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The yield-rate trade-off in
microbial populations
Nakul K. Barfa
Student No. 6185746
MS Research - Literature Thesis (EC 12)
University of Amsterdam, The Netherlands
1. Introduction
Heterotrophic organisms obtain their energy by the degradation of organic substrates into
products with lower free energy. The free energy difference between substrate and
product can in part be conserved by the production of ATP and in part be used to drive
the degradation reaction. ATP production occurs via substrate level phosphorylation and /
or electron transport chain. Theoretically the maximal ATP yield is obtained if the entire
free energy difference is conserved as ATP. However, in this case there is no energy to
drive the reaction and therefore the rates of substrate degradation and ATP production is
zero (figure 1) (MacLean, 2008). If some of the free energy difference is used to drive the
reaction, the rate of ATP production increases with decreasing yield until a maximum is
reached. Hence, for fundamental thermodynamic reasons there is always a trade-off
between yield (moles of ATP per mole of substrate) and rate (moles of ATP per unit of
time) of ATP production in isolated metabolic pathways of heterotrophic organisms
(Kreft & Bonhoeffer, 2005; Luckinbill, 2011).
Figure 1: The yield- rate trade-off. Schematic of the thermodynamic trade-off between
the rate and yield of ATP production in an individual catabolic reaction. Figure taken
from (MacLean, 2008).
The ATP production from sugar degradation by fermentation and respiration seems to be
in accordance with the yield-rate trade-off. As in the presence of oxygen and sugars,
many organisms are in principle capable of using both pathways to produce ATP.
Because the ATP production rate of respiration is rapidly saturated at high levels of
resource or limited oxygen supply, these organisms have the possibility to increase the
rate of ATP production by using fermentation in addition to respiration (Fitzsimmons,
Schoustra, Kerr, & Kassen, 2009; Novak, Pfeiffer, Lenski, Sauer, & Bonhoeffer, 2006).
However, because the yield of fermentation is much lower than that of respiration (2 mol
versus about 32 mol of ATP per mole of glucose), the use of fermentation in addition to
respiration increases the rate of ATP production at the cost of a lower total yield. If
energetic limitation has a large impact on fitness of organisms in their natural
environment, we expect that the properties of ATP-producing pathways have been under
strong selection pressure during evolution. However, the reason for choosing the
fermentation pathway might be due to some other factors and this trade-off is just the
consequence of it.
In order for resource competition to generate social conflict, it is clear that there must be
a trade-off between the benefit that an individual gains from resource exploitation and the
benefit that the group gains. Although there is some evidence for such trade-offs in
multicellular eukaryotes (for example, (Guo, Mueller, & Ayala, 1991)), no general
evidence has been offered to explain why such trade-offs must exist. In the case of
microorganisms, it is well-established that a trade-off between the rate and yield of
metabolism is a fundamental aspect of resource use, making microbes an ideal group of
organisms in which to investigate the social conflicts created by resource competition. In
this paper, theoretical studies relating to resource competition and social conflict in
microbial populations and experimental tests of this theory using experimental evolution
in microbial microcosms are reviewed. Possible avenues for future research and the
relevance of this work for understanding social evolution are also discussed.
2. Theoretical reasons for the existence of the yield-rate trade-off
a. Thermodynamics and other constraints
Thermodynamics suggest that there has to be a trade-off between the rate and the yield of
a reaction and, if there is no difference in the free energy between reactants, the reaction
will not proceed (figure 1). This phenomenon is true for the pathways as well as for a
whole organism, as living organisms also follows thermodynamic constraints, just that in
most of the cases they are far from the equilibrium contrary to chemical equilibrium.
Now the question is whether the thermodynamic yield-rate trade-off is relevant at the farfrom chemical equilibrium state at which most living organisms operate. A yield-rate
trade-off may however exist in living organisms because of other than (equilibrium)
thermodynamic constraints. For example Molenaar et al (2009) showed that how the shift
in metabolic efficiency originates from a tradeoff between investments in enzyme
synthesis and metabolic yields for different catabolic pathways. His model elucidates
how the optimization of growth by natural selection shapes growth strategies. His model
does not use thermodynamics, however still generates a trade-off between yield and rate
which explains that thermodynamics is not the only factor responsible for the yield-rate
trade-off, there are other constraints as well which have an effect on this phenomenon
(Molenaar, van Berlo, de Ridder, & Teusink, 2009). Fundamental assumption here was
(the observation) that organisms need longer pathways (more enzymes) to generate more
ATP from a certain amount of substrate.
b. Theoretical models and simulations
What are the evolutionary consequences of the metabolic rate-yield trade-off? Early
theoretical studies addressed this question by modeling pairwise competition between
hypothetical strains of microbe that consume resources rapidly or efficiently. The
outcome of these models is simple: under competition for a common resource, the selfish
strain with a high rate of ATP production always displaces the prudent strain with a high
yield of ATP production, revealing the potential for metabolic trade-offs to generate a
tragedy of the commons (Kreft, 2004; Pfeiffer, Schuster, & Bonhoeffer, 2001). However,
this outcome changes when individuals compete for local pools of resources with their
neighbors, as occurs in structured populations such as a bacterial biofilm (Kreft, 2004). In
this case, strains with a high yield of ATP metabolism can displace competitors with a
high rate of ATP metabolism by effectively exploiting their local pool of resources
(Pfeiffer et al., 2001; Kreft, 2004). In this scenario, rapid metabolism is still associated
with a fitness benefit, because it increases reproductive rate, but the cost of rapid ATP
production is not borne by the population as a whole. Instead, the cost of rapid ATP
production is paid exclusively by local groups of cells with rapid metabolism, which
leads to an indirect cost of selfishness. Although theoretical models of resource
competition and social conflict in microorganisms differ with respect to their ecological
and biochemical assumptions, they lead to the common prediction spatially structured
ecological interactions are the key to preventing the tragedy of the commons in microbial
populations (MacLean, 2008).
