A mathematical model of metabolic insulin signaling
pathways
Ahmad R.
Sedaghat1,
Arthur
Sherman2, and
Michael
J.
Quon1
1 Cardiology Branch, National Heart, Lung, and Blood
Institute, and 2 Mathematical Research Branch, National
Institute of Diabetes and Digestive and Kidney Diseases, National
Institutes of Health, Bethesda, Maryland 20892
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ABSTRACT |
We develop a
mathematical model that explicitly represents many of the known
signaling components mediating translocation of the insulin-responsive
glucose transporter GLUT4 to gain insight into the complexities of
metabolic insulin signaling pathways. A novel mechanistic model of
postreceptor events including phosphorylation of insulin receptor
substrate-1, activation of phosphatidylinositol 3-kinase, and
subsequent activation of downstream kinases Akt and protein kinase
C-
is coupled with previously validated subsystem models of insulin
receptor binding, receptor recycling, and GLUT4 translocation. A system
of differential equations is defined by the structure of the model.
Rate constants and model parameters are constrained by published
experimental data. Model simulations of insulin dose-response
experiments agree with published experimental data and also generate
expected qualitative behaviors such as sequential signal amplification
and increased sensitivity of downstream components. We examined the
consequences of incorporating feedback pathways as well as representing
pathological conditions, such as increased levels of protein tyrosine
phosphatases, to illustrate the utility of our model for exploring
molecular mechanisms. We conclude that mathematical modeling of signal
transduction pathways is a useful approach for gaining insight into the
complexities of metabolic insulin signaling.
signal transduction; metabolism; insulin resistance; GLUT4
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INTRODUCTION |
INSULIN IS AN
ESSENTIAL peptide hormone discovered in 1921 that regulates
metabolism (26). Interestingly, the ability of insulin to
promote glucose uptake into tissues was not demonstrated until 1949 (27). In 1971, specific cell surface insulin receptors were identified (12). The discovery that
insulin-stimulated glucose transport involves translocation of glucose
transporters (e.g., GLUT4) from an intracellular compartment to the
cell surface was made in 1980 (8, 53). Since genes
encoding the human insulin receptor and GLUT4 were cloned in 1985 (10, 54) and 1989 (5, 13), respectively,
steady progress has been made in identifying components of insulin
signal transduction pathways leading from the insulin receptor to
translocation of GLUT4 (see Ref. 32 for review).
On binding insulin, the insulin receptor undergoes receptor
autophosphorylation and enhanced tyrosine kinase activity.
Subsequently, intracellular substrates (e.g., insulin receptor
substrate-1, IRS-1) are phosphorylated on tyrosine residues that serve
as docking sites for downstream SH2 domain containing proteins,
including the p85 regulatory subunit of phosphatidylinositide
3-kinase (PI 3-kinase). The p85 binding to phosphorylated IRS-1
results in activation of the p110 catalytic subunit of PI 3-kinase
that catalyzes production of phosphoinositol lipids including
phosphatidylinositol 3,4,5-trisphosphates [PI(3,4,5)P3]
that activate the Ser/Thr kinase 3-phosphoinositide-dependent protein
kinase (PDK)-1. PDK-1 phosphorylates and activates other
downstream kinases, including Akt and protein kinase C (PKC)-
, that
mediate translocation of GLUT4. PTP1B is a protein tyrosine
phosphatase (PTPase) that negatively regulates insulin signaling
pathways by dephosphorylating the insulin receptor and IRS-1.
Interestingly, IRS-1 and PTP1B upstream from Akt and PKC-
have
recently been identified as substrates for these downstream kinases,
suggesting that feedback mechanisms exist (9, 33, 38, 39).
Elements downstream from Akt and PKC-
linking insulin signaling
pathways with trafficking machinery for GLUT4 are unknown (34). Thus a complete understanding of mechanisms
regulating the metabolic actions of insulin has remained elusive.
One reason it has been difficult to comprehend metabolic insulin
signaling pathways is that determinants of signal specificity are
poorly understood. Many signaling molecules are shared in common among
pathways initiated by distinct receptors. Moreover, cross talk
and feedback between a multitude of receptor-mediated pathways
generate signaling networks rather than linear pathways. Without
a theoretical framework, it is difficult to understand how complexities
evident from experimental data determine cell behavior. Now that the
human genome has been sequenced, it may be possible to generate a vast
experimental database for understanding cellular signaling. Alfred
Gilman has founded The Alliance for Cellular Signaling
(http://www.cellularsignaling.org/) with the goal of
integrating relevant experimental data (temporal and spatial
relationships of signaling inputs and outputs in a cell) into
interacting theoretical models. This comprehensive approach may enable
a full understanding of the complexities of cell signaling. In this
spirit, we now develop a mathematical model of metabolic insulin
signaling pathways that explicitly represents many known insulin
signaling components. Our goal is to define a comprehensive model that
not only accurately represents known experimental data but will also
serve as a useful tool to generate and test hypotheses. This modeling
approach may lead to novel insights regarding the molecular mechanisms
underlying insulin signal transduction pathways that regulate metabolic
actions of insulin.
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MODEL DEVELOPMENT |
We use our previously validated models of insulin receptor
binding kinetics (57), receptor recycling
(36), and GLUT4 translocation (35, 37) as
subsystems in conjunction with a novel mechanistic representation of
postreceptor signaling pathways to generate a complete model with 21 state variables. This complete model is then extended to incorporate
feedback pathways, and consequences of feedback are explored.
Differential equations derived from the structure of the complete model
were solved by use of a fourth order Runge-Kutta numerical integration
routine (42), using the WinPP version of XPPAUT (available
at http://www.math.pitt.edu/~bard/xpp/xpp.html; see
APPENDIX A for complete list of equations, initial conditions, and model parameters; see
http://mrb.niddk.nih.gov/sherman for WinPP source files used
to run simulations). A sufficiently small step size (0.001 min) was
used to ensure accurate numerical integrations for all state variables.
First order kinetics were assumed except where noted.
Complete Model without Feedback
Insulin receptor binding subsystem.
Our model of insulin receptor binding kinetics (57) (Fig.
1A) was extended here to
include additional steps representing insulin receptor
autophosphorylation and dephosphorylation (Fig. 1B). On
binding the first molecule of insulin, the receptor is rapidly
phosphorylated (1), resulting in receptors that may either
bind another molecule of insulin or dissociate from the first molecule
of insulin. Binding of a second molecule of insulin does not affect the
phosphorylation state of the receptor, whereas receptor
dephosphorylation occurs when insulin diffuses off of the receptor,
leaving a free receptor. In addition, protein tyrosine phosphatases
that dephosphorylate the insulin receptor and whose levels can vary
under pathological conditions (15) are explicitly represented as a multiplicative factor ([PTP]) that modulates receptor dephosphorylation rate. The differential equations for this
subsystem are
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(1)
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(2)
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(3)
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(4)
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(5)
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Definitions for state variables and rate constants are given in
legend to Fig. 1, A and B. Note that we do not
explicitly include an intermediate state of free receptors that are
still phosphorylated because receptor occupancy and phosphorylation are
tightly coupled, and we assume that there are virtually no receptors in
the unbound phosphorylated state.

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Fig. 1.
Schematic of insulin receptor binding and life cycle
subsystems. A: previously validated model of insulin binding
kinetics (57). x1, Free insulin
concentration (system input); x2, free receptor
concentration; x3, concentration of receptors
with 1 molecule of insulin bound; x4,
concentration of receptors with 2 molecules of insulin bound;
k1 and k 1, association
and dissociation rate constants, respectively, for the first molecule
of insulin to bind the receptor; k2 and
k 2, association and dissociation rate
constants, respectively, for the second molecule of insulin to bind the
receptor. B: receptor binding subsystem extended to include
receptor autophosphorylation and dephosphorylation.
x5, Concentration of once-bound phosphorylated
receptors; x4, redefined as concentration of
twice-bound phosphorylated receptors; k3, rate
constant for receptor autophosphorylation; k 3,
rate constant for receptor dephosphorylation; [PTP], a multiplicative
factor modulating k 3 that represents the
relative activity of protein tyrosine phosphatases (PTPases) in the
cell that dephosphorylate the insulin receptor. C:
previously validated model of insulin receptor recycling
(36). x6, Concentrations of
intracellular receptors; k4, endocytosis rate
constant for free receptors; k 4, exocytosis
rate constant; k4', endocytosis rate constant
for bound receptors; k5, zero order rate
constant for receptor synthesis; k 5, constant
for receptor degradation. D: extension of insulin receptor
binding and recycling subsystems that includes phosphorylated
receptors. x7 and x8,
concentration of twice-bound and once-bound intracellular
phosphorylated receptors, respectively; k 4',
exocytosis rate for twice-bound and once-bound intracellular
phosphorylated receptors; k6, dephosphorylation
rate constant for intracellular receptors that is modulated by the
multiplicative factor [PTP].
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Insulin receptor recycling subsystem.
Our previous model of insulin receptor life cycle explicitly represents
synthesis, degradation, exocytosis, and both basal and ligand-induced
endocytosis of receptors (36) (Fig. 1C). We now
extend this subsystem so that ligand-induced endocytosis is only
applied to phosphorylated cell surface receptors (Fig. 1D).
Both once- and twice-bound phosphorylated receptors are treated identically with respect to internalization. An additional step representing dephosphorylation of internalized phosphorylated receptors
and their incorporation into the intracellular pool is included. State
variables representing free surface insulin receptors
(x2) and phosphorylated surface receptors
(x4 and x5) are shared by
both binding and recycling subsystems. Thus differential equations for
these coupled subsystems (depicted in Fig. 1D) are
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(6)
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(7)
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(8)
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(9)
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(10)
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(11)
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(12)
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(13)
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Definitions for additional state variables and rate constants
are given in legend to Fig. 1, C and D.
Postreceptor signaling subsystem.
The postreceptor signaling subsystem developed here (Fig.
2) comprises elements in the metabolic
insulin signaling pathway that are well established (32).
It is assumed that this is a closed subsystem so that synthesis and
degradation of signaling molecules are not explicitly represented. The
concentration of phosphorylated surface insulin receptors is the input
to this subsystem. Activated insulin receptors phosphorylate IRS-1,
which then binds and activates PI 3-kinase. We modeled the dependence of IRS-1 phosphorylation on phosphorylated surface receptors as a
linear function. That is, the rate constant for IRS-1 phosphorylation, k7, is modulated by the fraction of
phosphorylated surface receptors (x4 + x5)/(IRp), where IRp is
the concentration of phosphorylated surface receptors achieved after
maximal insulin stimulation. The association of phosphorylated IRS-1
with PI 3-kinase is assumed to occur with a stoichiometry of 1:1.
