Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Artigo de Discussão Some insights into an integrative mathematical model: a prototype- model for bodyweight and energy homeostasis

Algumas discussões em um modelo matemático integrativo: um modelo protótipo para homeostase do peso corporal e energia

Algunos debates sobre un modelo matemático integrador: un modelo prototipo para la homeostasis del peso corporal y energía

Jorge Guerra Pires1 functions and roles seem fuzzy, most

seem to be piloting the same Abstract: The ambition of this undertaking. The key challenge from a document is to set in evidence the mathematical modeling perspective is prerequisite for integrative how to separate properly the (mathematical) models, mechanism- mechanisms of each . The kind based models, for appetite/bodyweight of pursuit presented herein could initiate control. For achieving this goal, it is an imperative cascade of mathematical provided a scrutinized literature review modeling applied to metabolism of and it is organized them in such a way bodyweight control and energy to make the point. The quantitative homeostasis. methods exploited by the authors are Descriptors: ; Glucose; called differential equations solved Homeostasis; Mathematical Models; numerically; they are discussed briefly Systems . since it is not our goal herein to handle details. On the current state of the art, Resumo: O escopo deste trabalho é there is no mathematical model to the colocar em evidência a necessidade de best of the author’s knowledge targeting modelos matemáticos integrativos, at integrating several hormones at once modelos baseados em mecanismos, para in mathematical descriptions: even for investigar controle de apetite e peso single hormones, the literature is either corporal. De forma a atingir essa meta, occasional or do not exist at all; it is uma revisão seletiva da literatura é depicted some results for simple models apresentada e o material é organizado already built. As it can be seen, the de modo a defender a visão. Os métodos quantitativos empregados são chamados 1 Department of Information Engineering, Computer Science and Mathematics (University of L'Aquila)/ Institute equações diferenciais resolvidas of Systems Analysis and Computer Science (IASI- CNR)/CAPES Foundation (Ministry of Education of Brazil). numericamente; estas não são discutidas E-mail: [email protected]

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... em detalhes devido ao fato de fugir do presenta y el material se organiza para desígnio do trabalho. No estado correte defender la visión. Los métodos da arte, aparentemente não existem cuantitativos utilizados son llamados modelos que buscam descrever ecuaciones diferenciales resuelven matematicamente hormônios de uma numéricamente; éstos no se discuten en forma única e integrada, mesmo para detalle debido al hecho de escapar del hormônios únicos, a literatura ou é alcance del trabajo. En el estado actual insuficiente ou não existe em muitos de la técnica correte, al parecer, non hay casos. Resultados preliminares são modelos que tratan de describir apresentados para algumas tentativas matemáticamente las hormonas de incipientes. Como pode ser visto, a manera única e integrada, incluso para funcionalidade e importância de cada las hormonas individuales, la literatura hormônio pode ser abstrusa, em muitas es escasa o inexistente. Los resultados casos poder-se-ia chegar à conclusão de preliminares se presentan en algunos que vários hormônios empenham a intentos incipientes. Como puede verse, mesma função. O desafio-chave do la funcionalidad y la importancia de ponto de vista matemático é como cada hormona pueden ser confusos, en entender a posição de cada hormônio no muchos casos se puede llegar a la processo como um todo. Trabalhos conclusión de que varias hormonas como o defendido aqui podem gerar cometen la misma función. El desafío uma onda de modelos matemáticos clave de un punto de vista matemático aplicados ao controle de peso e es cómo entender la posición de cada homeostase energético. hormona en el proceso como un todo. Descritores: Insulina; Glucose; Proyectos como abogado por aquí Homeostase; Modelos Matemáticos; puede generar una ola de modelos Biologia de Sistemas. matemáticos aplicados para el control de peso y la homeostasis energética. Resumen: El objetivo de este trabajo es Descriptores. Insulina; Glucosa; poner de relieve la necesidad de Homeostasis; Modelos Matemáticos; modelos matemáticos de integración, Biología de Sistemas. basado en modelos mecanismos para controlar el apetito y el peso corporal. 1. Introduction Con el fin de lograr este objetivo, una The determination to unify for revision selectivo de la literatura se integrating in the biological sciences is

