In vivo and in silico dynamics of the development of Metabolic Syndrome

The Metabolic Syndrome (MetS) is a complex, multifactorial disorder that develops slowly over time presenting itself with large differences among MetS patients. We applied a systems biology approach to describe and predict the onset and progressive development of MetS, in a study that combined in vivo and in silico models. A new data-driven, physiological model (MINGLeD: Model INtegrating Glucose and Lipid Dynamics) was developed, describing glucose, lipid and cholesterol metabolism. Since classic kinetic models cannot describe slowly progressing disorders, a simulation method (ADAPT) was used to describe longitudinal dynamics and to predict metabolic concentrations and fluxes. This approach yielded a novel model that can describe long-term MetS development and progression. This model was integrated with longitudinal in vivo data that was obtained from male APOE*3-Leiden.CETP mice fed a high-fat, high-cholesterol diet for three months and that developed MetS as reflected by classical symptoms including obesity and glucose intolerance. Two distinct subgroups were identified: those who developed dyslipidemia, and those who did not. The combination of MINGLeD with ADAPT could correctly predict both phenotypes, without making any prior assumptions about changes in kinetic rates or metabolic regulation. Modeling and flux trajectory analysis revealed that differences in liver fluxes and dietary cholesterol absorption could explain this occurrence of the two different phenotypes. In individual mice with dyslipidemia dietary cholesterol absorption and hepatic turnover of metabolites, including lipid fluxes, were higher compared to those without dyslipidemia. Predicted differences were also observed in gene expression data, and consistent with the emergence of insulin resistance and hepatic steatosis, two well-known MetS co-morbidities. Whereas MINGLeD specifically models the metabolic derangements underlying MetS, the simulation method ADAPT is generic and can be applied to other diseases where dynamic modeling and longitudinal data are available.

muscle. MINGLeD includes pathways for carbohydrate, lipid and cholesterol metabolism, and computes pool sizes (concentrations) of various metabolites present in these systems. Table A lists which metabolites are included in MINGLeD in each of the metabolically active tissues. Acetyl coenzyme A (ACoA) is the central intermediate metabolite interconnecting the carbohydrate and lipid metabolic pathways. The metabolic fluxes are based on first order mass action kinetics and listed in Table B. The type of equations is similar to those used in previous ADAPT studies [1][2][3][4]. These lumped flux and reaction equations were derived using previous (biological) knowledge about the processes were are modelling. Since the underlying regulation is often unknown (especially for lipid species), we refrained from composing our flux equations using stoichiometry coefficients. Therefore the underlying regulation is not explicatively modelled, but will be inferred by the time-dependent parameters using ADAPT.
MINGLeD aims to describe the metabolic pathways of the day's average. Therefore specific (detailed) pathways for neither the postprandial phase, nor the fasting state have been included. The overall metabolic fluxes are able to describe the day's average in a consistent manner, and describe both healthy metabolic states and various stages of metabolic derailment of the system as is present in the Metabolic Syndrome. Note that insulin has not been included since insulin synthesis, secretion and action are on a much shorter time scale (minutes) than we use the model for (day's average).
Below we provide a detailed description of the modelled metabolites, how they are biologically regulated, the motivation to include these in the computational model, and how these interactions and pathways have been implemented in a system of Ordinary Differential Equations (ODEs) to describe mass balance during steady state.

Macronutrient intake
The dietary intake is specified in the form of carbohydrates (in MINGLeD referred to as glucose substrates), fat (in MINGLeD referred to as triglycerides substrates), cholesterol and proteins. All these macronutrients are included such that the energy intake of the complete diet is taken into account. The values corresponding the dietary intake for the different diets are listed Table A in S1 Note.
In the model glucose is taken up into the plasma from the dietary glucose directly. Fat and cholesterol are packed into chylomicrons (CM). These undergo triglyceride hydrolysis and are delivered to the hepatic and peripheral tissues; the chylomicron remnants that contain cholesterol are delivered to the liver. Note that chylomicrons are not explicitly included in MINGLeD since we do not aim to create a specific model describing the postprandial phase. Including the chylomicron particles would not improve the ability of the model to describe the available experimental data.
Although the metabolic pathways of amino acid metabolism have not been included in MINGLeD, we do take dietary protein intake into account since 20% of the energy of the diet is derived from protein sources. The amino acids (AA) are taken up by the liver and the periphery, and in each of these tissues they can undergo either glucogenic or ketogenic metabolism.

