[gmx-users] Langevin dynamics

Tanos tccf at epq.ime.eb.br
Thu Jul 31 13:13:02 CEST 2003


Dear Jialin,
To say you the truth, I did not ever try yet to perform a LD in GROMACS
but I think the procedure is the same as to perform a MD. First I build
the .gro and .top files using pdb2gmx, then I use editconf to create the
box, and finally, grompp and mdrun. The only difference, I guess, is
that I do not use genbox because I do not want the explict solvent.
	Best,
	Tanos C. C. Franca
 

Hi;
     I would like to know how do you perform LD with not explicit
solvent. Did gromacs provide implict solvent model? If not, how did you
simulate the protein with LD method.  How did you make gro and top
files. Thanks in advance.

Jialin



-----Mensagem original-----
De: gmx-users-admin at gromacs.org [mailto:gmx-users-admin at gromacs.org] Em
nome de gmx-users-request at gromacs.org
Enviada em: quinta-feira, 31 de julho de 2003 04:06
Para: gmx-users at gromacs.org
Assunto: gmx-users digest, Vol 1 #906 - 10 msgs

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Today's Topics:

   1. Re: [gmx-user] a pyrene attached lipid: topology file
(taeho.kim at utoronto.ca)
   2. Re: Simulated annealing 10000K (Osmany Guirola Cruz)
   3. Re: Simulated annealing (Osmany Guirola Cruz)
   4. Re: Simulated annealing (David)
   5. Re: Re: [gmx-user] a pyrene attached lipid: topology file
(Christopher Yip)
   6. Re: Simulated annealing (Xavier Periole)
   7. Re: Restarting Pull Code (alexander.rhee at utoronto.ca)
   8. Re: Langevin dynamics (Jia-Lin Lo)
   9. Re: Simulated annealing 10000K (Kay Gottschalk)
  10. Re: Some questions on itp files. (Anton Feenstra)

--__--__--

Message: 1
Date: Wed, 30 Jul 2003 15:51:02 -0400
From:	taeho.kim at utoronto.ca
To:	gmx-users at gromacs.org
Subject: [gmx-users] Re: [gmx-user] a pyrene attached lipid: topology
file
Reply-To: gmx-users at gromacs.org

Hi, I?m wondering whether anyone has parameter files for any pyrene
labeled 
lipid.  
Although PRODRG server or using known parameters from similar 
structure may be the stating point now, is it necessary to do the 
parameterization for the labeled lipid molecule ?   I really appreciate
any 
help.
Thanks,

Taeho

--__--__--

Message: 2
From: Osmany Guirola Cruz <osmany.guirola at cigb.edu.cu>
To: gmx-users at gromacs.org
Date: Wed, 30 Jul 2003 16:00:13 -0700
Subject: Re: [gmx-users] Simulated annealing 10000K
Reply-To: gmx-users at gromacs.org

<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
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that was the problem in my simulation at 1000K my ten final structures
are
quite diferent after the SA. <br>
<br>
Xavier Periole wrote:<br>
<blockquote type="cite" cite="mid00d001c356d0$ff7b8fe0$d83a4a86 at fox">
  <title></title>
  
  <meta http-equiv="Content-Type" content="text/html; ">
 
  <meta content="MSHTML 6.00.2723.2500" name="GENERATOR">
 
  <style></style>  
  <div>&nbsp;</div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">Yop, sorry I meant 1000 K. 10000 K is
way too much.  </font></div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">Marco is right. With 11 residues it
is
unlikely  that your peptide has a unique</font></div>
 
  <div><font face="Arial" size="2">conformation in solvent. It probably
explore
 different conformations with diffenrent</font></div>
 
  <div><font face="Arial" size="2">probabilities. </font></div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">How did you generate your 10
structures
with  Modeler. I thought it needed a</font></div>
 
  <div><font face="Arial" size="2">template !! And what isthe point of
doing
an SA on  a specific conformation ?</font></div>
 
