An engineered human Fc domain that behaves like a pH-toggle switch for ultra-long circulation persistence
Code for the analysis in Lee et al.
Figure 4. The relative half-lives of each IgG mutant can be explained through a model of endosomal sorting and release. A) Graphical representation of the IgG endosomal sorting model. B) Posterior distributions of each volume and transport model. C) Endosomal and surface sorting parameters for each in vivo model. D) Predicted half-life of IgG with the specified endosomal (x) and surface (y) sorting fractions based on the fit model. E) Identical prediction to (D) for TODO: Marlene. F) Identical prediction to (D) for TODO: Scarlette.
All analysis was implemented in R and Stan, and can be found at [https://github.com/meyer-lab/FcRn-trafficking], release 1.0 (doi: 00.0000/arc0000000). Test conditions were identified throughout to ensure model accuracy.
The trafficking of exogenous IgG was modeled according to the following relationships, consistent with the graphic presented in Figure 4A. Exogenous IgG is modeled to exchange between three compartments representing a central extracellular, peripheral extracellular, and endosomal space. The central compartment is modeled as:
where
where
Implicit in this model are a few assumptions: First, there is no clearance outside of cellular uptake and lysosomal degradation. Each sorting fraction and model parameter is assumed to not vary with the concentration of exogenous IgG, therefore assuming that the modeled processes are not saturatable. Finally, sorting and release are assumed to vary in the same order as their measured affinities at pH 5.8 and 7.4, with IgG of no measurable affinity at 7.4 fully released (
As the model jacobian was invariant with respect to the IgG concentrations, the ODE model was solved through the matrix exponential of the jacobian. The half-life was found through root finding with either the Brent routine or Newton's method.
Model fitting was performed using Markov Chain Monte Carlo within Stan (1). Priors on
(1): Bob Carpenter, Andrew Gelman, Matthew D. Hoffman, Daniel Lee, Ben Goodrich, Michael Betancourt, Marcus Brubaker, Jiqiang Guo, Peter Li, and Allen Riddell. 2017. Stan: A probabilistic programming language. Journal of Statistical Software 76(1). DOI 10.18637/jss.v076.i01