Protein surface interpretation - help

Hi,
Could someone tell me whether I am right or wrong in understanding the idea
of different protein surfaces, please? Do the values of the surfaces area
that I have managed to calculate for a 15 kD protein seem reasonable?
1. van der Waals surface - the bigest area (covers van der Waals atomic
surfaces), eg. 14,000 squared Angstroms
2. molecular surface or contact surface covered by a rolling molecule of the
solvent, eg. 2,000 squared Angstroms
3. (solvent) accessible surface - described by the trace of the central
point of a solvent molecule rolling over the protein contact surface, eg.
7,000 squared Angstroms.

Are the values calculated for a 15 kD protein probable? Is the below true
for a typical protein:
molecular surface < accessible surface < van der Waals surface?

Which surface area is best to calculate in order to consider the geometry of
interacting surfaces
of proteinous antigen and an immunoglobulin? I would like to calculate
potential binding sites on a surface of an antigen assuming that the average
antigen surface covered by a monovalent antibody binding site is approx.
1500 squared Angstroms.
Thanks in advance for all your help.

Regards,
Stefek

Stefek Borkowski wrote:


If you told us how you calculated these values, we could comment on the
methods used rather than the results, which would probably be more
useful to you.

Dr Engelbert Buxbaum wrote:

Dear Dr. Buxbaum,
Thank you so much for offering your help. So again, I would like to
calculate the surface
of Rat Liver Fatty Acid Binding Protein (PDB file name: 1LFO).
It is a relatively small protein - approx. 15
kD molecular mass. I have a reliable literature value of the antibody
monovalent
binding surface area, that is equal to 1500 squared Angstroms, which is the
average value (true for all antibodies), I believe. My main goal is to
determine the number of potential binding sites (epitopes) on my protein
surface (that could be, just theoretically, simultaneously! and monovalently
bound by antibodies)
- this value is going to be an average, as I cannnot an won't model
antibodies specific to all possible epitopes!
Being a lay person at protein modelling and all, I used free software to do
the job (2 for Linux: spock, asv and 1 for Windows: ccp4). Once I had
installed the stuff, I managed to make the calculations. It took just a few
seconds actually, but the results are not all clear to me. Some nomenclature
seems misleading. Below I am enclosing summary of the results by each
software for comparison and some additional questions of mine.
The fundamental question for me, however, is whether the solvent accessible
surface area of a protein is the right choice to calculate the number of
potential antibody binding sites (i.e. the sites that can be bound at the
same time, skipping considerations of spatial hinderance between
antibodies). In other words, could the accessible surface be assumed as the
one interacting with antibody? If this assumption were true then I would be
happy just calculating this: approx. 7000 (the output value for solvent
accessible area - see below)
divided by 1500 is equal to approx. 4 or 5 possible simultaneous binding
sites on my protein.
I hope I have made myself clear now Do you think it would be
possible for you to find a few minutes of your precious time and have a
closer look at the output of my calculation files. They are not that big at
all - just text files of about dozen kilobytes. If you kindly agreed I would
be eager to send you them as attachments. Maybe it would also help if I sent
you the original PDB file with the crystal structure of the protein of
interest - approx. 120 kB?
Thanks again for any help you can offer.
Sincerely,
Stefek
P.S. Below is the summary from the output of my calculating software.
######################
SPOCK
van der Waals surface area:
Fractional surface area: 0.47 - what is that "fractional surface area" by
the way?!
Total surface area: 14619

Accessible surface area
Fractional surface area: 0.07
Total surface area: 7905 - again, what is that "fractional surface area"
here?!

van der Waals volume: 10116 cubic Angstroms

Molecular volume: 17567 cubic Angstroms - why does the program calculate
molecular volume and on the other hand I cannot find an option to calculate
molecular surface area ?!!! Maybe it is so rarely considered important
that I shouldn't
bother about it either?!

