "N9"
Catom = "C4"
else:
Natom = "N1"
Catom = "C2"
#rotate the sugar so the glycosidic bond is at the appropriate angle
#first, calculate an axis for this rotation
translatedBaseN = minus(baseAtoms[Natom], baseAtoms["C1'"])
sugarN = sugarAtoms[Natom]
axis = crossProd(sugarN, translatedBaseN)
angle = torsion(translatedBaseN, axis, (0,0,0), sugarN)
#if either angle or magnitude(axis) is 0, then the glycosidic bond is already oriented appropriately
if not(angle == 0 or magnitude(axis) == 0):
sugarAtoms = rotateAtoms(sugarAtoms, axis, angle)
#next, rotate the sugar so that chi is appropriate
translatedBaseC = minus(baseAtoms[Catom], baseAtoms["C1'"])
curChi = torsion(translatedBaseC, translatedBaseN, [0,0,0], sugarAtoms["O4'"])
sugarAtoms = rotateAtoms(sugarAtoms, translatedBaseN, curChi - STARTING_CHI)
#remove the unnecessary atoms from the sugarAtoms dict
del sugarAtoms["N1"]
del sugarAtoms["N9"]
#translate the sugar to the C1' atom of the base
sugarAtoms = dict([(atom, plus(coords, baseAtoms["C1'"])) for (atom, coords) in sugarAtoms.iteritems()])
return sugarAtoms
def __readBases(self, filename):
"""Read nucleotide structures from the specified PDB file
ARGUMENTS:
filename - the name of a PDB file containing structures of all four bases
RETURNS:
struc - a dictionary of file strucutres in the form base type => atom name => coordinates
"""
input = open(filename, 'r')
struc = dict(A = dict(), C = dict(), G = dict(), U = dict())
#read in the PDB file
for curline in input.readlines():
if curline[0:6] != "ATOM ":
continue
atomName = curline[12:16].strip()
resName = curline[17:20].strip()
x = float(curline[30:38])
y = float(curline[38:46])
z = float(curline[46:54])
#convert the atom name to PDB3 format
#we'll need to convert it back to PDB2 later, since that's what Coot uses, but internally, RCrane uses PDB3
atomName = atomName.replace("*", "'")
struc[resName][atomName] = [x,y,z]
input.close()
#translate each base so that the C1' atom is at [0,0,0]
for curRes in struc.keys():
c1loc = struc[curRes]["C1'"]
for curAtom in struc[curRes].keys():
struc[curRes][curAtom] = minus(struc[curRes][curAtom], c1loc)
return struc
def __readBases(self, filename):
"""Read nucleotide structures from the specified PDB file
ARGUMENTS:
filename - the name of a PDB file containing structures of all four bases
RETURNS:
struc - a dictionary of file strucutres in the form base type => atom name => coordinates
"""
input = open(filename, 'r')
struc = dict(A = dict(), C = dict(), G = dict(), U = dict())
#read in the PDB file
for curline in input.readlines():
if curline[0:6] != "ATOM ":
continue
atomName = curline[12:16].strip()
resName = curline[17:20].strip()
x = float(curline[30:38])
y = float(curline[38:46])
z = float(curline[46:54])
#convert the atom name to PDB3 format
#we'll need to convert it back to PDB2 later, since that's what Coot uses, but internally, RCrane uses PDB3
atomName = atomName.replace("*", "'")
struc[resName][atomName] = [x,y,z]
#translate each base so that the C1' atom is at [0,0,0]
for curRes in struc.keys():
c1loc = struc[curRes]["C1'"]
for curAtom in struc[curRes].keys():
struc[curRes][curAtom] = minus(struc[curRes][curAtom], c1loc)
return struc
def flipBase(self, curBase):
"""Flip the base anti/syn
ARGUMENTS:
curBase - the current base object in the form [baseType, baseCoordinates]
RETURNS:
the base object with rotated coordinates
NOTE:
This function does not necessarily simply rotate about chi. When flipping a purine, it also adjusts
the glycosidic bond position so that it the base a chance of staying in the density
"""
(baseType, curBaseCoords) = curBase
curC1coords = curBaseCoords["C1'"]
newBaseCoords = {}
#translate the base to the origin
for atomName, curAtomCoords in curBaseCoords.items():
newBaseCoords[atomName] = minus(curBaseCoords[atomName], curC1coords)
#the rotation axis is the same as the alignment vector for mutating the base
#for pyrimidines, the axis is C1'-C4
#for purines, the axis is from C1' to the center of the C4-C5 bond
axis = None
if baseType == "C" or baseType == "U":
axis = newBaseCoords["C4"]
else:
axis = plus(newBaseCoords["C4"], newBaseCoords["C5"])
axis = scalarProd(1.0/2.0, axis)
#rotate the base 180 degrees about the axis
newBaseCoords = rotateAtoms(newBaseCoords, axis, 180, curC1coords)
return [baseType, newBaseCoords]
def flipBase(self, curBase):
"""Flip the base anti/syn
ARGUMENTS:
curBase - the current base object in the form [baseType, baseCoordinates]
RETURNS:
the base object with rotated coordinates
NOTE:
This function does not necessarily simply rotate about chi. When flipping a purine, it also adjusts
the glycosidic bond position so that it the base a chance of staying in the density
"""
(baseType, curBaseCoords) = curBase
curC1coords = curBaseCoords["C1'"]
newBaseCoords = {}
#translate the base to the origin
for atomName, curAtomCoords in curBaseCoords.items():
newBaseCoords[atomName] = minus(curBaseCoords[atomName], curC1coords)
#the rotation axis is the same as the alignment vector for mutating the base
#for pyrimidines, the axis is C1'-C4
#for purines, the axis is from C1' to the center of the C4-C5 bond
axis = None
if baseType == "C" or baseType == "U":
axis = newBaseCoords["C4"]
else:
axis = plus(newBaseCoords["C4"], newBaseCoords["C5"])
axis = scalarProd(1.0/2.0, axis)
#rotate the base 180 degrees about the axis
newBaseCoords = rotateAtoms(newBaseCoords, axis, 180, curC1coords)
return [baseType, newBaseCoords]
def __rotateSugarCenter (self, phos5, phos3, sugarCenter):
"""rotate the sugar center by 360 degrees in ROTATE_SUGAR_INTERVAL increments
