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Diabetes is a chronic disease characterized by a decreased production of insulin and by a reduced efficacy of the insulin produced. This impaired condition is differently caused by both type 1 and type 2 diabetes. In type 1 diabetes, insulin-producing cells in the pancreas (

If untreated, both forms of diabetes result over time in a persistent high concentration of glucose in blood which leads to serious tissue damage, especially to the nervous and circulatory system with potentially fatal consequences. In 2015, diabetes caused five million deaths worldwide. The number of diabetic individuals has risen over the years from 285 million in 2010 to 387 million in 2014 and 415 in 2015, while projections estimate 642 million in 2040 [

There is no doubt that this kind of “pandemic” requires maximum attention and that besides clinical and biological research, mathematics could contribute to shed light on this complex pathology. In our study, we employed computational modeling and simulation to describe the effects of high calorie diets on the pathology of type 2 diabetes limiting our observation to the process of weight gain ultimately leading to the onset of an inflammation state.

Symptoms of type 2 diabetes (T2D) are not very pronounced, and as a result, the disease is usually diagnosed several years after its onset, once complications have already become established. The International Diabetes Federation estimated that 193 million people with diabetes are undiagnosed and are therefore at risk of developing complications. Since T2D comprises 90% of diabetes cases worldwide, by 2040, more than 570 million people will likely be living with diabetes, the majority of them being unaware of it [

A number of conceivable stress mechanisms (herein indicated as “stressors”) leading to and participating in insulin resistance and beta-cell dysfunction have been hypothesized to explain the complex landscape of T2D onset, such as oxidative stress, endoplasmic reticulum stress, amyloid (

The ultimate conceptualization identifies the hallmark of T2D in a chronic inflammatory state initiated by an excess of nutrients and referred to as metabolic inflammation or

This clear evidence is at the core of the present computer simulation study as it constitutes the primary working hypothesis of a mathematical model developed and used to assess the risk of developing an inflammatory state thus leading to T2D.

We used an agent-based model (ABM) of the immune system to study

The model is a derivation of a well-established general-purpose immune system simulator [

It is a multiscale discrete-event model, generic enough to account for the major hallmarks of the immune response. This computational model has been conceived to allow the dynamic representation of hypotheses and their preliminary testing [

Agent-based modeling is based on a general paradigm for complex systems inspired by von Neumann’s “cellular automata” [

In the used modeling framework, key immune cells such as monocytes-derived macrophages, dendritic cells, and B and T lymphocytes are represented by agents and follow a set of rules describing the different phases of the recognition and response of the immune system against a pathogen. In particular, the model incorporates key immune processes such as phagocytosis, antigen presentation, cytokine release, cell activation from inactive or anergic states, development of the immune memory, cytotoxicity, and antibody secretion [

The model represents a small volume of the body populated by a fraction of immune cells which is calculated according to generic leukocyte formulas. The discrete time step is equivalent to eight hours of real life.

For the work here presented, the above described model has been enriched for the ongoing purpose of studying the effects of excessive caloric intake by including specific mechanisms pertaining the (i) accumulation of fat in the adipose tissue, (ii) consequential growth of the adipose tissue, (iii) the generation of proinflammatory cytokines, and (iv) the endmost polarization of key innate immune mediators such as the macrophages into the proinflammatory phenotype establishing

Among the main risk factors of T2D is an excess in body weight which is often the result of fat accumulation over an extended period of time. This process is the result of an excess of caloric intake which is not balanced by a comparable caloric consumption due, for instance, to physical activity.

In the literature, there are very few attempts to quantify and model the link between the effects of high caloric intake [

Another value of use to set the initial condition of the model is the initial value of the fat mass FM

According to Westerterp’s regression equations in [

During periods of excessive calorie intake, adipocytes grow in order to stock the energy surplus (

To model the enlargement of the adipocyte due to a (daily) surplus of calorie intake indicated by

The volume of an adipocyte changes with an excess (or defect) of caloric intake. We model the

The probability functions

We now define the

Since we are representing cells as agents, we can model the increase of the volume of each single adipocyte individually. At each time step, the volume of an adipocyte changes with probability

Note that in equation (

To model the adipocyte recruitment from precursors at each step of the simulation, we first define the fraction

The newly generated adipocytes increase the total adipose tissue volume since each adipocyte is initialized with volume

Figure

The process described above simulates the weight gain process resulting from a prolonged highly caloric diet described in the following section. To compute the weight from the population of simulated adipocytes, we use equations (

Macrophages are at heart of many immune-related phenomena including inflammation, but their complexity and plasticity only recently have gained much appreciation. In particular, the differentiation of macrophages into the two phenotypes M1 (pro-) and M2 (anti-inflammatory) is the topic of one of our previous works [

The goal of our model is to determine how an excess of calorie triggers, in the long run, a state of low-grade inflammation through the accumulation in the adipose tissue of proinflammatory macrophages [

In this section, we describe the data used to find the parameters of the model (

The study from Diaz in reference [

In another study [

Figure

Simulation agreement with the overfeeding phase of the study of (a) Diaz [

For the second set of data, those of the study in [

To have a comprehensive view, simulations have been performed for diverse calories excess intake (here again each of them were run fifty times to account for stochastic variability).

Figure

Simulated body weight gain over a period of five years as a function of different excess calorie intake (kcal/day). The simulated individual is a 35-year-old male with an initial BMI of about 21,

As for the emergence of the inflammation, we recall that when the simulated adipocytes reach the critical volume

In the present simulations, to show the emergence of an inflammatory state, the population of macrophages is plotted in Figure

Number of macrophages in the two differentiation classes M1 and M2 per

Another way of looking at the effects of high calorie diets on the setup of the inflammation is by plotting the percentage of cases that did not trigger an inflammatory reaction for each dietary conditions over a time period of five years. These are the Kaplan–Maier curves of Figure

Kaplan–Meier curve of inflammation set-ups as a function of excess calories

Computational multiscale modeling of immune-related diseases is a growing field of the study [

The parameters of the model have been chosen to reproduce the weight gain increase in the relatively short period (

Concurrently to the weight gain, the simulation describes the emergence of the inflammatory state in terms of the relative fraction of macrophages differentiating into the proinflammatory M1 phenotype. As expected, the magnitude of the inflammation correlates with the calorie excess of the diet. Interestingly, it also shows the attempt of the immune system to counterbalance the inflammation eliciting a smaller fraction of anti-inflammatory macrophages M2 (Figure

A number of improvement to this model can be foreseen as, for instance, the effect of physical exercise on the release of the pro/anti-inflammatory cytokine IL-6 [

The data used in this study are from published literature articles and therefore are publicly available.

The authors declare that they have no conflicts of interest.

This study had been partially funded by the European Commission under the 7th Framework Programme (MISSION-T2D project, contract no. 600803).