Abstract for IBS2006
Aromatic Ring Current Shifts:
Implications for Conformations in Presence of Local and Global Torsional Motions With Respect to a Site in Macromolecules
S.Aravamudhan
Department of Chemistry
North Eastern Hill University
PO NEHU Campus Mawkynroh Umshing
SHILLONG 793022 Meghalaya
The aromatic ring current shifts are useful in certain contexts to infer the proton locations with respect to the aromatic ring present at a specified site within a biological macromolecule. But, there have been ambiguities in applying this method when it was found that the procedure and equations can be applied for using the calculated ring current shift values on the basis of the geometrical specifications. Since in solid crystals only fixed orientations are encountered, the sensitivity of the isotropic ring current shifts can be good enough by taking into consideration the possible range of variations in torsional angles. But, if it has to be applied in solution state the considerations are different due to the fact that there should be an explicit averaging of shift values corresponding to the displacements during torsional motions.
Considering the uncertainties reportedly encountered in such contexts, an effort is being made to find out the possibility of improving the efficacy of the ring current shift applications by calculating the full tensor form of the aromatic ring current shifts instead of using the equations given for the isotropic values of the ring current shifts.
1. One of the striking instance of possible improvement would be due to the fact that, the isotropic shifts are non zero only if the susceptibility tensor is anisotropic (49 x10^{6}) as in the case of Aromatic Ring. There could be similar contributions also from other groups but with much less anisotropy whose contributions to isotropic shift values would be negligible. This is the reason always aromatic ring current is considered predominantly to contribute by the "through space" magnetic dipole model.
It may be possible to find that the trace value range is much less than the range of variation of 'xx' (generalised reference to coordinate relating to the magnetic field direction) component by the full tensor calculation. Thus the sensitivity can be better for fixing the coordinates. When the motions are not fast enough, then the isotropic averaging over all orientations may not be applicable. The isotropic shift equation requires that during the motion the proton position remains unchanged in the Aromatic Molecule Fixed coordinate axes system. If the proton is not in any way fixed by chemical bonding relative to the aromatic system but there is a relative motion of the aromatic frame work and the radial vector of the proton with respect to the sixfold symmetry axis of the aromatic ring, then the equations for isotropic average shifts are no longer relevant but by the full tensor equation can be subjected to appropriate coordinate transformations and the full shielding tensor can be calculated for the displacements under a torsional motion and after from the set of the full tensors calculated appropriate averaging can be effected.
A simplified model calculation would be presented for the case (i) when the radial proton vector is fixed with respect to the six fold symmetry axis (local motion) and for the case (ii) when the radial vector oscillates (global motion) with respect to the six fold symmetry axes to examine for the advantages of the calculation of Full Tensor over the only isotropic ring current shift values.
 Original Message  From: "Gautam Basu" gautamda@gmail.com To: "Gautam Basu" gautamda@gmail.com Cc: soumen.basak@saha.ac.in; pinak@boseinst.ernet.in; sidroy@vsnl.com; chanchaldg2000@yahoo.com; soumalee@wbut.ac.in; vcwbut@sify.com Sent: Monday, December 05, 2005 4:30 AM Subject: IBS2006 POSTER > DEAR IBS2006 PARTICIPANT: > > Your abstract for IBS2006 is now accepted as a poster presentation. > Please find {POSTER BS019 in Session Biological Spectroscopy} the abstract number of your poster from the attached pdf > file  all abstracts have been divided into five broad categories: 1) > BS / Biological Spectroscopy, 2) PFD / Protein Folding and Design, 3) > CB / Computational Biology and Bioinformatics, 4) XR / Xray > Crystallography: Structure and Interaction, 5) NA / Nucleic Acids. > > There will be two poster sessions at IBS2006 (the information on the > website will soon be updated): > > Jan 07, 2006 / 2:00 PM  3:00 PM : all abstracts starting with "BS" and "PFD" > Jan 08, 2006 / 2:15 PM  3:15 PM : all abstracts starting with "CB", > "XR" and "NA" > > The poster display area will be 1m x 1m > > All displayed posters will be considered for five best poster award > during the symposium. > > Those who were selected for oral presentations from the submitted > abstracts have already been informed separately. > > Please feel free to ask me any questions about your abstract / poster. > > With best regards, > > Gautam Basu > >  > Gautam Basu > Jt.convener, IBS2006 > http://www.saha.ac.in/biop/ibs.2006  Original Message  From: "Gautam Basu" To: "Vaishali Shah" Cc: "Soumalee Basu" Sent: Sunday, January 01, 2006 11:42 PM Subject: IBS2006 Type II accommodation at Udayachal > Dear IBS2006 participant: > I am appending your IBS2006 accommodation details below. > Type II (double occupancy) at: > > Udyachal Tourist Lodge > (Landmark  Mishra's Restaurant and Purta Bhawan at Salt Lake): > Block  DG, Sector  II > Salt Lake City, Kolkata 700 091. > Phone: +91 33 2337 6246/2358 9347 > > To reach your place of accommodation from Howrah Station or the > Airport please take a taxi (you can get prepaid taxis if you specify > the area you want to go) to "Salt Lake". Use the landmark mentioned > above. If you have problems please call me on my mobile (9231874575). > > Venue of conference: > > Auditorium of Saha Institute of Nuclear Physics > (Near Baisakhi Island ask for "Saha Institute" Office): > Saha Institute of Nuclear Physics, Block  AF, Sector I > Salt Lake City, Kolkata 700 064. > Phone: +91 33 2337 1253 > > To reach SINP from Howrah Station or the Airport please take a taxi > (you can get prepaid taxis if you specify the area you want to go) to > "Salt Lake". The land mark is "Baishakhi Island" (here island means a > fourway crossing). Please ask anyone. If you have problems please > call me on my mobile (9231874575). > > To reach SINP from inside Salt Lake, take a bus / autorickshaw / > cycle rickshaw that goes to "Baishakhi" islnad. Ask for Saha > Institute of Nuclear Physics (SINP) there. If you have problems > please call me on my modile (9231874575). > > Please confirm the receipt of this letter. > > Gautam Basu > Jt.convener > IBS2006 > http://www.saha.ac.in/biop/ibs.2006 > > P.S. Please note that we have already paid for the entire period > (69) and arranged for breakfast during your stay. We will collect > the cost of accommodation from you on a flat basis (Rs. 250/day > including breakfast). Transportation will be available from your > place of stay to the conference and back. We will provide lunch and > tea during the conference (Jan 79). Dinners on Jan 7 and 8 are part > of the conference. For food on Jan 6, please coordinate with me since > each person will arrive at a different time. > > If you have any special request (like pick up from the airport or > Station, or accommodation beyond the normal dates, 69 Jan) please > let me know now. If you have already put in some special request, > please resend it again so that we can double confirm it. > > In the next mail I will respond to your special requests individually.  Original Message  From: Aravamudhan, S.Dr. To: Gautam Basu Sent: Monday, January 02, 2006 9:58 AM Subject: Re: IBS2006 Type II accommodation at Udayachal Dear Dr.Gautam Basu, Thank you for the message on accommodation and the approaches. Please take special note of the fact that due to flight booking considerations I had to book my ticket for travel on the 5th Jan. 2006 and hence I should be reaching Kolkata Airport on the 5th Jan. 2006 Flight Schedule particulars: Flight No: S2 312 Date of travel 5th Jan. 2006 Departure at Guwahati: 14:55 hrs Arrival in Kolkata: 16.05 hrs Hence I would require Boarding provisions also for 5th Dinner and through 6th Jan. 2006 Please let me know the conveniences for this early arrival at the Venue for the IBS2006. Best regards, S.Aravamudhan  Original Message  From: Gautam Basu To: Aravamudhan, S.Dr. Sent: Monday, January 02, 2006 10:26 AM Subject: Re: IBS2006 Type II accommodation at Udayachal We are aware of your special case. On 5th, as you walk out of the terminal, someone will wait for you outside the exit with your name on a placard to receive you and take you to your designated place of stay. It may so happen that for the first night you stay at some other place (not Udayachal). Please call me on my mobile if you have any problems after you arrive. Gautam 