ARGUMENTS:
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
sugarCenter - the coordinates of the sugar center to be rotated
RETURNS:
rotatedPoints - a list of the rotated points, each listed as [x, y, z, rotation angle]
"""
#calculate a unit vector along the rotation axis
axis = minus(phos3, phos5)
axis = scalarProd(axis, 1/magnitude(axis))
#perform the rotation
(u, v, w) = axis
(x, y, z) = minus(sugarCenter, phos5)
#make sure that the original location appears on the list with a rotation value of 0
sugarCenterRot = sugarCenter + [0]
rotatedPoints = [sugarCenterRot]
curAngle = SUGAR_ROTATION_INTERVAL
while curAngle < (2*pi - 0.5*SUGAR_ROTATION_INTERVAL):
cosTheta = cos(curAngle)
sinTheta = sin(curAngle)
a = u*x + v*y + w*z;
newX = a*u + (x-a*u)*cosTheta + (v*z-w*y)*sinTheta + phos5[0];
newY = a*v + (y-a*v)*cosTheta + (w*x-u*z)*sinTheta + phos5[1];
newZ = a*w + (z-a*w)*cosTheta + (u*y-v*x)*sinTheta + phos5[2];
rotatedPoints.append([newX, newY, newZ, curAngle])
curAngle += SUGAR_ROTATION_INTERVAL
return rotatedPoints
def __rotateSugarCenter (self, phos5, phos3, sugarCenter):
"""rotate the sugar center by 360 degrees in ROTATE_SUGAR_INTERVAL increments
ARGUMENTS:
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
sugarCenter - the coordinates of the sugar center to be rotated
RETURNS:
rotatedPoints - a list of the rotated points, each listed as [x, y, z, rotation angle]
"""
#calculate a unit vector along the rotation axis
axis = minus(phos3, phos5)
axis = scalarProd(axis, 1/magnitude(axis))
#perform the rotation
(u, v, w) = axis
(x, y, z) = minus(sugarCenter, phos5)
#make sure that the original location appears on the list with a rotation value of 0
sugarCenterRot = sugarCenter + [0]
rotatedPoints = [sugarCenterRot]
curAngle = SUGAR_ROTATION_INTERVAL
while curAngle < (2*pi - 0.5*SUGAR_ROTATION_INTERVAL):
cosTheta = cos(curAngle)
sinTheta = sin(curAngle)
a = u*x + v*y + w*z;
newX = a*u + (x-a*u)*cosTheta + (v*z-w*y)*sinTheta + phos5[0];
newY = a*v + (y-a*v)*cosTheta + (w*x-u*z)*sinTheta + phos5[1];
newZ = a*w + (z-a*w)*cosTheta + (u*y-v*x)*sinTheta + phos5[2];
rotatedPoints.append([newX, newY, newZ, curAngle])
curAngle += SUGAR_ROTATION_INTERVAL
return rotatedPoints
def __init__(self, c3pStruc, c2pStruc):
"""Initialize a BuildInitSugar object.
ARGUMENTS:
c3pstruc - the filename for a PDB file containing a C3'-endo sugar
c2pstruc - the filename for a PDB file containing a C2'-endo sugar
RETURNS:
an initialized BuildInitSugar object
"""
self.c3pStrucFilename = c3pStruc
self.c2pStrucFilename = c2pStruc
self.__c3pAtoms = readSugarPDB(c3pStruc)
self.__c2pAtoms = readSugarPDB(c2pStruc)
#translate the sugars so that the C1' atom is at the origin (so we don't have to do it every time we align a sugar)
for curSugar in (self.__c3pAtoms, self.__c2pAtoms):
c1p = curSugar["C1'"]
del curSugar["C1'"] #delete the C1' atom, since it's going to be zeroed anyway
#(and we don't want to return it since it doesn't need to be added to the pseudoMolecule object)
for (curAtom, curCoords) in curSugar.iteritems():
curSugar[curAtom] = minus(curCoords, c1p)
def buildPhosOxy(curResAtoms, prevResAtoms):
"""Calculate non-bridging phosphoryl oxygen coordinates using the coordinates of the current and previous nucleotides
ARGUMENTS:
curResAtoms - a dictionary of the current nucleotide coordinates (i.e. the nucleotide to build the phosphoryl oxygens on) in the format atomName: [x, y, z]
prevResAtoms - a dictionary of the previous nucleotide coordinates in the format atomName: [x, y, z]
RETURNS:
phosOxyCoords - a dictionary of the phosphoryl oxygen coordinates in the format atomName: [x, y, z]
or None if the residue is missing the P, O5', or O3' atoms
"""
try:
P = curResAtoms ["P"]
O5 = curResAtoms ["O5'"]
O3 = prevResAtoms["O3'"]
except KeyError:
return None
#calculate a line from O5' to O3'
norm = minus(O5, O3)
#calculate the intersection of a plane (with normal $norm and point $P) and a line (from O5' to O3')
#using formula from http://local.wasp.uwa.edu.au/~pbourke/geometry/planeline/
# norm dot (P - O3)
# i = ------------------------
# norm dot (O5 - O3)
#intersecting point = O3 + i(O5 - O3)
i = dotProd(norm, minus(P, O3)) / dotProd(norm, minus(O5, O3))
interPoint = plus(O3, scalarProd(i, minus(O5, O3)))
#move $interPoint so that the distance from $P to $interPoint is 1.485 (the length of the P-OP1 bond)
#we also reflect the point about P
PIline = minus(P, interPoint) #here's is where the reflection occurs, because we do $P-$interPoint instead of $interPoint-$P
#scaledPoint = scalarProd(1/magnitude(PIline) * PHOSBONDLENGTH, PIline)
scaledPoint = normalize(PIline, PHOSBONDLENGTH)
#to get the new point location, we would do P + scaledPoint
#but we need to rotate the point first before translating it back
#rotate this new point by 59.8 and -59.8 degrees to determine the phosphoryl oxygen locations
#we rotate about the axis defined by $norm
angle = radians(PHOSBONDANGLE / 2)
(x, y, z) = scaledPoint
#unitnorm = scalarProd( 1/magnitude(norm), norm)
unitnorm = normalize(norm)
(u, v, w) = unitnorm
a = u*x + v*y + w*z
phosOxyCoords = {}
for (atomName, theta) in (("OP1", angle), ("OP2", -angle)):
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation, and then add $P to the coordinates
newX = a*u + (x-a*u)*cosTheta + (v*z-w*y)*sinTheta + P[0]
newY = a*v + (y-a*v)*cosTheta + (w*x-u*z)*sinTheta + P[1]
newZ = a*w + (z-a*w)*cosTheta + (u*y-v*x)*sinTheta + P[2]
phosOxyCoords[atomName] = [newX, newY, newZ]
return phosOxyCoords
def mutateBase(self, curBase, newBaseType):
"""Change the base type.
