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Pfeiffer et al., (2001). Cooperation and competition in the evolution of ATP-producing pathways.

September 2012, model of the month by Massimo Lai
Original model: BIOMD0000000337

Pfeiffer and coworkers [1, BIOMD0000000337] explored the implications of a possible conundrum that our unicellular ancestors faced, when imposed to decide about the evolution of their metabolism. Nowadays, multicellular organisms produce most of their ATP through respiration, which is much more efficient than fermentation (their yield ratio is about 16:1) and therefore makes a much more rational use of available resources. However, fermentation is considerably faster.

There exist a trade-off between the efficiency of a metabolic pathway and its capability, to produce greater amount of ATP in a short time. Moreover, Waddell and coworkers [2] demonstrated, through thermodynamic considerations, that this trade-off is ineliminable.

The hypothetical scenario is that the two populations of organisms, namely respirators and fermenters, compete in the same ecosystem for a limited amount of nutrients. Despite their inefficient metabolism, fermenters could potentially outcompete the respirators by reproducing much more quickly. The paradoxical conclusion is that early respirators may have faced selective pressure to abandon aerobic metabolism in order to compete more effectively with fermenters. In other words, evolution could have pointed towards a less efficient use of shared resources, a situation that in game theory, is known as "The tragedy of the commons" [3].

The problem was modelled by means of a set of coupled partial differential equations, which expresses balance equations for the nutrients and cell concentrations at each grid point of a discretised spatial domain (Figure 1).

Figure 2

Figure 2 Snapshot of numerical simulation, showing grid cells populated by respirators (blue), fermenters (red), or both (yellow). Empty grid cells are shown in black (figure taken from [1]).

Figure 3 illustrates the outcome of the competitive struggle (i.e. population size of the surviving species), as a function of the availability of resource and diffusion speed. Fermenters can outcompete respirators only if resources are abundant and diffusion is fast (i.e. they can prey on the global amount of resources, and not only those available in their immediate surroundings, which get quickly depleted). However, the population size they can maintain is (predictably) much smaller. On the other hand, when resources become scarce and diffusion is lower, respirators outperform fermenters. Moreover, respirators are more likely to form aggregates, since neighbouring cells don't compete stiffly for nutrients in the same area, thanks to their energetic efficiency. Their capability to coexist could be seen as a stepstone towards multicellularity.

Interestingly, such behavioural patterns resemble those of a dimorphic fungus (Mucor Racemosus), that uses fermentation in its unicellular yeast-like form but shifts to respiration in its multicellular form [4].

In summary, this paper demonstrates that respiration does not necessarily overcome negative selective pressure when called to compete against organisms that relied on fermentation. This happens because, in a spatially structured environment, the development of cooperative behaviour (i.e. the more efficient use of shared resources, rather than an "all-you-can-eat" approach), actually produces a long-term competitive advantage. From a methodological point of view, it must be stressed that the inclusion of spatial effects in the formulation of the model (reaction-diffusion equation) was crucial to the outcome. In non-spatial (i.e. "single-compartment") simulations, which can be seen as a limit case with infinitely fast diffusion, fermenters always outperformed respirators.

On a more literary level, there is a measure of poetic justice in the success of slow but sensibly cooperative cells, against their greedy and individualistic counterparts.

Figure 1

Figure 1 Differential equations describing the model. (figure taken from [1]).

The modelling assumptions were the following:

  1. Both nutrients and cells are allowed to diffuse with prescribed diffusion coefficients.
  2. There are two competing populations of cells, respirators and fermenters, with different metabolic parameters.
  3. Both populations have the same yield and rate of ATP from aerobic metabolism, but fermenters are also allowed to use fermentation, and they have the highest rates of nutrient consumption and ATP pruduction.
  4. The source term for nutrients (\nu) is stochastic in time and space.
  5. The reproduction rate depends on the amount of available ATP.

In principle, this approach is applicable to any arbitrary number of competing species. A snapshot of the resulting spatial model is shown in Figure 2.

Figure 3

Figure 3 Simulation outcome, i.e. final population size of the surviving species, as a function of diffusion speed and resources availability. (figure taken from [1]).

Bibliographic References

  1. Pfeiffer T, Schuster S, Bonhoeffer S. Cooperation and competition in the evolution of ATP-producing pathways. Science. Apr;292(5516):504-7, 2001 [PMID:11283355]
  2. Waddell TG, Repovic P, Meléndez-Hevia E, Heinrich R, Montero F. Optimization of glycolysis: New discussions. Biochemical Education Jan ;27(1):12-13, 1999 [DOI: 10.1016/S0307-4412(98)00266-0]
  3. Hardin G. The tragedy of the commons. Science. Dec 13;162(3859):1243-8, 1968 [PMID:17756331]
  4. Inderlied CB, Sypherd PS. Glucose metabolism and dimorphism in Mucor. J Bacteriol. Mar ;133(3):1282-6, 1978 [PMID:641009]