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05/17/00 - GSC
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1.  Notation for matrices and arrays:

	matrix: @array
	vector: @{ $array[#i] }
	element: $array[#i][#j]

    This is all fine, but the element notation must be column by row rather 
    than row by column.  The whole issue comes down to using @{ $array[#i] } as     a convenient way to move vectors to and fro between subroutines.  We have 
    not been consistent, and this has led to a little bug with respect to 
    reading in the diffusion tensor under libYARM:file_io.c.  libYARM:file_io.c 
    was reading in the vectors correctly, but Structure_measure.pm:calcDiffPAS 
    was not passing the diffusion tensor in the vector form 
    File_io.pm:writeInput was outputting to yarm_input.  Adopting the above 
    method for arrays as a convention seems to break further things which were 
    already broken and perhaps should be fixed or permanently retired, i.e. 
    Csa.pm:rotateTensor in the call to the "C" implimentation.  The Csa.pm 
    routines don't follow this convention, but they should; however, they are 
    compartmentalized enough from the rest of the perl and C such that they 
    have maintained self-consistency.

2.  It is interesting that in the case of a DNA helix (at least with d12), 
    changing the orientation of the diffusion tensor by Pi/2 (as in the correcti    on noted in 1 above) doesn't change the outcome of the optimal correlation 
    times except in the 2nd decimal place which is significant only with 
    respect to the reported error under 100 Monte Carlo simultations.  This 
    may be purely a 13C CSA vs dipole contribution in nucleic acids, In 
    proteins, certainly, the 15N CSA principal axis and the dipole vector are 
    more aligned and might be more sensitive to this issue if this is the 
    source of the ambiguity.  In 13C the principal axis of the CSA tensor is 
    closer to Pi/2 with respect to the 1H-13C dipole vector and may render the 
    whole process slightly ambiguous.

3.  X2 vs S (variance)?  I don't believe that the X2 is a good statistic for 
    reporting the error and evaluating the best correlation times for several 
    reasons.  I have been reading "Data Reduction and Error Analysis for the 
    Physical Sciences" by Philip R. Bevington, and I don't think that 
    our 13C data makes up a normal distribution like the 15N amide data found 
    in proteins.  The experimental data is biased for certain couplings and 
    atom types because of the experimental equipment and the large spread in 
    chemical shifts for carbon (giving rise to decoupling and nutation 
    concerns) as well as the large spread in one bond couplings.  Not to 
    mention that we do not know the structure of d12 to the same degree as 
    found in proteins.  I don't know that this would fix things either, to 
    have a real structure for d12 derived from NMR measurements; we would 
    still only have a normal distribution among atom types, like C1', possibly.     In principle, we will always be dealing with sets of normal data, but they 
    will have radically different means under comparison of the atom types.
    See calcMin_Rot_Dyn.c:calc_R2R1.

4.  Which data set and why?  I don't think d12_v1 is as realiable as it should 
    be (for reasons already discussed:no errors, unsystematic treatment of C2' 
    results, repetition of highly overlapped data for C5' rather than omission 
    from the data set), and I think that the origin results, d12_v2 and d12_v3,
    are better but may be improved as well for several reasons.  The v800 can 
    only compensate under lock for field drift from Z0, but the Yale v800 
    magnet does, unfortunately, have a significant Z1 drift which causes the 
    peaks to move slightly in their chemical shifts.  This makes peaks picked 
    via intensities in the first data plane, not line up with peaks picked in 
    the final data planes.  The correlation among the data points in the 
    relaxation curves appear less than they should be, but this is not 
    observed when you integrate over a sizeable area for any one peak.  We 
    have since fixed this issue with v800, by having higher air pressure in 
    the legs of the magnet so that it no longer precesses under its own 
    lHe boiloff.  d12_v4 is complete crap, not because it was generated from 
    the odrfit implementation, but because it was generated looking for the 
    absolute minimum in X2 which led to the belief that an unphysical set of 
    parameters, namely the phase constant, reflected the data.  The phase 
    factor for the nonlinear fits should be positive and should be 5 ms (as was     accounted for in d12_v1 data analysis).  This delay comes from evolution 
    of the C-C couplings under the conversion to in-phase magnetization from 
    anti-phase at the beginning of the spin-echo period, and the conversion 
    from in-phase to anti-phase magnetization at the end of the spin-echo 
    period.  The X2 was coincidentally lower in some cases due to some 
    systematic error in the data for that atom type, but afterall not every atom    type was best fit by a negative phase constant.  This was a mistake we 
    made in evaluating the data.  I am fixing this now.