  <div><font face="Arial" size="2">You loose it at 1000K anyway !!
</font></div>
 
  <div><font face="Arial" size="2">I did some thing similar where I
generated
100 conf  from SA with an implicit </font></div>
 
  <div><font face="Arial" size="2">solvent (faster) and after that I
made&nbsp;clusters
of them. </font></div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">XAvier</font></div>
 
  <div>&nbsp;</div>
</blockquote>
<br>
</body>
</html>



--__--__--

Message: 3
From: Osmany Guirola Cruz <osmany.guirola at cigb.edu.cu>
To: gmx-users at gromacs.org
Date: Wed, 30 Jul 2003 16:02:37 -0700
Subject: Re: [gmx-users] Simulated annealing
Reply-To: gmx-users at gromacs.org

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<blockquote type="cite" cite="mid00eb01c356d1$ce867de0$d83a4a86 at fox">
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Sorry Xavier but i don't understand , i need that all my systems have
the
same number of h2o<br>
in gromacs , how i do that &nbsp; 
<blockquote type="cite" cite="mid00eb01c356d1$ce867de0$d83a4a86 at fox">
  <div>&nbsp;</div>
 
  <blockquote
 style="border-left: 2px solid rgb(0,0,0); padding-right: 0px;
padding-left: 5px; margin-left: 5px; margin-right: 0px;"> 
  
    <div>1- editconf -f p.gro -o p.gro -bt cubic -c -d 0.7<br>
2- genbox -cp p.gro    -cs spc216.gro -o p.gro -p p.top<br>
my peptides have diferent structure , and    then my BOX <br>
and my number of H2O are diferent, my question is<br>
hOW COULD    I GENERATE&nbsp; exactly the same number of solvent <br>
molecules and box    size.</div>
   
    <div>&nbsp;</div>
  </blockquote>
 
  <div><font face="Arial" size="2">include the solvent in your SA. I did
that too with  gromacs. It works</font></div>
 
  <div><font face="Arial" size="2">fine. And don't need a big box for 11
residues.  </font></div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">The implicit solvent SA I used before
was with  CHARMM implemented</font></div>
 
  <div><font face="Arial" size="2">in the lab by. S. Hassan. Can write
him
a  message&nbsp;at</font></div>
 
  <div><font face="Arial" size="2"><a
href="mailto:mago at inka.mssm.edu">mago at inka.mssm.edu</a>&nbsp;you'll
need CHARMM  though</font></div>
 
  <div>&nbsp;</div>
 
  <div><font face="Arial" size="2">XAvier</font></div>
</blockquote>
<br>
</body>
</html>



--__--__--

Message: 4
Subject: Re: [gmx-users] Simulated annealing
From: David <spoel at xray.bmc.uu.se>
To: gmx-users at gromacs.org
Organization: 
Date: 30 Jul 2003 22:09:34 +0200
Reply-To: gmx-users at gromacs.org

On Thu, 2003-07-31 at 00:30, Osmany Guirola Cruz wrote:
> Ok, David, but for generate my box i do:
> 1- editconf -f p.gro -o p.gro -bt cubic -c -d 0.7
> 2- genbox -cp p.gro -cs spc216.gro -o p.gro -p p.top
> my peptides have diferent structure , and then my BOX 
> and my number of H2O are diferent, my question is.
> hOW COULD I GENERATE  exactly the same number of solvent 
> molecules and box size.
> thanks

take the smallest number of any you get from genbox, and take away
molecules manually from the other ones.

