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</o:shapelayout></xml><![endif]--></head><body bgcolor=white lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:#1F497D'>Dear Mark and Justin,<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>I have a potentially silly question here. I have been trying to work out the figures from the various options of g_energy. You mentioned before that the bonded terms are not decomposable/require some hacking with the .top file. I am a bit confused with that.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>As mentioned previously, I did <o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>1)grompp –f new.mdp –n index.ndx –c old.tpr –o rerun1.tpr –p topol.top<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Where energy groups are added to the .mdp file<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>2)tpbconv –s rerun1.tpr –n index –o rerun2.tpr –nsteps 0 <o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>To produce individual .tpr files for i) System ii) Protein only iii) Lipid only iv) solv_ion only v) protein_lipid vi) protein_solv_ion vii) lipid_solv_ion<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>3)trjconv -f old.trr -n index.ndx -s rerun2.tpr -o rerun.trr<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>To produce a corresponding .trr files for (i) to (vii) in step 2<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>4) mdrun –s rerun2.tpr -rerun rerun.trr<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>To produce the .edr files for (i) to (vii)<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>With g_energy I derived these different components for (i) to (vii):<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>a-PE<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>b-Angle (lipid)/G96 angle (protein)<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>c-Proper dihedral<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>d-Improper dihedral<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>e-Ryckaert Belleman (lipid)<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>f-LJ 1-4<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>g-Coul 1-4<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>h-L J SR<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>i-Disp. Corr<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>j-Coul SR<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>k-Coul. Recip<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>After doing some maths, I got the below:<o:p></o:p></span></p><p class=MsoPlainText style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>the PEs for (i) to (vii) are the sum of their corresponding b-k values<o:p></o:p></span></p><p class=MsoPlainText style='margin-left:.5in'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>e.g. the PE for the system = Angle (lipid) + G96 angle (protein) + Prop. Dihedral + imp dihedral + Ryckaert Belleman (lipid) + LJ14 + Coul 1-4 + LJ SR + Disp Corr + Coul SR + Coul recip. <o:p></o:p></span></p><p class=MsoPlainText style='margin-left:.5in;text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>For bonded terms such as proper dihedral, I found that the proper dihedral of the system (i) = (ii) + (iii) i.e sum of proper dihedral values from protein and lipid. The same goes for the improper dihedral term. This is where I am confused. Doesn’t this show that the bonded terms can be decomposed?<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>I realize there has been a rather long pause between this email and the last, sorry about that, it’s because I have been trying to work out myself why you say the bonded terms cannot be decomposed easily.<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Perhaps as Justin pointed out, it is probably not worth the effort to derive individual energies of the various components that make up my system, but I would really appreciate a reply on this before I put the matter to rest. Thanks!<o:p></o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'><o:p> </o:p></span></p><p class=MsoPlainText><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>HW<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'> gmx-users-bounces@gromacs.org [mailto:gmx-users-bounces@gromacs.org] <b>On Behalf Of </b>Mark Abraham<br><b>Sent:</b> Friday, November 12, 2010 12:32 AM<br><b>To:</b> Discussion list for GROMACS users<br><b>Subject:</b> Re: [gmx-users] mdrun -rerun: bonded interactions of protein<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>On 11/11/2010 7:46 PM, NG HUI WEN wrote: <o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>Thanks a lot Justin and Mark for your useful input.</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>Indeed Justin was right, the quest to dissect the total energy of the system to get that contributed by the protein alone was not trivial at all! </span><o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>Indeed. If I'd observed you were doing PME, I'd have made the same point.</span><span style='font-size:12.0pt;font-family:"Times New Roman","serif";color:#1F497D'> <br></span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br><br><o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>I missed out this thread yesterday <a href="http://www.mail-archive.com/gmx-users@gromacs.org/msg34610.html">http://www.mail-archive.com/gmx-users@gromacs.org/msg34610.html</a> as well as Mark’s trick to decompose bonded terms by hacking the .top file. (However, I read from <a href="http://www.gromacs.org/Documentation/Gromacs_Utilities/g_energy">http://www.gromacs.org/Documentation/Gromacs_Utilities/g_energy</a> that the Coul-recip term is not decomposable regardless of the tricks used…)</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>Mark, following your advice, I added –nsteps 0 (-1 didn’t work) to tpbconv. I managed to get the interactive prompt succesfully this time. </span><o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>Yes, nsteps=-1 is a GROMACS 4.5-ism, sorry.