Endothelial dysfunction due to selective insulin resistance in vascular endothelium: insights from mechanistic modeling

Abstract

Previously, we have used mathematical modeling to gain mechanistic insights into insulin-stimulated glucose uptake. Phosphatidylinositol 3-kinase (PI3K)-dependent insulin signaling required for metabolic actions of insulin also regulates endothelium-dependent production of the vasodilator nitric oxide (NO). Vasodilation increases blood flow that augments direct metabolic actions of insulin in skeletal muscle. This is counterbalanced by mitogen-activated protein kinase (MAPK)-dependent insulin signaling in endothelium that promotes secretion of the vasoconstrictor endothelin-1 (ET-1). In the present study, we extended our model of metabolic insulin signaling into a dynamic model of insulin signaling in vascular endothelium that explicitly represents opposing PI3K/NO and MAPK/ET-1 pathways. Novel NO and ET-1 subsystems were developed using published and new experimental data to generate model structures/parameters. The signal-response relationships of our model with respect to insulin-stimulated NO production, ET-1 secretion, and resultant vascular tone, agree with published experimental data, independent of those used for model development. Simulations of pathological stimuli directly impairing only insulin-stimulated PI3K/Akt activity predict altered dynamics of NO and ET-1 consistent with endothelial dysfunction in insulin-resistant states. Indeed, modeling pathway-selective impairment of PI3K/Akt pathways consistent with insulin resistance caused by glucotoxicity, lipotoxicity, or inflammation predict diminished NO production and increased ET-1 secretion characteristic of diabetes and endothelial dysfunction. We conclude that our mathematical model of insulin signaling in vascular endothelium supports the hypothesis that pathway-selective insulin resistance accounts, in part, for relationships between insulin resistance and endothelial dysfunction. This may be relevant for developing novel approaches for the treatment of diabetes and its cardiovascular complications.

INTRODUCTION

Insulin resistance plays a key pathophysiological role in Type 2 diabetes and other diseases, including obesity, hypertension, coronary artery disease, dyslipidemias, and metabolic syndrome (71). Insulin helps regulate metabolic homeostasis by promoting glucose disposal in skeletal muscle and adipose tissue, and by inhibiting gluconeogenesis in liver (75). Insulin also has important physiological functions in the brain, pancreatic β-cells, heart, and vascular endothelium, which coordinate and couple metabolic and cardiovascular homeostasis (40, 55, 59). Vasodilator actions of insulin-stimulating production of nitric oxide (NO) from vascular endothelium increases blood flow that further enhances glucose uptake in skeletal muscle (13, 55). Endothelial dysfunction, characterized by reduced NO bioactivity, is a prominent feature of insulin-resistant states, including diabetes, obesity, and their cardiovascular complications (21, 29).

Insulin binding to its cognate cell-surface receptor activates two major branches of a complex insulin signal transduction network (82). Metabolic actions of insulin tend to be mediated by phosphatidylinositol 3-kinase (PI3K)-dependent signaling pathways (15, 55). Mitogen-activated protein kinase (MAPK)-dependent insulin signaling typically regulates mitogenesis, growth, and differentiation (51, 58). Insulin signaling pathways regulating endothelial production of NO are PI3K-dependent and exhibit striking parallels with metabolic insulin signaling (36, 50, 53, 93, 94). Insulin also has opposing vasoconstrictor actions to stimulate endothelin-1 (ET-1) production using MAPK-dependent (but not PI3K-dependent) signaling pathways in the endothelium (23, 62, 63). ET-1 is a potent vasoconstrictor synthesized and secreted from vascular endothelium that contributes to endothelial dysfunction and hypertension (38, 68). Both metabolic insulin resistance and vascular endothelial dysfunction are characterized by pathway-selective impairment in PI3K-dependent insulin signaling in metabolic (15) and vascular insulin target tissues (55). This contributes importantly to reciprocal relationships between insulin resistance and endothelial dysfunction that promote clustering of metabolic and cardiovascular diseases in insulin-resistant states (37). The insulin signaling network regulating vascular actions of insulin is characterized by cross talk among major signaling branches, as well as by both positive and negative feedback loops (70, 82). In addition, heterologous cross talk between other major signaling pathways (e.g., innate immune signaling) and insulin signaling is an important mechanism for regulating metabolic and vascular actions of insulin (28). Thus, it is a nontrivial undertaking to predict net vascular actions of insulin in response to physiological conditions interacting with intracellular insulin signaling networks in tissue-specific manners.

One useful approach for gaining additional insight into cellular and physiological systems regulated by insulin is to create homeomorphic mathematical models of insulin signaling using a systems approach that incorporates published experimental data, recent cellular and physiological concepts, and computer simulations to generate testable experimental hypotheses (67, 78). Interplay between experiment and modeling provides an efficient framework to advance understanding of reciprocal relationships between insulin resistance and endothelial dysfunction. In the present study, we develop and explore a mathematical model of insulin signaling in vascular endothelium that explicitly represents known signaling components mediating insulin-stimulated NO and ET-1 production. Novel subsystems regulating production of NO and ET-1 were corroborated independently using published experimental data. These were then coupled to a previously validated homeomorphic model of relevant insulin signaling pathways (78). We define a comprehensive, accurate model that can generate and test novel hypotheses. Our modeling approach reveals multiple plausible molecular mechanisms for insulin signal transduction pathways to create reciprocal relationships between insulin resistance and endothelial dysfunction. These insights may lead to novel therapeutic strategies for the treatment of diabetes and its cardiovascular complications.

METHODS

Model Description

The overall structure of our model developed here is strictly based on biochemical pathways determined from published and unpublished data on insulin signaling and insulin action in the vascular endothelium related to production of NO and secretion of ET-1. To derive a complete comprehensive final model, we used a modular approach as in the past (78), with extensive validation of discrete subsystems against experimental data to constrain model structure, parameter choice, and degrees of freedom. For example, we used our long-standing mathematical model of metabolic insulin signaling pathways (78) as the core subsystem to represent PI3K-dependent signaling from activation of the insulin receptor (IR) through activation of Akt (Fig. 1A). This PI3K-dependent subsystem is itself made up of various smaller independent subsystems. We directly linked this to a novel but straightforward nitric oxide synthase (eNOS)/NO subsystem in vascular endothelium developed in the present study (Fig. 1B). Moreover, we incorporated a detailed biochemical MAPK-dependent signaling subsystem based upon an amalgam of extensively validated models of receptor tyrosine kinase signaling (Fig. 2A) (27, 30, 34, 41, 65). This MAPK-dependent signaling subsystem was linked directly to ET-1 synthesis and secretion in vascular endothelium in the present model (Fig. 2B). The structure of the entire model with feedback pathways and crosstalk between the major PI3K- and MAPK-dependent signaling portions of the model is depicted in Fig. 3. Differential equations derived from the structure of the complete model were solved with a fourth-order Runge-Kutta numerical integration routine, using Berkeley Madonna (https://berkeley-madonna.myshopify.com/) and XPPAUT (http://www.math.pitt.edu/∼bard/xpp/xpp.html). A complete list of state variables, model equations, initial conditions, and model parameters, along with computer code (https://doi.org/10.6084/m9.figshare.12686072.v1) is presented in supplemental information (Supplemental Appendix S1; all other supplemental material is available at https://doi.org/10.6084/m9.figshare.12361085). 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. Selection of initial conditions, rate constants, and model parameters are based on previously published models or estimated from published or original experimental data, as indicated in Supplemental Appendix S2 in supplementary information.

Fig. 1.

Schematic of insulin signaling pathways stimulating nitric oxide (NO) production in endothelial cells. A: postreceptor insulin receptor substrate-phosphatidylinositol 3-kinase (IRS-PI3K)-Akt signaling subsystem. B: endothelial nitric oxide synthase (eNOS)-NO subsystem.

Fig. 2.

Schematic of insulin signaling pathways stimulating endothelin-1 (ET-1) production in endothelial cells. A: postreceptor MAPK signaling subsystem. B: ET-1 subsystem.

Fig. 3.

