Consider:
V + L <-> V^L
X + L <-> X^L
Before:
dV^L/dt = k_on * V * (L / n_v) − k_off * V^L
dV/dt = −k_on * V * (L / n_v) + k_off * V^L
d(L / n_v)/dt = −k_on * V * (L / n_v) + k_off * V^L
which implies:
dL/dt = −k_on * V * L + n_v * k_off * V^L
Now:
We are no longer explicitly modeling free lipid (or SN). Instead we enforce lipid conservation:
L = L_IC − n_v * V^L − n_x * X^L
dV/dt = −k_on * V * L + k_off * V^L
where:
L_TF is the remaining free lipid “pool” inferred from conservation
L_TF_IC is the initial total lipid (initial condition / total conserved amount)
V^L and X^L are lipid-bound complexes
nbs_v and nbs_x are the number of binding sites (or stoichiometric lipid usage) per complex formation event for V and X, respectively
So instead of integrating an ODE for lipid, lipid is computed algebraically at each time point from conservation of total lipid minus what is bound in complexes.
Consider:
Before:
Now:
We are no longer explicitly modeling free lipid (or SN). Instead we enforce lipid conservation:
where:
L_TF is the remaining free lipid “pool” inferred from conservation
L_TF_IC is the initial total lipid (initial condition / total conserved amount)
V^L and X^L are lipid-bound complexes
nbs_v and nbs_x are the number of binding sites (or stoichiometric lipid usage) per complex formation event for V and X, respectively
So instead of integrating an ODE for lipid, lipid is computed algebraically at each time point from conservation of total lipid minus what is bound in complexes.