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 __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 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