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 How to: Plateau followed by one phase association

## Introduction

In the standard one-phase association equation, the increase starts at time 0. This alternative equation is used when you measure a baseline for a while, then do some experimental intervention that starts the association at some time X0.

## Entering data

Create an XY data table. Enter time into X, and response (binding, concentration ..) into Y. If you have several experimental conditions, place the first into column A, the second into column B, etc.

After entering data, click Analyze, choose nonlinear regression, choose the panel of exponential equations, and choose Plateau followed by one phase association.

## Consider constraining X0 to a constant values

If you know the time at which you initiated the association, you should constrain X0 to that value. To do this, go to the Constrain tab of the nonlinear regression dialog, set the drop down next to X0 to "Constant equal to" and enter the value.

## Model

Y= IF( X<X0, Y0,Y0 + (Plateau-Y0)*(1 - exp(-K*(X-X0)))) X0 is the time at which the association begins. Often you will set that to a constant value based on your experimental design, but otherwise Prism can fit it. It is expressed in the same time units as X.

Y0 is the average Y value up to time X0. It is expressed in the same units as Y,

Plateau is the Y value at infinite times, expressed in the same units as Y.

K is the rate constant, expressed in reciprocal of the X axis time units. If X is in minutes, then K is expressed in inverse minutes.

Tau is the time constant, expressed in the same units as the X axis. It is computed as the reciprocal of K.

Half-life is in the time units of the X axis. It is computed as ln(2)/K.

Span is the difference between Y0 and Plateau, expressed in the same units as your Y values.

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