Minimal mathematical model for glycation of albumin

Background

Glycated albumin (GA) is often described as a reflection of glucose exposure over the past 2–4 weeks. We examined the scale of the operative interval for changes in %GA from the perspective of a theoretical model for GA formation, by simulating the time course of changes in %GA after changes in glucose.

Methods

Probability of survival of albumin (A) was according to first-order elimination based on t_1/2 of 17 days. Probability of formation of GA from A per unit time was proportional to glucose (G) and a glycation rate constant, k, deduced from reference values for %GA vs. G. We then simulated the kinetics of changes in %GA for conditions in which a prior steady-state (constant G) was followed by a step change in G.

Results

The glycation rate constant k was 9.79e-4/d/(mmol/L). We simulated changes in %GA for two scenarios involving step changes in G at time = 0: A. from 10 mmol/L to 15 mmol/L (%GA ultimately moves from 19.3% to 26.4%); B. from 15 mmol/L to 10 mmol/L (%GA ultimately moves from 26.4% to 19.3%). For both scenarios, the fractional transition of %GA between respective starting points and ultimate endpoints was after 30 days approximately 80% of the ultimate full transition.

Conclusions

Model-based calculations support the description of %GA as a reflection of G over the past 4–6 weeks, longer than the period of 2–4 weeks that is commonly cited.