5.  Just what exactly are the assumptions and issues with the data?
	- We don't have any statistics on the reproducibility of the data, but
	  we can derive the error associated with any given measurement in a dat	  a set.
	- The data, although collected as separate sets of aromatics and 
	  sugars, are susceptible to internal variations which reflect the 
	  inhomogeneity in J(CH) as used for the INEPT transfer and J(CC) as 
	  observed during the spin-echo period for the R2 measurement.  These 
	  issues cause the sensitivity and the correlation of the data points 
	  to suck a bit.  While I don't have a ready number for the 
	  translational diffusion which effects the R2 measurement, I believe 
	  that these issues I am addressing now are more significant and make 
	  translational diffusion a moot issue (however, it is still worth 
	  noting, I believe).
	- The R2 data was measured under a spin-echo method and not a CPMG 
	  method, but unlike Palmer's work, the data was collected under a 
	  decoupling field so we do not have to worry about averaging an 
	  in-phase and anti-phase CH-dipole term as part of the calculation of 
	  R2 (and we never did worry either).  See the previous note.
	- The v800, at the time of data collection, was suffering from a bit 
	  of Z1 drift which is not fixed by the lock, as a result the peaks 
	  move a bit in chemical shift in the subspectra.  This is not 
	  impossible to deal with, but remembering this effects how we extract 
	  the data from the 2-D maps.
	- We are treating C2' and C5' data points as an average of the values 
	  measured from H2'-C2' and H2''-C2' resonances.
	- Our reporting spins are 13C, which are just not going to make 
	  themselves amenable to the same analysis as in proteins.  It is not 
	  easy to collect relaxation data sets of 13C in nucleic acids which 
	  are susceptible to the same amount and type of error, even among atom 	  types in the same data set (i.e the sugars set).  We are never 
	  going to have as homogenous or as convincing data as the amide data 
	  in proteins unless we optimize the experiments for every atom type 
	  in the 13C spectrum.

6.  Changed _ck_ subroutines to _c2k_ in libNRF:ck.c to make room for the 
    implementation of _c1k_ and _c2ki_.

7.  Fixed some sign and sine errors in libNRF:ck.c  Updated all subsequent 
    subroutines to call appropriate _c2k_ entries.  I checked all of the 
    formulas, and in most cases I got the same results as the initial layout; 
    however, I noticed that some of the factoring of terms (i.e. 2/5, to 
    reflect the literature notation of J(w)) were totally inconsistent with 
    respect to some of the derivations of the anisotropic -> isotropic terms.  
    In fact many terms were not able to be recast from some of the less 
    assumptive forms.  This is no longer the case and the relationships are 
    self-consistent now, but I deleted the 2/5 factors from libNRF:spec_dens.c 
    and adopted the factors straight from Spiess, so see libYARM:relax_rates.c 
    as well.  I know that these are not the same numbers found in the 
    literature, and we can change them once we are sure that everything is 
    working properly; however, I don't know that it makes much difference.  
    Incidentally, how did the J(w) terms come to adopt an explicit factor of 
    2/5 in the literature?

9.  Fixed the dynamics calls in libYARM:relax_rates.c to call the system 

10. Added GPL license statement.  Added copyright statement to all code 
    headings as well as pointer to GPL license coverage.  Fixed 80 column 
    nonconformities when noticed.
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