</span><span style='font-size:12.0pt;font-family:"Courier New"'> <br></span><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br><br><o:p></o:p></span></p><p class=MsoPlainText><span style='font-family:"Courier New \;"'>Reading toplogy and shit from rerun1.tpr<br>Reading file rerun1.tpr, VERSION 4.0.7 (single precision)<br>Setting nsteps to 0<br>Group 0 ( System) has 100581 elements<br>Group 1 ( Protein) has 4002 elements<br>Group 2 ( Protein-H) has 3145 elements<br>Group 3 ( C-alpha) has 412 elements<br>Group 4 ( Backbone) has 1236 elements<br>Group 5 ( MainChain) has 1649 elements<br>Group 6 (MainChain+Cb) has 2027 elements<br>Group 7 ( MainChain+H) has 2039 elements<br>Group 8 ( SideChain) has 1963 elements<br>Group 9 ( SideChain-H) has 1496 elements<br>Group 10 ( Prot-Masses) has 4002 elements<br>Group 11 ( Non-Protein) has 96579 elements<br>Group 12 ( POPE) has 13052 elements<br>Group 13 ( SOL) has 83523 elements<br>Group 14 ( CL-) has 4 elements<br>Group 15 ( Other) has 96579 elements<br>Group 16 ( SOL_CL-) has 83527 elements<br>Group 17 (Protein_POPE) has 17054 elements<br>Select a group: </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>As suggested, I have also tried to compare the (average) values of subset.tpr and fullsystem.tpr, these are the total energies of:</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>System= -1.28209 e+06</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Protein= -9571.86</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Lipid= -296121</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>SOL_CL= -821353</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Other= -1.22684e+06</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>It was found that the: </span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Total energies (Protein + lipid + SOL_CL-) not equal to total energy of the system</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Total energies of (Lipid + SOL_CL-) not equal to total energy of other</span><o:p></o:p></p><p class=MsoListParagraph style='text-indent:-.25in'><span style='color:#1F497D'>Total energies of (others + protein) not equal to total energy of the system</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>I have yet to work out the reasons for the discrepancies, will spend some time pondering and trying to make sense of these (and other) values.</span><o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>Aren't you omitting the inter-group non-bonded terms? Anyway, I was suggesting this comparison for seeing whether the bonded components can be decomposed group-wise. It is already known that the non-bonded decomposition works.<br><br>Mark<br><br><br><o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>Thanks a bunch again!</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'>HW</span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><p class=MsoNormal><span style='color:#1F497D'> </span><o:p></o:p></p><div><div style='border:none;border-top:solid windowtext 1.0pt;padding:3.0pt 0in 0in 0in;border-color:-moz-use-text-color -moz-use-text-color'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'> <a href="mailto:gmx-users-bounces@gromacs.org">gmx-users-bounces@gromacs.org</a> [<a href="mailto:gmx-users-bounces@gromacs.org">mailto:gmx-users-bounces@gromacs.org</a>] <b>On Behalf Of </b>Mark Abraham<br><b>Sent:</b> Wednesday, November 10, 2010 9:08 PM<br><b>To:</b> Discussion list for GROMACS users<br><b>Subject:</b> Re: [gmx-users] mdrun -rerun: bonded interactions of protein</span><o:p></o:p></p></div></div><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>On 10/11/2010 11:29 PM, NG HUI WEN wrote: <o:p></o:p></p><p class=MsoNormal>Hi Gmxusers,<o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>I have been trying to run mdrun –rerun to get the energy of the protein in my protein-lipid system. I know similar questions have been raised on this topic before, I have tried to glean useful information from them to solve my problem but unfortunately to no avail. Thanks for your patience! <o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>As I did not have energygrps in the initial .mdp file, I included it this time <o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>integrator = md <br>nsteps = 0 <br>dt = 0.002 <br>nstxout = 50000 <br>nstvout = 50000 <br>nstenergy = 500 <br>nstlog = 500 <br>Continuation = yes <br>constraint_algorithm = lincs <br>constraints = all-bonds <br>lincs_iter = 1 <br>lincs_order = 4 <br>ns_type = grid <br>nstlist = 5 </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>rlist = 1.2 <br>rcoulomb = 1.2 <br>rvdw = 1.2 <br>coulombtype = PME <br>pme_order = 4 <br>fourierspacing = 0.16 <br>tcoupl = Nose-Hoover <br>tc-grps = Protein POPE SOL_CL- </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>tau_t = 0.1 0.1 0.1 <br>ref_t = 323 323 323 <br>pcoupl = Parrinello-Rahman <br>pcoupltype = semiisotropic </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>tau_p = 5.0 <br>ref_p = 1.0 1.0 <br>compressibility = 4.5e-5 4.5e-5 <br>pbc = xyz <br>DispCorr = EnerPres <br>gen_vel = no <br>nstcomm = 1<br>comm-mode = Linear<br>comm-grps = Protein_POPE SOL_CL-<br><b>energygrps = Protein SOL