Differential equations governing phosphorylation of IRS-1 and
subsequent formation of phosphorylated IRS-1/activated PI 3-kinase
complex are
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(14)
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(15)
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(16)
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(17)
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Activated PI 3-kinase converts the substrate
phosphatidylinositol 4,5-bisphosphate [PI(4,5)P2] to the
product PI(3,4,5)P3. This is modeled as a linear
function so that k9, the rate constant for
generation of PI(3,4,5)P3, is dependent on
x12, the amount of activated PI 3-kinase
(see APPENDIX B for detailed derivation). 5'-Lipid
phosphatases such as SHIP2 convert PI(3,4,5)P3 to
phosphatidylinositol 3,4-bisphosphate PI(3,4)P2]
(6), whereas 3'-lipid phosphatases such as PTEN convert
PI(3,4,5)P3 to PI(4,5)P2 (45). The
differential equations describing interconversion between these
phosphatidylinositides are
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(18)
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(19)
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(20)
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As with [PTP], the lipid phosphatase factors [SHIP] and
[PTEN] correspond to the relative phosphatase activity in the cell and are assigned a value of 1 under normal physiological conditions.

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Fig. 2.
Schematic of postreceptor signaling subsystem.
x9, Concentration of unphosphorylated insulin
receptor substrate (IRS)-1; x10, concentration
of tyrosine-phosphorylated IRS-1; x11,
concentration of free phosphatidylinositol 3-kinase (PI 3-kinase;
PI3-K); x12, concentration of the phosphorylated
IRS-1/activated PI 3-kinase complex; x13,
x14, and x15, percentages
of various phosphoinositol lipids in the cell;
x16 and x17, percentages
of unphosphorylated and phosphorylated Akt in the cell, respectively;
x18 and x19, percentages
of unphosphorylated and phosphorylated protein kinase C (PKC)- in
the cell, respectively. The rate constants k7 to
k12 and k 7 to
k 12 govern the conversion between state
variables as indicated. [PTP] is a multiplicative factor modulating
k 7 that represents the relative activity of
PTPases in the cell that dephosphorylate IRS-1. [PTEN] and [SHIP]
are multiplicative factors modulating k 9 and
k 10, respectively, that represent the relative
activity of these lipid phosphatases in the cell. Arrows with solid
lines indicate first-order reactions. Arrows with dashed lines indicate
reactions where the value of a state variable influences the value of
the rate constant.
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Activation of downstream Ser/Thr kinases Akt and PKC-
is dependent
on levels of PI(3,4,5)P3 (2, 49). In our
model, this is governed by rate constants that interact with the level
of PI(3,4,5)P3 (see APPENDIX B for detailed
derivation). The differential equations describing this are
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(21)
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(22)
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(23)
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(24)
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The output of this subsystem is represented as a metabolic
"Effect" due to Akt and PKC-
activity, with 80% of the
metabolic insulin signaling effect attributed to PKC-
and 20% of
the effect attributed to Akt (3, 7, 49)
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(25)
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where APequil is the steady-state level of combined
activity for Akt and PKC-
after maximal insulin stimulation
(normalized to 100%). Definitions for additional state variables and
rate constants in the postreceptor signaling subsystem are given in the
legend to Fig. 2.
GLUT4 translocation subsystem.
The final subsystem is our previous model of GLUT4 translocation
(35, 37) (Fig. 3). Under
basal conditions, GLUT4 recycles between an intracellular compartment
and the cell surface. The differential equations for this subsystem are
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(26)
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(27)
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Definitions for additional state variables and rate constants in
the GLUT4 translocation subsystem are given in the legend to Fig. 3. On
insulin stimulation, there may be a separate pool of intracellular
GLUT4 recruited to the cell surface (17, 18, 40). To
represent this aspect of GLUT4 trafficking, the insulin-stimulated exocytosis rate (k13') is increased to its
maximum value as a linear function of the metabolic effect produced by
phosphorylated Akt and PKC-
. By assuming that the basal equilibrium
distribution of 4% cell surface GLUT4 and 96% GLUT4 in the
intracellular pool transitions on maximal insulin stimulation to a new
steady state of 40% cell surface GLUT4 and 60% intracellular GLUT4,
the equations governing changes in k13 and
k13' are
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(28)
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(29)
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Thus changes in k13' are linearly
dependent on the output of the signaling subsystem (Effect).

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Fig. 3.
Schematic of GLUT4 translocation subsystem (35, 37).
x20, Percentage of intracellular GLUT4;
x21, percentage of GLUT4 at the cell surface;
k 13, rate constant for GLUT4 internalization;
k13, rate constant for translocation of GLUT4 to
the cell surface under basal conditions; k13',
rate constant for translocation of GLUT4; k14
(zero order) and k 14, rate constants for GLUT4
synthesis and degradation, respectively. The "metabolic Effect"
from postreceptor signaling subsystem increases
k13'.
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For our complete model without feedback, the four subsystems described
above were coupled by shared common elements (Fig. 4) (see APPENDIX B for
derivation of initial conditions, rate constants, and parameters).

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Fig. 4.
Complete model of metabolic insulin signaling pathways obtained by
coupling subsystem models for insulin receptor binding, receptor
recycling, postreceptor signaling, and GLUT4
translocation.
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Complete Model with Feedback
Recent evidence suggests that Akt and PKC-
may participate in
positive and negative feedback in metabolic insulin signaling pathways
(9, 33, 38, 39). To investigate potential functional consequences of these feedback pathways, we incorporated both positive
and negative feedback loops into our complete model (Fig. 5). Phosphorylation of PTP1B by Akt
impairs the ability of PTP1B to dephosphorylate insulin receptors and
IRS-1 by 25% (38). Because PTP1B itself negatively
modulates insulin signaling, the downstream negative regulation of an
upstream negative signaling element represents a positive feedback loop
for insulin signaling. We implemented this positive feedback loop by
assuming a linear effect of activated Akt (x17)
to inhibit PTP1B activity with a 25% decrease in [PTP] at maximal
insulin stimulation. Thus [PTP] is multiplied by 1
0.25x17/(100/11) (where 100/11 is the percentage of activated Akt after maximal insulin stimulation and for
x17
400/11; otherwise, [PTP] = 0; see
APPENDIX B for derivation).

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Fig. 5.
Complete model of metabolic insulin signaling pathways with
feedback. Identical to model shown in Fig. 4 except that new elements
comprising positive and negative feedback pathways are indicated by
dotted lines. PKC- serine phosphorylates IRS-1 to create a negative
feedback pathway, and Akt phosphorylates PTP1B to create a positive
feedback pathway.
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We also incorporated a negative feedback loop in which serine
phosphorylation of IRS-1 by PKC-
impairs formation of the
phosphorylated IRS-1/activated PI 3-kinase complex (39).
To represent this, we assumed that serine phosphorylation of IRS-1 by
activated PKC-
creates an IRS-1 species unable to associate with and
activate PI 3-kinase (represented by the state variable
x10a). The formation of
x10a tends to decrease the level of activated
PI 3-kinase in response to insulin stimulation (when compared with a
system without negative feedback). Additional differential equations
describing interconversion between unphosphorylated IRS-1
(x9) and serine-phosphorylated IRS-1
(x10a) are
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(30)
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(31)
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where Eq. 30 is an updated version of Eq. 14, k7' is the rate constant for serine
phosphorylation of IRS-1 by PKC-
, and k
7'
is the rate constant for serine dephosphorylation. We include a
multiplicative factor, [PKC], that modulates
k7' to model the ability of phosphorylated,
activated PKC-
(x19) to generate
serine-phosphorylated IRS-1. [PKC] is defined as a standard Hill
equation that is commonly used to represent enzyme kinetics, where
[PKC] = Vmaxx19(t
)n/[K
+ x19 (t
)n], where Vmax is
maximal velocity and Kd is dissociation
constant. This explicitly incorporates a time lag (
) into
the negative feedback loop. The parameters used in this equation are
listed in APPENDIX A.
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RESULTS |
Model Simulations without Feedback
We began evaluation of our complete model without feedback by
generating time courses for all state variables in response to a
maximally stimulating step input of 10
7 M insulin
that was turned off after 15 min (Figs. 6
and 7). Thirty seconds after the
initial insulin stimulation, ~98% of the free insulin receptors
became bound to insulin and underwent autophosphorylation (Fig. 6,
A-C). Phosphorylated once-bound insulin receptors at the cell surface made up ~75% of the surface receptor population, and phosphorylated twice-bound surface receptors comprised ~23% of
the surface receptor population. When insulin was removed after 15 min
of stimulation, the concentration of free insulin receptors returned to
basal levels with a half-time of ~3.5 min. A short transient rise in
the concentration of phosphorylated surface receptors bound to one
molecule of insulin was observed as phosphorylated twice-bound surface
receptors passed through the once-bound state to return to the unbound
free state. As expected, the state variables x6,
x7, and x8, which
represent intracellular insulin receptors, did not change very much
with an acute insulin stimulation (data not shown). These results are
in good agreement with both published experimental data and previous
results from our subsystem models of receptor binding and recycling
(36, 51, 57). In response to the rise in
autophosphorylated surface insulin receptors, unphosphorylated IRS-1
was rapidly converted to tyrosine-phosphorylated IRS-1 (Fig. 6D). Consistent with published experimental data
(29), maximal IRS-1 tyrosine phosphorylation was observed
within 1 min of the initiation of insulin stimulation. On removal of
insulin, IRS-1 underwent dephosphorylation back to basal conditions
with a half-time of ~8 min. This was also consistent with published
experimental data (24).

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Fig. 6.
Model simulations without feedback. Time courses for unbound
receptors (A), once- and twice-bound phosphorylated surface
receptors (B), total phosphorylated surface receptors
(C), and unphosphorylated and tyrosine-phosphorylated IRS-1
(D) after a step input of 10 7 M insulin for 15 min.
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Fig. 7.
Model simulations without feedback. Time courses for
activated PI 3-kinase (A), levels of phosphatidylinositol
3,4,5-trisphosphate [PI(3,4,5)P3] and
phosphatidylinositol 3,4-bisphosphate PI(3,4)P2]
(B), activated PKC- (C), and cell
surface GLUT4 (D) after a step input of
10 7 M insulin for 15 min.
