[gmx-users] Schlitter Configurational entropy 'NaN'
David van der Spoel
spoel at xray.bmc.uu.se
Fri May 16 07:53:04 CEST 2014
On 2014-05-16 06:03, tarak karmakar wrote:
>>
>> What does g_covar print?
>>
>> It seems the problem might be there, because the jump by 10 orders of
>> magnitude in eigenvalue does not seem reasonable.
>>
>
> g_covar prints the following
>
> Analysis is non-mass weighted
> Fit is non-mass weighted
> Diagonalized the 1386x1386 covariance matrix
> Trace of the covariance matrix before diagonalizing: 8.72034
> Trace of the covariance matrix after diagonalizing: 8.72034
>
> Wrote 1386 eigenvalues to eigenval.xvg
> Wrote reference structure to eigenvec.trr
> Wrote average structure to average.pdb and eigenvec.trr
> Wrote eigenvectors 1 to 1000 to eigenvec.trr
>
> Another more subtle issue might be the number of frames used for the
> analysis. Did you happen to have 1000 frames only? In that case the
> remaining degrees of freedom might be ill-defined.
>
> Yes. I do have 1000 frames only.
> In the previous case I had skipped some steps (trjconv with pbc -nojump
> -skip 10) to get a shorter trajectory. But when I took the full trajectory
> 10000 the eigenvalues are coming out good.
>
> 996 9.46356e-05
> 997 9.38922e-05
> 998 9.38014e-05
> 999 9.36644e-05
> 1000 9.33975e-05
> 1001 9.33863e-05
> 1002 9.296e-05
> 1003 9.28913e-05
> 1004 9.26346e-05
> 1005 9.25611e-05
>
> The Entropy due to the Quasi Harmonic approximation is 6239.63 J/mol K
> The Entropy due to the Schlitter formula is 6950.97 J/mol K
>
> Tarak
>
>
OK, thanks for your help in debugging this. I have now uploaded a fix to
gromacs 4.6. https://gerrit.gromacs.org/#/c/3447/
>
>
>
>
>
> On Thu, May 15, 2014 at 11:05 PM, David van der Spoel
> <spoel at xray.bmc.uu.se>wrote:
>
>> On 2014-05-15 19:20, David van der Spoel wrote:
>>
>>> On 2014-05-15 18:41, tarak karmakar wrote:
>>>
>>>> Hi Justin,
>>>> That's true and it is a C code and 0 index loop.
>>>> Then the strange jump 999 to 1000 came in to the picture.
>>>> But what about dealing with very small numbers?
>>>>
>>> What does g_covar print?
>>>
>>> It seems the problem might be there, because the jump by 10 orders of
>>> magnitude in eigenvalue does not seem reasonable.
>>>
>>
>> Another more subtle issue might be the number of frames used for the
>> analysis. Did you happen to have 1000 frames only? In that case the
>> remaining degrees of freedom might be ill-defined.
>>
>>
>>>
>>>>
>>>> Tarak
>>>>
>>>>
>>>> On Thu, May 15, 2014 at 9:30 PM, Justin Lemkul <jalemkul at vt.edu> wrote:
>>>>
>>>>
>>>>>
>>>>> On 5/15/14, 11:51 AM, tarak karmakar wrote:
>>>>>
>>>>> Part of the eigenval.xvg file
>>>>>>
>>>>>> 995 3.02979e-06
>>>>>> 996 2.98051e-06
>>>>>> 997 2.93131e-06
>>>>>> 998 2.75594e-06
>>>>>> 999 2.69955e-06
>>>>>> 1000 2.56434e-06
>>>>>> 1001 2.66401e-16
>>>>>> 1002 1.43252e-16
>>>>>> 1003 1.0735e-16
>>>>>> 1004 8.0728e-17
>>>>>> 1005 4.3465e-17
>>>>>> 1006 1.60571e-17
>>>>>> 1007 1.49006e-17
>>>>>> 1008 1.44694e-17
>>>>>> 1009 1.07083e-17
>>>>>> 1010 9.77564e-18
>>>>>> 1011 8.25739e-18
>>>>>> 1012 8.18473e-18
>>>>>> 1013 6.85267e-18
>>>>>> 1014 6.79135e-18
>>>>>> 1015 5.7498e-18
>>>>>> 1016 5.49917e-18
>>>>>> 1017 4.84525e-18
>>>>>> 1018 4.15989e-18
>>>>>> 1019 4.06407e-18
>>>>>> 1020 3.70677e-18
>>>>>> .............................
