in which the bracketed entries are options described below. The output can be piped to XMGR using the command string:

The output can be simultaneously directed to a file and piped to XMGR using the command string:

- -help
- Using this option alone will provide a brief synopsis of the program.
- -grid
- By default, curvefit assumes that the user will provide initial guesses for the parameter values to be optimized. If the -grid option is specified, then the the initial values will be chosen by a grid search. The user must provide lower bound, upper bound and number of grid steps to use for each parameter.
- -jack
- By default, curvefit provides estimates of the uncertainties in the fitted parameters both from the covariance matrix and from a Monte Carlo simulation. If -jack is specified, then a jackknife simulation is performed instead of the Monte Carlo simulation.
- -debug
- Echo the input back to the terminal for debugging purposes.
- -noerror
- By default, curvefit assumes that data will be input as (x, y, dy) triples (where dy is the uncertainty in y). If -noerror is specified, then only (x,y) pairs will be read. -noerror implies -jack because the Monte Carlo simulations cannot be done without uncertainties being provided.
- -xmgr
- Produce output for plotting using the XMGR software package.
- -raw
- The data will be read from a plain file without any header information. The user will be prompted for other information.
- -r seed
- Specifies an initial seed for the random number generator. If USE_GETSEED is defined in the Makefile for the program, then entering a seed is not necessary because the program will use the system clock to generate the seed. The routine getseed.f may need to be re-written for use on systems other than Silicon Graphics in order to use the USE_GETSEED compiler option.
- -m filename
- Specifies a filename to be used for writing the values of the fitted paramters determined for each Monte Carlo step in the Monte Carlo simulation of uncertainties. This file is useful for performing error analysis during subsequent calculations using fitted parameters.
- -f filename
- Specifies a filename to be read for input, rather than interactive data entry from the terminal. The format of the input file is given below.

The input associated with each keyword is described below:title string fields #fields field_1 .... field_n function string string [opt/fix] real real integer . . . string [opt/fix] real real integer xmgr string . . . string data real real real real . . . real real real real

- title string
- A title for the data of up to 80 characters
- fields
- This keyword is followed by the number of static magnetic fields used for data collection and then by the values of the static magnetic fields in units of tesla.
- function string
- String is one of the defined function names. The functions are listed using
the command
*curvefit -help*. The function keyword is followd by M input lines, one for each parameter in the function. In the default mode, each line consists of a string defining the name of the parameter and a real number defining the initial guess for the parameter. If*-grid*is specified, the parameter string is followed by three entries: a real number defining the lower bound for the parameter, a real number defining the upper bound for the parameter and an integer defining the number of search steps between the lower and upper bounds. The string defining the name of the parameter can be followed by an optional string with the value 'fix' or 'opt'. If the keyword 'opt' is specified, then the following values on the line are treated exactly as if the string 'opt' were omitted. If the string value is 'fix', then the next two fields are read as fixed values, not to be optimized, of the parameter and the error in the fixed parameter (which can be set to zero). The error is used to perform a Monte Carlo simulation of the uncertainties in the fitted parameters due to variations in the fixed parameters. - xmgr
- This keyword is followed by options used for XMGR. Each of these inputs consists of the keyword @ followed by a string setting some XMGR option. See the sample input files provided or the XMGR help pages for more information. If the -xmgr option is not specified, these entries are ignored.
- data
- This keyword is followed by N lines of data, one line for each data point.
The data is input as (x, y, dy, field) quadruples, unless the
*-noerror*option is specified. In this case, the data is input as (x,y, field) triples. x = 1/tcp, y = R2(1/tcp), in which tcp is the delay between 180 degree pulses in the CPMG experiment and R2(1/tcp) is the relaxation rate constant; dy is the experimental uncertainty in R2(1/tcp). If no uncertainties are specified for the y values, then the data may need to be scaled to obtain good convergence of the program.

General CPMG function for all time scales R2(1/tcp)=f(R2,papb,dw,kex) Function: Full_CPMG Parameters: R2, papb, dw, kex Fast limit cpmg function R2(1/tcp)=R2+Rex*(1 - (2*Tau/tcp)*tanh(1/(2*Tau/tcp))) Function: CPMG Parameters: R2, Rex, Tau Ishima and Torchia approximation for skewed populations and all time scales R2(1/tcp)=R2+Rex/(1+Tau*sqrt(144/tcp**4+PaDw**4)) Function: Ishima' Parameters: R2, Rex, PaDw, Tau Full CPMG function without R2 offset R2(1/tcp)=f(papb,dw,kex)' Function: Full_Rex Parameters: papb, dw, kex Fast limit cpmg function without R2 offset R2(1/tcp)=Rex*(1 - (2*Tau/tcp)*tanh(1/(2*Tau/tcp))) Function: Rex Parameters: Rex, Tau Fast limit cpmg function for 3 sites R2(1/tcp)=R2+Sum{Rex*(1 - (2*Tau/tcp)*tanh(1/(2*Tau/tcp)))} Function: 3-site_CPMG Parameters: R2,Rex1, Tau1, Rex2, Tau2 Fast limit cpmg function for 3 sites without R2 offset R2(1/tcp)=Sum{Rex*(1 - (2*Tau/tcp)*tanh(1/(2*Tau/tcp)))} Function: 3-site_CPMG Parameters: R2,Rex1, Tau1, Rex2, Tau2

In these expressions, pa and pb are the site populations, dw is the chemical shift difference between sites (in units of 1/s), kex = 1/Tau is the exchange rate constant, and Rex = pa pb dw^2 / kex. References for the above fitting functions are given below. Instructions for adding additional functions are given below.