Complete model of insulin signaling pathways stimulating nitric oxide (NO) and endothelin-1 (ET-1) production in endothelial cells with feedback and cross-talk. Insulin binding to its receptor results in receptor autophosphorylation and the phosphorylation of insulin receptor substrate (IRS-1) by the insulin receptor tyrosine kinase. Phosphorylated IRS-1 activates phosphatidylinositol 3-kinase (PI3K), which increases membrane-bound PI(3,4,5)P3 (PIP3). PIP3 recruits and activates 3-phosphoinositide-dependent protein kinase-1 (PDK-1), which phosphorylates and activates Akt and atypical PKCs. Activated Akt phosphorylates endothelial nitric oxide synthase (eNOS) to increase nitric oxide (NO), a vasodilator. Tyrosine phosphorylation of the insulin receptor (IR) also increases the association of Shc and Grb2 to the IR, leading to the activation of the Ras‐Raf‐MEK‐MAPK1/2 cascade. MAPK increases the production of ET-1, a vasoconstrictor. Positive and negative feedback pathways are indicated by dotted lines. Cross talk between the PI3K and MAPK branches is indicated (-˙˙-˙˙-). Atypical PKC serine phosphorylates IRS-1 to create a negative feedback pathway, and Akt phosphorylates PTP1B to create a positive feedback pathway. Akt directly phosphorylates and attenuates Raf activity to create crosstalk between the PI3K-Akt-NO and MAPK-ET-1 pathways. Under healthy conditions, insulin stimulated vasodilation counteracts the vasoconstrictive effects of insulin-stimulated ET-1.

Model Development

PI3K-dependent signaling core.

Published studies from our laboratory have elucidated a complete biochemical signaling pathway leading from the insulin receptor (IR) to activation of eNOS in vascular endothelial cells in primary culture (for review, see Ref. 54). This involves binding of insulin (x₁) to the IR (x₂-x₈), a ligand-activated tyrosine kinase that then phosphorylates intracellular insulin receptor substrate (IRS) family members (x₉) on tyrosine residues. Tyrosine phosphorylated IRS proteins (x₁₀) serve as docking molecules that form signaling complexes with downstream effectors. Tyrosine phosphorylation of IRS proteins at Src homology 2 (SH2)-domain binding motifs promotes interaction with SH2-domain-containing effectors, including phosphatidylinositol 3-kinase (PI3K; x₁₁). PI3K is a heterodimer composed of a regulatory p85 subunit and a catalytic p110 subunit (Fig. 1A). Binding of SH2 domains of the p85 subunit to tyrosine-phosphorylated motifs on IRS-1 (x₁₂) allosterically activates the preassociated p110 catalytic subunit to generate the lipid product phosphatidylinositol 3,4,5-trisphosphate [PI(3,4,5)P3] (x₁₃) from the substrate phosphatidylinositol 4,5-bisphosphate (x₁₄). PI(3,4,5)P3 binds to the pleckstrin homology domain in 3-phosphoinositide-dependent protein kinase-1 (PDK-1, not explicitly represented in this model for simplicity), resulting in its phosphorylation and activation to subsequently phosphorylate and activate other downstream serine-threonine kinases, including Akt (x₁₆, unphosphorylated Akt; x₁₇, phosphorylated, activated Akt) and atypical protein kinase C (aPKC) (x₁₈, unphosphorylated aPKC; x₁₉, phosphorylated, activated aPKC).

Our model also explicitly incorporates protein tyrosine phosphatases (e.g., PTP1B) that dephosphorylate IR and IRS-1, and lipid phosphatases (e.g., SHIP-2 and PTEN) that dephosphorylate PI(3,4,5)P3 because these protein and lipid phosphatases play important roles in negative regulation of insulin-signaling pathways. For simplicity, as in our previous model (78), we do not explicitly represent PI-5 lipid kinases, since these have not been definitively shown to play important roles in the biology relevant to the present model. In addition, positive and negative feedback pathways involving Akt and atypical PKC were incorporated into our model of PI3K-dependent signaling, as previously described (78). Phosphorylation of PTP1B by Akt impairs the ability of PTP1B to dephosphorylate insulin receptors and IRS-1 by 25% (69). Since 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 to inhibit PTP1B activity with a 25% decrease in [PTP] at maximal insulin stimulation. We also incorporated a negative feedback loop where serine phosphorylation of IRS-1 by aPKC impairs formation of the phosphorylated IRS-1/activated PI 3-kinase complex. To represent this, we assumed that serine phosphorylation of IRS-1 by activated aPKC creates a serine phosphorylated IRS-1 species (x_10a) unable to associate with and activate PI 3-kinase. Differential Eqs. 8–26, initial conditions, and model parameters for the PI3K-dependent signaling core subsystem are presented in Supplemental Appendix S1. This subsystem representing activation of the IR through Akt is virtually identical to the mathematical model we developed describing insulin-stimulated regulation of translocation of GLUT4 and glucose uptake in adipose cells (78).

eNOS/NO subsystem.

In the present model of insulin signaling in vascular endothelium regulating activation of eNOS and production of NO, we linked our previous model of PI3K-dependent IR signaling through Akt to a novel eNOS/NO subsystem (Fig. 1B), where direct phosphorylation of eNOS by Akt controls production of NO (Fig. 1B). Phosphorylated, activated Akt directly phosphorylates human eNOS at Ser¹¹⁷⁷ (equivalent to Ser¹¹⁷⁹ in bovine eNOS), resulting in enhanced eNOS activity (17, 50). Thus, the concentration of phosphorylated Akt (x₁₇) is the input to this subsystem. Activated Akt phosphorylates eNOS (x₂₀) to produce phosphorylated, activated eNOS (x₂₁), which then catalyzes conversion of the substrate l-arginine (Arg) to the products NO (x₂₂) and L-citrulline. Both eNOS phosphorylation/activation and NO production are represented in our model using Michaelis-Menten dynamics. The Michaelis-Menten equilibrium rate constant (K_m) is the ratio of the backward (dissociation) and the forward (association) first-order rate constants for formation and dissociation of the enzyme/substrate complex. We assume that the catalytic activity defining the rate of enzymatic conversion of substrate to product is much smaller than the rate constant for dissociation of the enzyme/substrate complex. Under these conditions, the value of K_m reflects the magnitude of the concentration of substrate required for effective enzymatic catalysis (80). In our present model, K_m values were obtained from estimates derived from published experimental studies (see Supplemental Appendix S2). After production of NO by eNOS, endothelium-derived NO diffuses into vascular smooth muscle cells, where it activates guanylate cyclase to increase cGMP levels, which subsequently evokes vasorelaxation and vasodilation (12, 55), a major output of our model.

Differential equations describing the eNOS/NO subsystem (Fig. 1B) are given here:

$$d\left(x_{20}\right)/dt=k_{-13}{x}_{21}\hspace{0.17em}–\hspace{0.17em}{k}_{13}{x}_{17}{x}_{20}/\left(K_{m13}+x_{20}\right)$$ (1)

$$d\left(x_{21}\right)/dt=k_{13}{x}_{17}{x}_{20}/\left(K_{m13}+x_{20}\right)-k_{-13}{x}_{21}$$ (2)

$$d\left(x_{22}\right)/dt=k_{14}{x}_{21}\left(\text{Arg}\right)/\left[K_{m14}+\left(\text{Arg}\right)\right]–k_{15}{x}_{22}$$ (3)

Here, x₂₂, represents the concentration of NO in the endothelial cell, which is directly related to vasodilation, a major output of our model. Arg represents the concentration of the eNOS substrate l-arginine in the cell.

MAPK-dependent signaling core.

In addition to PI3K-dependent insulin signaling, another major insulin signaling branch is the MAPK-dependent pathway. The Ras/MAPK is the most modeled and studied signaling pathway related to insulin signaling and other tyrosine kinase receptor signaling (61). Several mathematical models of MAPK-dependent signaling pathways (Fig. 2A) have been previously developed and extensively validated in the context of receptor tyrosine kinase signaling (including EGF, NGF, HGF, and PDGF receptor signaling) (27, 30, 34, 41, 65). Experimentally determined peak amplitudes and signal transfer efficiency of Akt and ERK pathways in various cell lines [PC12 cells, human umbilical vein endothelial cells (HUVECs), Swiss 3T3, and HeLa cells] are conserved (84). In our present model of insulin signaling in vascular endothelium, we adapted and amalgamated many aspects of these previous models to generate a reasonable quantitative representation of MAPK-dependent insulin signaling initiated by the insulin receptor. In cases where insufficient data exist to generate realistic estimates of particular rate constants, model parameters, or state variables, we have deliberately avoided explicit representation of these phenomena. In addition, we have endeavored to maintain comparable levels of complexity among our established representation of the PI 3-kinase-dependent signaling branch and our novel description of the insulin-stimulated MAPK-dependent signaling branch. Finally, we have eliminated complexities in the representation of MAPK-dependent signaling that are not directly related to ET-1 synthesis and secretion. These strategies help to minimize the degrees of freedom present in our complex model to increase the potential predictive power of our model.

