Introduction
Equilibrate is a program for calculating equilibria and dissociation constants for molecules that
interact with each other. Examples of biochemical interactions that occur
in living organisms or in vitro include signal transduction receptors
binding their ligand, transcription factors binding to their cognate sequence
element in DNA, regulatory subunits of enzymes interacting with the catalytic
subunit, and so on.
The extent to which the molecules bind to each other is dependent on a variety of factors, including concentration
of the molecules, ionic strenth (mono- and bivalent cations), temperature
and so on. In addition, binding is seldomly irreversible. The extent of
binding under a defined set of condtions is described by the dissociation
constant, KD (or by the inverse, the association constant, KA).
These interactions are of the type:
The dissociation constant is calculated using the concentrations (in M, (moles/ litre)) of the
bound and free forms of A and B as follows:
Despite the simplicity of the formula, how the interaction equilibrates is not intuitive if you just
now the total concentration of A, B and the KD (where [total A] =
[A] + [AB] , [total B] = [B] + [AB]).
The latter situation can be resolved by standard mathematical methods, but as the formulas resolve
in an abc-formula in which each of the constants are to be calculated with
another formula, the calculation of the equilibrium is tedious and thus
suitable for automation.
Features of Equilibrate
Equilibrate provides three utilities which work with graphic routines that support publication
quality figures:
(1) The Equilibrium Tool calculates steady state equilibria on basis of a minimum of three pieces of data entered
by the user. It calculates the remaining, unknown variables. In addition,
it plots a graph showing the steady state equilibrium at a range of concentrations.
(2)
The Dynamic Equilibrium Tool allows to perform a simulation of real time kinetics of the interaction
between two molecules. The tool allows the user to analyze the concentration
of the molecules and the rate with which the concentration changes as a
function of time. The tool also features a "Programmed Events" option,
which allows the user to perturb the equilibrium by increasing or decreasing
the concentration of one or more molecules at any given time. The software
plots a graph to facilitate the analysis, in addition the simulation data
are available in numeric form.
(3)
The Scatchard Analysis Tool calculates
the dissociation constant (KD)
of the interaction using three pieces of experimental data as a minimum.
It is known that the ratio of Bound-to-Free of one of the components is
a linear function of the concentration of Bound. Using linear regression
the data are analyzed statistically, including the calculation of a 95%
confidence interval for the calculated KD
The experimental data are plotted in a graph, along with the best fit of
the linear regression analysis.
The graph is highly customizable, supporting the following features:
Selection of variables to be plotted on the X and Y axes
Selection of a linear or logarithmic scale
Specifying the range of X and Y to be plotted
Editing X and Y axis titles
Moving and resizing the axis titles
Selection of preferred units
Multiple graphs in one chart
Copying the graph to the Windows clip board
Printing the graph
Using the multiple graph option the user is able to get a more intuitive understanding of the effect
of a different dissociation constant (KD) on the equilibrium at a range
of concentrations, or to plot the concentration of all the different components
in the interaction in one chart.
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