Optimization and evolution in metabolic pathways: Global optimization techniques in Generalized Mass Action models

Cells are natural factories that can adapt to changes in external conditions. Their adaptive responses to specific stress situations are a result of evolution. In theory, many alternative sets of coordinated changes in the activity of the enzymes of each pathway could allow for an appropriate adaptive readjustment of metabolism in response to stress. However, experimental and theoretical observations show that actual responses to specific changes follow fairly well defined patterns that suggest an evolutionary optimization of that response. Thus, it is important to identify functional effectiveness criteria that may explain why certain patterns of change in cellular components and activities during adaptive response have been preferably maintained over evolutionary time. Those functional effectiveness criteria define sets of physiological requirements that constrain the possible adaptive changes and lead to different operation principles that could explain the observed response. Understanding such operation principles can also facilitate biotechnological and metabolic engineering applications. Thus, developing methods that enable the analysis of cellular responses from the perspective of identifying operation principles may have strong theoretical and practical implications. In this paper we present one such method that was designed based on nonlinear global optimization techniques. Our methodology can be used with a special class of nonlinear kinetic models known as GMA models and it allows for a systematic characterization of the physiological requirements that may underlie the evolution of adaptive strategies.