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... ubiquitous in several areas these days, and co-works(4), it was also detected an eminent photograph of this key independently by Tam and co-works(5). attempt is Systems Biology, in theories comparable to multiscale modeling; e.g. 1.1 Objective(s) /motivations from gene to metabolism, from The objective of this work is to set in metabolism to cell behavior, from cell evidence the prerequisite for integrative behavior to tissue, and similar modeling mathematical models, mechanism-based paradigms. By taking advantage of the models, for appetite/bodyweight possibilities brought alongside systems control. This ambition was born from biology and alike, one can bump into the surveillance that no existent model audacious philosophies and paradigms; so far to the best of our knowledge had e.g. the virtual human(1), or virtual integrated efficaciously more than one (2). hormone, even for one hormone the Physiologically speaking, glucose models are infrequent or centered in one control, which implies in energy hormone, i.e. insulin; see(4) for a nice homeostasis and bodyweight changes, is case. Notwithstanding we provide a a quite dense and intricate bio-process. literature survey and some mathematical Accordingly, it is a process with players discussions, it is out of our scope to in different hierarchal phases and either discuss mathematical details or stages. As one illustration of such an make a complete literature review. As allegation, one could pick out “eating” sub-objectives, we can point out: a) (food intake) that is controlled by discuss some problems in the medical and fat mass controlled by literature when reporting hormone . On this paper, the researchers workings, that is, try to point out where dissert on an idealized insight called needs further investigations; b) pave the unceremoniously the “big glucose way for an upcoming (ongoing) model; model." In view of that, the perception c) captivate the reader regarding was born from the perceived lack of mathematical models in hormonal models that mathematically take a control. The motivation for pursuing glimpse of glucose control in an this goal(s) is that metabolic medical integrative line of attack, typically it is conditions related to eating is quite done using predominantly insulin(3); a common in our modern society, and seminar study is presented by Jacquier solutions rarely can be tested a priori, e.g. diets or medical products.

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result of this system failing to work 1.2 Organization of the manuscript properly or completely is diabetes and In the upcoming section, section 2, it is leptin resistance(7). Accordingly, discussed some literatures. In the metabolism is the imperative bio- following section, section 3, it is process in which living systems balance discussed briefly the methods. Since the energy available and the energy this work is not an “experimental” demanded on such a way that the work, this section is added for the sake organism will not find itself in of completeness. The authors plan to circumstances of lacking energy after a come back in other papers with more profusion of foodstuff(8-9); medical details since it is an ongoing project. conditions comparable to anorexia The next section, section 4, it is nervosa and morbid obesity are in provided some results and discussions, general positively correlated with it was overlapped in a single section due malfunctioning of the metabolic to the nature of the current work, which machinery. Independently of scientific is not presenting a set of experiments advances, our body works, and it is a and make the interpretation, rather it is miracle of control system in practice. to present an idea, the aim on this Accordingly, glucose is constantly section is to give the reader a flavor of converted to glycogen, "the battery of the current endeavors. Finally, section living systems," and it is constantly 5, presents the conclusions and final brought back to the bloodstream in remarks. Some references, scrutinized, times of necessity. As puts it(9), “This are given for the reader to have an idea [energy deposit mechanism] ensures an of the pillars of the current work. adequate plasma concentration of energy substrates to sustain tissue 2. Literature review metabolism at all times.” 2.1 The “big glucose model”: an Notwithstanding the astonishing integrative interpretation of glucose- advancements made over the past few bodyweight control decades in unscrambling many of the The overlapping of hormonal molecular pathways involved in energy receptiveness to nutrient (load) (homeostasis) regulation, a rather availability is primary for metabolic cloudy understanding of “how all the control(0); likely the best examples of pieces fit together to function as an medical conditions that appear as a integrated system”(5) is what can be

