Sure - that's fine. I'd like to get this word out and get more feedback like
yours.
Bob
On Tue, Sep 21, 2010 at 6:19 PM, Michael Evans <[email protected]> wrote:
> Thanks Bob! The PPT really cleared things up. I'm going to link to it in
> the tooltip, if you don't mind, as a way for users to find out more.
>
> Cheers, Mike
>
>
> On Tue, Sep 21, 2010 at 6:49 AM, Robert Hanson <[email protected]> wrote:
>
>> Mike, I know this is a bit obtuse -- we're still working on the manuscript
>> for this... There's a PowerPoint presentation I gave on the subject at last
>> year's ACS meeting. See
>>
>> http://chemapps.stolaf.edu/jmol/presentations/acs2009
>>
>>
>> On Mon, Sep 20, 2010 at 11:19 PM, Michael Evans <[email protected]>wrote:
>>
>>> Bob + other Lords of Jmol—I'm looking for some clarification of the "plot
>>> ramachandran r" specification from the Interactive Script Docs; particularly
>>> the definition of theta. It makes sense to me that theta is approximately
>>> the sum of delta phi and delta psi. I get lost with two points:
>>>
>>> - How theta relates to dq[i]/dq[i-1] (and what exactly is represented
>>> by this quantity...does it have something to do with the rotation of
>>> residues [i] and [i-1] w.r.t. one another? I'm thinking about the
>>> definition
>>> of quaternion division described in your wonderful post about
>>> quaternions,
>>> which I happened to come across today, as describing the relationship
>>> between two rotational states)
>>>
>>>
>> Each residue is assigned a frame -- an xyz axis set -- based on one or
>> another definition. This is the "C" or "P" or "N" in "set quaternionFrame"
>> ...
>>
>> "C" -- alpha carbon
>>
>> "P" -- peptide plane
>>
>> "N" -- peptide nitrogen, specifically for solid state NMR
>>
>> The orientation of these frames relative to the reference frame (the xyz
>> axes of the model) can be referred to by a quaternion -- four numbers.
>>
>> dq[i] is the quaternion difference (often written as division,not
>> subtraction) between the quaternion at residue i and the quaternion at
>> residue i - 1.
>>
>>
>>>
>>> - The distinction between "C" and "P" straightness, and how the "P"
>>> straightness approximation for theta was derived
>>>
>>>
>> If you load a protein and then issue
>>
>> wireframe only
>> set quaternionframe "C"
>> draw quaternion
>>
>> I think you will see what we are talking about. The xyz axes for each
>> residue are shown, and a yellow arrow with a number shows the axis and angle
>> required to rotate the reference frame (axes molecular) to this orientation.
>>
>>
>> I'll have to dig up that proof. It originated here at St. Olaf. We
>> discovered the relationship during the summer of 2008 (that's what my
>> research over the past two years has been about).
>>
>>
>>
>>> Related to point 1, I can't see how this is a second derivative. It looks
>>> like a derivative of the quaternion of residue [i] w.r.t. residue [i-1].
>>> What am I missing here? I'm trying to dumb down a description of the 3-D
>>> Rama plot as much as possible, to add it to a tooltip in an interface. With
>>> just a tooltip I don't have enough space to launch into a full-blown
>>> mathematical derivation, but if that's what it's going to take to really get
>>> at theta, I'll probably just leave it out :-)
>>>
>>>
>> If you call q[i-1] and q[i] the two quaternions for residues i-1 and i,
>> then dq[i] is q[i]/q[i-1], another quaternion. dq[i] indicates the axis and
>> angle in the standard reference plane that would rotate residue i-1 into the
>> orientation of residue i. That's the "first derivative." It also can be
>> thought of as the "local helical axis".
>>
>> If you load a protein and then issue
>>
>> draw quaternion difference
>>
>> you will see that the vectors produced pretty well define the axes of
>> helices and sheet strands. In fact, I might suggest that they be used to
>> DEFINE those axes, because it's a relatively simple matter to determine the
>> "average" quaternion and to specify the root mean square deviation of those.