Contents for the presentation of the materials at IBS2006 for the Abstract as above
The contents of this contribution addresses itself to the question of the rationales for estimating the ring current effects on the NMR chemical shifts in Bio(macro)molecules when the molecular moieties can undergo complicated motions, particularly in situations when the proton influenced by the ring current effects is not bonded to the molecule containing the aromatic ring (the source of ring current effects)
This situation is envisaged in Figure1 which is being reproduced from the earlier poster presentation by this author at the IBS meetings : http://geocities.com/inboxnehu_sa/NSCMB2004.html (Sheet12; IBS2004)
FIGURE1
Case (i) above is the familiar case where at appropriately fast rotational motions the ring current effects can be estimated by the Conventional Equations for the isotropic Chemical shift contributions. In this context it is suggested here that the relevant materials in this context may be looked for in the references included for the Abstract of IBS2004 as can be found at the Web Page http://aravamudhans.ucoz.com/Abstract_Particulars_NSCMB2004.html
These references are reproduced below:
[1] NMR in Medicine and Biology, K.H.Hausser and
H.R.Kalbitzer, p102, Springer
Verlag (1991).<br>
[2] Application
of Ring Current effects,Stephen J.Perkins in Biological
magnetic
resonance Vol.4 p193, Edited by Lawrence J.Berliner and Jaques Reuben,
Plenum Press(1982)<br>
[3] Investigating the Feasibility by
S.Aravamudhan page 501, Proceedings of
the Joint 29th Ampere13th ISMAR
International Conference,TU Berlin 1998. <br>
[4] Poster presentations
by S.Aravamudhan at the Annual Meetings of IBS at UOM
Chennai in 2002 and at
IIT Roorkee in
2003.
See the Webpage link http://aravamudhans.ucoz.com/amudhan20012000/Confview_link.html
at the reference for Abstract for IBS2005 http://aravamudhans.ucoz.com/Abstract_Particulars_NSCMB2004.html
The case (ii) in Figure1 above can be considered to be giving rise to two further possibilities. This is the consequence of the fact that the motions of the PAS (Principal Axes System for the Aromatic Ring Current Susceptibilities) in the aromatic molecule can be independent of the motions of the Position Vector of the Proton specified in the Laboratory FixedFrame of reference. This is illustrated in the following two figure: Figure2
FIGURE2
>
The above stated exceptional situations require the calculation of Full tensor for the Ring Current effects instead of only the Trace which is the average of all the three diagonal elements of the Tensor. However if the Full Tensor (9elements of the 3 x 3 Matrix) are available, then it is a simple matter to calculate the trace, and this value should be the isotropically averaged Shift value observable under very fast motions as in liquids. the advantages of USING the Tensor component σ_{zz} instead of the trace 'σ' would stand illustrated, to be convinced.
A beginning would be made with the familiarizing of the principal component values of the Aromatic Susceptibility Tensor and the anisotropy value for the same. Then a brief description of the procedure for the calculation would be given. Then a lead would be provided into the calculated results.
FIGURE3
http://saravamudhan.tripod.com/shield_demag_susceptibility/id2.html
Start with the situation when the laboratory fixed frame and the aromatic principal axes system are the same and the Magnetic field is applied along the ZAxis of the lab frame. Proton is located at appoint on the Zaxis at a distance of 20 A˚. In order to provide for the possible longer distances between proton and the aromatic rings in the situations like in FIGURE1, a 20 A˚ is set for the calculations. Comparisons with smaller distance values can be then much more easily tractable for the relevant differences in the shifts to be related to the time scales of the motions in the molecular systems.
FIGURE4
A TYPICAL CALCULATION OF ISOTROPIC VALUES
Graphical Display of Results
This above Value of 6.92 x 10^{9} may be compared with similar data reported in Literature for isotropic values calculated using the conventional equations for isotropic ring current shift values.