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... found for the most part in the scientific complex process of eating and community; this last sentence managing energy; "the regulation of summarizes well the motors (rationales) food intake in humans is an of the current ongoing endeavor. As a extraordinarily complicated process that representative case, recently a new researchers have only begun to hormone long ago guessed was finally understand"(7). See upcoming sections, identified, called neuromedin U(0), in special figure 1. firstly screened off in fruit fly, called limostatin. Basically this hormone 2.3 Food Intake vs. Metabolism: aforesaid works when we are fasting, it bodyweight control as a soup of avoids glucose to be stored in situations entangled hormones in which it supposes to be available; In the subsequent drawing, figure 1, it practically, it seems to inhibit the was systematized several hormones and master-hormone insulin. molecules (in general peptides) that A careful literature analysis provides us play an important role in glucose a substantial aggregate of hormones and control; it is the by-product of a molecules involved in the complex literature review done by the authors. process of food intake, feeding, and The coming text disserts on each of managing energy. Consequently, food is them, and others, in a brief approach, equal energy, energy is equal work. more information was added to the Undeniably, it is done work by the attached file; which also is not an human body from simple tasks, e.g. exhaustive discussion of them. The sleeping, to more complex and most imperative to apprehend is that elaborated tasks, e.g. playing our glucose is the main energy source of the favorite sport game. body and it must be refuelled from time to time. However, this time to time 2.2 A brief look at a dense and aforesaid is not always predictable, and intricate process how biological system must manage the A painstaking literature analysis endow energy already present until the next us with a large number of hormones and meal is the reason for this “web of molecules related somehow to the hormones.”

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Figure 1. Schematic viewpoint of the hormones involved in the appetite control and metabolism. In red are important players, but are not hormones. The dashed arrows intend to show hormones that play more than one control function on the diagram, the challenge is to build a complete diagram on this style, even in layers, that is, one hormone may control others; e.g. some researches point out that leptin can control insulin somehow(14). This diagram is mathematical modeling biased. The "fat" arrow between body weight and metabolism intends to say that the metabolism is a short-term dynamic process, from seconds to hours. whereas the body weight usually changes in a long-term scale, from days to months. Source: own elaboration(12).

2.4 A few import hormones and breaking down, glycogenolysis. players Furthermore, insulin levels in the blood 2.4.1 Insulin reflect both circulating energy (i.e., Insulin, essentially, lowers blood glucose) and stored energy (i.e., adipose glucose levels as it increases glucose tissue, visceral fat tissue) (0,7). The uptake in peripheral tissues(7) and ; scheme below attempts to depict this additionally, it inhibits glycogen picture, figure 2.

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Figure 2. The insulin- back-and-forth. On this picture one has the relationship between insulin, glucagon, glycogen, and glucose. Source: own elaboration.

In the coming scheme, figure 3, it is general recognized the role of insulin as highlighted other hormones that work in appetite controller, alongside leptin and parallel with insulin. Further, it is not in ghrelin.

Figure 3. Several players in the energy store-expenditure interplay. This scheme aims to depict a small network around glucose control, which implies in food intake and body weight changes. Source: own elaboration.

Several mathematical models were glucose control; however they have developed all over the years(3) on the been based just on a small number of hope to clarify the insulin importance in players, e.g. insulin-glucagon, insulin-

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... glucose, and so on; in spite of the positively/negatively correlated with success to explain several experimental bodyweight, which means different data. from insulin it is just a satiety hormone.

