Cooperation and Competition in the Evolution of ATP-Producing Pathways Thomas Pfeiffer, Stefan Schuster, and Sebastian Bonhoeffer

Supplementary Material

Supplemental Figure 1. Thermodynamic trade-off between rate and yield in ATP-producing pathways. In the main text we argue that for fundamental thermodynamic reasons there is a trade-off between rate and yield of ATP production in heterotrophic organisms. The quantitative relation between rate and yield, however, is determined by the specific biochemical properties of the ATP-producing pathway. Using glycolysis as an example, Waddell et al. [T. G. Waddell, P. Repovic, E. Melendez-Hevia, R. Heinrich, F. Montero, Biochem. Educ. 27, 12 (1999)] derived the following function to describe the dependence between rate and yield in ATP-producing pathways:

(eq. 1)

where J^ATP denotes the rate of ATP production, n^ATP denotes yield of ATP production, and c is a constant. The maximal yield, , is given by the ratio of the free energy difference between substrate and product, and the free energy required for the formation of ATP (). At maximal yield (n^ATP =) the rate of ATP production vanishes. The maximal rate of ATP production is obtained at a yield of = . The trade-off between rate and yield arises because a yield higher than can only be obtained at the cost of a lower rate.

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Supplemental Figure 2. Competition and invasion. The size that a population establishes on a given level of resource depends on the yield but not the rate of ATP production. However, the outcome of competition is determined by the rate of ATP production. As shown here (based on a numerical simulation of eq. 1 in the main text), a population with a high yield of ATP production (blue line) is at steady state with the resource (green line). At time t = 15 a new strain is introduced into the system with 20-fold higher rate, but 10-fold lower yield of ATP production. This strain outcompetes the resident population, but eventually establishes a lower population size because of its lower yield. (Parameters used in the simulation: v = 10, d = 1, J1^S = S/(1 + S), J2^S = 20S/(1 + S), J1^ATP = 10J1^S, J2^ATP = J2^S.)

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Supplemental Figure 3. Rates of resource consumption and ATP production as used in the spatial model [eq. 2 and (27) in the main text]. With increasing use of fermentation, the yield of the fermenter decreases asymptotically from 32 to 2, while the respirator obtains a constant yield of 32. Respirators and fermenters are indicated in blue and red, respectively. [Parameters are given in (27).]

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