>>
>>
>> --Straightness--
>>
>> Now you have to take two of those differences and take THEIR difference --
>> ddq[i] = dq[i+1] / dq[i] -- to get the "second" derivative. That's also a
>> quaternion. It is the first term of that quaternion (the quaternion dot
>> product of dq[i+1] and dq[i]) that we use in the straightness calculation:
>>
>> S[i] = 1 - arcCos(abs(dq[i+1] dot dq[i])) / (pi/2)
>>
>> This is in some ways analogous to what had been proposed earlier by others
>> [1] as a definition of "straightness", but they used the dot product of
>> regular three-dimensional vectors instead of quaternions, which makes
>> perfect sense, except that it doesn't allow the nice relationship to
>> Ramachandran angles. The definition of straightness we are using - defined
>> in terms of quaternions instead of just three-dimensional vectors - was the
>> (dare I say brilliant?) suggestion of Dan Kohler (St. Olaf '09, now at U.
>> Wisc.).
>>
>> Bob
>>
>>
>> [1] Kneller GR, Calligari P. Efficient characterization of protein
>> secondary structure in terms of
>> screw motions. Acta Crystallogr, Sect. D: Biol Crystallogr 2006; 62:
>> 302-311.
>>
>>
>>> Cheers and thanks as always, Mike
>>>
>>> --
>>> Mike Evans
>>> Organic Chemistry Graduate Student
>>> Moore Group
>>> University of Illinois, Urbana-Champaign
>>>
>>>
>>> ------------------------------------------------------------------------------
>>> Start uncovering the many advantages of virtual appliances
>>> and start using them to simplify application deployment and
>>> accelerate your shift to cloud computing.
>>> http://p.sf.net/sfu/novell-sfdev2dev
>>> _______________________________________________
>>> Jmol-users mailing list
>>> [email protected]
>>> https://lists.sourceforge.net/lists/listinfo/jmol-users
>>>
>>>
>>
>>
>> --
>> Robert M. Hanson
>> Professor of Chemistry
>> St. Olaf College
>> 1520 St. Olaf Ave.
>> Northfield, MN 55057
>> http://www.stolaf.edu/people/hansonr
>> phone: 507-786-3107
>>
>>
>> If nature does not answer first what we want,
>> it is better to take what answer we get.
>>
>> -- Josiah Willard Gibbs, Lecture XXX, Monday, February 5, 1900
>>
>>
>> ------------------------------------------------------------------------------
>> Start uncovering the many advantages of virtual appliances
>> and start using them to simplify application deployment and
>> accelerate your shift to cloud computing.
>> http://p.sf.net/sfu/novell-sfdev2dev
>> _______________________________________________
>> Jmol-users mailing list
>> [email protected]
>> https://lists.sourceforge.net/lists/listinfo/jmol-users
>>
>>
>
>
> --
> Mike Evans
> Organic Chemistry Graduate Student
> Moore Group
> University of Illinois, Urbana-Champaign
>
>
> ------------------------------------------------------------------------------
> Start uncovering the many advantages of virtual appliances
> and start using them to simplify application deployment and
> accelerate your shift to cloud computing.
> http://p.sf.net/sfu/novell-sfdev2dev
> _______________________________________________
> Jmol-users mailing list
> [email protected]
> https://lists.sourceforge.net/lists/listinfo/jmol-users
>
>
--
Robert M. Hanson
Professor of Chemistry
St. Olaf College
1520 St. Olaf Ave.
Northfield, MN 55057
http://www.stolaf.edu/people/hansonr
phone: 507-786-3107
If nature does not answer first what we want,
it is better to take what answer we get.
-- Josiah Willard Gibbs, Lecture XXX, Monday, February 5, 1900
------------------------------------------------------------------------------
Start uncovering the many advantages of virtual appliances
and start using them to simplify application deployment and
accelerate your shift to cloud computing.
http://p.sf.net/sfu/novell-sfdev2dev
_______________________________________________
Jmol-users mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/jmol-users
