Protein Synthesis, Trafficking, and Elimination
Zeroth-order ligand and receptor synthesis
Ligand and receptor are assumed to be produced with zeroth-order kinetics. This is to say the upstream process of transcription and translation is assumed to be at steady state and constant. Receptor synthesis occurs in all compartments, but ligand synthesis is assumed to only occur in the central compartment. The ligand in other compartments is modeled to arrive there via distribution from the central compartment.
\( \ce{ \phi ->[k_{synth}] Sol } \)
First-order soluble receptor synthesis
Soluble receptor is assumed to be produced via a first-order shedding of the membrane-bound receptor. This shedding process is assumed to be inhibited by drub binding to the target receptor. For expediency reasons, this process is assumed to only occur in the central compartment.
\( \ce{ R ->[k_{shed}] S } \)
Clearance of soluble proteins
All soluble proteins have a first-order elimination route. This is concentration independent and non-saturable. For large proteins in the plasma, this is typically fluid phase-pinocytosis from endothelial cells and hematopoietic cells (e.g. monocytes). For smaller proteins, this is typically renal filtration. For expediency reasons, this process is assumed to only occur in the central compartment.
This process is assumed to be inhibited by drug binding. Instead, the processes described in Drug Mechanisms are controlling for complexes.
\( \ce{ Sol ->[k_{deg}] \phi } \)
Clearance of membrane proteins
All membrane-bound proteins have a first-order elimination route, reflecting an internalization mechanism. This is concentration independent and non-saturable. The synthesis and elimination rates are computed from the macro-parameters that set the initial steady state for receptor expression (CSS) and for receptor turnover (T 1/2). By default, receptors bound to drug or to ligands in complexes will turn over at the same rate as the free receptor. This can be altered using the Drug:Receptor T 1/2 scale parameters, each of which is a multiplicative factor on the receptor half life parameter within its respective compartment.
\( \ce{ R ->[k_{deg}] \phi } \)
In the central compartment, soluble proteins bound to receptors will also be cleared when the receptor ligand complex is internalized and degraded. In the other compartments, the soluble proteins are released. This last assumption is made for expediency; it allows analytically computing the pre-drug steady-state concentrations soluble proteins.
Computing the initial conditions
The initial condition of receptors and ligands is computed by solving for the value of the micro parameters such that the steady state of the model is consistent with the macro parameters provided. For example in a multicompartment model with receptor binding for each state and each compartment there is an equation that can be solved. For example:
A system of these equations is solved symbolically to determine the initial steady state.