ARGUMENTS:
curBase - the current base object in the form [baseType, baseCoordinates]
newBaseType - the base type to mutate to
RETURNS:
baseObj - a list of [baseType, baseCoordinates]
"""
(curBaseType, curBaseCoords) = curBase
#calculate the vectors used to align the old and new bases
#for pyrimidines, the vector is C1'-C4
#for purines, the vector is from C1' to the center of the C4-C5 bond
curAlignmentVector = None
if curBaseType == "C" or curBaseType == "U":
curAlignmentVector = minus(curBaseCoords["C4"], curBaseCoords["C1'"])
else:
curBaseCenter = plus(curBaseCoords["C4"], curBaseCoords["C5"])
curBaseCenter = scalarProd(1.0/2.0, curBaseCenter)
curAlignmentVector = minus(curBaseCenter, curBaseCoords["C1'"])
#calculate the alignment vector for the new base
newBaseCoords = self.__baseStrucs[newBaseType]
newAlignmentVector = None
if newBaseType == "C" or newBaseType == "U":
newAlignmentVector = newBaseCoords["C4"]
else:
newAlignmentVector = plus(newBaseCoords["C4"], newBaseCoords["C5"])
newAlignmentVector = scalarProd(1.0/2.0, newAlignmentVector)
#calculate the angle between the alignment vectors
rotationAngle = -angle(curAlignmentVector, [0,0,0], newAlignmentVector)
axis = crossProd(curAlignmentVector, newAlignmentVector)
#rotate the new base coordinates
newBaseCoords = rotateAtoms(newBaseCoords, axis, rotationAngle)
#calculate the normals of the base planes
curNormal = None
if curBaseType == "C" or curBaseType == "U":
curNormal = crossProd(minus(curBaseCoords["N3"], curBaseCoords["N1"]), minus(curBaseCoords["C6"], curBaseCoords["N1"]))
else:
curNormal = crossProd(minus(curBaseCoords["N3"], curBaseCoords["N9"]), minus(curBaseCoords["N7"], curBaseCoords["N9"]))
newNormal = None
if newBaseType == "C" or newBaseType == "U":
newNormal = crossProd(minus(newBaseCoords["N3"], newBaseCoords["N1"]), minus(newBaseCoords["C6"], newBaseCoords["N1"]))
else:
newNormal = crossProd(minus(newBaseCoords["N3"], newBaseCoords["N9"]), minus(newBaseCoords["N7"], newBaseCoords["N9"]))
#calculate the angle between the normals
normalAngle = -angle(curNormal, [0,0,0], newNormal);
normalAxis = crossProd(curNormal, newNormal)
#rotate the new base coordinates so that it falls in the same plane as the current base
#and translate the base to the appropriate location
newBaseCoords = rotateAtoms(newBaseCoords, normalAxis, normalAngle, curBaseCoords["C1'"])
return [newBaseType, newBaseCoords]
def findBase(self, mapNum, sugar, phos5, phos3, baseType, direction = 3):
"""Rotate the sugar center by 360 degrees in ROTATE_SUGAR_INTERVAL increments
ARGUMENTS:
mapNum - the molecule number of the Coot map to use
sugar - the coordinates of the C1' atom
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
baseType - the base type (A, C, G, or U)
OPTIONAL ARGUMENTS:
direction - which direction are we tracing the chain
if it is 5 (i.e. 3'->5'), then phos5 and phos3 will be flipped
all other values will be ignored
defaults to 3 (i.e. 5'->3')
RETURNS:
baseObj - a list of [baseType, baseCoordinates]
"""
if direction == 5:
(phos5, phos3) = (phos3, phos5)
#calculate the bisector of the phos-sugar-phos angle
#first, calculate a normal to the phos-sugar-phos plane
sugarPhos5Vec = minus(phos5, sugar)
sugarPhos3Vec = minus(phos3, sugar)
normal = crossProd(sugarPhos5Vec, sugarPhos3Vec)
normal = scalarProd(normal, 1.0/magnitude(normal))
phosSugarPhosAngle = angle(phos5, sugar, phos3)
bisector = rotate(sugarPhos5Vec, normal, phosSugarPhosAngle/2.0)
#flip the bisector around (so it points away from the phosphates) and scale its length to 5 A
startingBasePos = scalarProd(bisector, -1/magnitude(bisector))
#rotate the base baton by 10 degree increments about half of a sphere
rotations = [startingBasePos] #a list of coordinates for all of the rotations
for curTheta in range(-90, -1, 10) + range(10, 91, 10):
curRotation = rotate(startingBasePos, normal, curTheta)
rotations.append(curRotation) #here's where the phi=0 rotation is accounted for
for curPhi in range(-90, -1, 10) + range(10, 91, 10):
rotations.append(rotate(curRotation, startingBasePos, curPhi))
#test electron density along all base batons
for curBaton in rotations:
curDensityTotal = 0
densityList = []
for i in range(1, 9):
(x, y, z) = plus(sugar, scalarProd(i/2.0, curBaton))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
densityList.append(curPointDensity)
curBaton.append(curDensityTotal) #the sum of the density (equivalent to the mean for ordering purposes)
curBaton.append(median(densityList)) #the median of the density
curBaton.append(min(densityList)) #the minimum of the density
#find the baton with the max density (as measured using the median)
#Note that we ignore the sum and minimum of the density. Those calculations could be commented out,
