NOE Calibration Using CYANA

Introduction

NOE calibration converts NOESY cross-peak intensities into upper distance limits. A certain functional relationship is assumed between peak intensities and UPLs for a given group of peaks. The most common is NOE peak volume proportional to interproton distance to the minus six:

 	V = A/d^6

where V is the peak volume (or intensity), d is the upper distance limit, and A is the calibration constant.

NOE Calibration Using CYANA 2.1

This section describes how to determine NOE calibration constants using CYANA 2.1.

Before running the calibration, the N chemical shifts in the peak list must be updated, and the peak lists separated into a list of N noes and C noes, using the UBNMR macro, macro1.

Command "calibrate"

A CYANA command calibrate is the basic calibration tool, unchanged since DYANA.

    Parameters: f(d)                      (required)
                dmin [d2 ...] dmax        (default: 2.4 5.5)
                weight=w                  (default: 1.0)
                plot=file  log  minimal   (default: none)

calibrate accepts a calibration function f(d) as the required argument.

This command uses "center" averaging. Explicit pseudoatom corrections are added to UPLs:

• Multiplicity correction is applied by dividing the peak volume by the numbers of 1H spins in pseudoatoms assigned to the peak. For instance, the volume of a cross peak between a Leu QQD pseudo atom and a Tyr QD pseudo atom is divided by a factor of 6 x 2 = 12 prior to applying the calibration function. The resulting UPL is the subject to the upper and lower cutoffs.
• Distance correction is applied by adding a distance between the pseudoatom and its constituent spins. It is applied after the application of upper and lower cutoffs. For example, for a Tyr QD pseudoatom this correction is equal to half the distance between the HD1 and HD2 spins. Distance correction can be manually performed with the distance correct command.

Type help calibrate at CYANA prompt for more information or see the DYANA documentation.

Macro "caliba"

CYANA macro caliba.cya is functionally the same as caliba.dya of DYANA. It is a more sophisticated calibration tool aimed at getting more nuanced calibration than a uniform 1/d6 dependence. CALIBA is recommended for manual structure calculation with CYANA 2.1. The caliba macro in fact uses calibrate, therefore, it also uses "center" averaging.

Caliba parameters:
                dmin=dmin                 (default: 2.4)
                dmax=dmax                 (default: 5.5)
                vmin=Vmin                 (default: 0.0)
                bb=A                      (default: calculated automatically)
                sc=B                      (default: A/dmin2)
                methyl=C                  (default: B/3)
                weight=w                  (default: 1.0)
                avedis=d                  (default: 3.4)
                plot=file                 (optional)

This macro divides each peaklist into three classes of peaks with different calibration functions and constants:

class	peaks/constraints	function
backbone	all HN/HA— HN/HA, and HN(i)/HA(i) — HB(j) with abs(i - j) < 5	V = A/d6
sidechain	neither "backbone" nor "methyl"	V = B/d4
methyl	all involving methyl groups	V = C/d4

By default, constant A is calculated from avedis - the assumed average distance between backbone atoms. It is also possible to specify the backbone constant A explicitly. Constant B is then calculated from A, and C from B

Parameters dmin and dmax are the lower and upper cutoff limits for UPLs, respectively.

Parameter vmin is useful to filter out peaks with intensities below a certain threshold. Without it even incorrectly picked peaks with intensities below S/N level will produce UPLs set at the upper cutoff.

plot is an optional parameter, used to create logarithmic plots of volumes versus corresponding minimal distances in the selected structures together with the calibration functions. It is useful for fine-tuning the calibration during structure refinement. Of course, a structure must be then loaded into CYANA before running caliba.

VERY IMPORTANT!!!. The default behavior of structure calculation (anneal, calc_all, noeassign) in CYANA 2.x is to use "sum of r^-6" averaging for UPLs. Setting expand=1 declares "sum of r^-6" averaging, and expand=0 declares "center" averaging. If your UPLs reflect "center" averaging (that is, they were created with caliba or calibrate), then

• They can be used with DYANA, CYANA 1.x and AutoStructure.
• They can be used with legacy macros in CYANA 2.1, such as habas.
• They can be used for manual structure calculation in CYANA 2.1, if expand=0 is set before calling anneal.
• Do not use them for automated structure calculation in CYANA 2.1 with noeassign. The noeassign macro employs peaks calibrate (see below) and sets expand=1. In general, do not mix them with UPLs calibrated with peaks calibrate.

Type help caliba at CYANA prompt or see the DYANA manual for more information. You can also look at the script itself in the macro subdirectory of a CYANA installation.

