# 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.