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BindingModels

Charles Pence edited this page Apr 24, 2013 · 1 revision

Binding Model Mathematics

This chapter describes the equations used to simulate the binding curves. Though some of these equations can be solved analytically, the calculations are performed numerically. The program breaks either the total [P] or total [L] range into a user-defined number of points and then calculates the concentration of free and bound A and free and bound MT at each point.

First Order Binding

This model is simple first order binding.

In first order binding, the relationship between P and L is:

equation

The dissociation constant is defined as:

equation

We can also write mass balances for total P and total L:

equation

equation

We can rearrange the equation for total L and solve for [L] free:

equation

We now can substitute this equation into the equation for total P:

equation

The program numerically finds the value of [P] free that solves this equation, then uses that to calculate all other necessary parameters.

Two Binding Sites

This model assumes that each ligand contains two binding sites for protein P, sites 1 and 2, with different dissociation constants. It is assumed that the two sites do not interact.

The binding relationships for this model are:

equation

The dissociation constants for this model are:

equation

The mass balances for this model are:

equation

equation

equation

The L1 and L2mass balances can be solved for free L1 and L2:

equation

equation

These equations can be substituted into the mass balance for P to get:

equation

This equation is numerically solved by the program to get free P, which is then used to calculate bound P and the fraction of P bound. Free L is not calculated because this model cannot be graphed against free L.

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