FIRM. Full Iterative Relaxation Matrix program

FIRM Full Iterative Relaxation Matrix program FIRM is a flexible program for calculating NOEs and back-calculated distance constraints using the full relaxation matrix approach. FIRM is an interactive program and will prompt for input parameters. Usually, however, FIRM will be run in the background and input will be redirected from a file. For more detailed descriptions of FIRM and its use, see the documentation that accompanies the program. Input PDB File FIRM calculates the 2-D NOE crosspeak intensities for a structural model whose coordinates are input in PDB format. To be recognized as a proton by FIRM, the first character of the atom name must be an 'H'. Except for the aromatic protons (which must be called HD1/HD2 and HE1/HE2), the names of protons are unimportant. However, for methyl groups to be recognized by FIRM, the methyl carbon atom names should be those used by AMBER 4.x, and methyl protons must follow the methyl carbon in the PDB file. Input Variables The mixing time, correlation time (tauc), and methyl rotation correlation time (taucm) are entered in seconds. Entering a negative value for tauc will turn on the option to use order parameters, as discussed later. Entering zero for taucm (or choosing an N-jump site methyl model of N=0) results in methyl groups being treated as static protons with no rotation about the methyl axis. The best value for the methyl taucm is probably 5e-11. An additional leakage term can be included to account for additional relaxation pathways. Input NOEs An NOE file of experimental intensities may be input. The format of the NOE file is comment line1 (can contain anything) comment line2 (can contain anything) atom1, res1, nres1, atom2, res2, nres2, noe... etc... format(a4,1x,a4,i3,1x,a4,1x,a4,i3,2x,f8.4) The atom names used in the NOE file must correspond to those in the PDB file. If there is no input NOE file, FIRM calculates the NOEs for the input model, writes any output files, and prompts for additional mixing times. Equivalent Protons The numerical value of the NOE input in the noe file may be substituted with the character "*". This NOE will then be flagged as equivalent with the preceding NOE. This is intended for unresolved methylene protons where only the summed intensity is observed. Although aromatic and methyl protons could also be handled in this fashion, they are best treated as described later. However, it is appropriate to use the equivalence flag with aromatic/methyl groups that have NOEs to unresolved methylene protons. Equivalencies made with "*" will result in summed NOE intensities for calculating R-factors. Also, the experimental NOE intensities will be distributed among the unresolved protons according to the calculated

intensities when merging. Note that this is NOT an averaging technique and in no way approximates methylene motions. To facilitate the input of NOEs for equivalent protons, a supplemental program equivnoe.f is provided to "flag" equivalent protons with "*". Equivnoe expects equivalent protons to be assigned with a "Q" prefix (QB = HB2/HB3; QD = HD2/HD3; etc). Methyl Groups Methyl NOEs are input as the summed intensity using the first proton of the methyl group. If the two methyl groups of Val and Leu cannot be resolved, the equivalence flag "*" should be used for the second methyl group, as described above. NOEs between protons and methyl rotor protons are calculated using an (r^-3)^2 to account for fast spinning of the methyl group. Each methyl proton is treated separately. The spectral density function is from the N-site jumping model of Tropp [J. Chem. Phys. 72, 6035 (80)]. Intra-methyl relaxation depends on the correlation time of the methyl rotor (50 ps) and is calculated using the spectral density function of Woessner [J. Chem. Phys. 36, 1 (62)]. NOEs between 2 methyl rotors are calculated in the same fashion, but a N^2-site jumping model is used to describe the proton positions on each methyl group. Acceptable input values for the N-site jump model are N=0, 3, 6, 12. Using N=12 instead of N=6 results in an NOE difference of less than 0.001. The value to use depends on if you want freely rotating methyl groups (N>3) or jumping between the 3 preferred positions (n=3) or static methyl groups (N=0). See J. Magn. Reson. 103B, 222-233 (94). Aromatic Protons In contrast to that for methyl groups, each equivalent aromatic proton must be specified in the input NOE file. Therefore, the NOE intensity used must be 1/2 (or whatever the appropriate fraction is) of the total integrated volume measured. For example, 4 entries are needed for an aromatic-aromatic NOE (2 protons from each aromatic ring are equivalent), and the noe input is the measured intensity divided by 4. The equivalence flag "*" may be used for the 3 redundant entries. This format is automatically constructed from the measured noe file (which contains a summed intensity) by the equivnoe program. NOEs between protons and equivalent aromatic protons are calculated using an r^-6 averaging to account for ring flipping [Konning et al. J. Magn. Res. 90, 111 (90)]. This is done by averaging all 4 of the crossrelaxation matrix elements (only 2 of these are unique, but they are averaged over both sides of the diagonal). For NOEs between equivalent aromatics on different residues, R is averaged over all 8 cross-relaxation elements (only 4 are unique). There is no averaging for aromatic protons on the same residue. Internal Motions As an option, internal motions may be simulated using atomic order parameters that are input in the thermalfactor column of the PDB file. The order parameter S is used to decrease the effective correlation time of an interproton vector by tau = tauc * S(i) * S(j) where tauc is the usual isotropic correlation time. The absolute value of S must range from 0.0 to 1.0. The value of order parameters may be assigned to individual protons or to groups of atoms. A more accurate method of including internal motions is to use spectral density functions Jn, which can be derived from correlation functions of molecular dynamics trajectories. If a file named "jn.dat" is present, this