>>>>>> .............................
>>>>>> 1362 -3.16429e-18
>>>>>> 1363 -3.40673e-18
>>>>>> 1364 -3.85766e-18
>>>>>> 1365 -4.16796e-18
>>>>>> 1366 -4.16839e-18
>>>>>> 1367 -4.17689e-18
>>>>>> 1368 -4.48977e-18
>>>>>> 1369 -4.54731e-18
>>>>>> 1370 -4.58794e-18
>>>>>> 1371 -4.86076e-18
>>>>>> 1372 -5.05864e-18
>>>>>> 1373 -5.73908e-18
>>>>>> 1374 -6.1385e-18
>>>>>> 1375 -6.98907e-18
>>>>>> 1376 -7.5897e-18
>>>>>> 1377 -1.23406e-17
>>>>>> 1378 -1.24701e-17
>>>>>> 1379 -1.41182e-17
>>>>>> 1380 -1.47709e-17
>>>>>> 1381 -1.50144e-17
>>>>>> 1382 -5.73596e-17
>>>>>> 1383 -1.03466e-16
>>>>>> 1384 -1.277e-16
>>>>>> 1385 -1.64873e-16
>>>>>> 1386 -3.2657e-16
>>>>>>
>>>>>> These eigenvalues are very less compared to the below 1000 numbers.
>>>>>> I see there is no strange jump from 999 to 1000 but from 1000 to 1001.
>>>>>>
>>>>>>
>>>>>> The array in the code is zero-indexed, so this is actually the
>>>>> location of
>>>>> the problem.
>>>>>
>>>>> -Justin
>>>>>
>>>>>
>>>>> Lambda values are considered to be zero in these cases and thus
>>>>>
>>>>>> w = sqrt(BOLTZMANN*temp/lambda)/NANO = infinity
>>>>>> &
>>>>>> dd = 1+kteh*eigval[i];
>>>>>> deter += log(dd)
>>>>>> is failed.
>>>>>>
>>>>>> i = 1000 w = inf lam = 0 hwkT = inf dS =
>>>>>> -nan
>>>>>> i = 1001 w = inf lam = 0 hwkT = inf dS =
>>>>>> -nan
>>>>>> i = 1002 w = inf lam = 0 hwkT = inf dS =
>>>>>> -nan
>>>>>>
>>>>>> So, there is precision problem in the code; 10^-16 is taken as zero!!
>>>>>>
>>>>>> Tarak
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Thu, May 15, 2014 at 5:23 PM, David van der Spoel
>>>>>> <spoel at xray.bmc.uu.se>wrote:
>>>>>>
>>>>>> On 2014-05-15 11:40, tarak karmakar wrote:
>>>>>>
>>>>>>>
>>>>>>> Dear Sir,
>>>>>>>
>>>>>>>>
>>>>>>>> Thank you again for guiding me towards this. Got some clue.
>>>>>>>> The g_anaeig code is
>>>>>>>> ............................................................
>>>>>>>> ............................................................
>>>>>>>> .................