POPE</b></span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'> </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>I then did </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>1)grompp –f new.mdp –n index.ndx –c old.tpr –o rerun.tpr –p topol.top</span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>2)trjconv –f old.trr –n index.ndx –s rerun.tpr –o rerun.trr (when prompted, I selected “0” system)</span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>3)mdrun –s rerun.tpr –rerun rerun.trr</span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'> </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'>I notice that the previous post <a href="http://oldwww.gromacs.org/pipermail/gmx-users/2009-January/038968.html">http://oldwww.gromacs.org/pipermail/gmx-users/2009-January/038968.html</a> suggested to use tpbconv (on rerun.tpr) and trjconv (on rerun.trr) to extract the protein only. While it was possible to do so with trjconv, it wasn’t feasible with tpbconv (I’m using gromacs 4.0.7) – I might have missed out something as I did not get any prompt/output (see below)</span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'> </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>tpbconv -s topol.tpr -n index_P.ndx -o rerun2.tpr</span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'> </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>Reading toplogy and shit from topol.tpr<br>Reading file topol.tpr, VERSION 4.0.7 (single precision)<br>0 steps (0 ps) remaining from first run.<br>You've simulated long enough. Not writing tpr file</span><o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>Looking at the code, tpbconv checks for whether there are any more steps to simulate before even considering letting you use it in the "create subset" mode. You could argue that this is buggy, because the way it computes whether there are any more steps will always indicate no more steps in such cases. However, the workaround is to use tpbconv -nsteps -1 (as well as the other stuff). Let me know how this goes and I'll update the documentation.<br><br><br><br></span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:10.0pt;font-family:"Courier New"'> </span><o:p></o:p></p><p class=MsoNormal>Using the g_energy command on the output energy.edr file, I got among others, these options to choose<o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>49 Coul-SR:Protein-Protein 50 LJ-SR:Protein-Protein </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>51 Coul-14:Protein-Protein 52 LJ-14:Protein-Protein </span><o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal>In order to get the energy of the protein, I reckon I have to add 49,50,51,52 (to account for the nonbonded components) and<o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>I think that you can make a case either way for 1-4 interactions - they're algorithmically similar to the other non-bonded interactions, but their parameter values should be tightly coupled to some other of the bonded parameters, but then in several forcefields those values are just scaled versions of the normal ones... I'd guess most people call them non-bonded.<br><br><br><br></span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>1 Angle 2 G96Angle 3 Proper-Dih. 4 Ryckaert-Bell. 5 Improper-Dih </span><o:p></o:p></p><p class=MsoPlainText><span style='font-size:9.0pt;font-family:"Courier New"'>f</span>or the bonded components. However, I think 1-5 is the bonded terms for the system and not the protein alone. Can anyone help me with this?<o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>Compare values from reruns on the subset-tpr and the full-tpr. I don't know whether/how well that works. In extremis, you should be able to reduce the .tpr to a single interaction.<br><br><br><br></span><o:p></o:p></p><p class=MsoPlainText> <o:p></o:p></p><p class=MsoPlainText> <o:p></o:p></p><p class=MsoPlainText>Also, on a slightly different note, this post <span style='font-size:10.0pt;font-family:"Courier New"'><a href="http://oldwww.gromacs.org/pipermail/gmx-users/2005-July/016307.html">http://oldwww.gromacs.org/pipermail/gmx-users/2005-July/016307.html</a></span> suggested that the force constant of the solvent (DMSO) to be adjusted to zero.<span style='font-size:10.0pt;font-family:"Courier New"'> Am I right to think that it does not apply to my case as my protein-lipid system </span>is solvated with SPC? (I read that SPC is rigid water. I did not add –DFLEXIBLE in .mdp)<o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><br>That was in the context of a full-tpr rerun. The point is that atoms that have been constrained don't contribute to relevant sums. Because you are using constraints, there's no "Bonds" energy sum for any atom pair. Because the DMSO was a flexible model, its bonded-interactions contributions need to be subtracted (i.e. parameters set to zero) to get a group-wise bonded-interaction value.<br><br>Mark<br><br><br><br></span><o:p></o:p></p><p class=MsoPlainText> <o:p></o:p></p><p class=MsoPlainText>Any help would be highly appreciated.Thanks!<o:p></o:p></p><p class=MsoPlainText> <o:p></o:p></p><p class=MsoPlainText>HW<o:p></o:p></p><p class=MsoNormal><span style='font-size:12.0pt;font-family:"Times New Roman","serif"'><< </span><o:p></o:p></p><p><span style='font-size:10.0pt;font-family:"Arial","sans-serif"'>This message and any attachment are intended solely for the addressee and may contain confidential information. If you have received this message in error, please send it back to me, and immediately delete it. 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