Assessment of glycemic response to an oral glucokinase activator in a proof of concept study: application of a semi-mechanistic, integrated glucose-insulin-glucagon model

Abstract

A proof of concept study was conducted to investigate the safety and tolerability of a novel oral glucokinase activator, LY2599506, during multiple dose administration to healthy volunteers and subjects with Type 2 diabetes mellitus (T2DM). To analyze the study data, a previously established semi-mechanistic integrated glucose-insulin model [1–5] was extended to include characterization of glucagon dynamics. The model captured endogenous glucose and insulin dynamics, including the amplifying effects of glucose on insulin production and of insulin on glucose elimination, as well as the inhibitory influence of glucose and insulin on hepatic glucose production. The hepatic glucose production in the model was increased by glucagon and glucagon production was inhibited by elevated glucose concentrations. The contribution of exogenous factors to glycemic response, such as ingestion of carbohydrates in meals, was also included in the model. The effect of LY2599506 on glucose homeostasis in subjects with T2DM was investigated by linking a one-compartment, pharmacokinetic model to the semi-mechanistic, integrated glucose-insulin-glucagon system. Drug effects were included on pancreatic insulin secretion and hepatic glucose production. The relationships between LY2599506, glucose, insulin, and glucagon concentrations were described quantitatively and consequently, the improved understanding of the drug-response system could be used to support further clinical study planning during drug development, such as dose selection.

Appendix

Glucose submodel equations

$$ \frac{{dG_{A} }}{dt} = - G{}_{A}(t) \cdot k_{a} $$

(12)

$$ \frac{{dG_{C} }}{dt} = k_{a} \cdot G{}_{A}(t) + G_{PROD} (t) + \frac{Q}{{V_{P} }} \cdot G{}_{P}(t) - (CL_{G} + CL_{GI} \cdot I_{E} (t) + Q) \cdot \frac{{G_{C} (t)}}{{V_{G} }} \, , \, $$

$$ \, G_{C} (0) = G{}_{SS} \cdot V_{G} $$

(13)

$$ \frac{{dG_{P} }}{dt} = Q \cdot \left( {\frac{{G_{C} (t)}}{{V_{G} }} - \frac{{G_{P} (t)}}{{V_{P} }}} \right) \, , \, G_{P} (0) = G_{SS} \cdot V_{P} $$

(14)

$$ \, G_{PROD} (t) = G{}_{PROD,0} = G_{SS} \cdot (CL_{G} + CL_{GI} \cdot I_{SS} ) $$

(15)

$$ \frac{{dG_{E} }}{dt} = k_{GE} \cdot \frac{{G_{C} (t)}}{{V_{G} }} - k_{GE} \cdot G_{E} (t) \, , \, G_{E} (0) = G_{SS} $$

(16)

G_A is glucose in the absorption compartment, k_a is first-order absorption, G_C and G_P are the glucose in the central and peripheral compartments, G_PROD is endogenous glucose production, Q is intercompartmental clearance, V_G and V_P are the central and peripheral volumes of distribution, CL_GI is insulin-dependent clearance and CL_G is insulin-independent clearance, G_SS is glucose in the central compartment at steady-state, G_E is the glucose effect compartment, k_GE is the equilibration rate constant to and from the glucose effect compartment, I_E is the insulin effect compartment, I_SS is insulin concentration at steady-state.

Insulin submodel equations

$$ \frac{dI}{dt} = I{}_{SEC}(t) - \frac{{CL_{I} }}{{V_{I} }} \cdot I(t), \, I(0) = I_{SS} \cdot V_{I} $$

(17)

$$ I_{SEC,o} = I_{SS} \cdot CL_{I} $$

(18)

$$ G_{CM} (t) = \left( {\frac{{G_{E} (t)}}{{G_{SS} }}} \right)^{IPRG} $$

(19)

$$ I_{ABSG} (t) = 1 + S_{incr} \cdot G_{A} (t) $$

(20)

$$ I_{SEC} (t) = I_{SEC,o} \cdot G_{CM} (t) \cdot I_{ABSG} (t) $$

(21)

$$ \frac{{dI_{E} }}{dt} = k_{IE} \cdot \frac{I(t)}{{V_{I} }} - k_{IE} \cdot I_{E} (t), \, I_{E} (0) = I_{SS} $$

(22)

I_SEC is endogenous insulin secretion, CL_I is insulin clearance, V_I is the volume of distribution of insulin, I_SEC,0 is baseline insulin secretion, G_CM is the fraction of insulin secretion regulated by the glucose concentration in the effect compartment, IPRG is the estimated power in the relationship, I_ABSG is the fraction of insulin secretion triggered by the incretin effect following glucose absorption from the gut, S_incr is the slope of a linear relationship, k_IE is the equilibration rate constant to and from the insulin effect compartment.