Glucose metabolism
Plasma glucose metabolism is controlled by glucose inflow from the diet, consecutive glucose uptake by liver and periphery and gluconeogenesis (GNG) in the liver. Insulin-independent, glucose-concentration independent glucose uptake by the brain and erythrocytes was not taken into account since these tissues were not explicitly specified, and no experimental data of these fluxes is available. Instead the brain and erythrocytes are part of the periphery since this compartment comprises of all other tissues apart from liver, intestine and plasma.
Glucose is trapped in the form of glucose-6-phosphate (G6P), and can be retrieved in the plasma through GNG in the liver. Glycogen pools were omitted since glycogenolysis and glycogenesis would both be connected to G6P, and on a day's average basis would not be separable (only the net effect is modelled).
The amino acids (AA) of which the dietary protein is composed of are converted to G6P via the glucogenic pathway and to acetyl coenzyme A (ACoA) via the ketogenic pathway in both liver and periphery. We impose that both pathways contribute equally to metabolism of the dietary protein uptake.
It is worth mentioning that all these pathways have been lumped and therefore no intermediates in e.g. the glycolysis pathway have been included. This yields a compact model of which the majority of the modelled variables can be estimated from the data with accuracy. If we would include detailed pathways with many intermediates, which cannot be coupled to experimental data, an identifiable model cannot be obtained, i.e. these intermediate metabolites and fluxes do not provide accurate predictions and may present unphysiological behavior.

Plasma lipoprotein metabolism
Lipoproteins are particles that have a hydrophobic core with a surrounding hydrophilic layer. This makes them ideal for the transport of triglycerides and cholesterol through the circulation. They are traditionally classified based on density, size, apolipoprotein composition and origin of synthesis. The density of a lipoprotein is determined by the amount of protein and lipid the particle contains. A higher density indicates that the lipoprotein has a higher ratio of protein to lipid content. HDL is the smallest and most dense particle.
Commonly, a distinction into five classes is made: chylomicrons (CM), very low density lipoproteins (VLDL), intermediate density lipoproteins (IDL), low density lipoproteins (LDL) and high density lipoproteins (HDL). In MINGLeD we distinguish between high density lipoproteins that carry cholesterol (HDL-C) and (very) low density lipoproteins that carry both cholesterol ((V)LDL-C) and triglycerides ((V)LDL-TG). All endogenously derived triglyceride-rich lipoproteins (TRL) have been packed under the name of (V)LDL, but inherently comprise of very low density (VLDL), intermediate density (IDL) and low density (LDL) lipoproteins. Note that HDL-TG has not been included since it is generally known that the majority of the molecules within HDL can be contributed to cholesterol particles and the TG content is negligible. Furthermore, the ratio between TG and cholesterol in HDL is not known (and not experimentally assessed).
HDL-C is formed from pre-HDL which originates from the periphery and is packed with cholesterol that has been esterified through lecithin-cholesterol acyltransferase (LCAT). Plasma HDL-C is subjected to plasma lipid transfer upon action of the cholesteryl ester transfer protein (CETP), and the remaining remnant particles are taken up by the liver via scavenger receptor class B1 (SR-B1). CETP collects triglycerides from TRL in exchange for cholesteryl esters from HDL and vice versa. However, since we did not include HDL-TG, MINGLeD only considers the cholesterol transfer from HDL-C to (V)LDL-C. Note that the rate equation for CETP was chosen to be dependent on plasma TG pools, since this is generally considered to be the driver behind CETP action. HDL-C also plays an important role in the reverse cholesterol transport (RCT) pathway: the transport of cholesterol from the peripheral tissues back to the liver, after which cholesterol can be secreted via the bile into the feces. The pathways in MINGLeD allow for this reverse cholesterol transport to take place.
(V)LDL is assembled in the liver from the hepatic triglyceride and cholesteryl ester pool, and then secreted into the plasma. Circulating (V)LDL is being lipolyzed and thereby delivers triglycerides and cholesterol to peripheral tissues. The remaining remnant particles are TG depleted and are taken up by LDL receptormediated uptake by the liver, where they are recycled into the cholesteryl ester pool.
(V)LDL can also undergo transport to the intestinal lumen through transintestinal cholesterol excretion (TICE). The TICE rate equation was chosen to be dependent on the VLDL-C pool. The plasma compartments contributing to TICE are not completely known, and may be both coming from ApoBcontaining lipoproteins as well as from erythrocytes, it was decided to make it dependent on VLDL-C only, since erythrocytes are not included in the model.

