# INRATE: help and advice

Consult the reference manual for further details and worked examples.
W.G.Bardsley, University of Manchester, U.K.

This program uses arbitrary models for what is essentially model free data smoothing, in order to estimate characteristic features of the data sets, such as initial rates in enzyme kinetics, or lag times or asymptotic rates in transport studies.
The models for y = f(t) are defined as follows.

1. The linear model (1/2 parameters)

               f(t) = Bt + C

   This can be used when the data are linear (approximately).
2. The quadratic model (2/3 parameters)

               f(t) = At^2 + Bt + C

   This should be used when only the initial data points are to be analysed to estimate an initial rate.
3. The exponential model (2/3 parameters)

               f(t) = alpha[1 - exp(-beta.t)] + C

   This can be used when initial rates and final horizontal asymptotes are to be estimated from the data.
4. The Hill/Michaelis-Menten model (2/3/4 parameters)

               f(t) = Vmax.t^n/(Km^n + t^n) + C

   This can be used when final horizontal asymptotes (also initial rates if n = 1) are to be estimated from the data.
5. The coupled assay, transient kinetic model (3/4 parameters)

               f(t) = Pt + Q[1 - exp(-R.t)] + C

   This is used for initial rates, lag times and/or inclined linear asymptotes as found with lag and/or burst kinetics.

Including a constant term C

Your data may have a nonzero f(0) baseline, e.g. absorbance or background count may not be zero when t = 0, so a model of the form g(t) + A, where g(0) = 0 and A is estimated, might be appropriate to correct for the uncertainty in f(0).

There could be uncertainty in the point t = 0, e.g. if the quenching time is not known exactly when a model of the form g(t - B) with B estimated might be required.

Models like f(t) = g(t - B) + A to cover both cases cannot be used since they are overdetermined, i.e. phi(A, B) = 0.

When t = 0 the models provided are equal to C, i.e. f(0) = C so you can have a best-fit curve through the origin or else estimate the extra constant term C. Unfortunately this can make the curve-fitting more difficult and, in some circumstances, can lead to biased estimates or even failure to converge to a useful solution.

Which models to use

- Model 1 is only useful with reasonably linear data sets.
- Model 2 fits monotonically bending types of curves but it can not be used to estimate final asymtotes. Select this model if you just have early time points.
- Model 3 fits data curving monotonically to an asymptote and estimates initial rates and asymptotes. Select this model if you have a complete time course and want the initial rate and final horizontal asymptote.
- Model 4 is like model 2 but also fits sigmoid (n > 1) or non sigmoid (n < 1) curves. You can fix n ( e.g. n = 1 is the Michaelis-Menten equation plus constant ) or else allow n to be estimated. If n < 1 the initial slope is infinite and if n > 1 it is zero, when this model can only estimate final asymptotes not initial rates. Use these models for saturation binding type curves.
- Model 5 estimates initial rates P + QR, relaxation times 1/R, lag times -(Q + C)/P, and asymptotes Pt + (Q+C), for coupled enzyme assays or transient kinetics.

Except for 2 and 5, these models do not fit turning points.

Test files for models 1 to 5

Test files are provided so that you can practise and see what is involved in fitting the various models. Observe the effect of fixing the zero point or letting the program estimate it. Note that the program will not accept negative data values.
Model 1
Use any linear data set such as line.tf1.
Model 2
Use inrate.tf1 which is an example of gently upward curving data.
Model 3
Use inrate.tf2 which is typical data for the movement of solute into or from vesicles, with no time lag but sufficient time to approach equilibrium. For emptying subtract readings from the initial one to transform your data into data that increases from zero.
Model 4
Use inrate.tf3. Note that you can fix n at a chosen value or let the program estimate n. This will only work if the best-fit n is close to 1 since estimation of parameters used as exponents depends critically on starting estimates. Estimate n first, then fix n.
Model 5
Use inrate.tf4 as an example of a lag phase leading to an inclined linear asymptote.

Advice

1. Input your data from a file, not directly from a terminal.
2. Use MAKFIL to prepare your data and EDITFL to edit/weight.
3. If you only have duplicates or triplicates it may be best to set all standard errors equal to 1 in the data file so the program will default to unweighted type of regression.
4. Prepare your data file so that f(t) increases with time t.
5. For g(t) as decreasing data supply f(t) = g(0) - g(t).
6. Prepare your data file so that f(0) = 0 if it is possible.
7. Select the best-fit curve through the origin if possible.
8. If there is an unknown baseline correction in either f(t) or t itself select the option to vary the constant term C.
9. If C is varied the program will attempt to find the point where f(t) = 0 by numerical methods in order to calculate df/dt when f(t) = 0 in case you want to correct bias in t.
10. Experiment with the models until you find the one that is best for your particular type of data. Usually it should only be necessary to use just one or two models routinely.
11. If your data has turning points or you require areas use programs CALCURVE, COMPARE, SPLINE.
12. For growth curves use GCFIT.