# but they may be useful at some point in the future. When we look at higher resolutions maybe?
# Besides, they're fast calculations.)
baseDir = max(rotations, key = lambda x: x[4])
#rotate the stock base+sugar structure to align with the base baton
rotationAngle = angle(self.__baseStrucs["C"]["C4"], [0,0,0], baseDir)
axis = crossProd(self.__baseStrucs["C"]["C4"], baseDir[0:3])
orientedBase = rotateAtoms(self.__baseStrucs["C"], axis, rotationAngle)
#rotate the base about chi to find the best fit to density
bestFitBase = None
maxDensity = -999999
for curAngle in range(0,360,5):
rotatedBase = rotateAtoms(orientedBase, orientedBase["C4"], curAngle, sugar)
curDensity = 0
for curAtom in ["N1", "C2", "N3", "C4", "C5", "C6"]:
curDensity += density_at_point(mapNum, rotatedBase[curAtom][0], rotatedBase[curAtom][1], rotatedBase[curAtom][2])
#this is "pseudoChi" because it uses the 5' phosphate in place of the O4' atom
pseudoChi = torsion(phos5, sugar, rotatedBase["N1"], rotatedBase["N3"])
curDensity *= self.__pseudoChiInterp.interp(pseudoChi)
if curDensity > maxDensity:
maxDensity = curDensity
bestFitBase = rotatedBase
baseObj = ["C", bestFitBase]
#mutate the base to the appropriate type
if baseType != "C":
baseObj = self.mutateBase(baseObj, baseType)
return baseObj
def findSugar(self, mapNum, phos5, phos3):
"""find potential C1' locations between the given 5' and 3' phosphate coordinates
ARGUMENTS:
mapNum - the molecule number of the Coot map to use
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
RETURNS:
sugarMaxima - a list of potential C1' locations, each listed as [x, y, z, score]
"""
#calculate the distance between the two phosphatse
phosPhosDist = dist(phos5, phos3)
#calculate a potential spot for the sugar based on the phosphate-phosphate distance
#projDist is how far along the 3'P-5'P vector the sugar center should be (measured from the 3'P)
#perpDist is how far off from the 3'P-5'P vector the sugar center should be
#these functions are for the sugar center, which is what we try to find here
#since it will be more in the center of the density blob
perpDist = -0.185842*phosPhosDist**2 + 1.62296*phosPhosDist - 0.124146
projDist = 0.440092*phosPhosDist + 0.909732
#if we wanted to find the C1' instead of the sugar center, we'd use these functions
#however, finding the C1' directly causes our density scores to be less accurate
#so we instead use the functions above to find the sugar center and later adjust our
#coordinates to get the C1' location
#perpDist = -0.124615*phosPhosDist**2 + 0.955624*phosPhosDist + 2.772573
#projDist = 0.466938*phosPhosDist + 0.649833
#calculate the normal to the plane defined by 3'P, 5'P, and a dummy point
normal = crossProd([10,0,0], minus(phos3, phos5))
#make sure the magnitude of the normal is not zero (or almost zero)
#if it is zero, that means that our dummy point was co-linear with the 3'P-5'P vector
#and we haven't calculated a normal
#if the magnitude is almost zero, then the dummy point was almost co-linear and we have to worry about rounding error
#in either of those cases, just use a different dummy point
#they should both be incredibly rare cases, but it doesn't hurt to be safe
if magnitude(normal) < 0.001:
#print "Recalculating normal"
normal = crossProd([0,10,0], minus(phos5, phos3))
#scale the normal to the length of perpDist
perpVector = scalarProd(normal, perpDist/magnitude(normal))
#calculate the 3'P-5'P vector and scale it to the length of projDist
projVector = minus(phos3, phos5)
projVector = scalarProd(projVector, projDist/magnitude(projVector))
#calculate a possible sugar location
sugarLoc = plus(phos5, projVector)
sugarLoc = plus(sugarLoc, perpVector)
#rotate the potential sugar location around the 3'P-5'P vector to generate a list of potential sugar locations
sugarRotationPoints = self.__rotateSugarCenter(phos5, phos3, sugarLoc)
#test each potential sugar locations to find the one with the best electron density
for curSugarLocFull in sugarRotationPoints:
curSugarLoc = curSugarLocFull[0:3] #the rotation angle is stored as curSugarLocFull[4], so we trim that off for curSugarLoc
curDensityTotal = 0
#densityList = [] #if desired, this could be used to generate additional statistics on the density (such as the median or quartiles)
#check density along the 5'P-sugar vector
phosSugarVector = minus(curSugarLoc, phos5)
phosSugarVector = scalarProd(phosSugarVector, 1.0/(DENSITY_CHECK_POINTS+1))
for i in range(1, DENSITY_CHECK_POINTS+1):
(x, y, z) = plus(phos5, scalarProd(i, phosSugarVector))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
#check at the sugar center
(x, y, z) = curSugarLoc
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
#check along the sugar-3'P vector
sugarPhosVector = minus(phos3, curSugarLoc)
sugarPhosVector = scalarProd(sugarPhosVector, 1.0/(DENSITY_CHECK_POINTS+1))
for i in range(1, DENSITY_CHECK_POINTS+1):
(x, y, z) = plus(curSugarLoc, scalarProd(i, sugarPhosVector))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
curSugarLocFull.append(curDensityTotal)