file is read to input Jn for selected proton pairs. The format of the file is i, j, J(1), J(2), J(3) format(i4,i4,3e15.4) The atom numbers i and j must correspond to the atom numbers of the selected proton pair in the input PDB file. Routines for calculating spectral density functions are not included with FIRM but are available from the author. Scaling Experimental NOEs If an NOE file is input, the experimental intensities must be scaled to the calculated intensities. A calibration file may be input to specify the proton pairs that will be used to determine the scaling factor. This allows you to scale the experimental intensities over selected NOEs. The format of the calibration file is identical to that of the NOE file but the last column of NOE intensities is not read. If a calibration file is not given, then the scaling factor is determined over all the experimental NOEs. The calculated NOEs can be compared to experimental NOEs by computing an NOE R-factor, and the experimental NOEs merged (substituted) in the calculated NOE matrix in an iterative refinement procedure as discussed below. It is probably best to exclude seminal protons in scaling (and maybe even merging). Calculating NOE from a Model If an experimental NOE file is not input (i.e., the return key is pressed when prompted for an NOE input file), the program assumes that you are calculating the NOE for a PDB model. You may specify a noise level to superimpose upon the calculated NOEs. For "squared" noise, a random number between -noise and +noise is added to the computed NOE. For Gaussian noise, the value input is the s.d. of the distribution. In each case, if the result is less than zero then the NOE is set to zero. (It appears best to select NOEs above some threshold intensity before adding noise or some distant (10 angstrom) protons will appear much shorter.) The NOE is computed, specified output files are written, and the program prompts for a new mixing time. Entering zero will exit the program. If another mixing time is entered, a new NOE will be calculated and the results appended to the output file. This facilitates the generation of NOESY buildup curves as a function of mixing time. Iterative Refinement by Merging NOEs In an iterative refinement procedure using FIRM, the experimental NOEs are merged in the calculated NOE matrix to back-calculate interproton distances for structural refinement. After merging, a new relaxation matrix is calculated from the hybrid NOE matrix. If the hybrid NOE matrix is not self-consistent, negative eigenvalues will be found which must be corrected to proceed. Two different methods are available for handling this problem. The simplest is to try merging a smaller amount of the experimental NOE intensities thereby allowing the hybrid NOE matrix to slowly approach the experimental values. If the magnitude of the most negative eigenvalue is not too great, then it is also possible to add a constant term to (i.e., increase the intensity of) the diagonal elements of the NOE matrix. If negative eigenvalues are found, FIRM computes the amount by which the diagonal needs to be increased and asks whether the diagonal should be increased. If you think the increase too large then you must resort to merging a smaller fraction of the experimental NOE intensities. The cutoff that we generally use is 0.05. After calculating a hybrid relaxation matrix, the rates from the model that do not correspond to measured NOEs may be substituted back in. The relaxation rates involving equivalent aromatic protons are averaged to account for ring flipping, and the diagonal rates computed from the off-diagonal rates. A new NOE matrix is