Hepatic lipid metabolism
The hepatic triglyceride pool is supplied by chylomicron remnant uptake, fatty acid uptake from the plasma, de novo lipogenesis (DNL; synthesis of triglycerides from ACoA substrates). Details about the reaction stoichiometry can be found in Table B. The triglyceride pool is drained by β-oxidation and for the assembly of (V)LDL particles.
Acetyl coenzyme A is a species that participates in many different metabolic processes. It plays a role in carbohydrate, lipid and cholesterol metabolism. It originates from breakdown of carbohydrate substrates (glycolysis) and from breakdown of fatty acids (β-oxidation). It is used as a substrate for de novo lipogenesis of triglycerides and for the biosynthesis of cholesterol (through the mevalonate pathway). It can also be oxidized via the citric acid cycle, yielding ATP.

Hepatic cholesterol metabolism
We distinguish between free cholesterol and cholesteryl ester as pools of cholesterol present in the liver (both species have been measured separately in the hepatic cholesterol pool). The hepatic free cholesterol pool is supplied by chylomicron remnant uptake, cholesterol biosynthesis and by cholesteryl ester hydrolase (CEH; hydrolysis of CE to FC) activity. The FC pool is drained by Acylcoenzyme A:cholesterol acyltransferase (ACAT; esterification of FC to CE) activity and biliary cholesterol excretion. Hepatic free cholesterol is also a precursor for bile acid synthesis.
The hepatic cholesteryl ester pool is supplied by (V)LDL-C and HDL-C remnant uptake and esterification of free cholesterol through ACAT. Cholesteryl esters are drained from the liver for (V)LDL-C assembly and by hydrolysis through CEH.

Hepatic bile acid metabolism
Bile acids are synthesized in the liver from endogenous cholesterol and can be secreted into the lumen of the intestine. Because of their amphipathic properties they are able to emulsify dietary lipids and they thereby facilitate lipid absorption. The majority of the intestinal bile acids will be recycled by the enterohepatic circulation. The bile acids can be taken up into the circulation, return to the liver and be resecreted.

Peripheral lipid metabolism
Many pathways in peripheral lipid metabolism resemble those of hepatic lipid metabolism. Triglycerides are included in the peripheral compartment by chylomicron remnant uptake, TG uptake resulting from lipolyzed (V)LDL and de novo lipogenesis. When triglycerides undergo lipolysisby activity of lipoprotein lipase (LPL)they are released in the plasma in the form of free fatty acids. Triglycerides are also removed from the peripheral TG pool by β-oxidation.
The peripheral ACoA pool is determined by many processes that yield ACoA particles: the ketogenic uptake of dietary proteins, from carbohydrate substrates originating after glycolysis and from lipid substrates originating after the β-oxidation of triglycerides. ACoA is a substrate for both lipid production (DNL) and for cholesterol production (biosynthesis). It can also be oxidized to generate energy.

Peripheral cholesterol metabolism
In the peripheral compartment, MINGLeD does not discriminate between free cholesterol and cholesteryl ester particles as no experimental data on the cholesterol pools in these tissues is available. Therefore we consider the peripheral cholesterol pool to be referred to as the total cholesterol content present in the periphery.
The cholesterol present in the HDL-C particles is retrieved from the peripheral cholesterol pool. The cholesterol pool is replenished by (V)LDL-C uptake and cholesterol biosynthesis from ACoA. ACoA is the common precursor that links TG and cholesterol synthesis and exists not only in the liver, but in every tissue (adipose tissue also expresses HMG-CoA reductase, which is the limiting step in cholesterol biosynthesis).             The factor 0.5 originates from our assumption that both the glucogenic and ketogenic pathway contribute equally to metabolism of the dietary protein uptake.
The flux equations are derived using stoichiometry rules: Triglycerides are esters derived from glycerol and three fatty acids per particle: The composition of triglycerides depends on the length and saturation of the fatty acid chains of which it is composed. The conversion of TG to Acetyl CoA is therefore derived based on energy content. We adjust the number of Acetyl CoA molecules derived from TG assuming that the energy density of body fat equals the energy density of the consumed food. This results in:

Implementation details
The mathematical model and optimization procedures were implemented in MATLAB (2013b, The Mathworks, Natick, Massachusetts). The ordinary differential equations were solved with compiled MEX files using numerical integrators from the SUNDIALS CVode package (2.6.0, Lawrence Livermore National Laboratory, Livermore, California) [5]. An absolute and relative tolerance of 10 -6 was used. The MATLAB nonlinear least-squares solver lsqnonlin (from the Optimization Toolbox), which uses an inferior reflective Newton method, was used to estimate model parameters [6]. The termination tolerances for the objective function and the parameter estimates were set to 10 -8 , the maximum number of iterations allowed was set to 10 3 and the maximum number of function evaluations allowed to 10 5 .