DOCUMENTATION FOR EZ-FIT V1.1
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*** EZ-FIT is an interactive computer software package that
fits experimental data to a variety of model equations. EZ-FIT
runs on an IBM-PC compatible microcomputer with a CGA graphics card
or equivalent, a requirement for the EZ-FIT plot routine. EZ-FIT
was developed specifically for the regression analysis of enzyme or
receptor kinetic data. It provides reliable parameter estimates and
determines the goodness of fit of the data to the selected model.
EZ-FIT has the facility for data entry, editing, filing, and plotting.
Up to 90 data pairs can be analyzed at once.

*** When entering data the default entries are always displayed in
square brackets [ ]. To choose the default value simply enter a
carriage return .







A menu of 14 model equations is incorporated in EZ-FIT.

1. Michaelis-Menten,
2. Iso-enzyme or two receptors,
3. Hill,
4. Competitive inhibition,
5. Noncompetitive inhibition,
6. Mixed competitive inhibition,
7. Uncompetitive inhibition,
8. Ping-Pong bi-bi,
9. Ordered bi-bi,
10. Random bi-bi,
11. Modified integrated Michaelis-Menten,
12. Agonist,
13. Antagonist (4 parameter logistic equation).
14. Substrate inhibition







*** Data from enzyme studies that are in the form of cpm,
dpm, or optical densities can be converted by EZ-FIT into moles or
Molar of product/min/mg protein. Similarly, receptor binding data can
be converted to moles bound/mg protein. EZ-FIT automatically
computes the decay of the nuclide given the number of days since its
manufacture.

As an example, we'll enter data in the form of 10,000 dpm bound
from a receptor binding study. EZ-FIT then requests the following:

ENTER THE ISOTOPE TYPE: (1)3H, (2)14C, (3)32P, (4) OTHER:[?] 3

We've entered 3 for 32P.

ENTER # DAYS ELAPSED SINCE MANUFACTURE OF ISOTOPE:[?] 14.3

We've entered 14.3.

ENTER INITIAL SPECIFIC ACTIVITY OF ISOTOPE (Ci/mmole):[?] 20

We've entered 20.

ENTER ASSAY VOLUME (ml):[?] 1000
Enter 1000 if you want your data converted to moles instead of MOLAR.
The conversion to 1000 ml negates the Molar conversion, but does not
alter the data, so that the effect is the same as converting it
to moles.

ENTER PROTEIN CONCENTRATION IN ASSAY (mg):[?] 0.050

We've entered 50 ug.

ENTER TIME OF INCUBATION (min):[?] 1

Enter 1 minute if you want your data converted to moles/min/mg. This
is the same as moles/mg for binding studies; the conversion to one
minute does not change the data and therefore has the same effect as
converting it to moles/mg.

ENTER MOLAR TYPE: (1)pM-, (2)nM-, (3)uM- /min/mg:[?] 1

We've entered 1 for pmoles.

That's all there is to it. EZ-FIT then converts the 10,000
dpm to 9 pmol/min/mg which is equivalent to 9 pmol/mg.

*** When a model function is chosen for fitting a set of data, the
user has the option of weighting or not weighting the fit. Weighting
of data may be necessary when the variance of Y(experimental) is
not constant. In this case, EZ-FIT generates the weights from an
empirical variance function or if the standard errors of Y(expt) are
included in the data set it uses them for weighting. The default
setting for weighting, when chosen, is proportional weighting.

*** When using the models 4 to 11, multiple sets of data (up to 6 sets)
can be analyzed simultaneously, thereby increasing the precision of
the Ki or Ka, Km, and Vmax values. An example of how to enter 2 sets
of data for competitive inhibition is shown below.

The first set of data contains no inhibitor, but subsequent
data sets contain increasing concentrations of inhibitor. The first
row is the velocity or specific binding, the second row is the
substrate or ligand concentration, and the third row is the inhibitor
concentration. Following each data set, enter four nines 9999 and
after the last 9999 of the last data set enter four ones 1111. This
allows EZ-FIT to keep track of the separate sets of data and to
produce separate curves for each data set. Once the data is entered,
it can be filed.

Example:
FIRST DATA GROUP:
8.7 'velocity' \
8.0 'substrate' } Do not include the comments.
0.0 'inhibitor' /

9.45
10.0
0.0

11.3
16.6
0.0

11.6
25.0
0.0

13.3
50.0
0.0

9999
NEXT DATA GROUP:
5.28 'velocity' \
8.0 'substrate' } Second curve
8.0 'inhibitor' /

6.11
10.0
8.0

8.2
16.6
8.0

9.80
25.0
8.0

11.7
50.0
8.0

9999

NEXT DATA GROUP:
1111
* END DATA SET *


Note that when entering more than one independent variable (e.g.
substrate A and inhibitor I, substrates A and B, or time and substrate B) with
each of the four competition models, with the three bi bi models, or with
the integrated MM equation, respectively, the first substrate entered in
each data sub-group is always the variable substrate A or time. Inhibitor
and substrate B are the second variables entered and are held constant in the
data sub-group.

To list your raw data files, use the 'DIRECTORY OF DATA FILES'
option on the main menu. The file name MUST contain the suffix
'.RAW' for the files to be listed.

