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Complex Systems Analysis and Mathematical Modeling of Insulin Resistance in Skeletal Muscle Cells and the Impact of Plasma Free Fatty Acids

Baris U. Agar1, Ali Cinar1, Emmanuel C. Opara2, and Gary Reznik3. (1) Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, IL 60616, (2) Department of Biomedical Engineering, Illinois Institute of Technology, 10 W. 32nd Street, Chicago, IL 60616, (3) Microbiology and Immunology Division, Illinois Institute of Technology Research Institute (IITRI), 10 W. 35th Street, Chicago, IL 60616

We have performed complex systems analysis on the pathways of energy metabolism of skeletal muscle cells towards understanding the key metabolites and processes involved in triggering insulin resistance and to incorporate these findings to a dynamic model of the system.

In United States, 20.8 million children and adults, making up 7% of the population, have been diagnosed with diabetes [1]. Type 2 diabetes is the most common form of diabetes, accounting for about 90% of the cases. The link between obesity and Type 2 diabetes has been emphasized in recent years. There is a strong correlation between excessive fat in diet and the progression from being overweight to obesity and ultimately to the development of diabetes. Plasma free fatty acids (FFA) play important roles in muscle, heart, liver, and pancreas. Elevated FFA concentrations lead to suppression of glucose transport into skeletal muscle cells causing insulin resistance. A better understanding of the alterations in insulin utilization in tissues caused by high levels of free fatty acids (FFA), will help identify the key steps to be targeted for treatment of Type 2 diabetes.

Mathematical modeling of system dynamics offers many opportunities for computational investigation of metabolic activities. Models permit the analysis of dynamic system behavior when frequent experiments are infeasible. Mathematical models of insulin utilization and the effects of FFAs on this metabolism can aid in focusing on certain sub-mechanisms of these pathways and test related hypotheses on these subsystems. In addition to traditional kinetic model development techniques of reaction systems, we rely on the principles of cybernetic modeling framework. Cybernetic modeling defines certain segments of a metabolic network (elementary pathways) assigned with certain universal objectives, which are assembled to form the network (topological realization) [2]. Cybernetic models involve the effect of the regulatory mechanisms working to achieve these objectives. Once dynamic models are available, simulation data can be generated, and time series data analysis, bifurcation analysis, and robustness assessment techniques can be used to determine the characteristics of the metabolic model. Concepts such as adaptation, robustness, error correction, feedback and feedforward control, self-regulation, hysteresis, and limit cycle become useful for characterizing and analyzing the metabolic network.

In order to develop a mathematical model of the energy metabolism of skeletal muscle cells, we have performed complex systems analysis to identify metabolites and reactions with key roles within the system. By utilizing current knowledge on biochemical reactions and activation/deactivation processes of the system, we have developed an "interaction network" which represents every possible direct influence that a certain metabolite can exert on another. The resulting network is a directed graph that consists of more than 64 nodes (metabolites) and 235 arrows (interactions). We have determined the diameter of the system which demonstrates the average number of influences that has to take place for a metabolite to affect the level of another metabolite. The metabolites with key roles within the system were identified according to their connection properties. We have analyzed the degree of emission (number of metabolites whose levels can be influenced by a certain metabolite), and the degree of reception (number of metabolites that influence the level of a certain metabolite) after n number of direct influences. By setting n=1, we have determined several metabolites (e.g. mitochondrial NAD+, mitochondrial FAD) as key metabolites according to the number of direct interactions with other metabolites. Further analysis was conducted by setting n>1 and metabolites such as oxygen were observed to interact with a significant number of metabolites of the system with n being as low as 3.

Certain sub-systems (composed of several metabolites, biochemical reactions and interactions) within the metabolic network may serve specific functions in the system. Such sub-systems should be incorporated properly into the mathematical model. In the case of insufficient experimental data, cybernetic modeling principles can be employed to introduce the function of a certain segment into the mathematical model. We have identified motifs [3] of the metabolic network, the patterns of interconnections occurring at numbers that are significantly higher than those in randomized networks. The significance of these structures raises the question of whether they have specific roles in the network. If they do, they might be used to understand the network dynamics in terms of elementary computational building blocks. Different networks that belong to a certain class (e.g. biological) may share the same unique network motifs. Therefore motifs can define broad classes of networks, each with specific types of elementary structures. Dr. Alon and co-workers have observed bi-fan and feed-forward loop motifs as common motifs of biological systems [3]. We have identified more than 3 unique motifs in the interaction network of the energy metabolism of skeletal muscle cells, none being bi-fan or feed-forward loop. We have investigated the number of occurrences of previously defined key metabolites in these motifs and observed that several metabolites participate only in specific motifs.

REFERENCES

1. Centers for Disease Control and Prevention, National Diabetes Fact Sheet. 2005

2. Varner J, Ramkrishna D., Metabolic engineering from a cybernetic perspective. 1. Theoretical preliminaries, Biotechnol. Prog., 1999, 15, 407-425.

3. Milo, R. et. al., Network motifs: Simple building blocks of complex networks, 2004, Science, 303, 15381542