> 
> 
> 
> David wrote:
> > On Wed, 2003-07-30 at 23:43, Osmany Guirola Cruz wrote:
> >   
> > > Thanks again Xavier,
> > > I have this problem:
> > > I have a peptide whit unknown structure, whit "modeler" i  get 10
> > > diferents structures of my peptide, and then.....
> > > i use SA whith the ten models to obtain a "superminimized
structure"
> > > but my final structures are NOT similar
> > > :-( . i have the idea that my simulations converge to a unique
> > > structure (my SA = "1000K" to 300K) you say 10 000 i will probe 
> > > with 10000 to see what happens. ???????  
> > > 
> > >     
> > 
> > I wouldn't use SA in this case, but rather simulated the peptides in
> > solvent (each of the ten with exactly the same number of solvent
> > molecules and box size) and then first let it relax and then do a
short
> > free simulation to measure the energy (Epot including solvent). Your
> > lowest energy is the most likely structure, although the forcefield
can
> > be wrong.
> > 
> > 
> >   
> > > Xavier Periole wrote:
> > >     
> > > >  I guess you have been reading papers from NMR procedures to 
> > > > generate their models corresponding to the data. If that what
you 
> > > > are doing It would be easier to get a program that NMR people 
> > > > use, is is probably implemented 
> > > > It seeems difficult to do that automatically in gromacs, at
least
> > > > for me.
> > > > I guess you that could modify the strength of the constant on
the
> > > > angles
> > > > and bonds in the parameter file and do that for each temperature
you
> > > > need but that's gonna to be a pain in the ...
> > > > I don't know what you are doing but I can assure you that at
10000 K
> > > > the system is pretty flexible. Try to simulate it for 10 ps at
10000
> > > > K 
> > > > and look at the trajectory !! It should convice you. But I don't
> > > > know if
> > > > it is relevant for your problem. 
> > > >  
> > > > XAvier
> > > >  
> > > > 
> > > >       
> > > 
> > > _______________________________________________ gmx-users mailing
list
> > > gmx-users at gromacs.org
> > > http://www.gromacs.org/mailman/listinfo/gmx-users Please don't
post
> > > (un)subscribe requests to the list. Use the www interface or send
it
> > > to gmx-users-request at gromacs.org.
> > >     
> 
> _______________________________________________ gmx-users mailing list
> gmx-users at gromacs.org
> http://www.gromacs.org/mailman/listinfo/gmx-users Please don't post
> (un)subscribe requests to the list. Use the www interface or send it
> to gmx-users-request at gromacs.org.
-- 
Groeten, David.
________________________________________________________________________
Dr. David van der Spoel, 	Dept. of Cell and Molecular Biology
Husargatan 3, Box 596,  	75124 Uppsala, Sweden
phone:	46 18 471 4205		fax: 46 18 511 755
spoel at xray.bmc.uu.se	spoel at gromacs.org   http://xray.bmc.uu.se/~spoel
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

--__--__--

Message: 5
Date: Wed, 30 Jul 2003 16:07:52 -0400
Subject: Re: [gmx-users] Re: [gmx-user] a pyrene attached lipid:
topology file
From:	Christopher Yip <christopher.yip at utoronto.ca>
To:	gmx-users at gromacs.org
Reply-To: gmx-users at gromacs.org

Taeho - we can get the coordinates from Julie as a starting point
On Wednesday, July 30, 2003, at 03:51 PM, taeho.kim at utoronto.ca wrote:

> Hi, I?m wondering whether anyone has parameter files for any pyrene 
> labeled
> lipid.
> Although PRODRG server or using known parameters from similar
> structure may be the stating point now, is it necessary to do the
> parameterization for the labeled lipid molecule ?   I really 
> appreciate any
> help.
> Thanks,
>
> Taeho
> _______________________________________________
> gmx-users mailing list
> gmx-users at gromacs.org
> http://www.gromacs.org/mailman/listinfo/gmx-users
> Please don't post (un)subscribe requests to the list. Use the
> www interface or send it to gmx-users-request at gromacs.org.
>
Christopher M. Yip, Ph.D., P.Eng.
Associate Professor - Canada Research Chair in Molecular Imaging
Departments of Chemical Engineering and Applied Chemistry
Department of Biochemistry
Institute of Biomaterials and Biomedical Engineering
University of Toronto
407 Rosebrugh Building
4 Taddle Creek Rd
Toronto, Ontario, CANADA M5S 3G9
(416) 978-7853
(416) 978-4317 (fax)
christopher.yip at utoronto.ca
http://bigten.ibme.utoronto.ca


--__--__--

Message: 6
From: "Xavier Periole" <periole at inka.mssm.edu>
To: <gmx-users at gromacs.org>
Subject: Re: [gmx-users] Simulated annealing
Date: Wed, 30 Jul 2003 16:19:46 -0400
Reply-To: gmx-users at gromacs.org

This is a multi-part message in MIME format.