*** Model equations 1-3 and 12-14 use only a SINGLE set of data. They
can NOT accept multiple data sets. As an example, a set of data to
be fit by the Michaelis-Menten or one-site receptor saturation model is
shown below. Notice that there are only two entries per group in this
example. The first entry is the velocity or specific binding, and the
second entry is the substrate or ligand concentration.
Example:

FIRST DATA GROUP:
8.7 'velocity' \ one curve only
8.0 'substrate' /

9.4
10.0

11.3
16.6

11.6
25.0

13.3
50.0

9999

NEXT DATA GROUP:
1111
* END DATA SET *
*** When analyzing the progress of a reaction, either enzyme or
receptor, with time, the integrated Michaelis-Menten model is
used. This model computes the initial velocity (Vo) of the reaction;
the computed values of Km and Vmax may not be accurate and caution should
be used when interpreting them. The estimates of Km and Vmax from progress
curves are most accurate when multiple curves are evaluated at different
substrate concentrations.

Since many in vitro biochemical reactions do not obey the
standard integrated form of this equation due to enzyme instability
during incubation, EZ-FIT uses a modified form of this equation that
includes a decay constant (Kvmax). This constant represents the
inactivation of the enzyme or receptor with time, during in vitro reactions.

When using this model, the units of the initial substrate (So)
concentration MUST be identical to those of the product of the
reaction (e.g. So = nmol, Product = nmol). For initial parameter
estimates, it is suggested to enter a value for Km equal to So, a
value for Vmax equal to 100 times the estimated value of Product/min,
and a Kvmax equal to 0.0001.



*** EZ-FIT requires that initial estimates of the fitted parameters be
provided. The initial estimates of the parameters (e.g. Km, Vmax, Ki, etc.)
can usually be an order of magnitude or two away from the true values.
EZ-FIT improves these rough estimates by using the Nelder-Mead Simplex
routine; convergence to a feasible area of the least-squares is likely,
given an appropriate step size. Using these values, the Gauss/Newton-
/Marquardt/Levenberg/Nash routine improves these estimates to final
values. The parameter values are always constrainted to values greater
than zero. The regression routine may be aborted at any time by press a
capital X.

A report of the results is printed and includes the original
data, the best fit curve data, the residuals, the standard error of
regression, the final parameter values (e.g. Km, Ki, Vmax, etc.) and
their asymptotic standard errors, a paired Student t test at p<0.05
to determine the accuracy of the parameter values, a Runs statistic
test of the residuals to determine if a systematic nonrandom departure
of the data from the fitted curve exists, and identification of
individual data points which depart by greater than 20 percent from the
behavior of the fitted curve (outliers). Parameter values that are not
significantly different from zero, as determined by the Student's t
test, are identified by an arrow (<--) to the right of the value.
Outlying data are also identified by arrows. The result of the Runs
test of residuals is returned as either a PASS or FAIL. To aide in discriminating between rival models for the same data
set, a goodness of fit test is used. The Akaike's information criterion
(AIC) provides an estimate of the goodness of fit for the fitted curve.
When comparing models, the model with a AIC value that is at least 2
units smaller than the rival model is the best fit.

When standard errors of Yobs are included in the data set, the
Chi-Square statistic can also be used to aide in determining the best fit
model. This is done by chosing the weighting option that uses standard
errors instead of the empirical weighting function. When comparing
models, the model with a Chi-Square value closest to 1.0 is the best fit.


*** EZ-FIT produces graphs of the data and fitted curve. Five
types of plots can be displayed for models 1 to 10. These include
X-Y, Scatchard, Eadie-Hofstee, Lineweaver-Burk, and residual plots.
Models 11, 12 and 14 display only an X-Y and residual plot. Model 13
displays four plots, an X-Y plot, a modified Scatchard plot of
(%inhibition/[Inhibitor]) vs (%inhibition), a semi-log inhibition plot,
and a residual plot.



To obtain a copy of the graph on a local printer, press the
SHIFT and PRTSC keys simultaneously while the graph is being displayed
on the monitor. NOTE: The MS-DOS program GRAPHICS.COM must be run
before the graphics screen dump will work.


*** The scale of each graph can be expanded or reduced by 30% by
entering either a '+' or '-' at the scale request statement. To
expand or reduce the graph further, exit the graph using a ,
reenter the same graph again, and enter either a '+' or '-' again.
This has the effect of expanding or reducing the expanded- or
reduced-graph by an additional 30%. This process can be repeated to
provide the proper scale so that the plotted curve can intersect an
axes instead of being clipped. If, however, an '=' is entered instead
of a '+' or '-', the scale defaults back to its original size.
Entering a '*' causes the expanded or reduced graph to be maintained
at that scale. In addition, two '++' or '--' can be used to change
the size of graph even further.


*** If upon inspection of a graph, outlying data points are observed,
the corresponding data points can be removed from the analysis using
the EDIT option and the fitting process can be repeated. A new report
is printed, and a new graph is displayed with the new fitted curve. EZ-FIT may be rerun as many times as you like, with different
models or data sets, without exiting the program.


*** END OF DOCUMENTATION **

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* *
* EZ-FIT was developed by *
* *
* Frank W. Perrella, Ph.D. *
* E.I. DuPont de Nemours & Co. *
* Glenolden Laboratory *
* 500 South Ridgeway Ave. *
* Glenolden, PA 19036 *
* *
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