The MAPK-dependent signaling core of our present model is a major new component added to our previous insulin signaling model. Although this portion of the model relies heavily on published validated models of MAPK signaling in response to other growth factors that stimulate tyrosine kinase receptors (e.g., heregulin, EGF) (27, 77), we generally follow the robust modeling principles that we previously used in developing the PI3K-dependent signaling core (78). This involves tyrosine phosphorylation of the insulin receptor substrate Shc (x₂₃) by the insulin receptor (phospho-Shc, x₂₄). Phosphorylated Shc then binds to the SH2 domain of Grb-2, resulting in activation of the GTP exchange factor SOS (son of sevenless, not explicitly represented in our model). SOS is preassociated with the small GTP-binding protein Ras in its GDP-bound state (x₂₅). Activated SOS catalyzes the exchange of GDP for GTP on Ras to activate it. Activated Ras (x₂₆) recruits cytoplasmic Raf (x₂₇) to the plasma membrane, which initiates a three-tier kinase phosphorylation cascade (not explicitly represented in our model). Activated Raf (x₂₈) sequentially phosphorylates two serine residues on MEK (x₂₉), resulting in singly (x₃₀) and doubly (x₃₁) phosphorylated MEK. As a simplification, we assume that the doubly phosphorylated MEK is solely responsible for subsequent phosphorylation of MAPK (x₃₂), which also undergoes sequential phosphorylation on tyrosine (x₃₃) and threonine (x₃₄) residues. Phosphorylated and activated MAPK (x₃₃, x₃₄) translocates to the nucleus to phosphorylate and activate a variety of transcription factors [e.g., c-Fos, Elk-1, and c-Myc (85)]. In our model, singly phosphorylated MAPK has less activity than doubly phosphorylated MAPK.

Our MAPK-dependent signaling model is negatively regulated at several points by explicit representation of dephosphorylation of key enzymes. For example, protein phosphatase (PP2A) dephosphorylates both Raf and MEK (at both phosphorylation sites), resulting in inactivation of these enzymes. In addition, MAPK phosphatase (MKP-3) dephosphorylates MAPK at both the tyrosine and threonine phosphorylation sites to reduce MAPK activity accordingly (95). Differential Eqs. 27–36, initial conditions, and model parameters for the MAPK-dependent signaling core subsystem are presented in Supplemental Appendix S1. We did not find evidence of ERK-dependent negative feedback regulation of SOS and Raf-1 in insulin-stimulated endothelial cells and thus did not include it in our model.

ET-1 synthesis and secretion subsystem.

Insulin acutely stimulates synthesis and secretion of ET-1 using MAPK-dependent (but not PI3K-dependent) signaling pathways (10, 23, 62, 63). Detailed kinetics of the nuclear events modulating insulin-stimulated ET-1 synthesis is not well understood. Therefore, in our model, this process is simply represented by a single first-order parameter k₂₉ that fits the kinetics of insulin-stimulated ET-1 secretion from primary vascular endothelial cells (x₃₅ = concentration of ET-1 in conditioned media) that we observed experimentally (Fig. 5D). We also used a first-order rate constant k₃₀ to represent the degradation rate for ET-1. Thus, ET-1 synthesis and secretion in response to MAPK activation are represented by the differential equation:

$$d\left(x_{35}\right)/dt=k_{29}\left(x_{34}+x_{33}\right)–k_{30}{x}_{35}$$ (4)

Fig. 5.

Model simulations of intracellular levels of phosphorylated Shc (p-Shc), GTP-bound Ras (Ras-GTP), phosphorylated MAPK (p-MAPK), and ET-1. A: model simulations for intracellular levels of p-Shc, Ras-GTP, and p-MAPK after a step input of insulin (100 nM, 15 min) are plotted as a function of time. B: insulin concentration-response curves generated by model simulations of peak p-Shc, Ras-GTP, and p-MAPK. The lines represent the best fit of the simulated data points. C: model simulations of the time course for ET-1 synthesis/secretion after a step input of insulin (100 nM, 15 min). D: insulin concentration-response generated by model simulations of peak ET-1 synthesis/secretion. Experimental data for ET-1 secreted into conditioned media from bovine aortic endothelial cells (n = 3) in primary culture were obtained, as described in methods.

Net vascular tone determined by cross talk between PI3K- and MAPK-dependent signaling.

Experimental studies suggest that Akt attenuates Raf activity by direct phosphorylation on Ser²⁵⁹. Phosphorylation of Raf on Ser²⁵⁹ promotes binding of 14-3-3 proteins to Raf, resulting in Raf inactivation (49, 96). Specifically, treatment of human vascular endothelial cells with insulin (50 nM) for 10 min significantly increased Raf-1 Ser²⁵⁹ phosphorylation levels. This was associated with simultaneous increases in phosphorylation of the mitogen-activated protein kinase kinase (MEK1/2) at Ser^217/221 and ET-1 expression. Pretreatment with the PI3-K inhibitor, LY294002 reduced Ser-259 phosphorylation of Raf-1. Moreover, pretreatment with LY294002 or an AKT-inhibitor reduced insulin-mediated vasorelaxation. These data from human vascular endothelial cells support our model assumptions (91). Noncompetitive inhibition of Raf by Akt is modeled in accordance with the equation, v = V_max S/([ K_m + S][1 + (1/k_i)^h]). Here k_i represents the inhibition constant for Raf inactivation by Akt. The Hill coefficient h represents the level of cooperativity for inhibitor binding (14). In our model, h is set to 1 to express noncooperative binding behavior, meaning that binding at one site has no effect on binding on other sites (64). Thus, the differential equations governing cross talk between PI3K- and MAPK-dependent insulin signaling are the following:

$$d\left(x_{27}\right)/dt=k_{19}{x}_{28}\left[\text{PP2A}\right]/\left[K_{m19}+x_{28}\right]\hspace{0.17em}–\hspace{0.17em}{k}_{20}{x}_{26}{x}_{27}/\left\{\left[K_{m20}+x_{27}\right]\left[1+{\left(x_{17}/k_i\right)}^{n2}\right]\right\}$$ (5)

$$d\left(x_{28}\right)/dt=k_{20}{x}_{26}{x}_{27}/\left\{\left[K_{m20}+x_{27}\right]\left[1+{\left(x_{17}/k_i\right)}^{n2}\right]\right\}-k_{19}{x}_{28}\left[\text{PP2A}\right]/\left[K_{m19}+x_{28}\right]$$ (6)

We have explicitly modeled cross talk between insulin-stimulated PI3K- and MAPK-dependent pathways to help determine the balance between vasodilator actions of NO and vasoconstrictor actions of ET-1 that are integrated to determine “net vascular tone”. In our model, the outputs of the PI3K- and MAPK-dependent insulin signaling subsystems are integrated to generate a “vascular effect” or “net vascular tone,” where vascular tone is defined as a percentage (100 – “vascular effect”). Net vascular tone is ultimately determined by the magnitude of vasodilator actions of NO (primarily regulated by PI3K-dependent signaling) that are opposed by vasoconstrictor actions of ET-1 (primarily regulated by MAPK-dependent signaling). Under normal balanced healthy physiological conditions, 60% of the vascular insulin signaling effect is attributed to NO, while 40% of the effect is attributed to ET-1 to represent the fact that under healthy conditions, direct insulin stimulation of the vasculature results in net vasodilator actions (8, 33, 62, 63). This is then normalized to NE_equil (net effect of NO and ET-1 at equilibrium after maximal insulin stimulation). That is, the steady-state level of net vasomotor tone considers both NO and ET-1 after maximal insulin stimulation. The equation describing this is

$$\text{Vascular Effect}=100·\left(0.6x_{22}-0.4x_{35}\right)/{\text{NE}}_{\text{equil}\text{.}}$$ (7)

Experimental Procedures

In the present study, model parameters were largely derived from our published experimental data, and the experimental data of others are taken from the literature. However, we also performed several new unpublished laboratory experiments to help test the predictive ability of our mathematical model and to provide more extensive validation both at the subsystem and whole model level.

Cell culture and transfection.

Bovine aortic endothelial cells (BAECs) (Clonetics, San Diego, CA) were grown in endothelial growth media (EBM), as described previously (23), and used at passages 3 and 4. BAEC at 60% confluence were transiently cotransfected with 0.1 μg of pCIS2-RFP (expression vector for red fluorescent protein) and 0.45 μg of pCIS2 (empty vector), expression vectors for wild-type PTEN (PTEN-WT), or PTEN-C124S (catalytically inactive point mutant with Ser substituted for Cys¹²⁴) using Lipofectamine Plus (Life Technologies), according to manufacturer’s instructions.