>>>>>>>> static void calc_entropy_qh(FILE *fp,int n,real eigval[],real
>>>>>>>> temp,int
>>>>>>>> nskip)
>>>>>>>> {
>>>>>>>> int i;
>>>>>>>> double hwkT,w,dS,S=0;
>>>>>>>> double hbar,lambda;
>>>>>>>>
>>>>>>>> hbar = PLANCK1/(2*M_PI);
>>>>>>>> for(i=0; (i<n-nskip); i++) {
>>>>>>>> if (eigval[i] > 0) {
>>>>>>>> lambda = eigval[i]*AMU;
>>>>>>>> w = sqrt(BOLTZMANN*temp/lambda)/NANO;
>>>>>>>> hwkT = (hbar*w)/(BOLTZMANN*temp);
>>>>>>>> dS = (hwkT/(exp(hwkT) - 1) - log(1-exp(-hwkT)));
>>>>>>>> S += dS;
>>>>>>>> if (debug)
>>>>>>>> fprintf(debug,"i = %5d w = %10g lam = %10g hwkT = %10g dS =
>>>>>>>> %10g\n",
>>>>>>>> i,w,lambda,hwkT,dS);
>>>>>>>> }
>>>>>>>> else {
>>>>>>>> fprintf(stderr,"eigval[%d] = %g\n",i,eigval[i]);
>>>>>>>> w = 0;
>>>>>>>> }
>>>>>>>> }
>>>>>>>> fprintf(fp,"The Entropy due to the Quasi Harmonic
>>>>>>>> approximation is
>>>>>>>> %g
>>>>>>>> J/mol K\n",
>>>>>>>> S*RGAS);
>>>>>>>> }
>>>>>>>>
>>>>>>>> static void calc_entropy_schlitter(FILE *fp,int n,int nskip,
>>>>>>>> real *eigval,real temp)
>>>>>>>> {
>>>>>>>> double dd,deter;
>>>>>>>> int *indx;
>>>>>>>> int i,j,k,m;
>>>>>>>> char buf[256];
>>>>>>>> double hbar,kt,kteh,S;
>>>>>>>>
>>>>>>>> hbar = PLANCK1/(2*M_PI);
>>>>>>>> kt = BOLTZMANN*temp;
>>>>>>>> kteh = kt*exp(2.0)/(hbar*hbar)*AMU*(NANO*NANO);
>>>>>>>> if (debug)
>>>>>>>> fprintf(debug,"n = %d, nskip = %d kteh = %g\n",n,nskip,kteh);
>>>>>>>>
>>>>>>>> deter = 0;
>>>>>>>> for(i=0; (i<n-nskip); i++) {
>>>>>>>> dd = 1+kteh*eigval[i];
>>>>>>>> deter += log(dd);
>>>>>>>> }
>>>>>>>> S = 0.5*RGAS*deter;
>>>>>>>>
>>>>>>>> fprintf(fp,"The Entropy due to the Schlitter formula is %g J/mol
>>>>>>>> K\n",S);
>>>>>>>> }
>>>>>>>> ............................................................
>>>>>>>> ..............................................................
>>>>>>>> What I got from the 'g_anaeig_d.debug' file is given below
>>>>>>>>
>>>>>>>> i = 0 w = 1.06303e+12 lam = 3.66537e-27 hwkT = 0.0270659 dS =
>>>>>>>> 4.60951
>>>>>>>> i = 1 w = 1.50699e+12 lam = 1.82384e-27 hwkT = 0.0383696 dS =
>>>>>>>> 4.26055
>>>>>>>> i = 2 w = 1.62965e+12 lam = 1.55961e-27 hwkT = 0.0414928 dS =
>>>>>>>> 4.18231
>>>>>>>> i = 3 w = 2.02202e+12 lam = 1.01306e-27 hwkT = 0.0514829 dS =
>>>>>>>> 3.96662
>>>>>>>> i = 4 w = 2.80273e+12 lam = 5.27285e-28 hwkT = 0.0713605 dS =
>>>>>>>> 3.64022
>>>>>>>> i = 5 w = 3.1712e+12 lam = 4.11871e-28 hwkT = 0.0807422 dS =
>>>>>>>> 3.51677
>>>>>>>> i = 6 w = 3.45782e+12 lam = 3.46419e-28 hwkT = 0.0880401 dS =
>>>>>>>> 3.43029
>>>>>>>> i = 7 w = 3.56568e+12 lam = 3.25778e-28 hwkT = 0.0907862 dS =
>>>>>>>> 3.39959
>>>>>>>> i = 8 w = 4.00962e+12 lam = 2.57633e-28 hwkT = 0.102089 dS =
>>>>>>>> 3.28234
>>>>>>>> i = 9 w = 4.4611e+12 lam = 2.08125e-28 hwkT = 0.113584 dS =
>>>>>>>> 3.17575
>>>>>>>> i = 10 w = 4.6037e+12 lam = 1.95431e-28 hwkT = 0.117215 dS =
>>>>>>>> 3.14431
>>>>>>>> i = 11 w = 5.01062e+12 lam = 1.64977e-28 hwkT = 0.127576 dS =