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Maximal formation of the phosphorylated IRS-1/activated PI 3-kinase
complex in response to 10
7 M insulin occurred within
~1.5 min (Fig. 7A). This is in good agreement with
published data showing that PI3-kinase and tyrosine-phosphorylated IRS-1 molecules associate quickly after insulin stimulation (2, 14). The time course for disappearance of activated PI 3-kinase after the removal of insulin followed the time course for
dephosphorylation of IRS-1. PI 3-kinase activated in response to
insulin stimulation catalyzed the conversion of PI(4,5)P2
to PI(3,4,5)P3, which in turn drove the formation of
PI(3,4)P2 (Fig. 7B). The level of PI(3,4,5)P3 increased from 0.31 to 3.1% of the total lipid
population, and the level of PI(3,4)P2 increased from 0.29 to 2.9% of the total lipid population as it equilibrated with
PI(3,4,5)P3. On removal of insulin, the
phosphatidylinositides returned to basal levels (time to half-maximal
levels was ~11 min). The levels of PI(3,4,5)P3 controlled
the formation of phosphorylated, activated PKC-
(Fig.
7C). Maximal PKC-
activation occurred within 3 min of
insulin stimulation. After insulin was removed, the level of activated
PKC-
declined back to basal levels (time to half-maximal levels was
~11 min). The time course for phosphorylated, activated Akt was
identical to that for PKC-
(data not shown). Insulin-stimulated activation of PKC-
and Akt mediates increased exocytosis of GLUT4 so
that 40% of total cellular GLUT4 was at the cell surface and 60% was
intracellular after maximal insulin stimulation (Fig. 7D).
Our simulations of insulin-stimulated GLUT4 recruitment occurred with a
half-time of ~3 min, matching published experimental results (18, 20). When insulin was removed, surface and
intracellular GLUT4 levels returned to their basal values (time to
half-maximal levels was ~16 min). Thus the overall response of our
complete model without feedback to an acute insulin input is in good
agreement with both a variety of published experimental data and
previously validated subsystem models.
Model Simulations with Feedback
Having developed a plausible mechanistic model of metabolic
insulin signaling pathways related to translocation of GLUT4, we next
explored the effects of including positive and negative feedback loops
to gain additional insight into the complexities of insulin signaling.
Phosphorylation of PTP1B by Akt partially inhibits the ability of PTP1B
to dephosphorylate the insulin receptor and IRS-1 (38). In
addition, PKC-
phosphorylates serine residues on IRS-1 and inhibits
the ability of IRS-1 to bind and activate PI 3-kinase
(39). As described in MODEL DEVELOPMENT, we
incorporated these positive and negative feedback interactions into our
model. As for the model without feedback, we generated time courses for all state variables in response to a maximally stimulating step input
of 10
7 M insulin for 15 min (Figs.
8 and
9). Time courses for the various insulin receptor states in response to insulin stimulation were qualitatively similar to results obtained from our model without feedback (cf. Fig. 6). However, after removal of insulin, the return of
free surface receptors to basal levels and the disappearance of total
phosphorylated surface receptors occurred a little more slowly than in
the model without feedback. These results are consistent with the
presence of a positive feedback loop at the level of the insulin
receptor. With incorporation of negative feedback at the level of
IRS-1, the time course for IRS-1 tyrosine phosphorylation in response
to insulin stimulation is quite different from model simulations
generated without feedback. In response to insulin, the level of
tyrosine-phosphorylated IRS-1 transiently reached a peak of 0.84 pM
within 1.5 min. This was followed by a rapid 60% decrease before a
final equilibration at ~0.30 pM by 11 min (Fig. 8D). Thus
the presence of negative feedback at the level of IRS-1 caused
transient oscillatory behavior and a lower steady-state level for
tyrosine-phosphorylated IRS-1. Levels of serine-phosphorylated IRS-1
first began to rise after 1.5 min of insulin stimulation. Similar to
tyrosine-phosphorylated IRS-1, the concentration of serine-phosphorylated IRS-1 equilibrated at 0.76 pM after 5 min of
insulin stimulation. Less than 10% of the total IRS-1 remained in the
unactivated state after maximal insulin stimulation. Removal of insulin
resulted in conversion of both serine- and tyrosine-phosphorylated IRS-1 back to unphosphorylated IRS-1 (time to return to half-maximal levels was ~17 min).

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Fig. 8.
Model simulations with feedback. Time courses for unbound receptors
(A), once- and twice-bound phosphorylated surface receptors
(B), total phosphorylated surface receptors (C),
and unphosphorylated, serine-phosphorylated, and
tyrosine-phosphorylated IRS-1 (D) after a step input of
10 7 M insulin for 15 min.
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Fig. 9.
Model simulations with feedback. Time courses for activated
PI 3-kinase (A), levels of PI(3,4,5)P3 and
PI(3,4)P2 (B), activated PKC- (C),
and cell surface GLUT4 (D) after a step input of
10 7 M insulin for 15 min.
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The transient oscillatory behavior observed for tyrosine-phosphorylated
IRS-1 in response to insulin stimulation was also observed for
activated PI 3-kinase (Fig. 9A). Activated PI 3-kinase transiently peaked at 5.6 fM within 1.8 min. This was followed by a
rapid undershoot and then equilibration at ~1.9 fM by 10 min. On
removal of insulin, the concentration of activated PI 3-kinase
returned to basal levels (time to half-maximal levels was ~17
min). The time courses for PI(3,4,5)P3,
PI(3,4)P2, PKC-
, and Akt displayed a qualitatively
similar dynamic (Fig. 9, B and C). That is,
after 1 min of insulin stimulation, the level of PI(3,4,5)P3 increased from 0.31% of the total lipid
population to a peak of ~6.1% followed by an undershoot before
equilibration at ~2.5%. The level of PI(3,4)P2 increased
from 0.21% to a peak of ~5.6% before equilibrating at a
steady-state level of ~2.4%. On removal of insulin, both
PI(3,4,5)P3 and PI(3,4)P2 returned to their
basal levels (time to half-maximal levels was ~17 min). In response
to insulin, the percentage of activated PKC-
transiently peaked at
~17.1% after ~1.5 min followed by an undershoot and equilibration
at ~7.4% by 11 min. After insulin was removed, the level of
activated PKC-
declined to basal levels with a time to half-maximal
levels of ~17 min. Because we modeled the behavior of Akt identically
to PKC-
, the time course for phosphorylated, activated Akt mirrored
that for PKC-
(data not shown). With respect to translocation of
GLUT4, the overall shapes of the time courses for cell surface GLUT4
with and without feedback were similar. However, with inclusion of
positive and negative feedback loops, described above, the half-time
for translocation of GLUT4 to the cell surface in response to insulin
was slightly shorter than that observed in the model without feedback
(~2.5 min), whereas the time for return to basal levels after insulin
removal was longer (time to half-maximal level was ~18 min). Thus the
inclusion of positive and negative feedback loops into our model of
metabolic insulin signaling generates predictions regarding the
dynamics of various signaling components that may be experimentally testable.
Insulin Dose-Response Characteristics
We generated simulations of insulin dose-response curves to
further explore characteristics of our model with and without feedback.
Step inputs ranging from 10
6 to 10
12 M
insulin for 15 min were used to construct dose-response curves for
maximum levels of bound insulin receptors at the cell surface, total
phosphorylated receptors at the cell surface, activated PI3-kinase, and
cell surface GLUT4 (Fig. 10). Published
experimental data corresponding to each of these elements were then
compared with simulation results. The experimental data used for
comparison were obtained from a series of experiments performed in the
same preparation of rat adipose cells (47). For bound
surface insulin receptors (x3 + x4 + x5), the
dose-response curve generated by our model without feedback had a
half-maximal effective dose (ED50) of 3.5 nM (Fig.
10A). Our model with feedback generated a curve with an
ED50 of 2.9 nM. Both of these simulation results were similar to the experimentally determined ED50 of 7 nM that
was reported by Stagsted et al. (47). With respect to
receptor autophosphorylation, model simulations without feedback
generated a dose-response curve for surface phosphorylated receptors
(x4 + x5) with an
ED50 of 3.5 nM (Fig. 10B). Model simulations
with feedback generated a dose-response curve with an ED50
of 2.9 nM. The experimentally determined ED50 for receptor
autophosphorylation was reported as 5 nM (47). The close
similarity between insulin dose-response curves for receptor binding
and receptor autophosphorylation observed in both our simulations and
the experimental data is consistent with the tight coupling of the
dynamics of these processes.

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|
Fig. 10.
Experimentally generated insulin dose-response curves adapted from
Ref. 47 were compared with dose-response curves generated
from our model with and without feedback for bound receptors
(A), phosphorylated receptors at the cell surface
(B), PI 3-kinase activity (C), and glucose
uptake (D; assumed to be directly proportional to GLUT4
levels at the cell surface).
|
|
For activated PI 3-kinase, model simulations without feedback
generated an insulin dose-response curve with an ED50 of
0.83 nM. Model simulations with feedback showed a slightly greater sensitivity with an ED50 of 1.43 nM. These simulation
results seem reasonable, since downstream components should have
greater insulin sensitivity than proximal events if one assumes that
signal amplification occurs for downstream elements. Interestingly, the experimentally determined ED50 for activated PI 3-kinase
reported by Stagsted et al. (47) is 8 nM. With respect to
insulin-stimulated translocation of GLUT4, model simulations without
feedback generated a dose-response curve with an ED50 of
0.53 nM, whereas model simulations with feedback generated a
dose-response curve with a slightly smaller ED50 of 0.19 nM. In rat adipose cells, the ED50 = 0.17 nM for
insulin-stimulated glucose uptake (47). Again, our
simulation results are not only consistent with kinetic expectations
but also closely match experimental results, including observations that maximal glucose uptake occurs with partial insulin receptor occupancy (47). A general result from these model
simulations is that insulin sensitivity increases for components
farther downstream in the signaling pathway. In addition, the presence
of feedback in our model resulted in slightly increased sensitivity for
each signaling component examined compared with simulations without feedback.
Biphasic Activation of PKC-
Biphasic activation of PKC-
in rat adipocytes in response to
insulin stimulation has been previously reported (48, 50). However, the mechanism underlying this dynamic is unknown. To determine
whether the presence of feedback in insulin signaling pathways might
account for this biphasic response, we compared published experimental
data on activation of PKC-
with model simulations in the presence or
absence of feedback. We used a step input of 10
8 M
insulin for 15 min to mimic the experimental conditions reported in
Standaert et al. (48). Intriguingly, the time course for activated PKC-
in response to insulin generated from the simulation with feedback displayed a biphasic dynamic that more closely matched the experimental data, whereas the model without feedback failed to
produce a biphasic response (Fig. 11).
Thus one possible mechanism to generate a biphasic activation of
PKC-
in response to insulin is the presence of feedback pathways.

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Fig. 11.