#curSugarLocFull.extend([curDensityTotal, median(densityList), lowerQuartile(densityList), min(densityList)])#, pointList])
#find all the local maxima
sugarMaxima = []
curPeakHeight = sugarRotationPoints[-1][4]
nextPeakHeight = sugarRotationPoints[0][4]
sugarRotationPoints.append(sugarRotationPoints[0]) #copy the first point to the end so that we can properly check the last point
for i in range(0, len(sugarRotationPoints)-1):
prevPeakHeight = curPeakHeight
curPeakHeight = nextPeakHeight
nextPeakHeight = sugarRotationPoints[i+1][4]
if prevPeakHeight < curPeakHeight and curPeakHeight >= nextPeakHeight:
sugarMaxima.append(sugarRotationPoints[i])
#sort the local maxima by their density score
sugarMaxima.sort(key = lambda x: x[4], reverse = True)
#adjust all the sugar center coordinates so that they represent the corresponding C1' coordinates
for i in range(0, len(sugarMaxima)):
curSugar = sugarMaxima[i][0:3]
#rotate a vector 148 degrees from the phosphate bisector
phosAngle = angle(phos5, curSugar, phos3)
phos5vector = minus(phos5, curSugar)
axis = crossProd(minus(phos3, curSugar), phos5vector)
axis = scalarProd(axis, 1/magnitude(axis))
c1vec = rotate(phos5vector, axis, 148.539123-phosAngle/2)
#scale the vector to the appropriate length
c1vec = scalarProd(c1vec, 1.235367/magnitude(c1vec))
#rotate the vector about the phosphate bisector
phosBisectorAxis = rotate(phos5vector, axis, -phosAngle/2)
phosBisectorAxis = scalarProd(phosBisectorAxis, 1/magnitude(phosBisectorAxis))
c1vec = rotate(c1vec, phosBisectorAxis, -71.409162)
sugarMaxima[i][0:3] = plus(c1vec, curSugar)
return sugarMaxima
def buildInitOrTerminalPhosOxy(curResAtoms, prevResAtoms = None):
"""build phosphoryl oxygens using only the O3' or O5'atom (intended for the first or last nucleotide of a chain/segment)
ARGUMENTS:
curResAtoms - a dictionary of the current nucleotide coordinates (i.e. the nucleotide to build the phosphoryl oxygens on) in the format atomName: [x, y, z]
this dictionary must contain at least the phosphate
OPTIONAL ARGUMENTS:
prevResAtoms - a dictionary of the previous nucleotide coordinates in the format atomName: [x, y, z]
if provided, the curResAtoms["P"] and prevResAtoms["O3'"] will be used to place the phosphoryl oxygens
if not provided, the curResAtoms["P"] and curResAtoms["O5'"]
RETURNS:
phosOxyCoords - a dictionary of the phosphoryl oxygen coordinates in the format atomName: [x, y, z]
or None if the residue is missing the necessary atoms
"""
try:
P = curResAtoms ["P"]
if prevResAtoms is not None:
O = prevResAtoms["O3'"]
C = prevResAtoms["C3'"]
else:
O = curResAtoms["O5'"]
C = curResAtoms["C5'"]
except KeyError:
return None
#place atom along the P-O5' bond that is the appropriate distance from P
phosOxy = minus(O, P)
phosOxy = normalize(phosOxy, PHOSBONDLENGTH)
#define plane with C5'-O5'-P
norm = crossProd( minus(C, O), minus(P, O))
norm = normalize(norm)
#rotate dummy atom in plane about P by INITPHOSANGLE (which is the appropriate O5'-OP1 angle)
(x, y, z) = phosOxy
(u, v, w) = norm
theta = -radians(INITPHOSANGLE) #use the negative angle so that we rotate away from the C5'
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation
a = u*x + v*y + w*z
phosOxy[0] = a*u + (x-a*u)*cosTheta + (v*z-w*y)*sinTheta
phosOxy[1] = a*v + (y-a*v)*cosTheta + (w*x-u*z)*sinTheta
phosOxy[2] = a*w + (z-a*w)*cosTheta + (u*y-v*x)*sinTheta
#rotate dummy atom about O5'-P axis by 59.8 and -59.8 degrees
norm = minus(O, P)
norm = normalize(norm)
(x, y, z) = phosOxy
(u, v, w) = norm
angle = radians(PHOSBONDANGLE / 2)
phosOxyCoords = {}
for (atomName, theta) in (("OP1", angle), ("OP2", -angle)):
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation, and then add $P to the coordinates
newX = a*u + (x-a*u)*cosTheta + (v*z-w*y)*sinTheta + P[0]
newY = a*v + (y-a*v)*cosTheta + (w*x-u*z)*sinTheta + P[1]
newZ = a*w + (z-a*w)*cosTheta + (u*y-v*x)*sinTheta + P[2]
phosOxyCoords[atomName] = [newX, newY, newZ]
return phosOxyCoords
def buildPhosOxy(curResAtoms, prevResAtoms):
"""Calculate non-bridging phosphoryl oxygen coordinates using the coordinates of the current and previous nucleotides
ARGUMENTS:
curResAtoms - a dictionary of the current nucleotide coordinates (i.e. the nucleotide to build the phosphoryl oxygens on) in the format atomName: [x, y, z]
prevResAtoms - a dictionary of the previous nucleotide coordinates in the format atomName: [x, y, z]
RETURNS:
phosOxyCoords - a dictionary of the phosphoryl oxygen coordinates in the format atomName: [x, y, z]
or None if the residue is missing the P, O5', or O3' atoms
"""
try:
P = curResAtoms["P"]
O5 = curResAtoms["O5'"]
O3 = prevResAtoms["O3'"]
except KeyError:
return None
#calculate a line from O5' to O3'
norm = minus(O5, O3)
#calculate the intersection of a plane (with normal $norm and point $P) and a line (from O5' to O3')
#using formula from http://local.wasp.uwa.edu.au/~pbourke/geometry/planeline/
# norm dot (P - O3)
# i = ------------------------
# norm dot (O5 - O3)
#intersecting point = O3 + i(O5 - O3)
i = dotProd(norm, minus(P, O3)) / dotProd(norm, minus(O5, O3))
