Pyruvate metabolism in rat liver mitochondria. What is optimized at steady state?

A representative model of mitochondrial pyruvate metabolism was broken down into its extremal independent currents and compared with experimental data obtained from liver mitochondria incubated with pyruvate as a substrate but in the absence of added adenosine diphosphate. Assuming no regulation of enzymatic activities, the free-flow prediction for the output of the model shows large discrepancies with the experimental data. To study the objective of the incubated mitochondria, we calculate the conversion cone of the model, which describes the possible input/output behaviour of the network. We demonstrate the consistency of the experimental data with the model because all measured data are within this cone. Because they are close to the boundary of the cone, we deduce that pyruvate is converted very efficiently (93%) to produce the measured extramitochondrial metabolites. We find that the main function of the incubated mitochondria is the production of malate and citrate, supporting the anaplerotic pathways in the cytosol, notably gluconeogenesis and fatty acid synthesis. Finally, we show that the major flow through the enzymatic steps of the mitochondrial pyruvate metabolism can be reliably predicted based on the stoichiometric model plus the measured extramitochondrial products. A major advantage of this method is that neither kinetic simulations nor radioactive tracers are needed.

Mathematical modeling of the regulation of caspase-3 activation and degradation.

Caspases are thought to be important players in the execution process of apoptosis. Inhibitors of apoptosis (IAPs) are able to block caspases and therefore apoptosis. The fact that a subgroup of the IAP family inhibits active caspases implies that not each caspase activation necessarily leads to apoptosis. In such a scenario, however, processed and enzymically active caspases should somehow be removed. Indeed, IAP-caspase complexes covalently bind ubiquitin, resulting in degradation by the 26S proteasome. Following release from mitochondria, IAP antagonists (e.g. second mitochondrial activator of caspases (Smac)) inactivate IAPs. Moreover, although pro-apoptotic factors such as irradiation or anti-cancer drugs may release Smac from mitochondria in tumor cells, high cytoplasmic survivin and ML-IAP levels might be able to neutralize it and, consequently, IAPs would further be able to bind activated caspases. Here, we propose a simple mathematical model, describing the molecular interactions between Smac deactivators, Smac, IAPs, and caspase-3, including the requirements for both induction and prevention of apoptosis, respectively. In addition, we predict a novel mechanism of caspase-3 degradation that might be particularly relevant in long-living cells.

Chromokinetics of metabolic pathways.

Some methods to study and intuitively understand steady-state flows in complicated metabolic pathways are discussed. For this purpose, a suitable decomposition of complex metabolic schemes into smaller subsystems is used. These independent subsystems are then interpreted as basic colors of a chromatic coloring scheme. The mixture of these basic colors allows an intuitive picture of how a steady state in a metabolic pathway can be understood. Furthermore, actions of drugs can be more easily investigated on this basis. An anaerobic variant of pyruvate metabolism in rat liver mitochondria is presented as a simple example. This experiment allows measurement of the percentage that each basic color contributes to the steady states resulting from different experimental conditions. Possible implementations of existing algorithms and rational design of new drugs are discussed. A MATHEMATICA program, based on a new algorithm for finding all basic colors of stoichiometric networks, is included.

Construction of an associative memory using unstable periodic orbits of a chaotic attractor.

Unstable periodic orbits are the skeleton of a chaotic attractor. We constructed an associative memory based on the chaotic attractor of an artificial neural network, which associates input patterns to unstable periodic orbits. By processing an input, the system is driven out of the ground state to one of the pre-defined disjunctive areas of the attractor. Each of these areas is associated with a different unstable periodic orbit. We call an input pattern learned if the control mechanism keeps the system on the unstable periodic orbit during the response. Otherwise, the system relaxes back to the ground state on a chaotic trajectory. The major benefits of this memory device are its high capacity and low-energy consumption. In addition, new information can be simply added by linking a new input to a new unstable periodic orbit.