Biphasic activation of PKC- in response to insulin
stimulation. Published data on insulin-stimulated activation of PKC-
(adapted from Ref. 48, Fig. 2A;
) were compared with simulation results from our model
with ( ) and without ( ) feedback using a
step input of 10 8 M insulin for 15 min.
|
|
Effects of Increased Levels of PTPases on Insulin-Stimulated
Translocation of GLUT4
To demonstrate the ability of our model to represent pathological
conditions, we ran model simulations without feedback where we examined
the effects of increased PTPase activity on translocation of GLUT4.
Simulations of the time courses for cell surface GLUT4 were generated
for 15-min insulin step inputs of 10
7, 10
9,
and 10
10 M and [PTP] = 1. These control curves
were then compared with simulations in which [PTP] = 1.5 (mimicking diabetes or obesity). As might be predicted,
increasing [PTP] resulted in a decreased amount of cell surface
GLUT4 at every insulin dose and a more rapid return to the basal
state when insulin is removed (Fig. 12). Moreover, the effect of increased
PTPase activity to reduce cell surface GLUT4 (in terms of percentage)
is more pronounced at lower insulin doses. Thus, at an insulin dose of
10
7 M, increasing [PTP] by 50% causes a 6.5% decrease
in peak insulin-stimulated GLUT4 at the cell surface, whereas at the
10
10 M insulin dose, a 50% increase in [PTP]
results in a 27.9% decrease in peak insulin-stimulated cell
surface GLUT4. These results are consistent with the
amplification properties of this signal transduction system and the
function of PTPases to negatively regulate insulin signaling at the
level of the insulin receptor and IRS-1. Model simulations with
feedback gave qualitatively similar results (data not shown).

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Fig. 12.
Effects of increasing PTP on time courses for
insulin-stimulated translocation of GLUT4. Simulations for cell surface
GLUT4 in response to a 15-min step input of 10 7 M insulin
(A), 10 9 M insulin (B), and
10 10 M insulin (C) are shown for [PTP] = 1.0 (open symbols) and [PTP] = 1.5 (solid symbols) using our model
without feedback.
|
|
 |
DISCUSSION |
Since the discovery of insulin over 80 years ago, tremendous
progress has been made in elucidating the molecular mechanisms of
insulin action. However, recent investigations of insulin signaling reveal biological complexities that are still not fully understood. For
example, the determinants of specificity for metabolic insulin signaling pathways are largely unknown. Rapid progress in the field of
signal transduction and genomics has inspired the foundation of groups
such as the National Resource for Cell Analysis and Modeling (NRCAM;
pioneers in the Virtual Cell project; see Ref. 41) and The
Alliance for Cellular Signaling. These groups strongly argue that a
theoretical approach with a comprehensive database is absolutely
necessary for a full understanding of cellular signaling behavior.
Model Development
Previous applications of mathematical modeling to insulin action
have focused on limited areas such as receptor binding kinetics and
GLUT4 trafficking (17, 35-37, 43, 44, 57). The
predictive power of these models has been useful for understanding
particular aspects of insulin action. In the present work, we
incorporate some of these models along with a novel current description
of insulin signal transduction elements into a complete model of metabolic insulin signaling pathways. Because some signaling elements represented in the model have just recently been discovered,
biochemical characterization of the kinetics for these elements
remains incomplete. For example, time courses of activation are often
reported with reference to insulin stimulation without
characterization relative to immediate upstream precursors. Moreover,
limitations in experimental approaches preclude the determination of
some time courses with sufficient resolution. Thus we did not
explicitly include an element for PDK-1 between the generation of
PI(3,4,5)P3 and the phosphorylation of PKC-
and Akt
because insufficient kinetic data are available in the literature.
Similarly, elements downstream from PKC-
and Akt that link metabolic
insulin signaling pathways with the machinery for GLUT4 trafficking are
unknown and therefore not explicitly represented.
One potential pitfall in developing such a complicated model is that
the number of arbitrary free parameter choices may decrease the
predictive power of the model. To address this issue, we incorporated previous models as subsystems in our complete model to significantly reduce the number of arbitrary elements. Rate constants and parameters for these subsystems had previously been independently obtained and
validated. The majority of remaining model parameters and rate
constants characterizing newly modeled steps of the metabolic insulin
signaling pathway were based on experimental data in the literature. We
also used boundary value conditions to derive fixed relationships among
various rate constants and model parameters to further decrease the
degrees of freedom in the structure of the model. Finally, as a
simplifying measure, we represented the numerous kinetic reactions in
our model as first-order reactions coupled by shared common elements.
We have attempted to thoroughly validate our complete model by
demonstrating that the behavior of each individual state variable in
response to a step insulin input closely matches experimental data from
a variety of independent sources. As further evidence of the validity
of our complete model, our system as a whole generated properties that
have been observed experimentally, including the presence of "spare
receptors" (e.g., maximal activation of GLUT4 translocation with
submaximal insulin receptor occupancy), signal amplification, and
increased insulin sensitivity for downstream components in the
signaling pathway. Because three of the four model subsystems have
previously been validated and the behavior of the overall model agrees
closely with published experimental data, we conclude that our
postreceptor signaling subsystem is reasonable and robust. Moreover,
the rate constants chosen for the signaling subsystem were based on
data in the literature. Although a more complete exploration of the postreceptor signaling subsystem is of interest, this is beyond the
scope of the current study.
In some cases where mechanisms regulating interactions between
signaling elements are not fully understood, we modeled these interactions as linear relationships. The rate of IRS-1 phosphorylation in response to activated insulin receptors, the rate of
PI(3,4,5)P3 generation in response to activated
PI 3-kinase, the rate of PKC-
and Akt phosphorylation in response
to increased levels of PI(3,4,5)P3, and the rate of
exocytosis for GLUT4 in response to phosphorylated PKC-
and Akt are
all modeled as simple linear functions. In the case of the negative
feedback loop where PKC-
phosphorylates IRS-1 on serine residues, we
modulated the rate constant for serine phosphorylation of IRS-1 using a
standard Hill equation to incorporate a reasonable time lag.
Importantly, we observed a good overall match between experimental data
and model simulations for both insulin dose-response curves and time
courses. Thus our coupling assumptions seem reasonable. Nevertheless,
these points in the model represent areas that could be further refined
in the future when a greater understanding of the molecular mechanisms
involved is achieved. Indeed, by modeling more complicated coupling
mechanisms, specific simulation results may give rise to experimentally
testable predictions. This interplay between theoretical predictions
and experimental results may yield important insights into the
molecular mechanisms of insulin action.
Model Simulations without Feedback
We validated the structure of our complete model by comparing
published experimental data with model simulations in response to an
acute insulin stimulus. In our model without feedback, the dynamics of
insulin-stimulated phosphorylation of IRS-1, activation of
PI 3-kinase, production of PI(3,4,5)P3 and
PI(3,4)P2, and phosphorylation of Akt and PKC-
all fit
well with published experimental data (2, 29, 46, 48, 55).
On removal of insulin, the dynamics of the return to basal states in
our simulations showed a time to half-maximal levels of ~8 min for
phosphorylated IRS-1 and activated PI 3-kinase and ~11 min for
PI(3,4,5)P3, phosphorylated Akt, and phosphorylated
PKC-
. Because minimal kinetic data exist regarding the return to
basal levels after removal of insulin, these simulation results
represent predictions of our model. Finally, as expected, time courses
for insulin receptor binding and GLUT4 translocation also matched
experimental data when these subsystems were placed into the context of
the overall model.
In our simulations we observed a time lag between the insulin input and
subsequent steps in insulin signaling that increased as the signal
propagated downstream. This lag was present for simulations of both
insulin stimulation and removal. Because the kinetics governing most
state variables were modeled as first-order events, recovery to basal
conditions of each component would be expected to appear as a
concave-up, exponential decay curve. Interestingly, in our simulations
of insulin removal (after 15-min insulin stimulation), we observed the
presence of a concave-down region immediately before the concave-up
exponential decay that became more pronounced for distal components and
is clearly evident in the simulations of GLUT4 translocation (Fig.
7D). This qualitative behavior is consistent with the
presence of a signaling cascade that controls insulin-stimulated
translocation of GLUT4 and has been observed experimentally in rat
adipose cells (20).
To further validate our complete model without feedback, we compared
published experimental data with simulations of insulin dose-response
curves for key state variables (Fig. 10). The usefulness of these
comparisons was substantially strengthened by the fact that data on
insulin receptor binding, receptor autophosphorylation, PI 3-kinase
activation, and glucose transport were obtained from a single
experimental preparation of rat adipose cells (47). Qualitatively, the sigmoidal shape of dose-response curves generated by
our model simulations (when plotted as a semi-log graph) is consistent
with the hyperbolic response characteristic of most receptor-mediated
biological events. In addition, we observed increased insulin
sensitivity for downstream components of the insulin signaling pathway.
That is, ED50 = 3.5 nM for receptor binding,
ED50 = 3.5 nM for receptor autophosphorylation,
ED50 = 0.83 nM for PI 3-kinase activation, and
ED50 = 0.53 nM for GLUT4 translocation. This increased
sensitivity of downstream components, consistent with the presence of a
signal amplification cascade, is a well-described characteristic for
biological actions of insulin. For example, only a fraction of insulin
receptors need to be occupied by insulin for maximal glucose uptake to
occur in adipose cells (20, 47). Stagsted et al.
(47) reported an ED50 of 8 nM for
insulin-stimulated PI 3-kinase activation. However, close inspection
of their data suggests that the actual value may be closer to 4 nM.
Nevertheless, this ED50 is still somewhat larger than the
ED50 of 0.83 nM derived from our simulations. However, the
measurement of PI 3-kinase activity in anti-phosphotyrosine immunoprecipitates derived from whole cell lysates is difficult to
perform in a quantitative manner. Thus it is possible that the small
discrepancy between our simulation results and experimental data with
respect to activation of PI3-kinase may be explained, in part, by
imprecision introduced by experimental variability. Of note, the shape
and ED50 of insulin dose-response curves for insulin
receptor binding, receptor autophosphorylation, and GLUT4 translocation
almost exactly match the corresponding experimentally determined
dose-response curves (Fig. 10). Thus the insulin sensitivity of key
components of our model is realistic. Moreover, given the fact that our
model structure, rate constants, and parameters were derived from a
large mixture of many different experimental systems, this remarkable
fit to experimental data from a single system across several key state
variables suggests that the overall structure of our model is quite robust.
