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On Oct 11, 2006, at 2:52 PM, Santarsiero, Bernard D. wrote:
It really has nothing to do with least-squares itself.
But it does. When I've used the term 'least-squares', I mean ordinary
(unweighted) least-squares (OLS), which has been used historically
for superpositions. OLS is fundamentally predicated on two strong
statistical assumptions (as stated in the Gauss-Markov theorem): (1)
all atoms in the superposition have the same variance and (2) none of
the atoms are correlated with each other. Both of these OLS
assumptions are false, in general, with macromolecular superpositions.
It's the implementation, and how you want to define the minimal
function. You don't want to superimpose elements that are really
different.
Sort of. The problem is knowing what is "really different" before
doing a superposition. Probably the primary motivation for performing
a superposition is to get an idea of what is different and what is
similar among multiple structures. In most cases, regions of
structures that are different are also similar to some extent. Thus
different regions carry at least some structural information that
should be incorporated in the superposition. Similar vs different is
a matter of degree; it is not an absolute category. The maximum
likelihood (ML) method implemented in THESEUS naturally accounts for
these issues by weighting structural regions according to their
structural similarity.
And not to argue the point much further, but least-squares IS a
maximum likelihood estimator.
The method of least squares can be justified in terms of likelihood,
given some additional assumptions, but least squares is not maximum
likelihood. Specifically, the OLS solution is identical to the ML
solution if you assume a Gaussian distribution for the data, and if
all data points have the same variance and are uncorrelated. On the
other hand, the statistical justification for OLS is given by the
Gauss-Markov theorem, and it guarantees the optimality of the OLS
solution (by frequentist measures, not likelihoodist or Bayesian
measures) regardless of whether the data have a Gaussian distribution
or not.
IOW, it is best to realize that LS and ML are very different methods,
historically, philosophically, and practically. In general, they will
lead to different solutions to the same problem. In certain special
cases they can lead to the same solution, as can Bayesian methods,
but that doesn't mean that OLS is ML or Bayesian.
Cheers,
Douglas
http://www.theseus3d.org/
bds
On Wed, October 11, 2006 1:34 pm, Douglas L. Theobald wrote:
On Oct 11, 2006, at 1:49 PM, Santarsiero, Bernard D. wrote:
the graphics program "O" is excellent at things like this.
Basically you do a rough superposition with lsq-exp (explicit)
and then improve it with lsq-imp. It leaves out calpha's that
aren't close, but pulls everything else in.
Yes, the way that O does it with lsq is much preferred over many
other methods. However, it really is just a kludge to overcome
the problems with least-squares, an optimization method that
really is inappropriate for the macromolecular superposition
problem. The advantage of the maximum likelihood method that
THESEUS implements, is that it removes the arbitrary and
subjective parameters for deciding what "isn't close". Maximum
likelihood instead inherently down-weights the variable parts
exactly by the (statistically) proper amount.
Additionally, lsq does not do a bona fide simultaneous
superposition with more than two structures, whereas THESEUS does.
Cheers,
Douglas
Bernie Santarsiero
On Wed, October 11, 2006 10:38 am, Douglas L. Theobald wrote:
On Oct 11, 2006, at 11:08 AM, Jenny wrote:
Hi, All,
I have three proteins that only differ in one big loop(resi
46-59).So I'm trying to superimpose three proteins and keep the
same part fixed.( basically, superimpose by residue 1-45 and
residue 60-120).Is there easy way to do this?
Hi Jenny,
It's easy to do with THESEUS from the command line:
http://www.theseus3d.org/
For a least squares fit, just use something like:
theseus -l -s1-45:60-120 protein1.pdb protein2.pdb protein3.pdb
or equivalently, exclude the range with:
theseus -l -S46-59 protein1.pdb protein2.pdb protein3.pdb
However, since THESEUS uses maximum likelihood you shouldn't
even have to specify a residue range, just do:
theseus protein1.pdb protein2.pdb protein3.pdb
and it should work well.
^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`^`
Douglas L. Theobald
Department of Biochemistry
Brandeis University
Waltham, MA 02454-9110
[EMAIL PROTECTED]
GPG key ID: 38E9EB53
https://www.molevo.org/keys/38E9EB53.gpgkey
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