| posSymmPot |
index |
Potential term restraining atomic positions relative to those in a
similar structure. This term is similar to the (nonstrict) NCS XPLOR
energy term, but there is no need that the equivalent pairs of atoms
have the same atom name, have the same residue name, or even be of the
same number. Additionally, an absolute fit is possible such that
coordinates overlay one another if one specified
setAbsoluteFit(True).
Constructor:
It is suggested that this potential term be created using the helper
function posSymmPotTools.create_PosSymmPot().
PosSymmPot(instanceName,
simulation ) - creates a potential term with the given name.
The second argument is optional, and defaults
to the current Simulation.
Methods:
calcEnergy() - calculate and return energy
calcEnergyAndDerivs(DerivList) - calcs energy and derivative info
addEquivAtomSelPair(atomSel,
atomSel,
weights1,
weights2) - specify a pair of atomSel.AtomSels,
the centroids of which will be restrained
to have the same relative position. The
optional weights arguments can be used to
specify nonuniform weighting used when
computing the centroids from the
constituent atomic positions.
equivAtomSelPairs() - return a list containing the current
set of AtomSel pairs.
removeEquivAtomSelPair(atomSel1,
atomSel2) - remove the specified pair.
addEquivAtoms(string1,
string2) - specify sets of atoms whose positions
will be restrained to have the same
relative position. This form must be
used for inhomogeneous ensembles.
rms() - returns the best-fit RMSD between the two
selection sets.
violations() - returns 0 if upperBound > rms > lowerBound,
1 otherwise.
individualRMSDs() - returns a list containg the distances
between each equivalent pair after
best-fitting
rotMat() - returns the rotation matrix which best-
fits the second selection sets to
the first when they are both
translated to the origin.
centroid(whichOne) - returns the centroid position of each
selection set, specified by whichOne
(either 0 or 1).
translatedCoords(whichOne) - returns a sequence of vec3.Vec3s
which represent the positions of the
specified selection set (by whichOne -
either 0 or 1).
calcVarTens(whichOne,i) - return the appropriate VarTensor (a
symmetric matrix, see below) for
equivalence set i.
deltaVariance() - return the matrix norm of the difference
in variance tensor (see below).
aveCoords(whichOne) - (ensemble and selection set) averaged
coordinates translated so they're
centered at the origin and fit.
fitCoords(whichOne,i,j,m) - return centered, rotated atomic coords
in selection set i, ensemble member j,
selection set index m.
getEnsWeight(whichOne, - return the ensemble weight used for
memberIndex) the specified ensemble member.
weight(whichOne,i,j,m) - return the weight for the atomic position
in selection set i, ensemble member j,
selection set index m.
Read-Write accessors:
scale - scale factor for the position/average position term.
varScale - scale factor for the delta variance term - only nonzero
for EnsembleSimulations [default: 0].
lowerBound - see below. If lowerBound>0, equivalent pairs
will be forced apart [default: 0].
upperBound - see below. This specifies the rmsd amount the equivalent
pairs are allowed to differ [default: 0].
absoluteFit - If True, do not perform rotation and translation before
difference calculation, such that fit regions will lie on
top of each other [default: False].
planarFit - If True, use alternate approach for determining
translatedCoords and rotMat where only translation
perpendicular to vector u is subtracted, and the rotation
matrix is only allowed to rotate about u [default: False].
u - The plane normal vector [default: Vec3(0,0,1)].
the above quantities may be retrieved using the member function form
quantity(), while they are set using the form setQuantity(value).
The potential term is defined as
E = 0.5 * scale() * Ni * (dRMSD^2 +
dVarRoot)
with
/ rmsd - upperBound, if rmsd > upperBound
dRMSD = | rmsd - lowerBound, if rmsd < lowerBound
\ 0 , if rmsd < upperBound and rmsd > lowerBound
and
rmsd^2 = 1/Ni sum_i |(q_1i-q_1c) - R(q_2i-q_2c)|^2
where q_1i and q_2i are the average position of the ith respective
equivalent pair, and the sum is over all pairs, and Ni is the number of
equivalent pairs. R is the rotation matrix which minimizes rmsd2.
q_1c and q_2c are the average positions of the equivalent pair
positions, e.g.
q_1c = 1/N1 * sum_i q_1i.
For an ensembleSimulation.EnsembleSimulation,
dVarRoot = varScale * sqrt(deltaVariance) is nonzero with a value, with
deltaVariance = sum_i sum_{a,b} (VarTensor0_i(a,b) - VarTensor1_i(a,b))^2
where the i sum is over all equivalent sets and VarTensorNu_i is a variance
tensor for equivalent set i which measures deviations from the ensemble mean
position:
VarTensorNu_i(a,b) = < deltaq_i(a) deltaq_i(b) >
where deltaq_i is the deviation of coordinate in equivalent set i from its
ensemble mean, and the average is over all atoms in the equivalence set and
all ensemble members. Note that it is acceptible for there to be no atoms
present for some ensemble members.
Note that this term scales as the number of equivalent pairs.
Members - for low-level, internal use only.
A - covariance matrix
sum_i ( deltaqb_0(i) * deltaqb_1^T(i) )
where deltaqb_eta is the ensemble,
selection set averaged coordinates,
relative to the appropriate
centroid for selection set i.
ATAMhalf - the matrix (A^T * A)^{-1/2}
vectors - eigenvectors of the matrix A^T * A
values - associated eigenvalues of A^T * A
gamma; - a arry containing. +/- 1 / sqrt(values)
The sign is chosen such that the
rotation matrix
R = A U Gamma U^T
does not possess an inversion
(i.e. the determinant= +1)
# This file was automatically generated by SWIG (http://www.swig.org).
# Version 4.0.2
#
# Do not make changes to this file unless you know what you are doing--modify
# the SWIG interface file instead.
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