2.4.2 Glucagon 2.4.3 Leptin Glucagon is a hormone secreted by the Leptin is a signal of adiposity(10,11), it is alpha cells of the pancreas that positively correlated with fat-mass, decreases food intake(7,13). Likewise, body mass index; it triggers food intake glucagon is the “hormone of when it is low and inhibit food intake starvation,” in contrast to leptin known when it is high*. Moreover, it has been as the "the hormone of satiety," and proposed as a co-worker with insulin to levels of glucagon do increase when control and monitor body adiposity and someone fasts. Further, glucagon metabolism(10). Consequently, several mainly stimulates glucose production researches has been carried out to either by breaking down glycogen or by understand it properly, more than just "producing" more glucose an adiposity-metabolism controller(11,14- (gluconeogenesis) in the liver/fat tissue, 6). It is not clear yet, but leptin seems to particularly during the fasting condition work with ghrelin on the food intake or when the body has an increased need control. Leptin and ghrelin can be for glucose(7). Glucagon seems to work placed into two big groups(13): in this directly on the liver to inhibit food case leptin and similar hormones would intake(7,13); recently some unknown work to increase/decrease the pathways between liver and brain began functionality of ghrelin and similar to be understood(18). As seen from hormones directed connected to meal- figures 2 and 3, it is the antagonist patterns control, i.e. short term signals molecule of insulin. Accordingly, and long-term signals. In view of that, it insulin asks the cells to store glucose is a long-term hormone signal, whereas either in the liver cells as glycogen or in ghrelin and insulin are short-term fat cells as triglycerides, whereas hormonal signals. glucagon orders them to be released. The hormones that control appetite can be classified into satiety/satiation * This sentence can be problematic if seen mathematically. It gives the idea of ‘threshold,’ related and fat-correlated(7,13): glucagon which is just a mathematical trick. There is no true evidence that biological systems work like is not fat-correlated, i.e. it is not threshold models.

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2.4.4 Glycogen released in times of hypoglycemia (low Glycogen is one of the molecules by levels of glucose in the bloodstream, in which energy is stored in humans, the contrast to hyperglycemia), it is second is in fat cells as triglycerides(9). triggered by glucagon. Accordingly, it is stored in the liver and

Figure 4. The metabolism can be steered towards anabolism (i.e. “synthesis of energy”) or catabolism (“burning of energy”) by the combination of several hormones, glycogen is generally controlled by glucagon and insulin. Source: based on(9).

2.4.5 Triglycerides Triglycerides can be hydrolyzed into Triglycerides (fat and oil) consist of glycerol and fatty acids. Fatty acids are three fatty acid molecules joined to a of individual significance because they molecule of glycerol(7). Hydrolysis of can be transformed into copious triglycerides, controlled by glucagon, molecules of acetyl CoA that can enter within releases free fatty Krebs cycles and generate a large acids into the blood and it is amount of ATP(9). compensated by insulin which increases fat storage as triglycerides. 2.4.6 Ghrelin Additionally, free fatty acids can be Ghrelin is an imperative hunger/satiety used as an immediate source of energy signal secreted by the (7,9) with by many organs, but the brain; they can effects in several places in the body, e.g. also be converted by the liver into ; it was discovered in derivatives called ketone bodies. 1999, about four years after its sister

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... leptin. Ghrelin secretion rises between Equations (ODE) organized in a system. meals*, when the stomach is empty, and The system was solved numerically, stimulates hunger, our propensity to using the automatic routines from start out a meal; furthermore, it has been Matlab®/Simulink™. The system was suggested a gastric emptying role. As building using the block diagrams of the stomach fills during a meal, the Simulink; it was set to be used adaptive secretion of ghrelin rapidly falls and steps and all the simulations were hunger is thereby reduced**; it has been carried out in a home-like computer: suggested a postgastric feedback Processor - Intel(R) Core(TM) i7-4500. influence by nutrient load, e.g. glucose CPU @ 1.80GHz 2.40 GHz. RAM: 8 control. However, one recent study GB. Operation System Windows 64 bit. demonstrated raised levels of ghrelin in None of the simulations lasted more dieters who lost weight. If this raised than seconds. A variable-step method ghrelin level enhances appetite, it may (Dormand-Prince) was applied for partially explain why it is so difficult solving numerically the ordinary for most dieters to maintain their weight differential equations available within loss. It is produced by several points Matlab, called by Simulink, where within the body such as pancreas (ɛ- Simulink was controlled and run from a cells), stomach, and . m-File properly designed for that. See(17) for discussion on this kind of 3. Methods strategy for solving systems of ODEs. All the data delivered herein are in silico, i.e. computer simulations; 4. Discussions/Results whenever compulsory, we shall indicate When a theoretical physicist comes to a third-part – i.e., in vivo and in vitro – lab for testing his ultimate model, likely results with references. The his/her model will be confronted with mathematics on this manuscript boils classical models, his/her math double- down to Ordinary Differential checked, his/her references controlled. In view of that, if everything is okay,

