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

saravamudhan@nehu.ac.in

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 six-fold 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.

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 Figure-1 which is being reproduced from the earlier poster presentation by this author at the IBS meetings : http://geocities.com/inboxnehu_sa/NSCMB2004.html  (Sheet-12; IBS2004)

FIGURE-1

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://aravamudhan-s.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 Ampere-13th 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://aravamudhan-s.ucoz.com/amudhan20012000/Confview_link.html at the reference for Abstract for IBS2005 http://aravamudhan-s.ucoz.com/Abstract_Particulars_NSCMB2004.html

The case (ii) in Figure-1 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 Fixed-Frame of reference. This is illustrated in the following two figure: Figure-2

FIGURE-2

>

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 (9-elements 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.

FIGURE-3

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 Z-Axis of the lab frame. Proton is located at appoint on the Z-axis 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 FIGURE-1, 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.

FIGURE-4

 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.

           FIGURE-5

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 X-axis, the Txx values would remain invariants and for proton rotation about Y-axis Tyy values would remain invariant. the symbol 'T' is used instead of  'σ'

FIGURE-6

Graphs are for the following combinations of independent rotations of ring (0-180 in steps of 20) and proton (0-180 in steps 0f 20) about the respective axes indicted in sequential list below

Please NOTE

For further details and   for the consequences on averaging for motions and  other particulars an appendix would be added to these materials.

The intended Appendix is now included in the TABLE displayed below as the poster materials to be downloaded. These are the finalised verison of the poster site materials for IBS2006 and the lay out is as below.

POSTER SITE of POSTER BS019: A lay-out
Sheets uploaded on 14-12-2005 at 7:11 PM by Dr.S.Aravamudhan

The Logo below is an image copied from the web site for the 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

saravamudhan@nehu.ac.in

Certificate of participation

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