Deductive functional assignment of elements in appetite regulation

Mathematical modeling of the human energy metabolism based on the Selfish Brain Theory

Deregulations in the human energy metabolism may cause diseases such as obesity and type 2 diabetes mellitus. The origins of these pathologies are fairly unknown. The key role of the brain is the regulation of the complex whole body energy metabolism. The Selfish Brain Theory identifies the priority of brain energy supply in the competition for available energy resources within the organism. Here, we review mathematical models of the human energy metabolism supporting central aspects of the Selfish Brain Theory. First, we present a dynamical system modeling the whole body energy metabolism. This model takes into account the two central control mechanisms of the brain, i.e., allocation and appetite. Moreover, we present mathematical models of regulatory subsystems. We examine a neuronal model which specifies potential elements of the brain to sense and regulate cerebral energy content. We investigate a model of the HPA system regulating the allocation of energy within the organism. Finally, we present a robust modeling approach of appetite regulation. All models account for a systemic understanding of the human energy metabolism and thus do shed light onto defects causing metabolic diseases.

Systemic investigation of a brain-centered model of the human energy metabolism

The regulation of the human energy metabolism is crucial to ensure the functionality of the entire organism. Deregulations may lead to severe pathologies such as diabetes mellitus and obesity. The decisive role of the brain as active controller and heavy consumer in the complex whole-body energy metabolism is the object of recent research. Latest studies suggest the priority of the brain energy supply in the competition between brain and body periphery for the available energy resources. In this paper, a systemic investigation of the human energy metabolism is presented which consists of a compartment model including periphery, blood, and brain as well as signaling paths via insulin, appetite, and ingestion. The presented dynamical system particularly contains the competition for energy between brain and body periphery. Characteristically, the hormone insulin is regarded as central feedback signal of the brain. The model realistically reproduces the qualitative behavior of the energy metabolism. Short-time observations demonstrate the physiological periodic food intake generating the typical oscillating blood glucose variations. Integration over the daily cycle yields a long-term model which shows a stable behavior in accordance with the homeostatic regulation of the energy metabolism on a long-time scale. Two types of abstract constitutive equations describing the interaction between compartments and signals are taken into consideration. These are nonlinear and linear representatives from the class of feasible relations. The robustness of the model against the choice of the representative relation is linked to evolutionary stability of existing organisms.

Compact energy metabolism model: brain controlled energy supply

The regulation of the energy metabolism is crucial to ensure the functionality of the entire organism. Deregulations may lead to severe pathologies such as obesity and type 2 diabetes mellitus. The decisive role of the brain as the active controller and heavy consumer in the complex whole body energy metabolism is the matter of recent research. Latest studies suggest that the brain's energy supply has the highest priority while all organs in the organism compete for the available energy resources. In our novel mathematical model, we address these new findings. We integrate energy fluxes and their control signals such as glucose fluxes, insulin signals as well as the ingestion momentum in our new dynamical system. As a novel characteristic, the hormone insulin is regarded as central feedback signal of the brain. Hereby, our model particularly contains the competition for energy between brain and body periphery. The analytical investigation of the presented dynamical system shows a stable long-term behavior of the entire energy metabolism while short time observations demonstrate the typical oscillating blood glucose variations as a consequence of food intake. Our simulation results demonstrate a realistic behavior even in situations like exercise or exhaustion, and key elements like the brain's preeminence are reflected. The presented dynamical system is a step towards a systemic understanding of the human energy metabolism and thus may shed light to defects causing diseases based on deregulations in the energy metabolism.

Unbuffered and buffered supply chains in human metabolism

The investigation of very complex dynamical systems like the human metabolism requires the comprehension of important subsystems. The present paper deals with energy supply chains as subsystems of the metabolism on the molecular, cellular, and individual levels. We form a mathematical model of ordinary differential equations and we show fundamental properties by Fourier techniques. The results are supported by a transition from a system of ordinary differential equations to a partial differential equation, namely, a transport equation. In particular, the behavior of supply chains with dominant pull components is discussed. A special focus lies on the role of buffer compartments.