Exemple #1
0
 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
Exemple #2
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 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
Exemple #3
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 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
Exemple #4
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 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
Exemple #5
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 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
Exemple #6
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 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
Exemple #7
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 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