Michaelis-Menten kinetic modeling of hemoglobin A_1c status facilitates personalized glycemic control

Discrepancy between measured HbA_1c and HbA_1c calculated from plasma glucose is associated with higher risk for diabetic complications. However, quantification of this difference is inaccurate due to the imperfect linear conversion models. We propose to introduce a mathematical formula that correlates with the observational data and supports individualized glycemic control.

We analysed 175,437 simultaneous plasma glucose and HbA_1c records stored in our laboratory database. Employing the Michaelis-Menten (MM) equation, we compared the calculated HbA_1c levels to the measured HbA_1c levels. Data from patients with multiple records were used to establish the patients' glycemic status and to assess the predictive power of our MM model.

HbA_1c levels calculated with the MM equation closely matched the population's average HbA_1c levels. The Michaelis constant (K_m) had a negative correlation with HbA_1c (r² = 0.403). Using personalized K_m values in the MM equation, 85.1% of HbA_1c predictions were within 20% error (ADAG calculation: 78.4%). MM prediction also performed better in predicting pathologic HbA_1c levels (0.904 AUC vs. 0.849 AUC for ADAG).

MM equation is an improvement over linear models and could be readily employed in routine diabetes management. K_m is a reliable and quantifiable marker to characterize variations in glucose tolerance.