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1) You can force "genbox" to insert extramolecules of solvent in your =
box.
    And equilibrate the whole thing, but your peptide conformations have
=

    been generated without solvent, right ! HOw good is that ? I am not
=
sure.

2) You can re-do your SAs with explicit solvent ! You beggin with a =
conformation
    of your peptide. You heat it up to 1000 K run for 50 ps and begin to
=
cool down.
    Much longer, but the size of the system is small. You can compare =
the=20
    structures at the end of the 50ps at 1000K and see if they are =
different enough.
    If they are you are can assume that you are going to explore enough
=
space.
    ideally. But I'd do more SAs.

Good luck
XAvier




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<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Diso-8859-1">
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</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>1) You can force "genbox" to insert =
extramolecules=20
of solvent in your box.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; And equilibrate the
=
whole thing,=20
but your peptide conformations have </FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; been generated =
without solvent,=20
right ! HOw good is that ? I am not sure.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>2) You can re-do your SAs with explicit
=
solvent !=20
You beggin with a conformation</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; of your peptide. You
=
heat it up=20
to 1000 K run for 50 ps and begin to cool down.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; Much longer, but the
=
size=20
</FONT><FONT face=3DArial size=3D2>of the system is small. You can =
compare the=20
</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; structures at the =
end of the=20
50ps at 1000K and see if they are different enough.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; If they are you are
=
can assume=20
that you are going to explore enough space.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>&nbsp;&nbsp;&nbsp; ideally. But I'd do
=
more=20
SAs.</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2>Good luck</FONT></DIV>
<DIV><FONT face=3DArial size=3D2>XAvier</FONT></DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=3DArial size=3D2></FONT>&nbsp;</DIV></BODY></HTML>

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Message: 7
Date: Wed, 30 Jul 2003 20:04:51 -0400
From:	alexander.rhee at utoronto.ca
To:	gmx-users at gromacs.org
Subject: [gmx-users] Re: Restarting Pull Code
Reply-To: gmx-users at gromacs.org

Semen,

I'm using the afm approach in 3.1.5_pre1 to pull apart molecules, and
it's
working quite nicely to the best of my knowledge.  You might have to dig
through
the mailing lists to find the current state of the constrained pull
code.

Regards,

Alex



Message: 6
Date: Sun, 27 Jul 2003 22:37:05 -0700 (PDT)
From: Semen Esilevsky <yesint4 at yahoo.com>
Subject: Re: [gmx-users] Restarting Pull Code
To: gmx-users at gromacs.org
Reply-To: gmx-users at gromacs.org

Which kind of pull simulation do you use?
It's something strange with the pull code - it seems
that constrained pull do not work at all in 3.1.4...

Semen

--- alexander.rhee at utoronto.ca wrote:
> Hullo,
> 
> I've recently been working with the pull code in
> 3.1.5_pre1 and have inevitably
> run into crashes.  It seems that when you restart
> the crashes using tpbconv the
> pull forces are reset to 0? so that when you merge
> the original run data and the
> new run data a sharp break will appear in the force
> curve where the pulling
> force just drops to 0.
> 
> I was wondering if there was a way around this so
> that you can get a clean force
> curve without any breaks, or am I just missing
> something really obvious?
> 
> Regards,
> 
> -Alex
> _______________________________________________
> gmx-users mailing list
> gmx-users at gromacs.org
> http://www.gromacs.org/mailman/listinfo/gmx-users
> Please don't post (un)subscribe requests to the
> list. Use the 
> www interface or send it to
gmx-users-request at gromacs.org.