Model Simulations with Feedback
To further explore the complexities of insulin signaling, we
simultaneously modeled positive and negative feedback loops based on
mechanisms proposed in the literature (9, 33, 38, 39). We
incorporated a positive feedback loop into our model by having Akt
phosphorylate PTP1B and impair its ability to dephosphorylate the
insulin receptor and IRS-1 (38). The slight increase in insulin sensitivity for insulin binding and receptor
autosphosphorylation observed in our model with feedback was an
expected result of positive feedback at the level of the insulin
receptor. That is, decreased activity of PTPases against phosphorylated
insulin receptors results in subtle shifts in the equilibrium states
for the various receptor state variables. Similarly, we observed
slightly decreased sensitivity for the activated PI 3-kinase
dose-response curve derived from our model with feedback. This is the
result of positive feedback with Akt phosphorylating PTP1B and
inhibiting tyrosine dephosphorylation of IRS-1. In addition, the
lower equilibrium level of PI 3-kinase after maximal insulin
stimulation (which defines the parameter PI3K) also contributes to a
shift in insulin sensitivity at the level of PI 3-kinase.
Dose-response curves for translocation of surface GLUT4 derived from
the model with feedback demonstrated greater insulin sensitivity than
simulations without feedback. This was due to the combined effects of
increased sensitivity of proximal signaling elements. Remarkably, the
experimental data for insulin-stimulated glucose uptake reported by
Stagsted et al. (47) indicated an ED50 of 1.7 nM that almost exactly matched the ED50 of 1.9 nM for cell
surface GLUT4 that we calculated from our model with feedback. In
addition to slightly increased insulin sensitivity, the half-times for
return to basal levels of all signaling elements were longer in our
simulations with feedback. These results are consistent with
experimental observations suggesting that positive feedback at the
level of the insulin receptor and IRS-1 slows the return of activated
signaling elements to basal levels (38).
We incorporated a negative feedback loop into our model by modeling the
ability of PKC-
to phosphorylate IRS-1 on serine residues and impair
its ability to bind and activate PI 3-kinase (39). Time
courses for insulin receptor binding and phosphorylation generated by
models with and without feedback were similar. However, the overall
dynamics of postreceptor signaling elements in our model were quite
different with inclusion of feedback. In response to insulin
stimulation, we observed a transient damped oscillatory behavior before
equilibrium was reached in all elements of the postreceptor signaling
subsystem. This oscillatory behavior was a direct result of negative
feedback by PKC-
. Immediately after insulin stimulation, effects of
PKC-
on upstream components are not apparent because of the time lag
present for distal signaling components. As levels of phosphorylated
PKC-
increase (and the value of parameter [PKC] approaches 1), the
rate constant for serine phosphorylation of IRS-1 increases, resulting
in depletion of the tyrosine-phosphorylated IRS-1 pool. As biochemical
reactions within the postreceptor signaling pathway shift and react to
effects of this negative feedback, time courses of postreceptor
elements exhibit a transient oscillatory behavior before a final
equilibrium state is reached. Although this qualitative behavior has
not been reported for insulin-stimulated PI 3-kinase activity, it is
possible that time courses with sufficiently fine resolution to capture this behavior have not been performed. Intriguingly, a damped oscillatory behavior or biphasic activation of PKC-
in response to
insulin stimulation previously has been reported in several studies
(48, 50). Only our model with feedback (but not without feedback) generated simulations for insulin-stimulated PKC-
activity that closely matched the complex dynamic for PKC-
present in published experimental data (48). Thus one novel result
from our model is the suggestion that negative feedback from PKC-
to
IRS-1 may be sufficient to explain the complex dynamic behavior of
PKC-
activity in response to insulin.
Modeling Increased Levels of PTPases
In addition to giving insight into normal physiology, our model
may also be useful for helping to understand pathological conditions.
Diabetes is a disease characterized by insulin resistance that may be
related, in part, to elevated levels of protein tyrosine phosphatases
such as PTP1B (15). We simulated a pathological condition
where activity of PTPases was 50% above normal ([PTP] = 1.5). Over a
range of insulin doses, this was associated with a decrease in peak
cell surface GLUT4 compared with simulations where [PTP] = 1. The
percent decrease in peak GLUT4 was greater for lower insulin doses, and
the half-times for recovery to basal conditions were significantly
shortened by increasing [PTP]. Similar effects were observed in the
models with and without feedback. Thus our model can make specific
predictions about the nature of insulin resistance due to increased
levels of PTPases such as PTP1B. Similarly, it may be possible to
explore mechanisms of insulin resistance due to altered lipid
phosphatase function by manipulation of the parameters [SHIP] and
[PTEN].
In conclusion, the mathematical model of metabolic insulin signaling
pathways developed here is based on previous subsystem models as well
as new elements characterizing the molecular mechanisms of insulin
signaling. The model structure was extensively validated and sufficient
to explain qualitative behaviors that are experimentally observed in
both normal and pathological states. In addition, our model with
feedback suggests a potential mechanistic explanation for the damped
oscillatory behavior of PKC-
activity in response to insulin that is
observed experimentally. Moreover, various mechanisms used to couple
model subsystems represent experimentally testable hypotheses.
Consequently, we hope that our model will be a useful predictive tool
for generating hypotheses to complement and motivate experimental
approaches. This may lead to a better understanding of the normal
physiology of insulin action as well as the pathophysiology underlying
insulin resistance that contributes to major public health problems
such as diabetes and obesity.
 |
APPENDIX A |
Model without Feedback
State variables are as follows
x1 |
= Insulin input
|
x2 |
= Concentration of unbound surface insulin receptors
|
x3 |
= Concentration of unphosphorylated once-bound surface receptors
|
x4 |
= Concentration of phosphorylated twice-bound surface receptors
|
x5 |
= Concentration of phosphorylated once-bound surface receptors
|
x6 |
= Concentration of unbound unphosphorylated intracellular receptors
|
x7 |
= Concentration of phosphorylated twice-bound intracellular receptors
|
x8 |
= Concentration of phosphorylated once-bound intracellular receptors
|
x9 |
= Concentration of unphosphorylated IRS-1
|
x10 |
= Concentration of tyrosine-phosphorylated IRS-1
|
x11 |
= Concentration of unactivated PI 3-kinase
|
x12 |
= Concentration of tyrosine-phosphorylated IRS-1/activated PI 3-kinase
complex
|
x13 |
= Percentage of PI(3,4,5)P3 out of the total
lipid population
|
x14 |
= Percentage of PI(4,5)P2 out of the total lipid
population
|
x15 |
= Percentage of PI(3,4)P2 out of the total lipid
population
|
x16 |
= Percentage of unactivated Akt
|
x17 |
= Percentage of activated Akt
|
x18 |
= Percentage of unactivated PKC-
|
x19 |
= Percentage of activated PKC-
|
x20 |
= Percentage of intracellular GLUT4
|
x21 |
= Percentage of cell surface GLUT4
|
Equations are as follows
x1 |
= insulin input
|
dx2/dt |
= k 1x3 + k 3[PTP]x5 k1x1x2 + k 4x6 k4x2
|
dx3/dt |
= k1x1x2 k 1x3 k3x3
|
dx4/dt |
= k2x1x5 k 2x4 + k 4'x7 k4'x4
|
dx5/dt |
= k3x3 + k 2x4 k2x1x5 k 3[PTP]x5 + k 4'x8 k4'x5
|
dx6/dt |
= k5 k 5x6 + k6[PTP](x7 + x8) + k4x2 k 4x6
|
dx7/dt |
= k4'x4 k 4'x7 k6[PTP]x7
|
dx8/dt |
= k4'x5 k 4'x8 k6[PTP]x8
|
dx9/dt |
= k 7[PTP]x10 k7x9(x4 + x5)/(IRp)
|
dx10/dt |
= k7x9(x4 + x5)/(IRp) + k 8x12 (k 7[PTP] + k8x11)x10
|
dx11/dt |
= k 8x12 k8x10x11
|
dx12/dt |
= k8x10x11 k 8x12
|
dx13/dt |
= k9x14 + k10x15 (k 9[PTEN] + k 10[SHIP])x13
|
dx14/dt |
= k 9[PTEN]x13 k9x14
|
dx15/dt |
= k 10[SHIP]x13 k10x15
|
dx16/dt |
= k 11x17 k11x16
|
dx17/dt |
= k11x16 k 11x17
|
dx18/dt |
= k 12x19 k12x18
|
dx19/dt |
= k12x18 k 12x19
|
dx20/dt |
= k 13x21 (k13 + k13')x20 + k14 k 14x20
|
dx21/dt |
= (k13 + k13')x20 k 13x21
|
Initial conditions are as follows
x1(0) |
= 0
|
x2(0) |
= 9 × 10 13 M
|
x3(0) |
= 0
|
x4(0) |
= 0
|
x5(0) |
= 0
|
x6(0) |
= 1 × 10 13 M
|
x7(0) |
= 0
|
x8(0) |
= 0
|
x9(0) |
= 1 × 10 12 M
|
x10(0) |
= 0
|
x11(0) |
= 1 × 10 13 M
|
x12(0) |
= 0
|
x13(0) |
= 0.31%
|
x14(0) |
= 99.4%
|
x15(0) |
= 0.29%
|
x16(0) |
= 100%
|
x17(0) |
= 0
|
x18(0) |
= 100%
|
x19(0) |
= 0
|
x20(0) |
= 96%
|
x21(0) |
= 4%
|
Model parameters are as follows
k1 |
= 6 × 107
M 1 · min 1
|
k 1 |
= 0.20 min 1
|
k2 |
= k1
|
k 2 |
= 100k 1
|
k3 |
= 2,500 min 1
|
k 3 |
= k 1
|
k4 |
= k 4/9
|
k 4 |
= 0.003 min 1
|
k4' |
= 2.1 × 10 3 · min 1
|
k 4' |
= 2.1 × 10 4 · min 1
|
k5 |
= 10k 5
M · min 1 if
(x6 + x7 + x8) > 1 × 10 13
=60k 5
M · min 1 if
(x6 + x7 + x8) 1 × 10 13
|
k 5 |
= 1.67 × 10 18 min 1
|
k6 |
= 0.461 min 1
|
k7 |
= 4.16 min 1
|
k 7 |
= (2.5/7.45)k7
|
k8 |
= k 8(5/70.775) × 1012
|
k 8 |
= 10 min 1
|
k9 |
= (k9(stimulated) k9(basal))(x12/PI3K) + k9(basal)
|
k9(stimulated) |
= 1.39 min 1
|
k 9 |
= (94/3.1)k9(stimulated)
|
k9(basal) |
= (0.31/99.4)k 9
|
k10 |
= (3.1/2.9)k 10
|
k 10 |
= 2.77 min 1
|
k11 |
= (0.1k 11)(x13 0.31)/(3.10 0.31)
|
k 11 |
= 10 ln (2) min 1
|
k12 |
= (0.1k 12)(x13 0.31)/(3.10 0.31)
|
k 12 |
= 10 ln (2) min 1
|
k 13 |
= 0.167 min 1
|
k13 |
= (4/96)k 13
|
k13' |
= [(40/60) (4/96)]k 13 · (Effect)
|
k14 |
= 96k 14
|
k 14 |
= 0.001155 min 1
|
effect |
= (0.2x17 + 0.8x19)/(APequil)
|
IRp |
= 8.97 × 10 13 M
|
[SHIP] |
= 1.00
|
[PTEN] |
= 1.00
|
[PTP] |
= 1.00
|
APequil |
= 100/11
|
PI3K |
= 5 × 10 15 M
|
Model with Feedback
Additional state variables are as follows
x10a = concentration of
serine-phosphorylated IRS-1
Additional equations are as follows
dx9/dt |
= k 7[PTP]x10 k7x9(x4 + x5)/(IRp) + k 7'x10a k7'[PKC]x9 (updated)
|
dx10a/dt |
= k7[PKC]x9 k 7'x10a
|
Additional initial conditions are as follows
Additional parameters are as follows
k7' |
= ln (2)/2 min 1
|
k 7' |
= k7' [(2.5/7.45)(3.70 × 10 13)]/[(6.27 × 10 13)
(2.5/7.45)(3.70 × 10 13)]
|
[PTP] |
= 1.00 [1 0.25(x17/(100/11)] for
x17 (400/11), otherwise [PTP] = 0 (updated)
|
PI3K |
= k8(3.70 × 10 13)(1 × 10 13)/[k8(3.70 × 10 13) + k 8] (updated)
|
[PKC] |
= Vmaxx19(t )n/[K + x19(t )n]
|
Vmax |
= 20
|
Kd |
= 12
|
n |
= 4
|
|
= 1.5
|
 |
APPENDIX B |
Initial Conditions, Rate Constants, and Parameter Choice for
Complete Model without Feedback
Where possible, initial conditions and model parameters were
determined by known boundary value conditions or experimental data as
previously described (35-37, 57). Table
1 lists initial conditions for the basal
state (no insulin) of state variables obtained from previous models.