>>>>>>>> 3.05972
>>>>>>>> i = 12 w = 5.31327e+12 lam = 1.46718e-28 hwkT = 0.135282 dS =
>>>>>>>> 3.00116
>>>>>>>> i = 13 w = 5.51169e+12 lam = 1.36345e-28 hwkT = 0.140334 dS =
>>>>>>>> 2.96455
>>>>>>>> i = 14 w = 5.70613e+12 lam = 1.27211e-28 hwkT = 0.145284 dS =
>>>>>>>> 2.92994
>>>>>>>> i = 15 w = 5.8637e+12 lam = 1.20466e-28 hwkT = 0.149296 dS =
>>>>>>>> 2.90275
>>>>>>>> i = 16 w = 6.01592e+12 lam = 1.14447e-28 hwkT = 0.153172 dS =
>>>>>>>> 2.87717
>>>>>>>> ----------------------
>>>>>>>> .......................
>>>>>>>> i = 996 w = 9.2246e+14 lam = 4.86757e-33 hwkT = 23.4869 dS =
>>>>>>>> 1.54425e-09
>>>>>>>> i = 997 w = 9.51359e+14 lam = 4.57635e-33 hwkT = 24.2226 dS =
>>>>>>>> 7.62131e-10
>>>>>>>> i = 998 w = 9.61243e+14 lam = 4.48271e-33 hwkT = 24.4743 dS =
>>>>>>>> 5.98465e-10
>>>>>>>> i = 999 w = 9.86259e+14 lam = 4.25819e-33 hwkT = 25.1113 dS =
>>>>>>>> 3.2445e-10
>>>>>>>> i = 1000 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1001 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1002 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> ......................
>>>>>>>> ..................
>>>>>>>> i = 1370 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1371 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1372 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1373 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1374 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1375 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1376 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1377 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1378 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> i = 1379 w = inf lam = 0 hwkT = inf dS =
>>>>>>>> -nan
>>>>>>>> n = 1386, nskip = 6 kteh = 4569.58
>>>>>>>> Opening library file /usr/share/gromacs/top/gurgle.dat
>>>>>>>>
>>>>>>>>
>>>>>>>> It is very interesting that the code printed 'nan' after 999 th term.
>>>>>>>> What
>>>>>>>> does this mean?
>>>>>>>> Is there any upper limit of number of atoms (c-alpha here)?
>>>>>>>>
>>>>>>>> Check your eigval.xvg file, what is the value at i = 1000?
>>>>>>>>
>>>>>>> It seems that lambda is the problem, hence I suspect the
>>>>>>> eigval[1000] to
>>>>>>> be strange.
>>>>>>>
>>>>>>>
>>>>>>> Tarak
>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> On Thu, May 15, 2014 at 2:54 PM, David van der Spoel
>>>>>>>> <spoel at xray.bmc.uu.se>wrote:
>>>>>>>>
>>>>>>>> On 2014-05-15 10:51, tarak karmakar wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>> | Is your system far out of equilibrium?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> It should not be as I have simulated the system for 100ns. Few
>>>>>>>>>> properties
>>>>>>>>>> to check to get the feelings of equilibrium are looking good.
>>>>>>>>>>
>>>>>>>>>> |Do the eigenvalues look reasonable?
>>>>>>>>>> Yes. File is attached.
>>>>>>>>>>
>>>>>>>>>> | Or is your system very large?