--__--__--

Message: 8
From: "Jia-Lin Lo" <jllo at phy.ncu.edu.tw>
To: <gmx-users at gromacs.org>
Subject: Re: [gmx-users] Langevin dynamics
Date: Thu, 31 Jul 2003 13:13:26 +0800
Reply-To: gmx-users at gromacs.org


Hi;
     I would like to know how do you perform LD with not explicit
solvent.
Did gromacs provide implict solvent model? If not, how did you simulate
the protein with LD method.  How did you make gro and top files.
Thanks in advance.

Jialin



> Tanos wrote:
> >             Hi folks,
> >             I would like to perform a Langevin Dynamics (LD) of 1 ns
in
> > a protein of about 900 residues enclosed in a water´s box in
physiologic
> > condictions, and I wonder if someone, experienced in this kind of
> > dynamics, has a suitable ld.mdp file to send me.
>
> AFAIK, LD is used when no explicit solvent is included. (The
stochastic
> part of LD replaces the solvent bumping into the solute). So, I don't
> see the sense in doing LD on a protein in a water box. Other than
> that, the only differences between MD and LD parameters would be
> the LD friction coefficient which may or may not depend on the (type
> of) protein you simulate.
>
>
> --
> Groetjes,
>
> Anton
>   _____________
_______________________________________________________
> |             |
|
> |  _   _  ___,| K. Anton Feenstra
|
> | / \ / \'| | | Dept. of Pharmacochem. - Vrije Universiteit Amsterdam
|
> |(   |   )| | | De Boelelaan 1083 - 1081 HV Amsterdam - Netherlands
|
> | \_/ \_/ | | | Tel: +31 20 44 47608 - Fax: +31 20 44 47610
|
> |             | Feenstra at chem.vu.nl - www.chem.vu.nl/~feenstra/
|
> |             | "If You See Me Getting High, Knock Me Down"
|
> |             | (Red Hot Chili Peppers)
|
>
|_____________|_______________________________________________________|
>
>
> _______________________________________________
> gmx-users mailing list
> gmx-users at gromacs.org
> http://www.gromacs.org/mailman/listinfo/gmx-users
> Please don't post (un)subscribe requests to the list. Use the
> www interface or send it to gmx-users-request at gromacs.org.


--__--__--

Message: 9
Date: Thu, 31 Jul 2003 09:21:23 +0300
Subject: Re: [gmx-users] Simulated annealing 10000K
From: Kay Gottschalk <kay.gottschalk at weizmann.ac.il>
To: gmx-users at gromacs.org
Reply-To: gmx-users at gromacs.org


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I'd do much more than ten structures. Do as many as you can in a=20
reasonable time and afterwards cluster the results! You cannot expect=20
your system to converge so easily...
On Thursday, July 31, 2003, at 02:00 AM, Osmany Guirola Cruz wrote:

> that was the problem in my simulation at 1000K my ten final
structures=20=

> are quite diferent after the SA.
>
> Xavier Periole wrote:
>
>
>
>
>
> =A0
> =A0
> Yop, sorry I meant 1000 K. 10000 K is way too much.
> =A0
> Marco is right. With 11 residues it is unlikely that your peptide
has=20=

> a unique
> conformation in solvent. It probably explore different
conformations=20=

> with diffenrent
> probabilities.
> =A0
> How did you generate your 10 structures with Modeler. I thought it=20
> needed a
> template !! And what isthe point of doing an SA on a specific=20
> conformation ?
> You loose it at 1000K anyway !!
> I did some thing similar where I generated 100 conf from SA with an=20
> implicit
> solvent (faster) and after that I made=A0clusters of them.
> =A0
> XAvier
> =A0
>
>
>
Dr. Kay-E. Gottschalk
Department of Biological Chemistry
Weizmann Institute of Science
Tel: ++972-8-9343639
Herzl St. 1
Rehovot 76100
Israel

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I'd do much more than ten structures. Do as many as you can in a
reasonable time and afterwards cluster the results! You cannot expect
your system to converge so easily...