Initial conditions for x4,
x5, x7, and
x8 were set to zero because, in the absence of
insulin, we assumed that no receptors are bound to insulin. Similarly, initial basal conditions for phosphorylated IRS-1, phosphorylated IRS-1/activated PI 3-kinase complex, and phosphorylated Akt and PKC-
(x10, x12,
x17, and x19) were set to
zero. The initial concentration for unphosphorylated IRS-1
(x9) was set to 10
12 M on the
basis of experimental results from 3T3-L1 adipocytes (21,
29). From published concentrations of purified PI 3-kinase obtained from rat liver and an estimate of the efficiency of
purification (4, 25), we set the basal intracellular
PI 3-kinase concentration (x11) at
10
13 M. Under basal conditions, the percentage
distribution of PI(3,4,5)P3 (x13),
PI(4,5)P2 (x14), and
PI(3,4)P2 (x15) in COS- 7 cells is 0.31, 99.4, and 0.29%, respectively, of the total pool
(23). Therefore, we used these values for the initial
basal conditions of x13,
x14, and x15. We assumed
that neither Akt nor PKC-
is in the phosphorylated, activated state
under basal conditions. Thus we set initial conditions for
unphosphorylated Akt (x16) and unphosphorylated
PKC-
(x18) equal to 100% of the amount of these proteins in the cell. We represented these state variables in
terms of percentages because we could not find published estimates of
cellular concentrations for either Akt or PKC-
.
Table 2 lists values for rate constants
obtained from previous subsystem models. For the rate constant for
insulin receptor autophosphorylation (k3), we
chose a value of 2,500 min
1 that was determined
experimentally in vitro (1). This is consistent with the
rapid autophosphorylation of insulin receptors in intact cells
(44, 58, 59). For the rate constant governing receptor dephosphorylation (k
3), we assumed that
release of insulin from the insulin receptor was rate limiting and that
receptors were immediately dephosphorylated once they returned to the
basal unoccupied state (11, 30, 31, 44). Therefore, we
chose k
3 = k
1.
The rate constant for phosphorylated receptor endocytosis
(k4') was chosen to be 2.1 × 10
3 min
1. This is the value used for the
endocytosis rate constant for bound insulin receptors in our previous
model (36). Because the rate of ligand-mediated
endocytosis exceeds the rate for exocytosis, we chose a ratio of
endocytosis and exocytosis rate constants for phosphorylated receptors
of 10:1 so that k
4' = 2.1 × 10
4 min
1. When phosphorylated receptors are
internalized, insulin dissociates and receptors undergo rapid
dephosphorylation. The half-time for internalized receptor
dephosphorylation (after maximal phosphorylation by insulin
stimulation) is ~1.5 min in rat liver endosomes (11). For a first-order rate constant
|
(B32)
|
Therefore, assuming half-time (t1/2) = 1.5 min for internalized receptor dephosphorylation, the rate
constant for intracellular receptor dephosphorylation
(k6) is 0.461 min
1.
For reactions in the postreceptor signaling subsystem, the choice of
rate constants was based on experimental data where possible. To
further limit the number of free parameters, we also used published data to derive fixed relationships among various rate constants. On
maximal insulin stimulation, most IRS-1 is tyrosine phosphorylated (52) with a half-time of ~10 s in 3T3-L1 adipocytes
(29). Under these conditions, ~5% of PI 3-kinase is
activated in Fao cells (16). By using initial conditions
described in APPENDIX A for the basal state and
assuming that 75% of all IRS-1 becomes tyrosine phosphorylated with
maximal insulin stimulation, equilibrium values for
x9 through x12 after
maximal insulin stimulation will be x9 = 2.5 × 10
13 M, x10 = 7.45 × 10
13 M, x11 = 9.5 × 10
14 M, and x12 = 5.0 × 10
15 M. By assuming the half-time for maximal
IRS-1 phosphorylation to be 10 s, k7 = 4.16 min
1 (using Eq. 32). Under normal
physiological conditions, where PTP = 1, Eq. 14 can be
simplified and rearranged as k
7 = (x9/x10)k7
in the equilibrium state after maximal insulin stimulation. Thus, under
conditions of maximal insulin stimulation,
k
7 = (2.5/7.45)k7.
Reassuringly, these values for k7 and
k
7 are consistent with the time course for
IRS-1 phosphorylation and dephosphorylation observed in rat adipose
cells (24). Similarly, at equilibrium, Eqs. 16 and 17 can be simplified and rearranged as
k8 = x12/(x10 x11)k
8.
Because we were unable to find data on rates for association or
dissociation of IRS-1 with PI 3-kinase, we chose
k
8 = 10 min
1 to be
consistent with the scale of other rate constants in the postreceptor
signaling subsystem. Thus, at maximal insulin stimulation, we
constrained k8 = (50/70.775) × 1012 M
1 · min
1.
On the basis of data from 3T3-L1 cells, we assumed that levels for both
PI(3,4,5)P3 and PI(3,4)P2 rise 10-fold after
maximal insulin stimulation (22, 46), resulting in a new
equilibrium distribution of 3.1, 94, and 2.9% for
PI(3,4,5)P3, PI(4,5)P2, and
PI(3,4)P2, respectively. Because insulin-stimulated
conversion of PI(4,5)P2 to PI(3,4,5)P3 is
mediated by the phosphorylated IRS-1/activated PI 3-kinase complex,
there is an increase in the rate constant governing this process
(k9) with insulin stimulation. We represented
the transition in k9 from the basal value
[k9 (basal)] to the insulin-stimulated value
[k9 (stimulated)] as a linear function of
activated PI 3-kinase present in the cell
|
(B33)
|
where PI3K is the equilibrium concentration of activated
PI 3-kinase obtained after maximal insulin stimulation. Data from 3T3-L1 preadipocytes suggest that conversion of PI(4,5)P2
to PI(3,4,5)P3 in response to insulin stimulation occurs
with a half-time of ~30 s (when a time lag from upstream signaling
events is considered) (46). Assuming a 30-s half-time for
conversion of PI(4,5)P2 to PI(3,4,5)P2 and
using Eq. 32, we calculated
k9 (stimulated) = 1.39 min
1.
For both basal and insulin-stimulated equilibrium states, Eq. 19 can be simplified and rearranged to show that
k9 = (x13/x14)k
9 (under normal physiological conditions, where PTEN = 1).
Therefore, k
9 and
k9 (basal) can be constrained:
k
9 = (94/3.1)k9 (stimulated) and
k9 (basal) = (0.31/99.4)k
9. Similarly, data from 3T3-L1
preadipocytes suggest that conversion of PI(3,4,5)P3 to
PI(3,4)P2 occurs with a half-time of ~15 s
(46). By assuming a 15-s half-time for conversion of
PI(3,4,5)P3 to PI(3,4)P2,
k
10 = 2.77 min
1. For both
basal and insulin-stimulated equilibrium states, Eq. 20 can
be simplified to constrain k10 = (3.1/2.9)k
10 (under normal physiological
conditions, where SHIP = 1).
To define kinetic rate constants for activation and deactivation of Akt
and PKC-
, we used data from rat skeletal muscle cells and rat
adipocytes showing that PKC-
and Akt are both activated by insulin
at approximately the same rate and that both enzymes reach maximal
activation within 5 min of insulin stimulation (48, 55).
There are no published data on the time course of activation in intact
cells for Akt or PKC-
by their immediate signaling precursors.
However, experimental data suggest that after taking into account the
time lag between insulin binding and generation of
PI(3,4,5)P3, the induced activation of Akt and PKC-
probably occurs within 2 min (50, 56). Thus we chose rate
constants for Akt and PKC-
activation, k11
and k12, to be the same and also assumed that
the half-time for maximal Akt and PKC-
activation was 1 min. Thus,
by using Eq. 32, k11 = k12 = [ln(2)] min
1 at
equilibrium after maximal insulin stimulation.
Because many other growth factors can activate Akt and PKC-
simultaneously (19, 28), we assumed that with maximal
insulin stimulation, both Akt and PKC-
exist in a 10:1
unactivated-to-activated distribution at equilibrium. Therefore, from
Eqs. 21-24, we can constrain k
11 = 10k11 = 10 ln(2) and k
12 = 10k12 = 10 ln(2). Because
PI(3,4,5)P3 formation mediates Akt and PKC-
activation (50, 56), we assumed that rate constants for activation of both Akt and PKC-
increase from zero to their maximal values as a
linear function of the increase in PI(3,4,5)P3 levels
|
(B34)
|
|
(B35)
|
where 0.31 is the basal value of PI(3,4,5)P3 and
3.10 is the value of PI(3,4,5)P3 in the cell after maximal
insulin stimulation. The values used for k
13,
k14, and k
14 were
previously defined for the GLUT4 translocation subsystem (Table 2), and the values for k13 and
k13' can be derived from this information using
Eqs. 28 and 29.
