A Mathematical Model of Granulopoiesis Incorporating the Negative Feedback Dynamics and Kinetics of G-CSF/Neutrophil Binding and Internalization.
We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating both the freely circulating concentration and the concentration of the cytokine bound to mature neutrophils. G-CSF concentrations are used to directly regulate neutrophil production, with the rate of differentiation of stem cells to neutrophil precursors, the effective proliferation rate in mitosis, the maturation time, and the release rate from the mature marrow reservoir into circulation all dependent on the level of G-CSF in the system. The dependence of the maturation time on the cytokine concentration introduces a state-dependent delay into our differential equation model, and we show how this is derived from an age-structured partial differential equation model of the mitosis and maturation and also detail the derivation of the rest of our model. The model and its estimated parameters are shown to successfully predict the neutrophil and G-CSF responses to a variety of treatment scenarios, including the combined administration of chemotherapy and exogenous G-CSF. This concomitant treatment was reproduced without any additional fitting to characterize drug-drug interactions.
Faculté de Pharmacie, Université de Montréal, Montréal, QC, H3T 1J4, Canada. morgan.craig@umontreal.ca.|Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, 02138, USA. morgan.craig@umontreal.ca.
M
M
Craig
Department of Mathematics and Statistics, McGill University, Montréal, QC, H3A 0B9, Canada.
A R
AR
Humphries
Departments of Mathematics, Physics and Physiology, McGill University, Montréal, QC, H3G 1Y6, Canada.
M C
MC
Mackey
D000818:Animals; D025461:Feedback, Physiological; D016179:Granulocyte Colony-Stimulating Factor / Q000008:administration & dosage / Q000493:pharmacokinetics / Q000502:physiology*; D006410:Hematopoiesis / Q000187:drug effects / Q000502:physiology*; D006801:Humans; D055641:Mathematical Concepts; D051379:Mice; D018345:Mice, Knockout; D008954:Models, Biological; D009504:Neutrophils / Q000166:cytology* / Q000187:drug effects / Q000502:physiology*; D016188:Receptors, Granulocyte Colony-Stimulating Factor / Q000172:deficiency / Q000235:genetics / Q000502:physiology
D016188:Receptors, Granulocyte Colony-Stimulating Factor; D016179:Granulocyte Colony-Stimulating Factor
Bound and unbound drug concentrations; G-CSF; Granulopoiesis; Mathematical modelling; Physiologically constructed pharmacokinetics; State-dependent delay differential equations