* There have been some controversies on the they are given green light for testing literature regarding its secreting laws; exactly their models. On the other hand, if the how it works, the stimuli that triggers its release or suppression. same thought experiment is carried out ** Be careful with this sentence, the falling down of ghrelin in bloodstream as result of with a theoretical biologist, the output eating is something complex, it is an ongoing research by the author mathematically speaking. probably will be different. It happens

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... because we have no way to ensure that a control ghrelin and vice versa. This mathematical model will work, it is portrays a network-like dynamics, not called the unreasonable effectiveness of modeled so far, except for insolated mathematics. Thus, the past goes in experiments. If one does their favor of physicists and alike, not for homework well, these kind of theoretical biology. There are two ways relationship could be predicted even to solve the aforesaid setback: 1) before one makes the experiments, what theoretical biologists struggler to copy has been done in physics for centuries the physicists' efforts, therefore for their own systems: the theory guides enjoying the same “privileges;” 2) new the experiments, not the experiments theories are developed specially for guide the theory. biology and medicine, “complicate” On this section we will discuss three (well-elaborated) models are developed cases: two already published by and tested, as the results go in favor, the independent groups(4,5) and the other field of studies starts to gain “respect.” being a model developed by the The former pathway is most likely to be authors(12). However, the cases are quite a dead end, whereas the latter is simple compared to all the discussions possibly the way. And this can be so far: as often happens in mathematical achieved just by models such as the one modelling, details are neglected. The discussed herein. challenge aimed is to improve these As we have seen from the previous models in future works. From the three sections, the control of glucose is pretty cases, one model can be built, which is complicate physiologically. Classically, an ongoing research*. any problem with glucose control, hyperglycemia, is treated with insulin; 4.1 Energy balance and defense of a insulin itself is not simple, it has several stable body weight: a leptin based time-scale, mainly short and long one. model** Some experiments have been pointing out that maybe facing the problem just *See ‘Logan, J. David and Wolesensky, Willian R. Mathematical methods in biology. Pure and Applied from the insulin standpoint is Mathematics: a Wiley-interscience Series of Texts, Monographs, and Tracts. John Wiley& Sons, Inc. comparable to trying to "hammer" any 2009’ for a nice account of mathematical models in biological and medical sciences. sharp edge you see. Some experiments ** See(17) for further discussions or https://www.researchgate.net/publication/23714748_ have been showing for instance that A_Mathematical_Model_of_Murine_Metabolic_Reg ulation_by_Leptin_Energy_Balance_and_Defense_of leptin can control insulin, insulin can _a_Stable_Body_Weight/reviews/118501.

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Below it is presented a mathematical rather than genetic susceptibility. We model for leptin dynamics(5,17). This are not going to discuss the details of model is applied for studying what is this model, see(5,17) for more details. called the settling point hypothesis: a theory that tries to explain the body weight changes based on diet patterns

Figure 5. A mathematical model for leptin dynamics. Source: based on(5).