now calculated from the resulting relaxation matrix. Negative eigenvalues may be found at this step also. However, they are not fatal, and you may proceed without adverse effects. Alternatively, the diagonal elements of the new NOE matrix may be increased by adding an additional relaxation (leakage) term. NOE R-factors R(NOE) and R(d) are computed. FIRM outputs these R-factors as well the numerator and denominator components of R(NOE). These components are useful for computing an R-factor extending over data from several mixing times. R-factors are calculated as the summed intensities of methyl protons, aromatic protons, and all proton pairs flagged with "*". Additional output includes the atom pairs with the largest deviation between the calculated and experimental NOEs. The latter information is useful for identifying errors in the input and structural regions that convergence poorly. Merging Equivalent Protons The "merging" of experimental NOEs is done somewhat differently for unresolved protons flagged with an "*". The experimental NOE intensity is divided unequally among the NOEs with a greater fraction going to the interaction with the greater calculated NOE. That is, the relative amounts of the experimental NOE associated with each of the equivalent interactions is directly proportional to the relative intensity of the calculated NOEs. Therefore, this "merging" will be model dependent. The NOE R-factors of equivalenced protons will be calculated using the summed intensities of the equivalent interactions. Automatic Refinement Procedure FIRM refinement (i.e., merging experimental and calculated NOEs) can also be done automatically. This option is useful for running FIRM in batch mode where input (and output) has been redirected from a control file. FIRM merging is performed as described above except that it is no longer possible to intervene if negative eigenvalues are found. In this case, a set of rules that are coded in the program (see source) are used to determine the action taken. As supplied, FIRM will increase the diagonal intensities by the required amount if it is less that 0.05; otherwise, the fraction of experimental intensities that are merged will be reduced by 50%. NOE Output File There are 2 major output files that can be produced by FIRM. The NOE output file contains NOESY crosspeak intensities. The format is identical to the input NOE format previously described. Crosspeaks to be output can be selected by specifying a minimum NOE or by giving a test_file containing a list of selected proton pairs. The format of the test_file is the same as the noe_file format. If a minimum NOE is used for selecting NOEs, then there is an additional option to include the diagonal intensities as well. NOE intensities are also included in the distance output file and therefore the noe output file may not be needed. The NOE outputs may also be limited by the (back-calculated) distance between protons. Entering a maximum distance of 10 or greater will ignore this method of selecting NOEs for output. Distance Output File The distance output file contains the back-calculated distances, the original PDB model distances, the calculated NOE intensities, the experimental intensities, and an estimate of the error in back-calculated distances (derived from the fit of the NOEs). The format is similar to the noe_file format with some additional fields. The atom pairs for output are determined by the input noe file. This distance file can be converted into constraint files for AMBER 4.x and DIANA structure refinement using the program dis2con.f

supplied with this distribution. Multiple Mixing Times FIRM can also be used for refinement using multiple data sets acquired with different mixing times. See documentation accompanying program for more detail. mcfirm - Monte Carlo Error Analysis By setting an optional flag in the source code, a version of FIRM can be compiled that automatically implements the Monte Carlo error analysis procedure used to determine the precision of an NMR-refined structure. Briefly, multiple NOE data sets are generated by superimposing Gaussian noise onto the NOEs calculated for the refined structure, and the error in the resulting structures represent the imprecision of the structure determination. For a discussion of this procedure, see Methods in Enzymology 240, 415-438 (1994) and Biochemistry 32, 1610-1617 (1993). Input and output for mcfirm are similar to those of FIRM. The difference is that mcfirm will cycle to facilitate multiple calculations. Instead of entering distinct NOE and distance file names, the root file name is given, and multiple output files are constructed by appending onto the root file name a numerical suffix. Shell scripts are provided that illustrate the process. Auxiliary Programs Included with FIRM Example Input File Return to NMR Software Page