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Add SMA-like binding model with pseudo pH dependence #14

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sleweke opened this issue Mar 4, 2020 · 0 comments
Closed

Add SMA-like binding model with pseudo pH dependence #14

sleweke opened this issue Mar 4, 2020 · 0 comments

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@sleweke
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sleweke commented Mar 4, 2020

Add a new binding model based on Huuk et al. 2017.
The binding model is an extension of the SMA model and adds a pseudo molecule that provides the local pH.

The equations are given by

\frac{\partial q_i}{\partial t} = k_{a,i}(c_p, q, pH) * (Lambda - \sum_j \frac{nu_j(pH) + sigma_j}{f_j} * q_j )^(nu_i(pH)) * c_{p,i} - k_{d,i}(c_p, q, pH) * c_{p,0}^(nu_i(pH)) * q_i
nu_i(pH) = nu_{i,0} + pH * nu_{i,1} + pH^2 * nu_{i,2}
k_{a,i}(c_p, q, pH) = k_{a,i,0} * exp(k_{a,i,1} * pH + k_{a,i,2} * pH^2) * exp(k_{a,i,salt} * c_{p,0} + k_{a,i,prot} * c_{p,i})
k_{d,i}(c_p, q, pH) = k_{d,i,0} * exp(k_{d,i,1} * pH + k_{d,i,2} * pH^2) * exp(k_{d,i,sdlt} * c_{p,0} + k_{d,i,prot} * c_{p,i})

The pH pseudo component will have index 1, since by convention salt already has index 0.
The pH component is non-binding.

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