The model is composed of two ordinary “inversely” proportional to leptin in the differential equations and three brain, and energy expenditure is algebraic equations. The first ordinary proportional to body mass and leptin in equations, the first equation, describes the brain. The functions used to create the production of leptin and elimination saturation effects are called Michaelis in blood plasma: all the relations are Menten equation, developed in the first order, they are proportional to a context of biochemistry. The third constant and a state variable. For the equation, an algebraic equation, leptin production, it is proportional to describes the transference of leptin from fat mass, whereas for leptin elimination blood plasma to the brain: it is not clear from plasma, it is proportional to from the paper(5) why it was used an clearance rate and glomerular filtration algebraic equation instead of a rate of the kidneys. The second ordinary differential equation, after discussions differential equation is for energy with co-workers, it seems that a expenditure, it says that food intake is differential equation would be better in

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... order to model “delays” rates. The fourth equation is used to model the relation between energy and fat mass: it is considered fat mass density, energy content to make the conversion. The last equation is for body mass: the sum of fat and free-fat mass. This model cannot be applied when muscle mass increases, once the free-fat mass is considered constant; in(4) it is discussed a possibility to consider free-fat mass, see upcoming system (1-10). It is employed the body mass to “validate” the model against samples from mice; the parameters are taken from the literature. For the case, the authors of the aforementioned model were able to get a good representation*.

4.2 A Predictive Model of the Dynamics of Body Weight and Food Intake: leptin, ghrelin and glucose

* See for an alternative formulation of the problem using optimal control theory Pires, JG. Some discussions into biomathematics: mathematical biology, biomathematics, and theoretical biology and alike. http://www.academia.edu/15185683/Algumas_discus s%C3%B5es_em_Biomatem%C3%A1tica_biologia_ matem%C3%A1tica_bioengenharia_biologia_te%C3 %B3rica_e_Cia. Retrieved on 23/07/2016.

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Figure 6. A mathematical model for leptin dynamics. Source: based on(4).

The explanation for the equations, from rate; see that this a simplified model(3). left to right, from up to down, is The next equation is for ghrelin, see following. The first equation is for body upcoming section for more: it is fat: it says that fat is produced as a inhibited as food is eaten and eliminated response to energy intake, which is from bloodstream. The next one is for given by the equation 8. Furthermore, hunger, an abstract concept made fat will inhibit its production “touchable:” Ghrelin and leptin exponentially, equation 9. The second influences hunger. By applying the equation is for free-fat mass: it says the reasoning of(13), we are saying that same for fat, except that we have an ghrelin increases appetite linearly, with activation, the higher x, the more free- leptin influencing the sensitivity of the fat mass is produced, with a limit given brain/valgus nervous to leptin. The next by equation 8, which is the energy equation, which influences equations 1 balance, matter cannot be created unless and 2, is an energy balance: energy there exist enough energy for that. comes by food intake and it is Equation 3 is for food available for eliminated by a basal rate, consumption: it is the mass balance transformation to matter, and between input and consumption. The metabolism (thermogenesis). The next next equation is for leptin: it is just the equation is a way for saying the balance between production and response to fat mass increase is slow for elimination. The next equation is small values but significant for high glucose: glucose is entered by food values: it makes the Michaelis- consumption and eliminated by a linear Menten/Hill equation goes to zero or

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... maximum value faster than normal, a 4.3 Ghrelin Mathematical Modeling way to achieve the system saturation centered on the Gastrointestinal faster. The last equation is a way to Tract simulate thermogenesis: it disappears Consider the upcoming system. when no food restriction is applied. For further details, see the original publication(4).

Figure 7. A mathematical model for ghrelin dynamics. Source: based on own work(12).

The aforementioned system was created C Where: i  1; xi , are factors, e.g. to model ghrelin mechanisms coming i1 from the gastrointestinal tract(12,19). The glucose, that controls ghrelin. This term first equation is for ghrelin dynamics: it replaces the first term in the first says that ghrelin production is inhibited equations of figure 7. from a constant-basal rate by stimuli This model for ghrelin is different from coming from stomach and . figure 6, previous section, in several The alpha parameter was introduced to points. First of all, this model tries to make a model “controversy-proof”: make a distinction between preprandial some says the stomach is key, others and postprandial signal, whereas the point out the key role of the duodenum, previous just food consumption. by changing alpha from 0 to 1, it is Secondly, some suggests that ghrelin possible to change the role of each does not work significantly with low compartment compared to each other. concentration, a linear relation as before The last part is just the elimination rate. cannot grasp it. Thirdly, the previous This equation can be generalized: model uses ghrelin alongside leptin in an “unmeasurable” quantity, subjective; i.e., hunger. Last but not least, the

