Single-Site Binding¶
- A basic, single-site binding model.
- indiv_models.SingleSite
Scheme¶
Scheme is for binding of titrant \(T\) to a stationary species \(S\):
To describe this, we use the following equilibrium constant:
Parameters¶
parameter | variable | parameter name | class |
---|---|---|---|
association constant | \(K\) | K |
thermodynamic |
binding enthalpy | \(\Delta H\) | dH |
thermodynamic |
fraction competent | — | fx_competent |
nuisance |
slope of heat of dilution | — | dilution_heat |
nuisance |
intercept of heat of dilution | — | dilution_intercept |
nuisance |
Species¶
We can only manipulate \([T]_{total}\) and \([S]_{total}\) experimentally, so our first goal is to determine the concentration of \([ST]\), which we cannot manipulate or directly observe.
The real root of this equation describes \([ST]\) in terms of \(K\) and the total concentrations of \([S]\) and \([T]\):
The mole fraction \(ST\) is:
Heat¶
The heat for each shot \(i\) (\(q_{i}\)) is:
where \(V_{0}\) is the volume of the cell (fixed) and \(\Delta H\) is the enthalpy of binding. Note that we do not deal with dilution here, as pytc calculates \(x_{ST,i}\) for the entire titration, accouting for dilution at each step. \(V_{0}\) is held constant as the total cell volume (not the volume of solution including the neck) as only the cell, not the neck, is detected in the signal.