NO measurement.

One day after transfection, transiently transfected endothelial cells grown to 95% confluence on chamber slides were serum-starved for 2 h and then loaded with the NO-reactive dye 4,5-diaminofluorescein diacetate (DAF-2 DA; Calbiochem) (final concentration, 3 µM; 20 min, 37°C). DAF-2 DA is a cell-permeable compound converted to DAF-2 by intracellular esterases that forms a triazole derivative in the presence of NO (emits light at 515 nm upon excitation at 489 nm in proportion to the amount of NO present) (50). After DAF-2 loading, cells were rinsed three times in DMEM-A supplemented with 100 µM l-arginine or EBM-A, kept in the dark, and maintained at 37°C with a warming stage (Bioptechs) on a Zeiss Axiovert S100 TV-inverted microscope (Carl Zeiss, Thornwood, NY) equipped with an argon laser, PentaMAX camera (Princeton Instruments, Trenton, NJ), and appropriate filters for fluorescence microscopy. To identify transiently transfected cells, RFP expression was visualized by emission of red light (583 nm) upon excitation at 558 nm. Typically, two to five transfected cells were identified in a field of view at ×32 magnification. Cells were then treated with insulin or lysophosphatidic acid (LPA), and NO production was visualized by emission of green light (515 nm) upon excitation at 489 nm. Green fluorescence intensity was quantified using IP Laboratories Software (Scanalytics, Fairfax, VA) to integrate intensity over all pixels within the boundary of each transfected cell. Data for each experiment were normalized to a reference image of the basal state.

ET-1 assay.

BAEC grown in 35-mm dishes were serum-starved overnight. The next day, medium was replaced with fresh endothelial basal medium before treatment. BAEC were pretreated with vehicle or wortmannin (100 nM, 1 h) followed by treatment with vehicle or insulin (100 nM, 20 min). Conditioned media were collected from each dish, and cell lysates were prepared for determination of protein concentration. For each sample, measurement of ET-1 in 100 μL of diluted conditioned media (1:1 dilution with PBS) was performed using an ELISA kit (Assay Designs, Ann Arbor, MI), according to the manufacturer’s protocol. All samples were assayed in duplicate. Optical density (OD) was determined using a microplate reader, Power Wave X (Bio-Tek Instruments, Winooski, VT) and KC4 software (Bio-Tek) at a wavelength of 450 nm and 580 nm. Reading at 450 nm was corrected by subtraction of readings at 580 nm to correct for optical imperfections in the plate. Results were determined by comparison to standard curves and normalized to total protein concentration of cells for each sample.

RESULTS

Please see methods and supplemental information (Supplemental Appendices S1 and S2) for model development section. Definitions of model state variables and justifications for initial conditions are shown in Supplemental Appendix Table S1. Complete differential equations are also shown in Supplemental Appendix S1. List, definitions, and justification of model parameter values are shown in Supplemental Appendix Table S2. The structure of the PI3K-dependent subsystem, MAPK-dependent subsystem, and overall complete model structure are shown in Figs. 1–3.

Model simulations of signaling pathways mediating insulin-stimulated NO production.

We began evaluation of our complete model 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. The temporal kinetics of the IR and IRS-1 phosphorylation, PI3K, Akt, and PKC activation in response to a 15-min step input of insulin has been previously reported by us (78). In response to insulin, phospho-Akt levels transiently peaked at ∼1.5 nM after ∼2 min followed by a transient decrease, then increase to equilibration at ∼0.7 nM by 10 min (Fig. 4A). The biphasic activation of Akt by insulin observed in our model is consistent with in vitro studies in endothelial cells (43). The time course for activated PKC mirrored that for Akt (data not shown). Upon insulin stimulation, cellular levels of phospho-eNOS increased to a peak of 3 nM at ∼0.5 min followed by a transient decrease, then an increase to equilibrium at 2.3 nM by 12 min. Similar to Akt, biphasic activation of eNOS by insulin in our model was also observed in endothelial cells in culture (81). When insulin was removed at 15 min, there was a return of phospho-eNOS to basal levels (time to half-maximal levels ∼18 min). Similarly, insulin promptly increased cellular NO production with NO levels peaking at 325 nM at ∼5 min and a plateau of 300 nM by 15 min. Upon insulin removal at 15 min, NO returned to basal levels by 60 min (Fig. 4A).

Fig. 4.

Comparison between model simulations and experimental data from vascular endothelium regarding the dynamics of insulin-stimulated phosphorylation of Akt and eNOS. A: model simulations for intracellular levels of phosphorylated Akt (p-Akt), phosphorylated eNOS (p-eNOS), and nitric oxide (NO) production after a step input of insulin (100 nM, 15 min) plotted as a function of time. B: insulin concentration-response curves generated by model simulations of peak p-Akt were compared with experimental data for p-Akt in response to insulin stimulation as determined by quantification of immunoblotting studies taken from the published literature (43). The line represents the best fit of the simulated data points. C: insulin concentration-response curves generated by model simulations of peak p-eNOS were compared with experimental data for p-eNOS (43). The line represents the best fit of the simulated data points.

Concentration-response curves for IR autophosphorylation, IRS-1 tyrosine phosphorylation, PI(3,4,5)P3 levels, and PKC activation have been previously reported (78). To further characterize our present model, we generated simulations of insulin concentration-response curves for phospho-Akt and phospho-eNOS. Step inputs ranging from 10⁻⁵ to 10⁻¹² M insulin for 15 min were used to construct concentration-response curves for maximum levels of phospho-Akt and phospho-eNOS (Fig. 4, B and C). Published experimental data corresponding to each of these elements were then compared with simulation results (44). Model simulations generated a concentration-response curve with an EC₅₀ of 1.2 nM, and 0.6 nM, for phospho-Akt and phospho-eNOS, respectively. The experimentally determined EC₅₀ (44) were 1.9 nM and 1.6 nM, for Akt and eNOS phosphorylation, respectively. The EC₅₀ for insulin-stimulated NO production from model simulations was 0.41 nM (data not shown).

Model simulations of signaling pathways mediating insulin-stimulated ET-1 production.

We examined the simulated time courses for changes in cellular levels of signaling intermediaries in the MAPK/ET-1 pathway in response to a maximally stimulating step input of 10⁻⁷ M insulin that was turned off after 15 min. Upon insulin stimulation, phosphorylated Shc levels peaked at 0.12 μM (∼24% of total cellular Shc) within 1.5 min. Levels of GTP-bound Ras increased from 7% of total Ras at baseline to 43% within ∼1.5 min (Fig. 5A). In response to insulin, total levels of phosphorylated MAPK (MAPK-P and MAPK-PP) peaked at 42 nM after ∼6.5 min followed by equilibration at ∼33 nM by 12 min (Fig. 5A). The time course of the activation of phosphorylated MAPK by insulin observed in our model is consistent with in vitro studies in endothelial cells and brown adipocytes (16, 39, 43). Upon removal of insulin, Shc and MAPK underwent dephosphorylation and Ras-GTP levels returned to basal conditions with a half-time of ∼5 min. Both MEK and Raf activation profiles were similar to MAPK (data not shown). Simulated insulin concentration-response curves for peak phospho-Shc, Ras-GTP, and phospho-MAPK resulted in EC₅₀ values of 2.5 nM, 2.7 nM, and 6.2 nM insulin, respectively (Fig. 5B). Via MAPK activation, insulin stimulated an acute increase in ET-1 levels that peaked at 1.8 nM after ∼18 min. After insulin removal at 15 min, this gradually decreased to basal levels (time to half-maximal levels ∼20 min) (Fig. 5C). For comparison, new experimental data assessing insulin-stimulated ET-1 secretion from primary vascular endothelial cells are also shown (Fig. 5D). Treatment of endothelial cells with 10 nM insulin stimulates ∼60% of maximal ET-1 levels. Model simulation with 10 nM insulin stimulation predicts ET-1 levels at ∼59% of the maximal insulin response.

Model simulations of vascular “effect” determining net vascular tone.

In our present model, the integrated output of two major insulin signaling branches (PI3K-dependent and MAPK-dependent) is represented as an effect on vascular tone or blood vessel diameter due to vasodilator actions of NO and vasoconstrictor actions of ET-1, respectively. In our model, we attribute 60% of the vascular insulin signaling effect to NO and 40% to ET-1 to achieve a net vasodilator effect under healthy conditions, consistent with experimental observations of insulin stimulation in the vasculature in the presence and absence of ET-1 receptor antagonists in animal models and humans (8, 33, 62, 63).