A Figure below Depicts the envisaged independent rotations of the Aromatic Ring and the Proton for which the graphical results of Full tensor Calculations would be given.
FIGURE5
Below are the graphical Results of calculating Full Tensor values and only the diagonal elements and the trace are plotted. If the protons are rotated about Xaxis, the Txx values would remain invariants and for proton rotation about Yaxis Tyy values would remain invariant. the symbol 'T' is used instead of 'σ'
FIGURE6
Graphs are for the following combinations of independent rotations of ring (0180 in steps of 20) and proton (0180 in steps 0f 20) about the respective axes indicted in sequential list below
Graph No Ring (aromatic) Proton (not bonded )
Rotation about Angle Rotation about Angle
1. NONE 0 deg LabY axis 0180 degrees
Tyy is invariant, 'trace' same trend as Tzz, range of Tzz is more than trace
2. NONE 0 deg LabX axis 0180 degrees
'trace' same as for 1. and Txx is invariant. Other features similar to 1.
3. LabX axis Held fixed at 40 deg LabY axis 0180 degrees
Tyy invariant, trace and Tzz trend similar, variation ranges are less; all features similar to 1.
4. LabX axis Held fixed at 40 deg LabX axis 0180 degrees
Trends are describable in similar ways as for 1., 2., &3.
5. LabX axis Held fixed at 80 deg LabYaxis 0180 degrees
Variations in trace much less and other trends are similar to the previous cases
6. LabX axis Held fixed at 80 deg LabX axis 0180 degrees
the trends being as per the earlier graphs, the ranges of variations in Tyy are more
FIGURE7
Please NOTE
For further details and for the consequences on averaging for motions and other particulars an appendix would be added to these materials.
Aromatic Ring Current Shifts:
Implications for Conformations in Presence of Local and Global Torsional Motions With Respect to a Site in Macromolecules
S.Aravamudhan
Department of Chemistry
North Eastern Hill University
PO NEHU Campus Mawkynroh Umshing
SHILLONG 793022 Meghalaya
















Sheet_1: Abstract Sheet_2: Index Sheet_3: Molecular and Laboratory axes systems which are relevant for calculation methods when the motions in macromolecules are recognized as interdependent or independent motions locally and globally Sheet_4: Diagrammatic illustration of the possible motions of the aromatic ring and the protons in the neighborhood of the aromatic ring Sheet_5: Further details and explanations for the motions referred to earlier and depicted [in Sheet_4]. Sheet_6: The equations and the methods used for the chemical shift calculations which are essentially a calculation of induced fields due to aromatic ring currents. Sheet_7: Aromatic ring Susceptibility as the Benzene ring Susceptibility Tensor; Some shift values calculated using this tensor for certain specific contexts to familiarize the methods and tabulations in this context; Further indications and comments on the motions and the consequences on the induced fields at protons due to the ring current effect. Sheet_8: A typical graphical display of the calculations using the Tensor Form equations; isotropic shift values to be compared with already reported values in literature; these values are for the protonring centre distance of 20 Angstrom. Values for a distance of 5 Angstrom can be obtained by multiplying the induced field values by 64 since the distance is reduced by a factor of 4; the shift values are inversely dependent on [distance raised to the power of 3 ]. Sheet_9: More elaborate tabulation of calculated results to become familiar with the reading of reported data for purposes of applying for the cases of vibrations and torsional motions. Sheet_10: A graphical display of the results in the form of a rotation pattern for appropriately interpolating and reading out values for specific motional situations. Sheet_11: A specific hypothetical case of how the Tensor Form can be useful when the isotropic values cannot be indicative of the motional state of the system. And further results as captions for graphical plots in the subsequent sheets. This sheet contains the main conclusions which resulted from the Calculations made at this instance of IBS2006 Sheet_12 to Sheet16: Different variations of considering the motions in the system and their corresponding displays as rotation patterns to become conversant with the required visualizations for applications 
http://aravamudhans.ucoz.com/BHU2006/NSWBCB2006_BHU.html 