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# Self Association¶

This binding model is similar to the steric mass action model (see Section Steric Mass Action) but is also capable of describing dimerization [10, 16]. The dimerization, which is the immobilization of protein at some already bound protein, is also termed “self-association”. It is modeled by adding a quadratic (in $$c_{p,i}$$) term to the adsorption part of the equation.

\begin{split}\begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} &= c_{p,i}\left( \frac{\bar{q}_0}{q_{\text{ref}}} \right)^{\nu_i} \left[ k_{a,i,1} + k_{a,i,2} c_{p,i} \right] - k_{d,i}\: q_i\: \left(\frac{c_{p,0}}{c_{\text{ref}}}\right)^{\nu_i} && i = 1, \dots, N_{\text{comp}} - 1, \\ q_0 &= \Lambda - \sum_{j=1}^{N_{\text{comp}} - 1} \nu_j q_j, \end{aligned}\end{split}

where the number of available binding sites is given by

\begin{aligned} \bar{q}_0 = \Lambda - \sum_{j=1}^{N_{\text{comp}} - 1} \left( \nu_j + \sigma_j \right) q_j = q_0 - \sum_{j=1}^{N_{\text{comp}} - 1} \sigma_j q_j. \end{aligned}

The concept of reference concentrations ($$c_{\text{ref}}$$ and $$q_{\text{ref}}$$) is explained in the respective paragraph in Section Reference concentrations.

For more information on model parameters required to define in CADET file format, see Self Association.