In our model simulation, a step input of insulin for 15 min decreased vascular tone from basal levels (this vasorelaxation results in increased vessel diameter) with a nadir of 47% of basal levels at ∼5 min. Upon insulin removal, vascular tone returns toward baseline (half-time ∼15 min) with a slight overshoot (∼2%) that settles back to baseline by ∼90 min (Fig. 6A). Consistent with model predictions, previous studies with isolated skeletal muscle vessels demonstrate that arteriolar diameter increases rapidly (time to half-maximal effect ∼1 min) and reaches a maximum at ∼5–10 min after acute exposure to insulin (12). Experimental data for maximal vasodilation of skeletal muscle arterioles in response to increasing insulin concentrations are similar to model predictions (Fig. 6B).

Fig. 6.

Comparisons between model simulations of insulin-induced changes in vascular tone and experimental data in blood vessels. A: model simulations of vascular tone as a function of time after a step input of insulin (100 nM, 15 min). B: insulin concentration-response generated by model simulations of peak change in vascular tone. Experimental data representing changes in vessel diameter in response to insulin were taken from published studies (12).

Effects of increased levels of PTEN, PTP1B, and SHIP2 phosphatases on insulin-stimulated NO production, ET-1 secretion, and net vascular tone.

PTP1B is a tyrosine phosphatase implicated in the pathogenesis of insulin resistance that dephosphorylates the insulin receptor and IRS-1 to negatively modulate downstream insulin signaling (9, 11, 26, 92). PTEN and SHIP2 are lipid phosphatases that dephosphorylate the lipid product of PI3K and impair signaling downstream from PI3K (57, 83). To evaluate the ability of our model to generate appropriate simulations in response to modulation of these phosphatases, we examined effects of increasing PTP1B, PTEN, and SHIP2 activity on insulin-stimulated NO/ET-1 production and vascular tone in our model simulations (Fig. 7). Control simulations of the time courses for NO, ET-1, and vascular tone in response to 15-min insulin step input ranging from 10⁻¹² M to 10⁻⁵ M were compared with simulations in which the values for PTP1B, PTEN, and SHIP2 were increased to [PTP] = 1.5, [PTEN] = 2, or [SHIP2] = 2. Larger values for PTP1B, PTEN, and SHIP2 resulted in decreased maximal insulin responsiveness for NO production. Larger values for PTP, PTEN, but not SHIP2, resulted in an increased EC₅₀. These results are shown quantitatively in Table 1. Similarly, with respect to ET-1 secretion, larger values for PTP1B, PTEN, but not SHIP2, increased maximal insulin response, suggesting a reciprocal increase in MAPK signaling when PI3K signaling is decreased (Table 1). In addition, we observed the expected increase in EC₅₀ for insulin-stimulated ET-1 secretion with larger values of PTP, PTEN, and SHIP2 (Table 1). Thus, these simulations are consistent with the expected promotion of insulin resistance that is due to altering activity of a variety of phosphatases that decrease PI3K-dependent Akt activity and subsequently increase signaling from Ras to Raf (Fig. 3). With respect to net vascular tone determined by the net effect of NO-mediated vasodilation and ET-1-mediated vasoconstriction, larger values for PTEN, SHIP2, and PTP1B resulted in increases in net vascular tone that correspond to decreased vessel diameter (Fig. 8A and Table 1). With respect to EC₅₀ for insulin-stimulated increase in vessel diameter, a larger value for PTP1B caused a decrease consistent with insulin resistance. However, larger values for PTEN and SHIP2 resulted in decreased EC₅₀ for insulin-stimulated increase in vessel diameter, which may be due to interactions between PI3K/Akt and Ras/Raf (Fig. 3).

Fig. 7.

Model simulations of insulin-concentration response curves under conditions of different phosphatase activities for phosphatase and tensin homolog (PTEN), protein tyrosine phosphatase 1B (PTP1B), and Src homology 2 (SH2)-domain-containing inositol phosphatase 2 (SHIP2A) with the output of peak NO (A), peak ET-1 (B), and peak vascular tone (C).

Table 1.

Predictions of complete model for V_max and EC₅₀ for NO, ET-1, and vascular effect in response to insulin stimulation using different magnitudes of values for PTEN, PTP1B, and SHIP2

NO	Vmax	EC50, nM
Normal	321 ± 7	0.43
PTEN (2×)	230 ± 5	0.45
PTP (1.5×)	280 ± 4	0.53
SHIP (2×)	315 ± 7	0.39
ET-1
Normal	1.90 ± 0.03	6.73
PTEN (2×)	2.50 ± 0.03	7.46
PTP (1.5×)	2.21 ± 0.03	10
SHIP (2×)	1.90 ± 0.03	6.8
Vascular effect
Normal	47 ± 1.0	0.37
PTEN (2×)	31 ± 0.6	0.33
PTP (1.5×)	41 ± 0.5	0.48
SHIP (2×)	45 ± 1.0	0.34

Values are expressed as means ± SE.

Fig. 8.

Effects of modulating phosphatase and tensin homolog (PTEN) activity to alter insulin-stimulated vascular tone, and production of nitric oxide (NO) and endothelin (ET-1). A: model simulations of insulin-stimulated changes in vascular tone after a step input of insulin (100 nM, 15 min) with baseline PTEN levels (solid line), a twofold increase and a twofold decrease in PTEN levels (dashed line; [PTEN] = 2 and 0.5, respectively). B and C: bovine aortic endothelial cells (BAEC) in primary culture were transiently cotransfected with an expression vector for red fluorescent protein (RFP) and pCIS2 (empty vector), PTEN-WT, or PTEN-C124S, as described in methods. Cells were then serum-starved overnight, loaded with 4,5-diaminofluorescein diacetate (DAF2-DA), and then stimulated with lysophosphatidic acid (LPA, 5 μM) or insulin (100 nM, 5 min). Production of NO in the cotransfected cells (determined by expression of RFP) was detected using an epifluorescent microscope and quantified using a digital camera, as described in methods. Data are expressed as means ± SE of 3 or 4 independent experiments and are expressed as the percentage of peak NO production in the control group (cells cotransfected with RFP/pCIS2 empty vector and treated with insulin). Overexpression of PTEN-WT attenuated the insulin response while expression of PTEN-C124S augmented this (P < 0.05). Bars labeled with different letters (a, b, c) are significantly different from each other, P < 0.05 (by ANOVA and Bonferroni’s post hoc test).

To compare predictions of our model system with new experimental data in a physiologically relevant cell type, we assessed insulin-stimulated NO production in BAEC in primary culture in the absence or presence of wild-type PTEN overexpression or expression of a dominant inhibitory mutant of PTEN (Fig. 8B). Cells cotransfected with RFP, eNOS, and either empty control vector (pCIS2) or PTEN constructs [wild-type PTEN (PTEN-WT) or dominant inhibitory PTEN mutant (C124S)] were stimulated with insulin (100 nM, 20 min). Insulin-induced peak NO production was reduced by ∼20% in cells overexpressing PTEN-WT. However, in BAEC overexpressing PTEN-C124S, insulin-induced NO production was increased by ∼40% over that of control cells (Fig. 8B). These results are qualitatively consistent with model simulations. (Fig. 8 and Table 1).

Insulin resistance and endothelial dysfunction present in diabetes, obesity, and their cardiovascular complications are characterized by pathway-selective impairment in PI3K-dependent insulin signaling combined with intact or augmented MAPK-dependent insulin signaling (37, 55). In cell culture experiments, treatment of primary endothelial cells with the specific PI3K inhibitor wortmannin is a useful approach for mimicking the PI3K-dependent impairment in insulin signaling (51). This generates endothelial cell and vascular dysfunction with respect to NO and ET-1 representative of that observed in diabetes and its cardiovascular complications (51, 62, 63, 94). To simulate the effect of pathway-selective inhibition of PI3K signaling in our model, we set the model parameter (k₁₁) representing the rate of insulin-activated Akt phosphorylation to 1/100th of the normal value. Under these conditions, model simulations generated a substantial increase in peak insulin-stimulated ET-1 level (an approximately threefold increase) with a concomitant reciprocal inhibition of NO production (∼100-fold decrease) (Fig. 9, A and B). To help evaluate the predictive power of the model, we designed new experiments to test the effects of wortmannin on insulin-stimulated production of ET-1 in primary endothelial cells in the absence or presence of insulin without or with wortmannin pretreatment. Experimental results demonstrated a substantial increase in peak insulin-stimulated ET-1 level (∼30% increase) (Fig. 9C).

