Figure 1.
GSIS and AASIS machinery in the pancreatic β-cell.
A. Schematic diagram of metabolic processes accounted for in model 1. Reactions are represented as arrows (either uni- or bidirectional) and labelled to
(Table 2). Red arrows represent D-glucose specific pathways, blue arrows indicate L-alanine-related reactions whereas black arrows denote viable metabolic routes common to both D-glucose and L-alanine. B. Schematic representation of downstream electrophysiologic events and ion fluxes included in model 2. In clockwise order: Na+/L-Alanine Co-transport (
), delayed rectifying K+ current (
), K+ ATP-dependent current (
), K+ Ca2+-activated current (
), Ca2+ plasma membrane pump (
), Ca2+ Uniporter (voltage-dependent) current (
), Na+ voltage-gated current (
), Na+/K+ pump current (
), Na+/Ca2+ exchanger current (
). Current equations are given in Table 3. C. Experimental workflow. BRIN-BD11 cells were washed with pre-warmed PBS and starved at 37°C for 40 min in 1.1 mmol/l D-glucose KRBB. The cells were then washed again with PBS and stimulated for 20 minutes in KRBB supplemented with different concentrations of D-glucose (G) only (1.1, 5, 16.7 and 30 mM), L-alanine (A) only (0.5, 1, 2, 5 and 10 mM) or their combination (G + A). After incubation, an aliquot of supernatant was removed for later quantification of D-glucose and L-alanine consumption, L-lactate production and insulin secretion. Intracellular
concentration was assessed by flow cytometry. Cells were then washed with ice-cold PBS and lysed to assess viability, intracellular ATP concentration, intracellular L-glutamate concentration and protein content. (*) Different lysis buffers were used depending on the biochemical parameter being measured.
Table 1.
BRIN-BD11 cells viability following 1 h incubation in stimuli-supplemented KRBB.
Figure 2.
Effects of D-glucose and L-alanine on acute insulin secretion from BRIN-BD11 cells.
BRIN-BD11 cells were cultured, allowed to adhere overnight prior to being pre-incubated (40 min) in 1.1 mmol/l D-glucose and the acute (20 min) insulinotropic effects of D-glucose (GLC) only (A), L-alanine (ALA) only (B) and combinations of both substrates (C, D) were tested. Values are mean ± SD of at least 3 independent experiments. In A, a vs basal (1.1 mmol/l) D-glucose KRBB; in B, b
vs stimuli-free KRBB, c
vs basal (0.5 mmol/l) L-alanine KRBB; in C, c as in B, d
vs absence of 10 mmol/l L-alanine; in (D), e
vs absence of 1.1 mmol/l, f
vs absence of 16.7 mmol/l D-glucose and g
L-alanine KRBB supplemented with 1.1 mmol/l D-glucose compared to same concentrations supplemented with 16.7 mmol/l D-glucose.
Figure 3.
Effects of D-glucose and L-alanine on ATP and L-lactate production.
All experiments were performed following 40 min pre-incubation in 1.1 mmol/l D-glucose and 20 min acute stimulation. Values are mean ± SD of at least 3 independent experiments. A. Experimental D-glucose consumption as a function of D-glucose concentration. a 5 mmol/l D-glucose vs 5 mmol/l D-glucose plus 10 mmol/l L-alanine (), b D-glucose vs same concentration of D-glucose supplemented with 10 mmol/l L-alanine (
). B. Experimental L-alanine consumption as a function of L-alanine concentration. C. Experimental total intracellular ATP concentration as a function of D-glucose influx in the absence or presence 10 mmol/l L-alanine (red diamonds and green triangles, respectively). c D-glucose vs addition of 10 mmol/l L-alanine (
). Simulated steady state ATP concentrations as a function of D-glucose influx (red and green solid lines) were fitted with a least square criterion to ATP observations by adjusting the parameters
,
,
,
,
,
,
,
,
and
. D. Experimental L-lactate concentrations as a function of D-glucose influx in the absence or presence of 10 mmol/l L-alanine (red diamonds and green triangle, respectively). d 16.7 mmol/l vs 30 mmol/l D-glucose (
), e 5 mmol/l D-glucose vs 5 mmol/l D-glucose plus 10 mmol/l L-alanine (
) and f D-glucose vs addition of 10 mmol/l L-alanine (
). Predicted steady state L-lactate concentrations (red and green solid lines) were simulated using the standard set of parameters listed in Table S1 that were obtained by fitting to ATP observations in panel C.
Figure 4.
Steady state concentration sensitivity analysis for mathematical model 1.
All simulations were performed using mathematical model 1 with standard parameters listed in Table S1. Parameters were varied individually by a factor of ,
,
,
and the resulting steady state
concentrations as a function of D-glucose influx are shown.
Figure 5.
Relationship between intracellular L-glutamate levels and insulin output.
