Dapagliflozin stimulates glucagon secretion at high glucose: experiments and mathematical simulations of human A-cells

Glucagon is one of the main regulators of blood glucose levels and dysfunctional stimulus secretion coupling in pancreatic A-cells is believed to be an important factor during development of diabetes. However, regulation of glucagon secretion is poorly understood. Recently it has been shown that Na+/glucose co-transporter (SGLT) inhibitors used for the treatment of diabetes increase glucagon levels in man. Here, we show experimentally that the SGLT2 inhibitor dapagliflozin increases glucagon secretion at high glucose levels both in human and mouse islets, but has little effect at low glucose concentrations. Because glucagon secretion is regulated by electrical activity we developed a mathematical model of A-cell electrical activity based on published data from human A-cells. With operating SGLT2, simulated glucose application leads to cell depolarization and inactivation of the voltage-gated ion channels carrying the action potential, and hence to reduce action potential height. According to our model, inhibition of SGLT2 reduces glucose-induced depolarization via electrical mechanisms. We suggest that blocking SGLTs partly relieves glucose suppression of glucagon secretion by allowing full-scale action potentials to develop. Based on our simulations we propose that SGLT2 is a glucose sensor and actively contributes to regulation of glucagon levels in humans which has clinical implications.


Mathematical model equations and parameters
For completeness we report all equations and parameters here.
A mathematical Hodgkin-Huxley-type model that describes electrical activity in human pancreatic A-cells was developed based on patch clamp data from human pancreatic A-cells (1). The model includes ATPsensitive K + channels (KATP-channels), a passive leak current, voltage-gated Na + -, K + -and Ca 2+ -channels, and the electrogenic sodium glucose co-transporter SGLT2.
The evolution of the membrane potential V is driven by the contribution from the different currents, dV/dt = -(I KATP + I leak + I Na + I Kv + I KA + I CaT + I CaL + I CaPQ + I SGLT2 )/C m , where C m =3.3 pF is the cell membrane capacitance. Voltage-gated membrane currents are modeled as where X stands for the channel type, V X is the associated reversal potential, g X the maximal whole-cell channel conductance, and m X and h X describe activation and inactivation of the channel, respectively.
Activation (similarly inactivation) is described by where m X,∞ (V) is the steady-state voltage-dependent activation function, and τ mX is the time-constant of activation, which in some cases depends on the membrane potential.
SGLT2 was modeled as a six-state model as described below.

ATP-sensitive K + and leak currents
The KATP current was modeled as a linear, passive current with low conductance g KATP =0.15 nS (1). The K + reversal potential was set to V K =-75 mV. Similarly, the leak current was modeled as with conductance g leak =0.1 nS and reversal potential V leak =-20 mV.

Voltage-sensitive Na + current
The voltage sensitive Na + current was modeled as in the original Hodgkin-Huxley model with activation m Na and inactivation h Na described as in Eqs. order to obtain action potentials in the whole cell model simulated currents needed to be increased compared to published data. The whole-cell conductance was set to g Na =1.6 nS, and the reversal potential was V Na =70 mV. Experimental currents are adopted from (1).

Voltage-sensitive K + currents
Voltage gated K + currents in human A-cells consist of 2 pharmacologically and kinetically separable components. The Kv2.x channel blocker stromatoxin inhibits the slow delayed-rectifier component revealing a fast inactivating A-type current sensitive to Kv4.x channel blocker heteropodatoxin-2 (1). The delayed-rectifier current was modeled as A-type currents were modeled as (1)

Voltage-sensitive Ca 2+ currents
Human A-cells contain at least three types of Ca 2+ channels: low-voltage-activated T-type channels, and high-voltage-activated L-and P/Q-type channels (1).
The three types of Ca 2+ currents were modeled as All three currents were assumed to activate rapidly (τ mCaT = τ mCaL = τ mCaPQ = 0.1 ms), whereas inactivation occurred on different timescales (τ hCaT = 7 ms, τ hCaL = 20 ms, τ hCaPQ = 1000 ms). Steady-state activation and inactivation functions for T-and L-type Ca 2+ channels were described as in Eq. (4). The L-type Ca2+ currents in human A-cells show two distinct parts (1). We assumed therefore that the steady-state activation function for L-type Ca 2+ channels was described as a sum of two Boltzmann functions, Inactivation was assumed to be identical for the two subpopulations of L-type Ca 2+ channels, and was thus described as in Eq. (4). All inactivation parameters were taken from (1), assuming that L-and P/Qtype Ca 2+ channels inactivation showed similar voltage-dependence, but different kinetics. This assumption was made because of the poor characterization of P/Q-type Ca 2+ current inactivation.
Experimentally obtained Ca 2+ -currents in response to voltage ramps adopted from (1) and corresponding simulated currents are depicted in Fig

SGLT2-mediated current
The sodium/glucose co-transporter 2 (SGLT2) utilizes a concentration gradient of Na + to transport glucose into the A-cells. Mechanistically SGLT1 and SGLT2 work similarly, with the main divergence being the different stoichometry: SGLT2 transports only one Na + ion, whereas SGLT1 transport two, for each molecule of glucose transported into the cell. Moreover, in absence of sodium in the external medium, glucose is not transported (2). The model equations describe translocation between the different states of the transporter, dC 1 /dt = (k 21 C 2 + k 61 C 6 ) -(k 12 + k 16 ) C 1 , dC 2 /dt = (k 12 C 1 + k 32 C 3 + k 52 C 5 ) -(k 21 + k 23 + k 25 ) C 2 , dC 4 /dt = (k 34 C 3 + k 54 C 5 ) -(k 45 + k 43 ) C 4 , dC 5 /dt = (k 45 C 4 + k 65 C 6 + k 25 C 2 ) -(k 54 + k 52 + k 56 ) C 5 , dC 6 /dt = (k 16 C 1 + k 56 C 5 ) -(k 61 + k 65 ) C 6 ,  where F is the Faraday constant, n the number of transporters, N A the Avogadro's number, k xy is the rate constant describing the transition between state x and state y, C z is the fraction of carriers in state z, and α and δ are phenomenological coefficients representing fractional dielectric distances. Finally, μ is the reduced potential F V/RT, where R is the gas constant and T is the temperature. The SGLT2 current depends on glucose and sodium concentrations inside and outside the cell, as well as on the membrane voltage V, because of the dependence of the rate constants on these factors.
The magnitude of the SGLT2 current is directly proportional to the number of transporters n in the cell.
We use n=1.5 x 10 9 . The number of SGLT2 transporters is constrained by the electrophysiology.
Increasing n 5 or 10 fold disturbs simulated activity, which no longer appears similar to experimental recordings (