Fig. 9.

Model simulations of the effect of wortmannin (PI3K inhibitor) treatment on insulin actions. Akt activation rate was restricted to 1/100th of its normal model value (k₁₁) to mimic the behavior of wortmannin. A: effect on peak NO production of insulin+wortmannin compared with insulin alone. B: effect on peak ET-1 production of insulin+wortmannin compared with insulin alone. C: experimental results showing ET-1 concentration in conditioned media after treating endothelial cells with insulin in the absence or presence of wortmannin (n = 4), as described in methods.

Effects of glucotoxicity, lipotoxicity, and inflammatory cytokines on insulin-stimulated NO, ET-1, and vascular tone.

Glucotoxicity, lipotoxicity, and inflammation are all putative mechanisms underlying both metabolic insulin resistance and endothelial dysfunction related to diabetes, obesity, and their cardiovascular complications (6, 22, 79). Federici et al. (20) previously demonstrated that culturing endothelial cells in high glucose (20 mM) for 72 h impairs insulin activation of PI3K/Akt/eNOS pathway. Under these conditions, stimulation with insulin (50 nM, 10 min) results in decreased Akt phosphorylation, eNOS phosphorylation, and eNOS activity (NO formation) by 30%, 37%, and 27%, respectively, when compared with control conditions. Simultaneously, they observed a reciprocal increase in MAPK phosphorylation of 49% (Fig. 10A). As a further validation of our new model, we mimicked these experimental glucotoxic conditions by constraining maximal insulin-stimulated Akt phosphorylation to 30% of normal in our model and then examined the resulting model predictions for eNOS and MAPK phosphorylation levels, as well as NO production as a proxy for eNOS activity. Results from these simulations and the actual experimental results were qualitatively similar (Fig. 10A).

Fig. 10.

Effects of glucotoxicity, lipotoxicity, and proinflammatory cytokines on insulin-stimulated phosphorylated endothelial nitric oxide synthase (p-eNOS), p-MAPK, nitric oxide (NO), and endothelin-1 (ET-1) production, and vascular tone: comparisons between experimental data and model predictions. A: high glucose-induced (20 mM, 72 h) impairment of insulin-stimulated p-Akt levels determined from published experiments (20) was used to constrain p-Akt levels in our mathematical model. Then, peak levels of p-eNOS, p-MAPK, and NO production in response to insulin (50 nM, 15 min) were generated from model simulations. These model predictions were plotted next to the published experimental results for insulin-stimulated p-eNOS, p-MAPK, and eNOS activity (NO formation) in endothelial cells exposed to high glucose (20 mM, 72 h) (20). Data are expressed as percent change relative to basal conditions. B: palmitic acid-induced impairment in insulin-stimulated Akt activity derived from published experimental results (90) was used to constrain p-Akt levels in our mathematical model. Then, model-generated levels of insulin-stimulated p-eNOS were compared with corresponding insulin-stimulated p-eNOS levels in endothelial cells exposed to varying concentrations of palmitic acid (0–0.8 mM) from the published literature (3, 90). The solid line represents the linear-least squares regression for the data points shown. C: model-predictions of insulin-stimulated NO and ET-1 levels in cells exposed to varying concentrations of palmitic acid. The solid and dashed lines represent the linear-least squares regression for the data points for NO and ET-1, respectively. D: TNF-α-induced impairment in insulin-stimulated Akt activity in vascular endothelium derived from published experimental results (19) was used to constrain p-Akt levels in our mathematical model. Model-generated changes in insulin-stimulated vascular tone (□) are plotted on the same graph as experimentally determined changes in insulin-stimulated vascular diameter in arteries treated with TNF-α (■) (19). Data are expressed as a percentage of peak response of vascular tone.

Elevated levels of free fatty acids (FFAs; comprising 30–40% palmitate) contribute to endothelial dysfunction and insulin resistance (79). Wang et. al. (90) examined effects of treating endothelial cells in primary culture with the saturated fatty acid to alter insulin-stimulated activation of eNOS. Treatment of human aortic endothelial cells with palmitate (0.1–0.8 mM) reduced Akt phosphorylation in response to insulin stimulation (100 nM) in a concentration-dependent manner (Fig. 10B). To evaluate the predictive ability of our model with respect to simulating lipotoxicity, we constrained the Akt output in our model in response to insulin, according to the experimental results reported for each palmitate concentration tested (90). Results from model simulations for phospho-eNOS were plotted against experimental results reported by Wang et. al. (90) (Fig. 10B). Model simulations are in good agreement with experimental results. Under these same conditions, we also used our model to simulate peak NO production and ET-1 secretion in response to insulin as a function of increasing palmitate concentrations (Fig. 10C). As expected, we observed a palmitate concentration-dependent increase in insulin-stimulated peak ET-1 secretion with a reciprocal decrease in peak NO production consistent with lipotoxic effects on vascular function in response to insulin. Thus, by constraining Akt to levels seen with experimental lipotoxicity, our model predicts diminished net vasodilator actions of insulin in a concentration-dependent manner, as observed under experimental conditions.

Among circulating proinflammatory cytokines, tumor necrosis factor-α (TNF-α) is implicated in the pathophysiology of both endothelial dysfunction and metabolic insulin resistance (35, 86). TNF-α impairs vasodilator actions of insulin in skeletal muscle vasculature, in part, through inhibition of PI3K/Akt-mediated activation of eNOS (19). In isolated arterioles from rat cremaster muscle, insulin induced a 3.4-fold increase in Akt phosphorylation that was nearly abolished by pretreatment with TNF-α (19). We simulated these conditions in our model by constraining Akt output to the extent determined experimentally by TNF-α treatment (19). Model predictions of TNF-α-mediated impairment in peak vasodilation in response to increasing concentrations of insulin were in good agreement with experimental results (Fig. 10D). Taken together, results from our model simulations are in good qualitative agreement with published experimental results under pathological conditions of glucotoxicity, lipotoxicity, and proinflammatory states, which are the principal mediators of endothelial dysfunction and insulin resistance in disorders of metabolic and cardiovascular homeostasis.

DISCUSSION

In the past several decades, the explosion of molecular biological techniques has helped to elucidate a complex insulin signal transduction network initiated by cell surface insulin receptors (member of the receptor tyrosine kinase family). For particular cell types or organs, insulin receptors mediate specific biological actions that may be directly related to metabolism or that may synergize with metabolism. Mathematical modeling of insulin signaling pathways used in conjunction with experimental studies is a productive approach for increasing understanding of insulin signaling and actions in health and disease (66, 67, 78, 89).

Model development.

The PI3K-dependent insulin signaling pathway regulating GLUT4 translocation in adipose cells is essentially identical to the insulin signaling pathway regulating activation of eNOS and production of NO in vascular endothelium (55). Therefore, we used our model of metabolic insulin signaling (78) en bloc to represent the PI3K-dependent branch of insulin signaling regulating eNOS activity and NO production (Fig. 1). The small novel piece of the PI3K-dependent subsystem in the current model is a representation of Akt-stimulated activation of eNOS and subsequent production of NO that uses a Michaelis-Menten approach supportable by published literature (Fig. 1B) (5, 48).

One major advance of the present mathematical model over our previous metabolic insulin signaling model (78) is the incorporation of a MAPK-dependent insulin signaling branch (Fig. 2A). This subsystem is then linked to a simple representation of synthesis and secretion of the potent vasoconstrictor ET-1 (Fig. 2B). Unnecessary or unsupportable details of the MAPK-dependent signaling branch were omitted to help limit the degrees of freedom and to provide overall balance to the complete model. Although, a slightly more complex model of insulin signaling through PI3K-dependent pathways has been published (4), that work does not incorporate a major MAPK-dependent insulin signaling branch and is not sufficient to model the balance between insulin-stimulated NO production and ET-1 secretion. There is another mathematical model of insulin signaling related to eNOS that does include MAPK signaling pathways, but the sole output of the model is NO (without ET-1) (74). Thus, our current model represents a major advance over previous models in that it incorporates two major relatively independent branches of the insulin signal transduction network (PI3K- and MAPK-dependent) that regulate opposing vascular actions of insulin to result in a final model output of “net vascular tone”.