Command "peaks calibrate"

Command peaks calibrate is a new feature of CYANA 2.x, which produced a "sum of r^-6"-averaged calibration. The documentation for it is scarce. For example, the manual structure calculation script ~/demo/manual/CALC.cya contains these lines:

peaks      := c13,n15,aro            # names of peak lists
prot       := demo                   # names of proton lists
tolerance  := 0.040,0.030,0.45       # chemical shift tolerances
                                     # order: 1H(a), 1H(b), 13C/15N(b), 13C/15N(a)
calibration:= 6.7E5,8.2E5,8.0E4      # calibration constants (will be determined
                                     #   automatically, if commented out)
dref       := 4.2                    # average upper distance limit for
                                     #   automatic calibration
  
  calibration prot=$prot peaks=$peaks constant=$calibration dref=$dref
  peaks calibrate "**" simple
  write upl $name-in.upl

Line calibration prot=$prot peaks=$peaks constant=$calibration dref=$dref calls the macro calibration.cya, which iteratively sets calibration constants for each peaklist. If the calibration list variable is defined, its values are taken as calibration constants. If it is left blank, calibration constants are calibrated based on assumed average distance dref between all atoms of the molecule. Note that dref here is inherently different from avedis of caliba - the latter refers only to distances between backbone protons.

Line peaks calibrate "**" simple generates UPLs assuming simple C/d^6 functions with calibration constants C from the previous step. These calibration constants are thus closely related the "backbone" class constants A of caliba.

To modify upper and lower cutoffs for NOE calibration with peaks calibrate add a line set upl_values:=2.4,6.0. The defaults are 2.4 and 5.5.

The main difference from calibrate and caliba is that pseudoatom correction are not applied to resulting UPLs.

VERY IMPORTANT!!!. The default behavior of structure calculation (anneal, calc_all, noeassign) in CYANA 2.x is to use "sum of r^-6" averaging for UPLs. Setting expand=1 declares "sum of r^-6" averaging, and expand=0 declares "center" averaging. If you UPLs use "sum of r^-6" averaging (if created with peaks calibrate), then

• Do not use them with DYANA, CYANA 1.x and AutoStructure.
• Do not use them with legacy macros in CYANA 2.1, such as habas.
• They can be used for manual structure calculation in CYANA 2.1, if expand=1 is set before calling anneal.
• They can be used for automated structure calculation in CYANA 2.1 with noeassign. The noeassign macro employs peaks calibrate (see below) and sets expand=1.

The aim of this new calibration method is likely to facilitate automated NOE assignment and structure calculation with noeassign. Unlike caliba and calibrate, peaks calibrate effectively generates UPLs even for unassigned peaks assuming NOEs between single protons. If such a peak gets assigned to a pseudoatom, the required correction is applied implicitly during the calculation.

Initial NOE Calibration

After simulating and filtering one typically has three initial NOESY peaklists, for example, n.peaks, ali.peaks, and aro.peaks. The assigned peaks are intra-residue and short-range within secondary structure elements. Initial calibration is needed to verify these assignments for consistency with molecular geometry and, if possible, to derive stereospecific assignments with HABAS in CYANA. If your SequenceList and AtomList were generated with XEASY, you will need to convert them to the format of CYANA 2.1 (see the ~/demo/details/MigrateFromDyanaCyana1.cya example script). SequenceList and AtomList from CARA are already compatible.

Amide, aliphatic and aromatic protons tend to have different relaxation properties in a simultaneous 3D ¹⁵N-, ¹³C-resolved NOESY.  NOESY spectra acquired separately may have varying acquisition times. Therefore, it is recommended to run caliba separately for each peaklist.

Here is a sample run_caliba.cya script for running caliba on all three peaklists:

protocol:=caliba.log
read prot $name
 
read peaks n
peaks select "**"
peaks set volume=abs(volume)
caliba
 
read peaks ali
peaks select "**"
peaks set volume=abs(volume)
caliba
 
read peaks aro
peaks select "**"
peaks set volume=abs(volume)
caliba bb=1.0E+06
 
write upl short.upl
protocol:=

Note that you need to convert volumes to absolute values before calling caliba, otherwise negative intensities will be misinterpreted.

Macro caliba should work fine for n.peaks and ali.peaks with default parameters. Aromatic peaklist aro.peaks requires special treatment because it does not have any peaks of the backbone class. For aromatic peaklists caliba should be run either with a single bb parameter or with both bb and sc parameters. Calling it without bb parameter will cause an error.

The sc and bb parameters for aro.peaks can be estimated from the aliphatic calibration. Typically the aromatic part of the simultaneous NOESY spectrum is less sensitive than the aromatic, therefore the values should be somewhat lower.

Verifying Initial NOE Calibration

Inspect resulting UPL files to make sure the the calibration is correct. You should avoid making UPLs too tight or too loose.

Known short-range distances in the secondary structure elements constitute good reference points. Consult the table below (adapted in short form from Ref. 1).

distance	α-helix	3_10-helix	β-sheet (A)	β-sheet (P)
d_αN	3.5	3.4	2.2	2.2
d_αN(i,i+2)	4.4	3.8
d_αN(i,i+3)	3.4	3.3
d_αN(i,i+4)	4.2	3.3
d_NN	2.8	2.6	4.3	4.2
d_NN(i,i+2)	4.2	4.1

For calibration of aromatic peaklists the characteristic distances are:

	distance	center averaging
d_δβ	2.33 - 3.77	5.00 - 6.75
d_δε	2.48	7.4

Note that aromatic QD and QE are pseudoatoms and the constraints in "center" averaging mode are much larger than the distances between individual atoms.

References

1.   Wuthrich, K. (1986)  "NMR of Proteins and Nucleic Acids", page 127.