The parameter [PTP] was defined as the relative activity of protein
tyrosine phosphatases in the cell. Thus [PTP] = 1 under normal
physiological conditions, whereas pathological variations in PTPase
activity can be represented by altering [PTP]. Similarly, model
parameters [SHIP] and [PTEN] were defined as the relative activity
of 5' and 3' lipid phosphatases, respectively, in the cell ([SHIP] = 1 and [PTEN] = 1 under normal conditions). The value for
IRp (used in Eqs. 14 and 15) was
determined to be 8.97 × 10
13 M, based on
calculations using equilibrium conditions obtained during maximal
insulin stimulation for Eqs. 6-13 and assuming that receptor downregulation is negligible during acute insulin stimulation. The value for APequil (used in Eq. 29) was
determined to be 100/11 (based on a 10:1 unactivated-to-activated
distribution of both Akt and PKC-
). The value for PI3K (used in
Eq. B33) was chosen as 5 × 10
15 M based
on experimental data indicating that ~5% of PI 3-kinase is
activated on maximal insulin stimulation (16).
Additional Initial Conditions, Rate Constants, and Parameter
Choice for Complete Model with Feedback
We assume that there is no serine phosphorylation of IRS-1 in
the absence of insulin stimulation. Therefore, we chose the initial
value of x10a = 0. In NIH-3T3IR
cells, the phosphotyrosine content of IRS-1 after maximal insulin stimulation decreases by ~50% at 60 min (39). Thus,
with inclusion of this negative feedback circuit, we chose the
insulin-stimulated equilibrium value of x10 = 3.7 × 10
13 M to reflect this 50% decrease. With
the use of steady-state conditions for Eq. 17 and initial
conditions x11 + x12 = 1 × 10
13 M, the
insulin-stimulated equilibrium level for x12 was
calculated to be k8(3.70 × 10
13)(1 × 10
13)/[k8(3.70 × 10
13) + k
8] = 2.54 × 10
15 M. Because the total amount of IRS-1 is constant
(x9 + x10 + x10a + x12), the
insulin-stimulated equilibrium level of x9 + x10a = 6.27 × 10
13 M. Values for k7, k
7,
k8, and k
8 remained the
same as for the model without feedback. We assumed the half-time for IRS-1 serine phosphorylation was 2 min. From Eq. B32, we
calculated k7' = ln(2)/2
min
1. With the use of the parameter constraints and
derived equilibrium concentrations described in APPENDIX A
as well as Eqs. 30 and 31,
k
7' = k7'[(2.5/7.45)(3.70 × 10
13)]/[(6.27 × 10
13)
(2.5/7.45)(3.70 × 10
13)] at equilibrium after
maximal insulin stimulation. Finally, to properly incorporate this
negative feedback loop into our model, the factor PI3K from Eq. B33 was redefined as 2.54 × 10
15 M, the
insulin-stimulated equilibrium value of x12
calculated. This change was necessary to satisfy all of the constraints
imposed by the new equilibrium after maximal insulin stimulation.
Consistent with the 50% decrease in phosphotyrosine content of IRS-1
described above, this new value for PI3K is approximately one-half of
that derived for the model without feedback. We chose values for
Vmax, Kd, n,
and
that seemed moderate and reasonable for introducing a time
delay on the order of a few minutes. By altering these parameters, it
is possible to generate behavior that ranges from biphasic changes in
activity of PKC-
to sustained oscillations (data not shown). At
present, there are no experimental data available to further refine
these parameter choices.
 |
ACKNOWLEDGEMENTS |
This work was supported in part by the Whitaker/National Institutes
of Health Biomedical Engineering Summer Internship Program (A. R. Sedaghat) and an American Diabetes Association Student Mentor Award (to
M. J. Quon).
 |
FOOTNOTES |
Address for reprint requests and other correspondence: M. J. Quon, Cardiology Branch, National Heart, Lung, and Blood Institute, National Institutes of Health, Bldg. 10, Rm. 8C-218, 10 Center Dr. MSC
1755, Bethesda, MD 20892-1755 (E-mail: quonm{at}nih.gov).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
July 2, 2002;10.1152/ajpendo.00571.2001
Received 31 December 2001; accepted in final form 25 June 2002.
 |
REFERENCES |
1.
Ablooglu, AJ,
and
Kohanski RA.
Activation of the insulin receptor's kinase domain changes the rate-determining step of substrate phosphorylation.
Biochemistry
40:
504-513,
2001[ISI][Medline].
2.
Backer, JM,
Myers MG, Jr,
Shoelson SE,
Chin DJ,
Sun XJ,
Miralpeix M,
Hu P,
Margolis B,
Skolnik EY,
Schlessinger J,
and
White MF.
Phosphatidylinositol 3'-kinase is activated by association with IRS-1 during insulin stimulation.
EMBO J
11:
3469-3479,
1992[Abstract].
3.
Bandyopadhyay, G,
Standaert ML,
Sajan MP,
Karnitz LM,
Cong L,
Quon MJ,
and
Farese RV.
Dependence of insulin-stimulated glucose transporter 4 translocation on 3-phosphoinositide-dependent protein kinase-1 and its target threonine-410 in the activation loop of protein kinase C-
.
Mol Endocrinol
13:
1766-1772,
1999[Abstract/Free Full Text].
4.
Carpenter, CL,
Duckworth BC,
Auger KR,
Cohen B,
Schaffhausen BS,
and
Cantley LC.
Purification and characterization of phosphoinositide 3-kinase from rat liver.
J Biol Chem
265:
19704-19711,
1990[Abstract/Free Full Text].
5.
Charron, MJ,
Brosius FC, III,
Alper SL,
and
Lodish HF.
A glucose transport protein expressed predominately in insulin-responsive tissues.
Proc Natl Acad Sci USA
86:
2535-2539,
1989[Abstract].
6.
Clement, S,
Krause U,
Desmedt F,
Tanti JF,
Behrends J,
Pesesse X,
Sasaki T,
Penninger J,
Doherty M,
Malaisse W,
Dumont JE,
Le Marchand-Brustel Y,
Erneux C,
Hue L,
and
Schurmans S.
The lipid phosphatase SHIP2 controls insulin sensitivity.
Nature
409:
92-97,
2001[ISI][Medline].
7.
Cong, LN,
Chen H,
Li Y,
Zhou L,
McGibbon MA,
Taylor SI,
and
Quon MJ.
Physiological role of Akt in insulin-stimulated translocation of GLUT4 in transfected rat adipose cells.
Mol Endocrinol
11:
1881-1890,
1997[Abstract/Free Full Text].
8.
Cushman, SW,
and
Wardzala LJ.
Potential mechanism of insulin action on glucose transport in the isolated rat adipose cell. Apparent translocation of intracellular transport systems to the plasma membrane.
J Biol Chem
255:
4758-4762,
1980[Free Full Text].
9.
De Fea, K,
and
Roth RA.
Protein kinase C modulation of insulin receptor substrate-1 tyrosine phosphorylation requires serine 612.
Biochemistry
36:
12939-12947,
1997[ISI][Medline].
10.
Ebina, Y,
Ellis L,
Jarnagin K,
Edery M,
Graf L,
Clauser E,
Ou JH,
Masiarz F,
Kan YW,
Goldfine ID,
Roth RA,
and
Rutter WJ.
The human insulin receptor cDNA: the structural basis for hormone-activated transmembrane signalling.
Cell
40:
747-758,
1985[ISI][Medline].
11.
Faure, R,
Baquiran G,
Bergeron JJ,
and
Posner BI.
The dephosphorylation of insulin and epidermal growth factor receptors. Role of endosome-associated phosphotyrosine phosphatase(s).
J Biol Chem
267:
11215-11221,
1992[Abstract/Free Full Text].
12.
Freychet, P,
Roth J,
and
Neville DM, Jr.
Insulin receptors in the liver: specific binding of (125I)insulin to the plasma membrane and its relation to insulin bioactivity.
Proc Natl Acad Sci USA
68:
1833-1837,
1971[Abstract].
13.
Fukumoto, H,
Kayano T,
Buse JB,
Edwards Y,
Pilch PF,
Bell GI,
and
Seino S.
Cloning and characterization of the major insulin-responsive glucose transporter expressed in human skeletal muscle and other insulin-responsive tissues.
J Biol Chem
264:
7776-7779,
1989[Abstract/Free Full Text].
14.
Giorgetti, S,
Ballotti R,
Kowalski-Chauvel A,
Cormont M,
and
Van Obberghen E.
Insulin stimulates phosphatidylinositol-3-kinase activity in rat adipocytes.
Eur J Biochem
207:
599-606,
1992[Abstract].
15.
Goldstein, BJ,
Li PM,
Ding W,
Ahmad F,
and
Zhang WR.
Regulation of insulin action by protein tyrosine phosphatases.
Vitam Horm
54:
67-96,
1998[ISI][Medline].
16.
Hayashi, T,
Okamoto M,
Yoshimasa Y,
Inoue G,
Yamada K,
Kono S,
Shigemoto M,
Suga J,
Kuzuya H,
and
Nakao K.
Insulin-induced activation of phosphoinositide 3-kinase in Fao cells.
Diabetologia
39:
515-522,
1996[Medline].
17.
Holman, GD,
Lo Leggio L,
and
Cushman SW.
Insulin-stimulated GLUT4 glucose transporter recycling. A problem in membrane protein subcellular trafficking through multiple pools.
J Biol Chem
269:
17516-17524,
1994[Abstract/Free Full Text].
18.
Holman, GD,
and
Cushman SW.
Subcellular trafficking of GLUT4 in insulin target cells.
Seminars Cell Dev Biol
7:
259-268,
1996.
19.
Kandel, ES,
and
Hay N.
The regulation and activities of the multifunctional serine/threonine kinase Akt/PKB.
Exp Cell Res
253:
210-229,
1999[ISI][Medline].
20.
Karnieli, E,
Zarnowski MJ,
Hissin PJ,
Simpson IA,
Salans LB,
and
Cushman SW.
Insulin-stimulated translocation of glucose transport systems in the isolated rat adipose cell. Time course, reversal, insulin concentration dependency, and relationship to glucose transport activity.
J Biol Chem
256:
4772-4777,
1981[ISI][Medline].
21.
Keller, SR,
Kitagawa K,
Aebersold R,
Lienhard GE,
and
Garner CW.
Isolation and characterization of the 160,000-Da phosphotyrosyl protein, a putative participant in insulin signaling.