Another essential novel addition to our current model is explicit representation of cross talk among major PI3K- and MAPK-dependent branches of insulin signaling. (Fig. 3). This provides one mechanism to alter the balance between insulin signaling through PI3K- and MAPK-dependent subsystems. This contributes to the ability of the overall model to accurately mimic pathway-selective insulin resistance (i.e., impaired PI3K-dependent insulin signaling combined with normal or enhanced MAPK-dependent signaling (36, 37, 55). Pathway-selective insulin resistance with resulting compensatory hyperinsulinemia to maintain normoglycemia is an important whole body pathophysiological mechanism that helps create reciprocal relationships between metabolic insulin resistance and endothelial dysfunction mediated by vascular insulin resistance (37). Reciprocal relationships between endothelial dysfunction and metabolic insulin resistance underlie the ability of insulin sensitizers to improve endothelial dysfunction. Conversely, therapies that improve endothelial dysfunction (e.g., angiotensin-converting-enzyme inhibitors) simultaneously reduce insulin resistance. In future work, our model may be able to quantitatively predict improvement in endothelial dysfunction due to therapeutic improvement in vascular insulin resistance.

Choice of initial conditions and model parameters.

Choice of initial conditions and model parameters was greatly limited by constructing the complete model out of many smaller subsystems. For novel parts of our present model that have not previously been validated, parameter choices and initial conditions were based on both our own and published experimental data. Taken together, these approaches greatly reduce the degrees of freedom present in the final model. No fitting of model parameters or initial conditions was performed to generate any of the overall model simulations. Indeed, all these many factors were selected a priori before model simulations were conducted. In cases where we explored effects of altering levels of various phosphatase model parameters or changed activity of Akt to mimic effects of pathophysiological states on model output, only these specific model parameters were altered to make model predictions. The ability of our model to make accurate predictions of novel or published experiments a priori without fitting model parameters or initial conditions is a major strength of the present work that supports the robustness of our model structure.

Complete model simulations focused on output of the PI3K-dependent subsystem.

Even with cross talk between PI3K- and MAPK-dependent subsystems, simulations with the complete model yielded temporal kinetic results for upstream state variables in the PI3K-dependent subsystem that were virtually identical to results from our published model of metabolic insulin signaling (78). This confirms proper implementation of our PI3K-dependent subsystem. The predicted biphasic temporal responses of Akt (Fig. 4A) have been observed experimentally in primary endothelial cells (44). Since Akt directly phosphorylates eNOS to catalyze production of NO from the substrate l-arginine (17, 24), it is not surprising, that p-eNOS (activated form) and NO, the product of eNOS, also display biphasic temporal responses. This is a reassuring validation of the novel terminal portion of the PI3K-dependent subsystem. This is important as eNOS and NO, PI3K-dependent subsystem outputs, contribute to specificity in our current insulin signaling model of vascular endothelium (vs. GLUT4 translocation in adipose cells). Simulation results of insulin concentration response curves for both p-Akt and its downstream target p-eNOS (Fig. 4, B and C) generated a best fit that very closely approximated actual experimental results (44). This provides substantial validation of the PI3K-dependent subsystem regulating insulin-stimulated activation of eNOS and subsequent production of the vasodilator NO. Thus, the modular structure of the PI3K-dependent subsystem is extremely robust with respect to vasodilator output.

Complete model simulations focused on output of the MAPK-dependent subsystem.

Simulations of key intermediate state variables in the MAPK-dependent insulin signaling branch (Fig. 5, A and B) showed an almost immediate response to the insulin-step input. This is in good agreement with published data for Shc and Ras (42, 76) and seem reasonable in light of previous models using similar state variables in MAPK-dependent signaling models of other receptor tyrosine kinase (27, 30, 34, 41, 65, 77). Simulations of the end effector ET-1 in response to insulin (Fig. 5C) generally match what is observed in vitro in primary endothelial cells (10, 23, 72) and also in new experiments performed for the current work (Fig. 5D). Data in Fig. 5D show good agreement with the overall scale and minimum and maximum responses. Note that we measured ET-1 concentrations in the culture media of HUVECs treated with different doses of insulin, whereas the model predicts intracellular ET-1. Relatively new evidence suggests that PI3K pathways can inhibit ET-1 secretion through the phosphorylation of FOXO1 by Akt (10, 72). FOXO1 is a transcription factor that enhances activity of the ET-1 promoter. When phosphorylated, FOXO-1 is excluded from the nucleus and the activity of the ET-1 promoter is decreased. Inclusion of this additional mechanism of in a future iteration of our model may achieve better simulation predictions for insulin-concentrations response curves for ET-1 levels.

Complete model simulations focused on final output of “net vascular tone”.

Simulation of temporal kinetics and insulin concentrations response curves of “net vascular tone” in response to insulin (Fig. 6) agrees with data from healthy skeletal muscle arterioles (12). The ability of our model to accurately simulate previously untested experimental results without fitting initial conditions or parameter choices (especially for major subsystem outputs and final model output) is indicative of the robustness of our complete model.

Complete model simulations in response to alterations of specific phosphatases.

Pathway-selective impairment of PI3K-dependent insulin signaling is implicated in the pathophysiology of metabolic and vascular insulin resistance (55). Therefore, we focused on phosphatases in the PI3K-dependent branch. PTP1B dephosphorylates both the insulin receptor and IRS-1 and has been implicated in the pathophysiology of diabetes (1, 9, 25, 69). SHIP2 and PTEN are lipid phosphatases implicated in the pathophysiology of insulin resistance that dephosphorylate the active lipid product of PI3K. Model simulations of insulin concentration response curves for peak NO production, peak ET-1 secretion and peak vascular tone are shown for normal conditions and also conditions where the activity of PTEN, SHIP2, or PTP1B is increased (Fig. 7). The maximal insulin response with respect to NO production was greatly reduced by increasing PTEN activity. There was a substantial but smaller effect of increasing PTP1B activity, while the effect of SHIP2 resulted in a small reduction of maximal NO that was nearly undetectable (Fig. 7A). This is consistent with the expected effects of these phosphatases to decrease NO production through the impaired PI3K-dependent pathway. Furthermore, our model predicts that, of the lipid phosphatases regulating PI3K products, PTEN has a larger effect than SHIP2 to promote development of PI3K-specific vascular insulin resistance. With respect to the insulin concentration response curves of peak ET-1, we observed an inverse effect (Fig. 7B). Taken together, these results are consistent with experimentally observed effects of pathway-selective impairment of PI3K-dependent with enhanced MAPK-dependent insulin signaling (10, 23, 52). Thus, our model is able to appropriately predict important pathophysiological conditions relative to the change in balance between vasodilator actions of NO and vasoconstrictor actions of ET-1. Indeed, our model predicts the appropriate decreased percent change in maximal “net vascular tone” given alterations in various phosphatases. Table 1 quantifies the predictions of V_max and EC₅₀ for NO, ET-1, and “net vascular effect” (Fig. 7C). Moreover, our simulations are consistent with what is known about the pathophysiology of abnormalities in these phosphatases relative to metabolic insulin resistance and Type 2 diabetes (32, 88).

We observed the largest changes to decrease NO and increase ET-1 with increasing PTEN levels. Therefore, we next simulated the effects on vascular tone of both increased and decreased PTEN levels relative to baseline values in response to a step input of insulin (Fig. 8A). As expected, relative to the baseline PTEN levels, decreasing PTEN levels resulted in net peak vasodilation that was greater than observed with baseline PTEN levels. Conversely, increasing PTEN levels resulted in net peak vasoconstriction relative to baseline levels. We then performed experiments in primary vascular endothelial cells to confirm these model predictions using overexpression of wild-type PTEN or transfections of a dominant negative mutant of PTEN (Fig. 8B). These new experimental results are qualitatively consistent with the predictions made by our model of simulating changes in PTEN. This further validates our model and demonstrates its utility in predicting unknown experimental results.

Pathway-selective insulin resistance.

Both metabolic and vascular insulin resistance are characterized by pathway-selective impairment in PI3K-dependent signaling with augmented MAPK-dependent signaling (51, 55). In vascular endothelial cells, this results in decreased NO production, increased ET-1 secretion, and a net vasoconstrictor response in the vasculature (51, 62, 63, 94). We published experiments in which we mimicked pathway-selective insulin resistance with compensatory hyperinsulinemia by treating endothelial cells with wortmannin (relatively specific PI3K inhibitor) and high insulin levels (51). To emulate the conditions of wortmannin treatment in our model, we constrained the rate (parameter k₁₁) of Akt activation to 1/100 of its normal value. We chose to alter Akt rather than PI3K because this is what experimental articles report. In model simulations, insulin-stimulated production of NO was nearly ablated (Fig. 9A). Conversely, insulin-stimulated ET-1 levels were elevated threefold over normal (Fig. 9B). These model predictions are completely consistent with published experiments in endothelial cells with respect to both NO production and ET-1 promoter activity (10, 23, 36, 37, 51). To further confirm model predictions, we conducted new experiments in endothelial cells treated with insulin in the absence or presence of wortmannin. ET-1 levels in conditioned media from these new experiments corresponded well to model predictions (Fig. 9C). Thus, our model is able to appropriately predict the consequences of PI3K-selective insulin resistance in endothelial cells with respect to changes in NO and ET-1.