>>>>>>>>>> My system is a protein dimer.
>>>>>>>>>>
>>>>>>>>>> It creates the following covariance matrix (c-alpha atoms)
>>>>>>>>>>
>>>>>>>>>> Constructing covariance matrix (1386x1386)
>>>>>>>>>>
>>>>>>>>>> That is big.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>> Try running g_anaeig -debug 1 and check the output file
>>>>>>>>> g_anaeig.debug.
>>>>>>>>> Then check the source code (gmx_anaeig.c) to see whether the
>>>>>>>>> evaluation
>>>>>>>>> of
>>>>>>>>> the entropy can be made more numerically stable.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> eigenvec.trr file is also attached.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> Mail with the attached files
>>>>>>>>>> "Needs moderator approval because of the file size."
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Thanks,
>>>>>>>>>> Tarak
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> On Thu, May 15, 2014 at 2:19 PM, tarak karmakar
>>>>>>>>>> <tarak20489 at gmail.com
>>>>>>>>>>
>>>>>>>>>> wrote:
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> | Is your system far out of equilibrium?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> It should not be as I have simulated the system for 100ns. Few
>>>>>>>>>>> properties
>>>>>>>>>>> to check to get the feelings of equilibrium are looking good.
>>>>>>>>>>>
>>>>>>>>>>> |Do the eigenvalues look reasonable?
>>>>>>>>>>> Yes. File is attached.
>>>>>>>>>>>
>>>>>>>>>>> | Or is your system very large?
>>>>>>>>>>> My system is a protein dimer.
>>>>>>>>>>>
>>>>>>>>>>> It creates the following covariance matrix (c-alpha atoms)
>>>>>>>>>>>
>>>>>>>>>>> Constructing covariance matrix (1386x1386)
>>>>>>>>>>>
>>>>>>>>>>> eigenvec.trr file is also attached.
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Thanks,
>>>>>>>>>>> Tarak
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> On Thu, May 15, 2014 at 2:06 PM, David van der Spoel <
>>>>>>>>>>> spoel at xray.bmc.uu.se
>>>>>>>>>>>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> On 2014-05-15 10:30, tarak karmakar wrote:
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Dear Sir,
>>>>>>>>>>>>
>>>>>>>>>>>> Thanks for the quick reply.
>>>>>>>>>>>>
>>>>>>>>>>>>> Using g_anaeig_d I've got both of them as 'nan'
>>>>>>>>>>>>>
>>>>>>>>>>>>> The Entropy due to the Quasi Harmonic approximation is -nan
>>>>>>>>>>>>> J/mol K
>>>>>>>>>>>>> The Entropy due to the Schlitter formula is nan J/mol K
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Interesting. Is your system far out of equilibrium? Do the
>>>>>>>>>>>>>
>>>>>>>>>>>>> eigenvalues
>>>>>>>>>>>> look reasonable? Or is your system very large?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Tarak
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>> On Thu, May 15, 2014 at 1:30 PM, David van der Spoel
>>>>>>>>>>>>> <spoel at xray.bmc.uu.se>wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 2014-05-15 09:07, tarak karmakar wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Dear All,
>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I wanted to calculate configurational entropy of a
>>>>>>>>>>>>>> protein by
>>>>>>>>>>>>>> using
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> g_covar
>>>>>>>>>>>>>>> and g_anaeig as follows,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> g_covar -f ../traj.xtc -s ../npt_prod -o eigenval -v
>>>>>>>>>>>>>>> eigenvec.trr
>>>>>>>>>>>>>>> -av
>>>>>>>>>>>>>>> average.pdb
>>>>>>>>>>>>>>> g_anaeig -v eigenvec.trr -entropy -temp 300
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I got the following results
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The Entropy due to the Quasi Harmonic approximation is 31440.3
>>>>>>>>>>>>>>> J/mol
>>>>>>>>>>>>>>> K
>>>>>>>>>>>>>>> The Entropy due to the Schlitter formula is nan J/mol K
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I went back to check the eigenvector file by dumping it to
>>>>>>>>>>>>>>> a new
>>>>>>>>>>>>>>> file
>>>>>>>>>>>>>>> 'dump'. There is no 'nan' indeed.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Could anyone comment on why I'm getting Schlitter entropy as
>>>>>>>>>>>>>>> 'nan'?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thanks and regards,
>>>>>>>>>>>>>>> Tarak
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Numerical error due to large numbers. Try compiling
>>>>>>>>>>>>>>> gromacs
>>>>>>>>>>>>>>> in
>>>>>>>>>>>>>>> double
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> precision.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> David van der Spoel, Ph.D., Professor of Biology
>>>>>>>>>>>>>> Dept. of Cell & Molec. Biol., Uppsala University.