A sample input file is given below:

If the -raw flag is used, the input file format consists only of data in (x,y,dy,field) quadruples or (x,y,field) triples:title cys38 fields 2 11.74 14.1 function CPMG R2 4 10 20 Rex 0 100.0 100 tex 0 10.0 100 xmgr @ XAXIS LABEL "1/tcp (1/ms)" @ YAXIS LABEL "R2(tcp) (1/s)" @ XAXIS TICKLABEL FORMAT DECIMAL @ YAXIS TICKLABEL FORMAT DECIMAL @ XAXIS TICKLABEL CHAR SIZE 0.8 @ YAXIS TICKLABEL CHAR SIZE 0.8 @ WORLD XMIN 0.0 data 1.000 7.39 0.07 11.74 0.667 8.35 0.10 11.74 0.500 9.29 0.06 11.74 0.250 11.24 0.24 11.74 0.152 12.49 0.23 11.74 0.0926 13.23 0.15 11.74 0.0155 15.07 0.07 11.74 # 1.000 8.38 0.38 14.08 0.667 9.64 0.14 14.08 0.500 11.53 0.31 14.08 0.250 14.08 0.30 14.08 0.152 15.78 0.14 14.08 0.0926 16.56 0.34 14.08 0.0155 18.69 0.41 14.08

A sample input file is given below:real real real real . . . real real real real

1.000 7.39 0.07 11.74 0.667 8.35 0.10 11.74 0.500 9.29 0.06 11.74 0.250 11.24 0.24 11.74 0.152 12.49 0.23 11.74 0.0926 13.23 0.15 11.74 0.0155 15.07 0.07 11.74 1.000 8.38 0.38 14.08 0.667 9.64 0.14 14.08 0.500 11.53 0.31 14.08 0.250 14.08 0.30 14.08 0.152 15.78 0.14 14.08 0.0926 16.56 0.34 14.08 0.0155 18.69 0.41 14.08

The output from the program is given below for the above input file:

# Least-Squares Curve Fitting Results # # title cys38 # function CPMG # equation y=R2+Rex*(1 - 2*Tau*x*tanh(1/(2*Tau*x))) # points 14 # X2 57.2108 # X2(red) 5.2010 # # Parameter Fitted_Value Fitted_Error Sim_value Sim_error # R2 6.4222 0.1075 6.4234 0.1046 # Rex 8.6279 0.1047 8.6274 0.1045 # Tau 0.7754 0.0223 0.7760 0.0210 # # %tile X2 # 0.0500 4.8460 # 0.1000 5.6655 # 0.1500 6.7263 # 0.2000 7.2215 # 0.2500 8.0515 # 0.3000 8.5073 # 0.3500 9.0708 # 0.4000 9.6372 # 0.4500 10.1745 # 0.5000 10.6080 # 0.5500 11.1242 # 0.6000 11.5896 # 0.6500 12.3084 # 0.7000 12.9874 # 0.7500 13.7660 # 0.8000 14.6704 # 0.8500 16.0189 # 0.9000 17.8107 # 0.9500 20.1585 #

Additional output is appended to the above if the *-xmgr option*
is specified. The output is mostly self-explanatory. The reduced chi-square
variable [X2(red)] is given by X2/(N-M), in which X2 is the chi-square value
for the best-fit model, N is the number of data points, and M is the number of
parameters in the function. If Monte Carlo simulations are performed, the
distribution of X2 is estimated and the percentiles of the distribution (from
5% to 95%) are reported.
The XMGR output produced using the above input file appears below.

will fit all files with names of the form string.DATA and produce output files string.DATA.out.

- Increase the variable
*nfuncs*by one. This is the total number of defined functions. - Set
*fnames(i) = 'string'*, where string is the function name without embedded spaces or tabs and i is the index of the function in the library. - Set
*feqs(i) = 'string'*, where string is the functional form y=f(x) without embedded spaces and i is the index of the function in the library. - Set
*nparms(i) = M*, in which M is equal to the number of parameters in the function. - For k=1 to M, set
*parnam(k,i) = 'string'*in which string is the name of the parameter, without embedded spaces, and i is the index of the function in the library.

in which string is the function name and expression is the FORTRAN representation of the function. The parameters of the function are a(1) to a(M).elseif (fname.eq.'string') then func='expression'

in which string is the function name and expression is the FORTRAN representation of the derivatives of the function with respect to a(1) to a(M).elseif (fname.eq.'string') then dyda(1)='expression' . . . dyda(M)='expression'

Arthur G. Palmer

Department of Biochemistry and Molecular Biophysics

Columbia University

630 West 168th Street

New York, NY 10032

email: agp6@columbia.edu

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the

Free Software Foundation, Inc.

59 Temple Place - Suite 330

Boston, MA 02111-1307, USA.

This program uses some software routines copyrighted by Numerical Recipes Software. You should obtain a license from Numerical Recipes if you do not have one already. You can obtain an academic workstation license by sending your name, address, email address, workstation hostname, workstation internet address, workstation brand and model number, and a check for $50.00 to

Numerical Recipes Software

P.O. Box 243

Cambridge, MA 02238

Be certain to state that you want the FORTRAN version of the software. You will also need the BLAS library installed on your workstation. This library is normally supplied by the workstation vendor, or can be obtained from www.netlib.org.

- Version 1.0 - Initial release August 3, 2001
- Version 1.1 -Updated for Linux (4/26/02)
- Version 1.2 - December 15, 2006
- Version 1.21 - fixed error with Monte Carlo output - August 2, 2008
- Version 1.30 - added 3-site CPMG functions, but not released publically
- Version 1.40 - added option to fix parameter values - May 8, 2009
- Version 1.42 - minor update
- Version 1.43 - minor update, September 15, 2009