Simulations of insulin resistance caused by glucotoxicity, lipotoxicity, and inflammation.

Under a variety of pathophysiological conditions (high glucose, high lipids, increased inflammation), pathway-selective impairment in PI3K-dependent insulin signaling is experimentally observed with metabolic insulin resistance in skeletal muscle and adipose tissue with respect to glucose uptake. Importantly for the current model, this pathway-selective insulin resistance is also observed experimentally in vascular endothelium leading to decreased production of insulin-stimulated NO and increased insulin-stimulated secretion of ET-1 (10, 23, 36, 37, 51). To test whether our model is able to predict pathophysiological effects of high glucose, we compared model simulations with published experiments where endothelial cells were exposed to high glucose to represent glucotoxicity (20), or palmitic acid to represent lipotoxicity (90). We also used published experiments where isolated arterioles were exposed to TNF-α to represent inflammation (19). In each of these experimental conditions, the impairment of Akt was reported as a proxy for PI3K impairment, and we used these values to constrain maximal Akt responses in our model simulations as appropriate. We then compared the difference in mean experimental outcomes relative to baseline for p-eNOS, p-MAPK, and eNOS activity with simulation outputs. Model simulations accurately reproduced both the direction and rough magnitude of changes in p-eNOS, p-MAPK, and NO production under high glucose conditions (Fig. 10A). With respect to a range of concentrations of palmitic acid (a free fatty acid), p-eNOS levels as a percent of the normal basal response was compared with the actual experimental data (Fig. 10B). Simulations were in good agreement with experimental data across a range of palmitic acid concentrations. We also plotted simulations of NO production and ET-1 secretion (relative to baseline) as a function of increasing palmitic acid concentrations (Fig. 10C). In these simulations, as the concentration of palmitic acid increased, NO production decreased while ET-1 secretion increased. This represents a model prediction that seems reasonable. That is, increasing lipotoxicity results in increasing pathway-selective PI3K impairment with augmented MAPK activity. The end effectors of PI3K and MAPK (NO and ET-1) decrease and increase, respectively, leading to an increased net vasoconstrictive state with increasing concentrations of insulin. With respect to proinflammatory states, we compared model simulations with experimental data from arterioles pretreated with TNF-α and then stimulated with increasing concentrations of insulin. Our model simulations were able to accurately reproduce the experimental results (Fig. 10D). Thus, we evaluated a range of pathogenic conditions that contribute directly to the pathophysiology of diabetes and endothelial dysfunction due, in part, to pathway-selective insulin resistance. Our model of vascular insulin signaling was able to accurately replicate published experimental results and make new experimental predictions that seem reasonable. This is predicated on adjusting impairment in Akt to experimentally observed levels. This suggests that Akt is a control point in the model that enables accurate simulations of model outputs in both PI3K-dependent and MAPK-dependent branches to arrive at an accurate overall model output. Moreover, it is likely that the cross talk between Akt and Raf contributes to the ability of MAPK pathways to become enhanced when PI3K pathways are impaired.

Pathophysiological implications of selective insulin resistance.

Endothelial dysfunction and insulin resistance are frequently present in obesity, metabolic syndrome, hypertension, and diabetes (37, 54, 55, 56). Previously, we have reported that the pooled univariate correlation coefficient between insulin resistance and endothelial function from cross-sectional studies (N = 3,190) was −0.14 (P = <0.001, 95% confidence interval: −0.09 – −0.20) (56). Insulin resistance and the metabolic factors that are associated with it have been known to induce endothelial dysfunction (37). However, endothelial dysfunction characterized by impairment of endothelial NO production may also contribute to insulin resistance (31). These studies suggest that the relationship between endothelial dysfunction is complex and bidirectional in nature. Selective insulin resistance in both the macrovasculature and microvasculature leads to vascular dysfunction. Indeed, microvascular dysfunction in skeletal muscle, splanchnic tissue, adipose tissue, heart, retina, and brain play a causal role in many features often observed in diabetes, including metabolic abnormalities, cardiac dysfunction, retinopathy, stroke, and cognitive dysfunction (18, 45, 55, 87).

Reduced NO and accentuated ET-1 action/activity are observed in insulin-resistant states such as obesity (47), hypertension (7), and diabetes (47). Indeed, blockade of ET-1 receptors improves insulin sensitivity, supporting the notion that improvement in endothelial function improves the metabolic actions of insulin (2, 55). Insulin activation of eNOS is impaired, but ET-1 expression is accentuated, in skeletal muscle arterioles in patients with diabetes compared with lean healthy controls (46). In fact, vascular ET-1 expression was inversely related, while phosphorylated eNOS levels were positively correlated, with insulin-mediated glucose disposal, a measure of insulin sensitivity (46, 73). Persistent hyperinsulinemia and stimulation of MAPK/ET-1 combined with impaired PI3K-NO pathway lead to vasoconstriction, as predicted by our model (60).

Selective insulin resistance in the endothelium affects not only vascular tone, but other functions of the endothelium as well. Cell-cell interactions between circulating inflammatory cells and vascular endothelium are regulated by endothelial expression of cellular adhesion molecules, such as intercellular adhesion molecule-1, vascular cell adhesion molecule (VCAM-1), and E-selectin. Insulin increases the endothelial expression of VCAM-1 and E-selectin through the MAPK-dependent, but not the PI3K-dependent, pathway (51). Concurrent blockade of PI3K-dependent pathways enhances the stimulatory effects of insulin on these adhesion molecules (51). Thus, in the setting of insulin resistance, chronic hyperinsulinemia via the unopposed activation of MAPK pathway leads to increased VCAM-1/E-selectin, which may initiate a proinflammatory cascade and premature atherosclerosis.

Summary and Conclusions

We developed a model of vascular insulin signaling that is a significant advance over our previous metabolic insulin signaling model. We used our published metabolic insulin signaling model (78) as the framework for the PI3K-dependent subsystem regulating output of NO. A major addition to the present model is incorporation and integration of a MAPK-dependent subsystem. The output of the MAPK-dependent subsystem is secretion of the vasoconstrictor ET-1. Thus, our new model can explore the behavior and consequences of interactions between two major branches of the insulin signaling network that regulate opposing vasoactive actions that are integrated into a “net vascular tone”. When compared with experimental data, our model successfully simulated pathway-selective insulin resistance in the PI3K-dependent subsystem with augmented signaling through the MAPK-dependent subsystem leading to a shift in balance of “net vascular tone”. This pathway selective insulin resistance is a key pathophysiological feature in metabolic and vascular insulin resistance present in both diabetes and endothelial dysfunction. It would not be possible to simulate these results using our previous PI3K-dependent insulin signaling model alone. In addition, current model simulations accurately predicted experimental results for a variety of pathogenic conditions, including glucotoxicity, lipotoxicity, and inflammation. Thus, our model has the ability to predict previous and new experimental outcomes related to pathophysiology in vascular insulin signaling. We conclude that our present model is a robust representation of a vascular insulin signaling network that may be a useful tool for designing informative experiments. Our model may help explore and refine important hypotheses regarding the role of insulin signaling in reciprocal relationships between endothelial dysfunction and insulin resistance. Finally, our model may help increase understanding of endothelial dysfunction and its role in metabolic diseases characterized by insulin resistance, such as diabetes and obesity.

GRANTS

For R.M. and A.S., this work was supported by the Intramural Research Program, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health; For M.J.Q., this work was supported, in part, by a grant from the American Diabetes Association (1-13-BS-150).

DISCLAIMERS

This content is solely the responsibility of the authors and does not necessarily represent the official view of the National Institutes of Health.

DISCLOSURES

The authors declare that they have no conflicts of interest with the contents of this article.

AUTHOR CONTRIBUTIONS

R.M. and M.J.Q. conceived and designed research; R.M., H.C., and M.M. performed experiments; R.M., H.C., M.M., A.S., and M.J.Q. analyzed data; R.M., H.C., A.S., and M.J.Q. interpreted results of experiments; R.M. prepared figures; R.M., H.C., A.S., and M.J.Q. drafted manuscript; R.M., H.C., M.M., A.S., and M.J.Q. edited and revised manuscript; R.M., H.C., M.M., A.S., and M.J.Q. approved final version of manuscript.