On Thursday, July 31, 2003, at 02:00 AM, Osmany Guirola Cruz wrote:


<excerpt>that was the problem in my simulation at 1000K my ten final
structures are quite diferent after the SA.


Xavier Periole wrote:






=A0

=A0

<fontfamily><param>Arial</param><smaller>Yop, sorry I meant 1000 K.
10000 K is way too much.</smaller></fontfamily>

=A0

<fontfamily><param>Arial</param><smaller>Marco is right. With 11
residues it is unlikely that your peptide has a =
unique</smaller></fontfamily>

<fontfamily><param>Arial</param><smaller>conformation in solvent. It
probably explore different conformations with =
diffenrent</smaller></fontfamily>

=
<fontfamily><param>Arial</param><smaller>probabilities.</smaller></fontf
am=
ily>

=A0

<fontfamily><param>Arial</param><smaller>How did you generate your 10
structures with Modeler. I thought it needed a</smaller></fontfamily>

<fontfamily><param>Arial</param><smaller>template !! And what isthe
point of doing an SA on a specific conformation ?</smaller></fontfamily>

<fontfamily><param>Arial</param><smaller>You loose it at 1000K anyway
!!</smaller></fontfamily>

<fontfamily><param>Arial</param><smaller>I did some thing similar
where I generated 100 conf from SA with an =
implicit</smaller></fontfamily>

<fontfamily><param>Arial</param><smaller>solvent (faster) and after
that I made=A0clusters of them.</smaller></fontfamily>

=A0

<fontfamily><param>Arial</param><smaller>XAvier</smaller></fontfamily>

=A0




</excerpt>Dr. Kay-E. Gottschalk

Department of Biological Chemistry

Weizmann Institute of Science

Tel: ++972-8-9343639

Herzl St. 1

Rehovot 76100

Israel


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--__--__--

Message: 10
Date: Wed, 30 Jul 2003 17:51:59 +0200
From: Anton Feenstra <feenstra at chem.vu.nl>
To: gmx-users at gromacs.org
Subject: Re: [gmx-users] Some questions on itp files.
Reply-To: gmx-users at gromacs.org

Senthil Kandasamy wrote:
> I have a few nagging doubts that need to be clarified.
> 
> 1. The parameters specified in the molecule.itp file override those in
> the ffgmx*.itp. Is that correct? e.g. in urea.itp
> 
> [bonds]
> 3   4 	1	1.000e-01	3.744e+05
> ...
> 
> Here b0 and kb from this file are used rather than the values in
> ffgmxbon.itp.  If I do not specify these values, then the values from
> ffgmxbon.itp will be used. correct?

Absolutely.

> 2. [pairs]:
> 
> If I specify a pair of atoms under the pairs directive, then the 1-4
non
> bonded interactions "ARE" calculated. If C6 and C12 are zeros, then
this
> effectively means that the LJ interaction is zero, but coulombic
forces
> will be calculated. Am I correct?

Close, actually the 1-4 LJ is a bonded interaction in Gromacs, and it
has it's own directive in the ff*bon.itp under [ pairtypes ]. Check
the manual, this is actually rather well and thoroughly described!


-- 
Groetjes,

Anton
  _____________ _______________________________________________________
|             |                                                       |
|  _   _  ___,| K. Anton Feenstra                                     |
| / \ / \'| | | Dept. of Pharmacochem. - Vrije Universiteit Amsterdam |
|(   |   )| | | De Boelelaan 1083 - 1081 HV Amsterdam - Netherlands   |
| \_/ \_/ | | | Tel: +31 20 44 47608 - Fax: +31 20 44 47610           |
|             | Feenstra at chem.vu.nl - www.chem.vu.nl/~feenstra/       |
|             | "If You See Me Getting High, Knock Me Down"           |
|             | (Red Hot Chili Peppers)                               |
|_____________|_______________________________________________________|




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