J Biol Chem
266:
12817-12820,
1991[Abstract/Free Full Text].
22.
Kelly, KL,
and
Ruderman NB.
Insulin-stimulated phosphatidylinositol 3-kinase. Association with a 185-kDa tyrosine-phosphorylated protein (IRS-1) and localization in a low density membrane vesicle.
J Biol Chem
268:
4391-4398,
1993[Abstract/Free Full Text].
23.
King, WG,
Mattaliano MD,
Chan TO,
Tsichlis PN,
and
Brugge JS.
Phosphatidylinositol 3-kinase is required for integrin-stimulated AKT and Raf-1/mitogen-activated protein kinase pathway activation.
Mol Cell Biol
17:
4406-4418,
1997[Abstract].
24.
Kublaoui, B,
Lee J,
and
Pilch PF.
Dynamics of signaling during insulin-stimulated endocytosis of its receptor in adipocytes.
J Biol Chem
270:
59-65,
1995[Abstract/Free Full Text].
25.
Lamphere, L,
Carpenter CL,
Sheng ZF,
Kallen RG,
and
Lienhard GE.
Activation of PI 3-kinase in 3T3-L1 adipocytes by association with insulin receptor substrate-1.
Am J Physiol Endocrinol Metab
266:
E486-E494,
1994[Abstract/Free Full Text].
26.
Levine, R.
Insulin action: 1948-80.
Diabetes Care
4:
38-44,
1981[Abstract].
27.
Levine, R,
Goldstein M,
Klein S,
and
Huddlestun B.
The action of insulin on the distribution of galactose in eviscerated nephrectomized dogs.
J Biol Chem
179:
985-990,
1949[Free Full Text].
28.
Liu, WS,
and
Heckman CA.
The sevenfold way of PKC regulation.
Cell Signal
10:
529-542,
1998[ISI][Medline].
29.
Madoff, DH,
Martensen TM,
and
Lane MD.
Insulin and insulin-like growth factor 1 stimulate the phosphorylation on tyrosine of a 160 kDa cytosolic protein in 3T3-L1 adipocytes.
Biochem J
252:
7-15,
1988[ISI][Medline].
30.
Mooney, RA,
and
Anderson DL.
Phosphorylation of the insulin receptor in permeabilized adipocytes is coupled to a rapid dephosphorylation reaction.
J Biol Chem
264:
6850-6857,
1989[Abstract/Free Full Text].
31.
Mooney, RA,
and
Green DA.
Insulin receptor dephosphorylation in permeabilized adipocytes is inhibitable by manganese and independent of receptor kinase activity.
Biochem Biophys Res Commun
162:
1200-1206,
1989[ISI][Medline].
32.
Nystrom, FH,
and
Quon MJ.
Insulin signalling: metabolic pathways and mechanisms for specificity.
Cell Signal
11:
563-574,
1999[ISI][Medline].
33.
Paz, K,
Liu YF,
Shorer H,
Hemi R,
LeRoith D,
Quon M,
Kanety H,
Seger R,
and
Zick Y.
Phosphorylation of insulin receptor substrate-1 (IRS-1) by protein kinase B positively regulates IRS-1 function.
J Biol Chem
274:
28816-28822,
1999[Abstract/Free Full Text].
34.
Pessin, JE,
Thurmond DC,
Elmendorf JS,
Coker KJ,
and
Okada S.
Molecular basis of insulin-stimulated GLUT4 vesicle trafficking. Location! Location! Location!
J Biol Chem
274:
2593-2596,
1999[Free Full Text].
35.
Quon, MJ.
Advances in kinetic analysis of insulin-stimulated GLUT-4 translocation in adipose cells.
Am J Physiol Endocrinol Metab
266:
E144-E150,
1994[Abstract/Free Full Text].
36.
Quon, MJ,
and
Campfield LA.
A mathematical model and computer simulation study of insulin receptor regulation.
J Theor Biol
150:
59-72,
1991[ISI][Medline].
37.
Quon, MJ,
and
Campfield LA.
A mathematical model and computer simulation study of insulin-sensitive glucose transporter regulation.
J Theor Biol
150:
93-107,
1991[ISI][Medline].
38.
Ravichandran, LV,
Chen H,
Li Y,
and
Quon MJ.
Phosphorylation of PTP1B at Ser(50) by Akt impairs its ability to dephosphorylate the insulin receptor.
Mol Endocrinol
15:
1768-1780,
2001[Abstract/Free Full Text].
39.
Ravichandran, LV,
Esposito DL,
Chen J,
and
Quon MJ.
Protein kinase C-
phosphorylates insulin receptor substrate-1 and impairs its ability to activate phosphatidylinositol 3-kinase in response to insulin.
J Biol Chem
276:
3543-3549,
2001[Abstract/Free Full Text].
40.
Satoh, S,
Nishimura H,
Clark AE,
Kozka IJ,
Vannucci SJ,
Simpson IA,
Quon MJ,
Cushman SW,
and
Holman GD.
Use of bismannose photolabel to elucidate insulin-regulated GLUT4 subcellular trafficking kinetics in rat adipose cells. Evidence that exocytosis is a critical site of hormone action.
J Biol Chem
268:
17820-17829,
1993[Abstract/Free Full Text].
41.
Schaff J and Loew LM. The virtual cell. Pac Symp
Biocomput: 228-239, 1999.
42.
Scraton, RE.
Basic Numerical Methods: an Introduction to Numerical Mathematics on a Microcomputer. London: E. Arnold, 1984.
43.
Shymko, RM,
De Meyts P,
and
Thomas R.
Logical analysis of timing-dependent receptor signalling specificity: application to the insulin receptor metabolic and mitogenic signalling pathways.
Biochem J
326:
463-469,
1997[ISI][Medline].
44.
Shymko, RM,
Dumont E,
De Meyts P,
and
Dumont JE.
Timing-dependence of insulin-receptor mitogenic versus metabolic signalling: a plausible model based on coincidence of hormone and effector binding.
Biochem J
339:
675-683,
1999[ISI][Medline].
45.
Simpson, L,
and
Parsons R.
PTEN: life as a tumor suppressor.
Exp Cell Res
264:
29-41,
2001[ISI][Medline].
46.
Sorisky, A,
Pardasani D,
and
Lin Y.
The 3-phosphorylated phosphoinositide response of 3T3-L1 preadipose cells exposed to insulin, insulin-like growth factor-1, or platelet-derived growth factor.
Obes Res
4:
9-19,
1996[Abstract].
47.
Stagsted, J,
Hansen T,
Roth RA,
Goldstein A,
and
Olsson L.
Correlation between insulin receptor occupancy and tyrosine kinase activity at low insulin concentrations and effect of major histocompatibility complex class I-derived peptide.
J Pharmacol Exp Ther
267:
997-1001,
1993[Abstract].
48.
Standaert, ML,
Bandyopadhyay G,
Perez L,
Price D,
Galloway L,
Poklepovic A,
Sajan MP,
Cenni V,
Sirri A,
Moscat J,
Toker A,
and
Farese RV.
Insulin activates protein kinases C-
and C-
by an autophosphorylation-dependent mechanism and stimulates their translocation to GLUT4 vesicles and other membrane fractions in rat adipocytes.
J Biol Chem
274:
25308-25316,
1999[Abstract/Free Full Text].
49.
Standaert, ML,
Bandyopadhyay G,
Sajan MP,
Cong L,
Quon MJ,
and
Farese RV.
Okadaic acid activates atypical protein kinase C (
/
) in rat and 3T3/L1 adipocytes. An apparent requirement for activation of Glut4 translocation and glucose transport.
J Biol Chem
274:
14074-14078,
1999[Abstract/Free Full Text].
50.
Standaert, ML,
Galloway L,
Karnam P,
Bandyopadhyay G,
Moscat J,
and
Farese RV.
Protein kinase C-
as a downstream effector of phosphatidylinositol 3-kinase during insulin stimulation in rat adipocytes. Potential role in glucose transport.
J Biol Chem
272:
30075-30082,
1997[Abstract/Free Full Text].
51.
Standaert, ML,
and
Pollet RJ.
Equilibrium model for insulin-induced receptor down-regulation. Regulation of insulin receptors in differentiated BC3H-1 myocytes.
J Biol Chem
259:
2346-2354,
1984[Abstract/Free Full Text].
52.
Sun, XJ,
Miralpeix M,
Myers MG, Jr,
Glasheen EM,
Backer JM,
Kahn CR,
and
White MF.
Expression and function of IRS-1 in insulin signal transmission.
J Biol Chem
267:
22662-22672,
1992[Abstract/Free Full Text].
53.
Suzuki, K,
and
Kono T.
Evidence that insulin causes translocation of glucose transport activity to the plasma membrane from an intracellular storage site.
Proc Natl Acad Sci USA
77:
2542-2545,
1980[Abstract].
54.
Ullrich, A,
Bell JR,
Chen EY,
Herrera R,
Petruzzelli LM,
Dull TJ,
Gray A,
Coussens L,
Liao YC,
Tsubokawa M,
Mason A,
Seepurg PH,
Grunfeld C,
Rosen OM,
and
Ramachandran J.
Human insulin receptor and its relationship to the tyrosine kinase family of oncogenes.
Nature
313:
756-761,
1985[ISI][Medline].
55.
Van der Kaay, J,
Batty IH,
Cross DA,
Watt PW,
and
Downes CP.
A novel, rapid, and highly sensitive mass assay for phosphatidylinositol 3,4,5-trisphosphate [PtdIns(3,4,5)P3] and its application to measure insulin-stimulated PtdIns(3,4,5)P3 production in rat skeletal muscle in vivo.
J Biol Chem
272:
5477-5481,
1997[Abstract/Free Full Text].
56.
Vanhaesebroeck, B,
and
Alessi DR.
The PI3K-PDK1 connection: more than just a road to PKB.
Biochem J
346:
561-576,
2000[ISI][Medline].
57.
Wanant, S,
and
Quon MJ.
Insulin receptor binding kinetics: modeling and simulation studies.
J Theor Biol
205:
355-364,
2000[ISI][Medline].
58.
White, MF,
Shoelson SE,
Keutmann H,
and
Kahn CR.
A cascade of tyrosine autophosphorylation in the
-subunit activates the phosphotransferase of the insulin receptor.
J Biol Chem
263:
2969-2980,
1988[Abstract/Free Full Text].
59.
Wilden, PA,
Kahn CR,
Siddle K,
and
White MF.
Insulin receptor kinase domain autophosphorylation regulates receptor enzymatic function.
J Biol Chem
267:
16660-16668,
1992[Abstract/Free Full Text].
Am J Physiol Endocrinol Metab 283(5):E1084-E1101