interPoint = plus(O3, scalarProd(i, minus(O5, O3)))
#move $interPoint so that the distance from $P to $interPoint is 1.485 (the length of the P-OP1 bond)
#we also reflect the point about P
PIline = minus(
P, interPoint
) #here's is where the reflection occurs, because we do $P-$interPoint instead of $interPoint-$P
#scaledPoint = scalarProd(1/magnitude(PIline) * PHOSBONDLENGTH, PIline)
scaledPoint = normalize(PIline, PHOSBONDLENGTH)
#to get the new point location, we would do P + scaledPoint
#but we need to rotate the point first before translating it back
#rotate this new point by 59.8 and -59.8 degrees to determine the phosphoryl oxygen locations
#we rotate about the axis defined by $norm
angle = radians(PHOSBONDANGLE / 2)
(x, y, z) = scaledPoint
#unitnorm = scalarProd( 1/magnitude(norm), norm)
unitnorm = normalize(norm)
(u, v, w) = unitnorm
a = u * x + v * y + w * z
phosOxyCoords = {}
for (atomName, theta) in (("OP1", angle), ("OP2", -angle)):
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation, and then add $P to the coordinates
newX = a * u + (x - a * u) * cosTheta + (v * z -
w * y) * sinTheta + P[0]
newY = a * v + (y - a * v) * cosTheta + (w * x -
u * z) * sinTheta + P[1]
newZ = a * w + (z - a * w) * cosTheta + (u * y -
v * x) * sinTheta + P[2]
phosOxyCoords[atomName] = [newX, newY, newZ]
return phosOxyCoords
def findBase(self, mapNum, sugar, phos5, phos3, baseType, direction = 3):
"""Rotate the sugar center by 360 degrees in ROTATE_SUGAR_INTERVAL increments
ARGUMENTS:
mapNum - the molecule number of the Coot map to use
sugar - the coordinates of the C1' atom
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
baseType - the base type (A, C, G, or U)
OPTIONAL ARGUMENTS:
direction - which direction are we tracing the chain
if it is 5 (i.e. 3'->5'), then phos5 and phos3 will be flipped
all other values will be ignored
defaults to 3 (i.e. 5'->3')
RETURNS:
baseObj - a list of [baseType, baseCoordinates]
"""
if direction == 5:
(phos5, phos3) = (phos3, phos5)
#calculate the bisector of the phos-sugar-phos angle
#first, calculate a normal to the phos-sugar-phos plane
sugarPhos5Vec = minus(phos5, sugar)
sugarPhos3Vec = minus(phos3, sugar)
normal = crossProd(sugarPhos5Vec, sugarPhos3Vec)
normal = scalarProd(normal, 1.0/magnitude(normal))
phosSugarPhosAngle = angle(phos5, sugar, phos3)
bisector = rotate(sugarPhos5Vec, normal, phosSugarPhosAngle/2.0)
#flip the bisector around (so it points away from the phosphates) and scale its length to 5 A
startingBasePos = scalarProd(bisector, -1/magnitude(bisector))
#rotate the base baton by 10 degree increments about half of a sphere
rotations = [startingBasePos] #a list of coordinates for all of the rotations
for curTheta in range(-90, -1, 10) + range(10, 91, 10):
curRotation = rotate(startingBasePos, normal, curTheta)
rotations.append(curRotation) #here's where the phi=0 rotation is accounted for
for curPhi in range(-90, -1, 10) + range(10, 91, 10):
rotations.append(rotate(curRotation, startingBasePos, curPhi))
#test electron density along all base batons
for curBaton in rotations:
curDensityTotal = 0
densityList = []
for i in range(1, 9):
(x, y, z) = plus(sugar, scalarProd(i/2.0, curBaton))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
densityList.append(curPointDensity)
curBaton.append(curDensityTotal) #the sum of the density (equivalent to the mean for ordering purposes)
curBaton.append(median(densityList)) #the median of the density
curBaton.append(min(densityList)) #the minimum of the density
#find the baton with the max density (as measured using the median)
#Note that we ignore the sum and minimum of the density. Those calculations could be commented out,
# but they may be useful at some point in the future. When we look at higher resolutions maybe?
# Besides, they're fast calculations.)
baseDir = max(rotations, key = lambda x: x[4])
#rotate the stock base+sugar structure to align with the base baton
rotationAngle = angle(self.__baseStrucs["C"]["C4"], [0,0,0], baseDir)
axis = crossProd(self.__baseStrucs["C"]["C4"], baseDir[0:3])
orientedBase = rotateAtoms(self.__baseStrucs["C"], axis, rotationAngle)
#rotate the base about chi to find the best fit to density
bestFitBase = None
maxDensity = -999999
for curAngle in range(0,360,5):
rotatedBase = rotateAtoms(orientedBase, orientedBase["C4"], curAngle, sugar)
curDensity = 0
for curAtom in ["N1", "C2", "N3", "C4", "C5", "C6"]:
curDensity += density_at_point(mapNum, rotatedBase[curAtom][0], rotatedBase[curAtom][1], rotatedBase[curAtom][2])
#this is "pseudoChi" because it uses the 5' phosphate in place of the O4' atom
pseudoChi = torsion(phos5, sugar, rotatedBase["N1"], rotatedBase["N3"])
curDensity *= self.__pseudoChiInterp.interp(pseudoChi)
if curDensity > maxDensity:
maxDensity = curDensity
bestFitBase = rotatedBase
baseObj = ["C", bestFitBase]
#mutate the base to the appropriate type
if baseType != "C":
baseObj = self.mutateBase(baseObj, baseType)
return baseObj
def mutateBase(self, curBase, newBaseType):
"""Change the base type.