>>>>>>>>>>>>>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>>>>>>>>>>>>>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> Gromacs Users mailing list
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> * Please search the archive at http://www.gromacs.org/
>>>>>>>>>>>>>> Support/Mailing_Lists/GMX-Users_List before posting!
>>>>>>>>>>>>>>
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>>>>>>>>>>>>>> gmx-usersor
>>>>>>>>>>>>>> send a mail to gmx-users-request at gromacs.org.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> David van der Spoel, Ph.D., Professor of Biology
>>>>>>>>>>>>>
>>>>>>>>>>>> Dept. of Cell & Molec. Biol., Uppsala University.
>>>>>>>>>>>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>>>>>>>>>>>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>>>>>>>>>>>> --
>>>>>>>>>>>> Gromacs Users mailing list
>>>>>>>>>>>>
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>>>>>>>>>>>> Support/Mailing_Lists/GMX-Users_List before posting!
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>>>>>>>>>>>>
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>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>>
>>>>>>>>> David van der Spoel, Ph.D., Professor of Biology
>>>>>>>>> Dept. of Cell & Molec. Biol., Uppsala University.
>>>>>>>>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>>>>>>>>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>>>>>>>>> --
>>>>>>>>> Gromacs Users mailing list
>>>>>>>>>
>>>>>>>>> * Please search the archive at http://www.gromacs.org/
>>>>>>>>> Support/Mailing_Lists/GMX-Users_List before posting!
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>>>>>>>>>
>>>>>>>>> send a mail to gmx-users-request at gromacs.org.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> --
>>>>>>> David van der Spoel, Ph.D., Professor of Biology
>>>>>>> Dept. of Cell & Molec. Biol., Uppsala University.
>>>>>>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>>>>>>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>>>>>>> --
>>>>>>> Gromacs Users mailing list
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>>>>>>> * Please search the archive at http://www.gromacs.org/
>>>>>>> Support/Mailing_Lists/GMX-Users_List before posting!
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>>>>>>>
>>>>>>>
>>>>>>> --
>>>>> ==================================================
>>>>>
>>>>> Justin A. Lemkul, Ph.D.
>>>>> Ruth L. Kirschstein NRSA Postdoctoral Fellow
>>>>>
>>>>> Department of Pharmaceutical Sciences
>>>>> School of Pharmacy
>>>>> Health Sciences Facility II, Room 601
>>>>> University of Maryland, Baltimore
>>>>> 20 Penn St.
>>>>> Baltimore, MD 21201
>>>>>
>>>>> jalemkul at outerbanks.umaryland.edu | (410) 706-7441
>>>>> http://mackerell.umaryland.edu/~jalemkul
>>>>>
>>>>> ==================================================
>>>>>
>>>>> --
>>>>> Gromacs Users mailing list
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>>>
>>>
>>
>> --
>> David van der Spoel, Ph.D., Professor of Biology
>> Dept. of Cell & Molec. Biol., Uppsala University.
>> Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
>> spoel at xray.bmc.uu.se http://folding.bmc.uu.se
>> --
>> Gromacs Users mailing list
>>
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--
David van der Spoel, Ph.D., Professor of Biology
Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone: +46184714205.
spoel at xray.bmc.uu.se http://folding.bmc.uu.se
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