A. Simulated steady state intracellular L-glutamate concentrations produced in response to a step increase in D-glucose influx in the absence (solid red line) and presence of a fixed L-alanine input equivalent to 10 mmol/l concentration administered in experiments (solid green line). B. Simulated intracellular L-glutamate concentrations as a function of L-alanine input flux only (solid blue line) and with a fixed D-glucose input equivalent to 16.7 mmol/l concentration administered in the experiments (solid dark green line). Both in A and B simulations results were obtained using mathematical model 1 with parameter values listed in Table S1. C. BRIN-BD11 cells were cultured, allowed to adhere over a 24 h period prior to being pre-incubated (40 min) in 1.1 mmol/l D-glucose, acutely stimulated for 20 min with either D-glucose only (16.7 mmol/l), L-alanine only (10 mmol/l), combinations of both substrates, 16.7 mmol/l D-glucose supplemented with 5 mmol/l DMGLU and 16.7 mmol/l D-glucose plus 1 µmol/l FCCP. Supernatant was assayed for insulin secretion and lysates were analysed for intracellular L-glutamate content. Values are mean ± SD of at least 3 independent experiments. Statistical significance: L-glutamate: a 16.7 mmol/l D-glucose vs 16.7 mmol/l D-glucose plus FCCP (), b 16.7 mmol/l D-glucose vs 16.7 mmol/l D-glucose supplemented with 10 mmol/l L-alanine (
), c 16.7 mmol/l D-glucose vs 16.7 mmol/l D-glucose plus 5 mmol/l DMGLU (
), d 10 mmol/l L-alanine vs 16.7 mmol/l D-glucose plus 10 mmol/l L-alanine (
).Insulin: e 16.7 mmol/l D-glucose vs presence of 10 mmol/l L-alanine (
), f 16.7 mmol/l D-glucose vs addition of DMGLU (
), g 10 mmol/l L-alanine vs supplementation with 16.7 mmol/l D-glucose (
), h 16.7 mmol/l D-glucose plus 10 mmol/l L-alanine vs 16.7 mmol/l D-glucose supplemented with 5 mmol/l DMGLU (
).
Figure 6.
Effects of D-glucose and/or L-alanine on intracellular Ca2+ and insulin secretion.
BRIN-BD11 cells were cultured, allowed to adhere over a 24 h period prior to being pre-incubated (40 min) in 1.1 mmol/l D-glucose, acutely stimulated for 20 min with either D-glucose only (16.7 mmol/l), L-alanine only (10 mmol/l, with/without 1.8 µg/ml oligomycin), combinations of both substrates with/without oligomycin, 16.7 mmol/l D-glucose supplemented with 10 mmol/l AIB and 10 mmol/l AIB only. Samples were assayed for insulin secretion and intracellular Ca2+ concentration as described in the Materials and Methods section. Values are mean ± SD of at least 3 independent experiments. Statistical significance: Intracellular Ca2+ concentration: a D-glucose only vs addition of 10 mmol/l L-alanine (), b D-glucose only vs addition of 10 mmol/l AIB (
), c D-glucose plus L-alanine vs addition of oligomycin (
), d D-glucose plus L-alanine vs D-glucose plus AIB (
), e L-alanine vs AIB (
), f L-alanine vs addition of oligomycin (
). Insulin secretion: g D-glucose vs addition of 10 mmol/l L-alanine (
), h D-glucose plus L-alanine vs L-alanine only (
), i D-glucose vs addition of 10 mmol/l AIB (
), l D-glucose plus L-alanine vs addition of oligomycin (
), m D-glucose plus L-alanine vs D-glucose plus AIB (
), n L-alanine vs AIB (
), o L-alanine vs addition of oligomycin (
), p D-glucose vs addition of AIB (
).
Figure 7.
Electrical activity and intracellular concentrations of and cations.
Time-dependent changes in the membrane potential (A), intracellular
concentration (B), intracellular
concentration (C) and intracellular
concentration (D) are depicted. The simulation with the default parameters given in Table S2 and
is represented by the solid black curve. The effect of applying
to model Na+/L-alanine co-transport was simulated by increasing
from 0 to 50 in equation 69 (solid blue line).
Figure 8.
Mean ,
,
concentrations and main channels’ currents modulated by
and
.
handling model simulations were run until an oscillatory steady state was reached and subsequently the mean was computed over time for each state variable and current in the system. Standard parameter values listed in Table S2 were used. The effect of a step increase in
(in the range
) for various values of the parameter
on intracellular
,
,
concentrations is reported in panels A–C. The effect of a step increase in
(in the range
) for the parameter
assuming the values
on the main currents included in the model,
,
,
,
,
,
is shown in panels D–I.
Figure 9.
Comparison of simulated mean levels and experimental insulin secretion dose-response curves.
A. Simulated steady state concentrations as a function of
(top x axis and right y axis, in red) are overlaid onto the experimental D-glucose insulin secretion dose-response curve (bottom x axis and left y axis, in black). The top x axis was scaled to the bottom x axis with
and the right y axis was scaled to the left y axis with
, both found with the fitting. B. Simulated steady state
concentrations as a function of
(top x axis and right y axis, in blue) are overlaid to the experimental L-alanine insulin secretion dose response curve (bottom x axis and left y axis, in black). The top x axis was scaled to the bottom x axis with
and the right y axis was scaled to the left y axis with
, both found with the fitting. The line annotated
shows the simulated steady state
concentration if
and L-alanine concentration follow assumption (ii). The patch delimited by the lines annotated
and
, correspondent to simulated steady state value from 10 mmol/l L-alanine (or 16.7 mmol/l D-glucose) and a
of it, shows that even a large variation in
has only a modest effect on
. Administration of 10 mmol/ AIB with or without supplementation with 16.7 mmol/l D-glucose can be simulated by setting
(same value as 10 mmol/l L-alanine) in both cases and
corresponding to 16.7 mmol/l D-glucose-derived ATP production (blue square) or
corresponding to virtually no metabolism-derived ATP production (cyan square), respectively. All simulations were performed using standard parameter values enumerated in Table S2 except for
and
that assumed the values herein specified.
Table 2.
Mathematical model of core metabolic processes in pancreatic β-cells: reactions list.
Table 3.
Mathematical model of handling in pancreatic β-cells: Nernst potential and channels currents list.