previous model spite of the fact food is

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... introduced, it is what is called “closed”; the duodenum: which is governed by the mice eat as much as they can: linear relations. Studies point out to a minimum between food available or feedback coming from the small hunger. Other differences could be intestine to control the pointed out, but this is not the scope of stomach/appetite, on this version of the the current paper. model these details are neglected. One The second equation of figure 7 is for example of such a detail is the fact that the stomach: which is given food in ghrelin seems to create a feedback, discrete modes. The third equation is for controlling gastric emptying.

Figure 8. Some simulations for the generalized ghrelin suppression/production term. The parametrization was arbitrarily chosen just for illustration purposes. Source: based on own work(12).

4.4 Discussing the model/mathematics many signal one pleases; see(18) for The model by(5) seems to be first model discussions on tastants. Several on the mechanism-based approach to challenges come up when trying to appetite/bodyweight control, and the integrate those hormones, e.g. ghrelin model by(4) appears to be the first to go works in minutes, whereas leptin works one step forward: considering better in days. As Tam and co-workers dynamics and one extra hormone and presents(5), it was possible to validate one nutrient signal (i.e., glucose). The their model against real data, model for ghrelin dynamics given by nonetheless these model was applied to the author(12) seems to be the first to mice, not human, and studied in the take into account the gastrointestinal scale of days; curiously, in spite of the tract and to suggest a way to add as ghrelin was already discovered at the

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative... time of the publication, no mention was can be seen, the functions and roles done to it. When these kind of seem fuzzy, most hormones seem to be modelling is pursued, several problem carrying the same undertake. The key comes up. In the SysBio (Milan, 2016), challenge from a mathematical it was highlighted one of this modeling standpoint is how to separate problematic: it is almost impossible to properly the workings of each hormone. find parameters in the literature, they One possibility is quite simple: like in are scattered; not to mention the reports the net force, we have several players, are not mathematical based, that is, easy but just one appears, an imaginary to incorporate in mathematical models. force, which is coordinated by all the hormones. If so, the question is how to 5. Conclusion and final remarks project each component on such a way On this short article, we have discussed to see clearly the contribution of each of the importance of an integrated model them. of glucose control. Glucose control poses before us a big challenge to Acknowledgement. This paper is the science to understand it properly, pieces output of a literature review done by the are understood day by day such as a author, and several discussions at the new hormone discovered in fruit flies(0) IASI-CNR-Rome and BioMathLab- called limostatin, in human suggested as CNR-Rome in 2015 (February to July). being represented by neuromedin U. In Important names are, in alphabetic 1996 leptin was discovered, Ghrelin in order: Andrea De Gaetano, Alessandro 1999, and so on. What is missing are Borri, Costanzo Manes, Pasquale efforts towards gathering the pieces of Palumbo. the puzzle and start to make sense of the big picture. Independent of our efforts 6. References and limitations, the system works, we 1. Kolodkin A, Boogerd FC, Plant N, Bruggeman FJ, Goncharuk V, Lunshof J, et al. are the proof, our brain is supplied with Emergence of the silicon human and network targeting drugs. European Journal of glucose in an almost constant rate, but Pharmaceutical Sciences. 2012. 46: 190–197. we can stay even days without eating. Our muscles are given energy to work, 2. Chassin LJ, Wilinska ME, Hovorka R. Evaluation of glucose controllers in virtual however we never need to assign it in environment: methodology and sample application. Artificial Intelligence in Medicine. our thoughts. It is certainly a miracle of 32: 171-181. 2004.

(bio) engineering control theory. As it

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Revista Eletrônica Gestão & Saúde ISSN: 1982-4785 Pires JG Some insights into a integrative...

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