ARGUMENTS:
curBase - the current base object in the form [baseType, baseCoordinates]
newBaseType - the base type to mutate to
RETURNS:
baseObj - a list of [baseType, baseCoordinates]
"""
(curBaseType, curBaseCoords) = curBase
#calculate the vectors used to align the old and new bases
#for pyrimidines, the vector is C1'-C4
#for purines, the vector is from C1' to the center of the C4-C5 bond
curAlignmentVector = None
if curBaseType == "C" or curBaseType == "U":
curAlignmentVector = minus(curBaseCoords["C4"], curBaseCoords["C1'"])
else:
curBaseCenter = plus(curBaseCoords["C4"], curBaseCoords["C5"])
curBaseCenter = scalarProd(1.0/2.0, curBaseCenter)
curAlignmentVector = minus(curBaseCenter, curBaseCoords["C1'"])
#calculate the alignment vector for the new base
newBaseCoords = self.__baseStrucs[newBaseType]
newAlignmentVector = None
if newBaseType == "C" or newBaseType == "U":
newAlignmentVector = newBaseCoords["C4"]
else:
newAlignmentVector = plus(newBaseCoords["C4"], newBaseCoords["C5"])
newAlignmentVector = scalarProd(1.0/2.0, newAlignmentVector)
#calculate the angle between the alignment vectors
rotationAngle = -angle(curAlignmentVector, [0,0,0], newAlignmentVector)
axis = crossProd(curAlignmentVector, newAlignmentVector)
#rotate the new base coordinates
newBaseCoords = rotateAtoms(newBaseCoords, axis, rotationAngle)
#calculate the normals of the base planes
curNormal = None
if curBaseType == "C" or curBaseType == "U":
curNormal = crossProd(minus(curBaseCoords["N3"], curBaseCoords["N1"]), minus(curBaseCoords["C6"], curBaseCoords["N1"]))
else:
curNormal = crossProd(minus(curBaseCoords["N3"], curBaseCoords["N9"]), minus(curBaseCoords["N7"], curBaseCoords["N9"]))
newNormal = None
if newBaseType == "C" or newBaseType == "U":
newNormal = crossProd(minus(newBaseCoords["N3"], newBaseCoords["N1"]), minus(newBaseCoords["C6"], newBaseCoords["N1"]))
else:
newNormal = crossProd(minus(newBaseCoords["N3"], newBaseCoords["N9"]), minus(newBaseCoords["N7"], newBaseCoords["N9"]))
#calculate the angle between the normals
normalAngle = -angle(curNormal, [0,0,0], newNormal);
normalAxis = crossProd(curNormal, newNormal)
#rotate the new base coordinates so that it falls in the same plane as the current base
#and translate the base to the appropriate location
newBaseCoords = rotateAtoms(newBaseCoords, normalAxis, normalAngle, curBaseCoords["C1'"])
return [newBaseType, newBaseCoords]
def buildInitOrTerminalPhosOxy(curResAtoms, prevResAtoms=None):
"""build phosphoryl oxygens using only the O3' or O5'atom (intended for the first or last nucleotide of a chain/segment)
ARGUMENTS:
curResAtoms - a dictionary of the current nucleotide coordinates (i.e. the nucleotide to build the phosphoryl oxygens on) in the format atomName: [x, y, z]
this dictionary must contain at least the phosphate
OPTIONAL ARGUMENTS:
prevResAtoms - a dictionary of the previous nucleotide coordinates in the format atomName: [x, y, z]
if provided, the curResAtoms["P"] and prevResAtoms["O3'"] will be used to place the phosphoryl oxygens
if not provided, the curResAtoms["P"] and curResAtoms["O5'"]
RETURNS:
phosOxyCoords - a dictionary of the phosphoryl oxygen coordinates in the format atomName: [x, y, z]
or None if the residue is missing the necessary atoms
"""
try:
P = curResAtoms["P"]
if prevResAtoms is not None:
O = prevResAtoms["O3'"]
C = prevResAtoms["C3'"]
else:
O = curResAtoms["O5'"]
C = curResAtoms["C5'"]
except KeyError:
return None
#place atom along the P-O5' bond that is the appropriate distance from P
phosOxy = minus(O, P)
phosOxy = normalize(phosOxy, PHOSBONDLENGTH)
#define plane with C5'-O5'-P
norm = crossProd(minus(C, O), minus(P, O))
norm = normalize(norm)
#rotate dummy atom in plane about P by INITPHOSANGLE (which is the appropriate O5'-OP1 angle)
(x, y, z) = phosOxy
(u, v, w) = norm
theta = -radians(
INITPHOSANGLE
) #use the negative angle so that we rotate away from the C5'
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation
a = u * x + v * y + w * z
phosOxy[0] = a * u + (x - a * u) * cosTheta + (v * z - w * y) * sinTheta
phosOxy[1] = a * v + (y - a * v) * cosTheta + (w * x - u * z) * sinTheta
phosOxy[2] = a * w + (z - a * w) * cosTheta + (u * y - v * x) * sinTheta
#rotate dummy atom about O5'-P axis by 59.8 and -59.8 degrees
norm = minus(O, P)
norm = normalize(norm)
(x, y, z) = phosOxy
(u, v, w) = norm
angle = radians(PHOSBONDANGLE / 2)
phosOxyCoords = {}
for (atomName, theta) in (("OP1", angle), ("OP2", -angle)):
cosTheta = cos(theta)
sinTheta = sin(theta)
#perform the rotation, and then add $P to the coordinates
newX = a * u + (x - a * u) * cosTheta + (v * z -
w * y) * sinTheta + P[0]
newY = a * v + (y - a * v) * cosTheta + (w * x -
u * z) * sinTheta + P[1]
newZ = a * w + (z - a * w) * cosTheta + (u * y -
v * x) * sinTheta + P[2]
phosOxyCoords[atomName] = [newX, newY, newZ]
return phosOxyCoords
def findSugar(self, mapNum, phos5, phos3):
"""find potential C1' locations between the given 5' and 3' phosphate coordinates
ARGUMENTS:
mapNum - the molecule number of the Coot map to use
phos5 - the coordinates of the 5' phosphate
phos3 - the coordinates of the 3' phosphate
RETURNS:
sugarMaxima - a list of potential C1' locations, each listed as [x, y, z, score]
"""
#calculate the distance between the two phosphatse
phosPhosDist = dist(phos5, phos3)
#calculate a potential spot for the sugar based on the phosphate-phosphate distance
#projDist is how far along the 3'P-5'P vector the sugar center should be (measured from the 3'P)
#perpDist is how far off from the 3'P-5'P vector the sugar center should be
#these functions are for the sugar center, which is what we try to find here
#since it will be more in the center of the density blob
perpDist = -0.185842*phosPhosDist**2 + 1.62296*phosPhosDist - 0.124146
projDist = 0.440092*phosPhosDist + 0.909732
#if we wanted to find the C1' instead of the sugar center, we'd use these functions
#however, finding the C1' directly causes our density scores to be less accurate
#so we instead use the functions above to find the sugar center and later adjust our
#coordinates to get the C1' location
#perpDist = -0.124615*phosPhosDist**2 + 0.955624*phosPhosDist + 2.772573
#projDist = 0.466938*phosPhosDist + 0.649833
#calculate the normal to the plane defined by 3'P, 5'P, and a dummy point
normal = crossProd([10,0,0], minus(phos3, phos5))
#make sure the magnitude of the normal is not zero (or almost zero)
#if it is zero, that means that our dummy point was co-linear with the 3'P-5'P vector
#and we haven't calculated a normal
#if the magnitude is almost zero, then the dummy point was almost co-linear and we have to worry about rounding error
#in either of those cases, just use a different dummy point
#they should both be incredibly rare cases, but it doesn't hurt to be safe
if magnitude(normal) < 0.001:
#print "Recalculating normal"
normal = crossProd([0,10,0], minus(phos5, phos3))
#scale the normal to the length of perpDist
perpVector = scalarProd(normal, perpDist/magnitude(normal))
#calculate the 3'P-5'P vector and scale it to the length of projDist
projVector = minus(phos3, phos5)
projVector = scalarProd(projVector, projDist/magnitude(projVector))
#calculate a possible sugar location
sugarLoc = plus(phos5, projVector)
sugarLoc = plus(sugarLoc, perpVector)
#rotate the potential sugar location around the 3'P-5'P vector to generate a list of potential sugar locations
sugarRotationPoints = self.__rotateSugarCenter(phos5, phos3, sugarLoc)
#test each potential sugar locations to find the one with the best electron density
for curSugarLocFull in sugarRotationPoints:
curSugarLoc = curSugarLocFull[0:3] #the rotation angle is stored as curSugarLocFull[4], so we trim that off for curSugarLoc
curDensityTotal = 0
#densityList = [] #if desired, this could be used to generate additional statistics on the density (such as the median or quartiles)
#check density along the 5'P-sugar vector
phosSugarVector = minus(curSugarLoc, phos5)
phosSugarVector = scalarProd(phosSugarVector, 1.0/(DENSITY_CHECK_POINTS+1))
for i in range(1, DENSITY_CHECK_POINTS+1):
(x, y, z) = plus(phos5, scalarProd(i, phosSugarVector))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
#check at the sugar center
(x, y, z) = curSugarLoc
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
#check along the sugar-3'P vector
sugarPhosVector = minus(phos3, curSugarLoc)
sugarPhosVector = scalarProd(sugarPhosVector, 1.0/(DENSITY_CHECK_POINTS+1))
for i in range(1, DENSITY_CHECK_POINTS+1):
(x, y, z) = plus(curSugarLoc, scalarProd(i, sugarPhosVector))
curPointDensity = density_at_point(mapNum, x, y, z)
curDensityTotal += curPointDensity
#densityList.append(curPointDensity)
curSugarLocFull.append(curDensityTotal)
#curSugarLocFull.extend([curDensityTotal, median(densityList), lowerQuartile(densityList), min(densityList)])#, pointList])
#find all the local maxima
sugarMaxima = []
curPeakHeight = sugarRotationPoints[-1][4]
nextPeakHeight = sugarRotationPoints[0][4]
sugarRotationPoints.append(sugarRotationPoints[0]) #copy the first point to the end so that we can properly check the last point
for i in range(0, len(sugarRotationPoints)-1):
prevPeakHeight = curPeakHeight
curPeakHeight = nextPeakHeight
nextPeakHeight = sugarRotationPoints[i+1][4]
if prevPeakHeight < curPeakHeight and curPeakHeight >= nextPeakHeight:
sugarMaxima.append(sugarRotationPoints[i])
#sort the local maxima by their density score
sugarMaxima.sort(key = lambda x: x[4], reverse = True)
#adjust all the sugar center coordinates so that they represent the corresponding C1' coordinates
for i in range(0, len(sugarMaxima)):
curSugar = sugarMaxima[i][0:3]
#rotate a vector 148 degrees from the phosphate bisector
phosAngle = angle(phos5, curSugar, phos3)
phos5vector = minus(phos5, curSugar)
axis = crossProd(minus(phos3, curSugar), phos5vector)
axis = scalarProd(axis, 1/magnitude(axis))
c1vec = rotate(phos5vector, axis, 148.539123-phosAngle/2)
#scale the vector to the appropriate length
c1vec = scalarProd(c1vec, 1.235367/magnitude(c1vec))
#rotate the vector about the phosphate bisector
phosBisectorAxis = rotate(phos5vector, axis, -phosAngle/2)
phosBisectorAxis = scalarProd(phosBisectorAxis, 1/magnitude(phosBisectorAxis))
c1vec = rotate(c1vec, phosBisectorAxis, -71.409162)
sugarMaxima[i][0:3] = plus(c1vec, curSugar)
return sugarMaxima