Accessible volume: 27063 cubic Angstroms

Probe radius: 1.4 Angstrom

At least in the case of SPOCK the values of protein volumes seem doubtless



######################
ASV

S =12923 - just by comparison with spock I can get that this regards to the
van der Waals surface
V =10555 - and this regards most probably to van der Waals volume

This software, as far as I can gather, cannot calculate the solvent
accessible volume


######################
CCP4

ANALYSIS OF ACCESSIBLE AREAS BY RESIDUE
TOTAL AREA: 6534 - guess that is the solvent accessible surface area -
roughly resembles that of SPOCK

ANALYSIS OF CONTACT AREAS BY RESIDUE
TOTAL CONTACT AREA: 1965 - that small !!!???

And now what is that "CONTACT AREA"?! Is it the same as "molecular area"? If
so, is such a huge difference between solvent accessible area and molecular
area possible then?! Looks improbable...

Any comments highly appreciated. Thanks

On Sun, 3 Oct 2004 20:24:30 +0200, "Stefek Borkowski" <[Only registered users see links. ]>
wrote:


Numbers seem reasonable. CryCo gives SAS for 1flo as 6426 A^2
[Only registered users see links. ]

I always thought of your #2 and #3 definitions as equivalent. That
is, molecular surface = SAS (kinda makes sense, doesn't it?)
IMHO, only it makes real physical sense in general and for what
you want it for in particular. I always use CNS to calculate it - it gives
numbers very close to GRASP which is used by many/most.

I suspect that your number for #2 is in reality total area of
_crystal contacts_ of a single protein molecule with other molecules
in the crystal lattice. 1749 A^2 in your case, accordidng to CryCo.

To answer your question, definitely SAS - what is not accesible
for water (those 1.4A), would equally not be accessible by protein
atoms.

DK

D.K. wrote:

Thank you so much DK. Your answer is very convincing. Now I am much more
confident that my calculations make sense. The SAS area seems the most
rationale to be used in my analysis. I am not going to bother about the
contact area as it looks useless for my considerations. Thanks for the link
to CryCo - it really gives in no time an on-line and moreover free
calculation of SAS, confirming my results obtained by offline software. You
have done a real perfect job for me. Lots of thanks again!!! May you have a
nice day and every success in the future!
Warm greetings from still sunny Poland (quite unusual for this time of
year!).
Yours,
Stefek

In article <ck16qo$msu$[Only registered users see links. ].gda.pl>, "Stefek Borkowski" <[Only registered users see links. ]> wrote:


You are very welcome! Good luck.

DK

Stefek Borkowski wrote:


The value you calculated would be some upper limit, because not all
patches of the surface will be equally immunogenic. In other words, you
calculate how many antibodies would (mechanically) fit onto the surface,
the number of potential binding sites will be lower.


PDB-files are easily available from the internet - it is thus sufficient
to just give the PDB-number, as you have done.


Small differences between values are to be expected and result from
different implementations.

Additionally, there is the problem of non-integer dimension of the
protein surface: Because the surface of a protein is not smooth, but has
protrusions and groves, its area is not a purely 2-dimensional value.
Mathematically, you can assign it a dimensionality between 2 and 3, thus
it is something between a surface and a volume. This is called a fractal
dimension, and is topic of fractal mathematics (you may have seen the
beautiful plots of Mandelbrodt- and Julia-sets, which are also
fractals).

Thus if you want to assign a 2-dimensional value "area" to the surface,
the result depends on how fine a ruler you apply, as the ruler becomes
finer, the area will move towards infinity. Of course one can argue that
for practical purposes rulers smaller than the diameter of a hydrogen
atom will not be useful, and that is essentially what your programs use.


The definitions should be in the documentation that comes with the
programs. As I had to deleted my Linux-stuff due to interference with my
Windoze-installation, I can not check right now.

A good way to learn about basic molecular modelling is the
Protein-Explorer, [Only registered users see links. ].

Dr Engelbert Buxbaum wrote:

Thank you so much again for all your comments. I have read them with
interest.
Kind regards and warm greetings from Poland.
Yours,
Stefek