CADETProcess.tools.yamamoto.yamamoto_equation

CADETProcess.tools.yamamoto.yamamoto_equation(log_c_salt_at_max_M: float, lambda_: float, nu: float, k_eq: float) → ndarray

Calculate the theoretical normalized gradient slope using Yamamoto’s method.

Yamamoto’s method is used in ion-exchange chromatography to model the relationship between the normalized gradient slope (GH) and the peak salt concentration (I_R) during a linear salt gradient elution. This method is based on the steric mass action (SMA) model and allows for the determination of key chromatographic parameters such as the characteristic charge (ν) and the equilibrium constant (k_eq).

The underlying equation is:

\[\log(GH) = (ν + 1) \log(I_R) - \log(k_{eq} \cdot \lambda^ν \cdot (ν + 1))\]

where:

• GH: Normalized gradient slope (logarithmic scale)

• I_R: Salt concentration at the protein peak maximum (in M)

• ν (nu): Characteristic charge of the protein

• k_eq: Equilibrium constant (binding affinity)

• λ (lambda_): Resin capacity in mM

Parameters:

log_c_salt_at_max_Mnp.ndarray

Log10 of salt concentrations at protein peak maximum in M.

lambda_float

Resin capacity in mM.

nufloat

Characteristic charge of the molecule.

k_eqfloat

Equilibrium constant of the binding model.

Returns:

np.ndarray

Calculated normalized gradient slope (GH) values in logarithmic scale.