Evolutionary adaptations in metabolic networks are fundamental to evolution of microbial growth. Studies on unneededprotein synthesis indicate reductions in fitness upon nonfunctional protein synthesis, showing that cell growth is limited by constraints acting on cellular protein content. Here, we present a theory for optimal metabolic enzyme activity when cells are selected for maximal growth rate given such growth-limiting biochemical constraints. We show how optimal enzyme levels can be understood to result from an enzyme benefit minus cost optimization. The constraints we consider originate from different biochemical aspects of microbial growth, such as competition for limiting amounts of ribosomes or RNA polymerases, or limitations in available energy. Enzyme benefit is related to its kinetics and its importance for fitness, while enzyme cost expresses to what extent resource consumption reduces fitness through constraint-induced reductions of other enzyme levels. A metabolic fitness landscape is introduced to define the fitness potential of an enzyme. This concept is related to the selection coefficient of the enzyme and can be expressed in terms of its fitness benefit and cost. E NVIRONMENTAL conditions set the selective pressures acting on unicellular organisms. Microbial fitness is often related to growth properties, such as biomass yield, growth rate, or antibiotic resistance. As a large part of the available resources is spent on the synthesis of metabolic machinery, regulation of the levels of metabolic enzymes can have large influences on fitness (Dean 1989; Dong et al. 1995; Dekel and Alon 2005; Stoebel et al. 2008). Selection on growth rate may then direct the evolution of microorganisms to optimal allocation of resources for fitness enhancement (Dekel and Alon 2005; Molenaar et al. 2009). Alternatively, evolution may be directed by metabolic trade-offs (Beardmore et al. 2011; Wenger et al. 2011), which may cause sympatric speciation (Friesen et al. 2004). To improve our understanding of the driving processes of metabolic evolution, the interplay between selective pressures and the biochemistry and organization of metabolic networks must be taken into account.Studies on the growth effects of unneeded-protein expression, sometimes called gratuitous or nonfunctional protein expression, indicate significant reductions in growth rate in batch cultivations of Escherichia coli (Novick and Weiner 1957; Dong et al. 1995; Dekel and Alon 2005; Shachrai et al. 2010) and Zymomonas mobilis (Snoep et al. 1995) and strong selective disadvantages in chemostat cultivations using E. coli (Dean et al. 1986;Dean 1989; Lunzer et al. 2002; Stoebel et al. 2008). In Saccharomyces cerevisiae, a trade-off related to unneeded-protein expression was found (Lang et al. 2009). Dong, Nilsson, and Kurland found that unneeded protein can be expressed up to 30% of the total protein content before E. coli growth halts (Dong et al. 1995). They concluded that growth reduction was caused by competition for protein syn...
Background: Dynamic modeling of metabolic reaction networks under in vivo conditions is a crucial step in order to obtain a better understanding of the (dis)functioning of living cells. So far dynamic metabolic models generally have been based on mechanistic rate equations which often contain so many parameters that their identifiability from experimental data forms a serious problem. Recently, approximative rate equations, based on the linear logarithmic (linlog) format have been proposed as a suitable alternative with fewer parameters.
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