﻿ Multiline models

# Multiline models

Equations can be written over several lines. Here is an example, the mixed model enzyme inhibition model built-in to Prism:

VmaxApp=Vmax/(1+I/(Alpha*Ki))

KmApp=Km*(1+I/Ki)/(1+I/(Alpha*Ki))

Y=VmaxApp*X/(KmApp + X)

Prism follows the convention of all computer languages. It starts at the top and goes down.

First it computes the intermediate variable VmaxApp. It knows this is an intermediate variable, and not a parameter to fit, because it appears to the left of the equals sign.

Next Prism computes the value of KmApp.

Finally it uses those two values to compute Y.

Math textbooks tend to write equations in the opposite order. A math text might first define Y as a function of VmaxApp and KmApp, and then lower on the page define how to calculate VmaxApp and KmApp from Vmax, Km, Alpha and I. Prism (like all computer languages) requires that you define an intermediate variable before you use it.

Here is a second example:

Specific=X*Bmax/(X+Kd)

Nonspecific=NS*X

<A>Y=Specific + Nonspecific

<B>Y=Nonspecific

The first line calculates the intermediate variable Specific. The second line defines the intermediate variable Nonspecific.

The third line is preceded by <A>. This means that this line only applies to data set A. The second line is preceded by <B> so only applies to data set B. This allows the model to fit a table of data where column A is the total binding and column B is the nonspecific binding. Read more about the syntax used to specify that a particular line only applies only to selected data sets.

You can define constants right in the multiline equation. This makes sense for defining true  constants, whose value will never change. If the constant is something like a concentration that changes from experiment to experiment, it is better to not define it in the equation itself, but rather define it in the Constrain tab. If it first appears on the right side of the equation, Prism will treat it like a parameter. You can use the Constrain tab to fix that parameter to a constant value. If the variable name appears first to the left of the equals sign, it is used only within the equation and won't appear in the constraints tab. For example, this line defines Pi:

Pi=3.141529