Kreft et al (2004) mentioned in his study that biofilms enrich altruists, enrichment
cultures select for highest growth rate (Kreft, 2004) and Beardmore et al (2011) in his
model mentioned that the metabolic and physiologic trade-offs translate into a fitness
landscape in which the most fit has unfit near-mutational neighbours, and a lower fitness
peak also exists that is more mutational robust. The ‘survival of the fittest’ applies at
lower mutation rates, giving way to ‘survival of the flattest’ at high mutation rates. They
also showed a transition zone in which both fittest and flattest co-exist (Beardmore et al.,
2011).
A trade-off between rate and yield might be due to a crowding constraint. For example –
the trade-off is may be due to the limitation on the amount of protein that can be present
in the cytosol. The study suggest that molecular crowding represents a bound on the
achievable functional states of a metabolic network, and they indicate that models
incorporating this constraint can systematically identify alterations in cellular metabolism
activated in response to environmental change (Beg et al., 2007).
Similar to Beg et al (2007), (Zhuang, Vemuri, & Mahadevan, 2011) also predicts that a
trade off exists because of a crowding constraint. However in this case it was limited to
the membrane enzymes. They hypothesize that the outcome of a competition for
membrane space between glucose transporters and respiratory chain, which they refer to
as economics of membrane occupancy, proteins influences respiration and fermentation.
By incorporating a sole constraint based on this concept in the genome-scale metabolic
model of E. coli, they were able to simulate respirofermentation. Further analysis of the
impact of this constraint revealed differential utilization of the cytochromes and faster
glucose uptake under anaerobic conditions than under aerobic conditions. Based on these
simulations, they propose that bacterial cells manage the composition of their
cytoplasmic membrane to maintain optimal ATP production by switching between
oxidative and substrate-level phosphorylation. As these results suggest that the membrane
occupancy constraint may be a fundamental governing constraint of cellular metabolism
and physiology, and establishes a direct link between cell morphology and physiology.
3. Experimental evidence
a. Metabolic constraint and social conflicts
The logic of this trade-off can be illustrated in Figure 1. Metabolic pathways, of course,
are made up of many reactions, only some of which produce ATP. Are tradeoffs between
rate and yield still present at the level of entire organisms? The simplest method to test
for a rate yield trade-off is to measure the yield of microbial cultures grown at different
resource uptake rates. Such experiments consistently find evidence of a trade-off between
the rate and yield of entire metabolic pathways (Beardmore et al., 2011; Kreft, 2004;
Weusthuis, Pronk, van den Broek, & van Dijken, 1994). For example, a very convincing
trade-off between the rate and yield of glucose metabolism has been demonstrated in the
yeast Saccharomyces cerevisiae (Figure 2a). Evidence that the rate versus yield trade-off
acts as an evolutionary constraint, and not just a physiological constraint, comes from the
observation that the rate and yield of glucose metabolism are negatively correlated among
species of yeasts (Figure 2b) (MacLean, 2008).
a
b
Figure 2. Plotted points in panel a show the rate and yield of glucose metabolism in
glucose-limited chemostat cultures of Saccharomyces cerevisiae. Data taken from Postma
et al. (1989). Plotted points in panel b show the rate and yield of glucose metabolism in
exponentially growing cultures of yeast species. Data are taken from Merico et al. (2007).
Species that ferment glucose to produce ethanol are shown with open symbols and those
species that do not produce ethanol are shown with filled symbols. The negative
correlation between the rate and yield of metabolism is significantly different from zero
after correcting for phylogeny, as revealed by comparing the sign of the correlation
between the rate and yield of metabolism between sister taxa (P = 0.03). Figure taken
from (MacLean, 2008).
The figure 2b looks interesting and it suggests that trade-off could be fundamental and
independent of the specific characteristics of the organisms. However, the data used to
plot this figure are obtained from different studies and grown in different medium.
Therefore, if these strains are allowed to adapt in the same medium they might not fall on
the same point on the hypothetical yield-rate trade-off line.
Evolutionary experiment by Novak et al (2006)
Novak et al. (2006) assayed the rate and yield of glucose metabolism in populations of E.
coli that were propagated in a spatially homogeneous glucose-limited environment under
strong selection for increased growth rate for 20,000 generations. Initially, populations
increased both the rate and yield of glucose metabolism and, after 20,000 generations of
selection, no evidence of a rate-yield trade-off could be found by comparing the mean
growth rate and yield of 12 replicate populations (Figure 3a and b). However, assays of
clones isolated from 4 focal populations after 20,000 generations of selection revealed
conclusive evidence of a trade-off between the rate and yield of growth in all 4
populations (Figure 3c).
Novak et al. (2006) explain these results as follows. The ancestor that was used to start
this experiment was poorly adapted to its environment and was able to increase both its
growth rate and yield because it had never been strongly selected for either rate or yield
in its recent evolutionary past. Populations diverged during the course of experiment,
because chance and epistasis resulted in the fixation of different beneficial mutations in
different replicate populations (Travisano et al., 1995). The negative genetic correlation
between rate and yield within populations provides evidence of the existence of a tradeoff between the rate and yield of ATP production, but the lack of a negative correlation
between populations suggests that this constraint was in part attributable to mechanistic
constraints imposed by the different adaptations to glucose limitation in different
populations. In other words, although all 12 of these populations faced the same
underlying thermodynamic constraints on the rate and yield of ATP production, the
actual trade-offs that emerged were dictated by both a common thermodynamic
constraint and by a population-specific constraint that emerged as a consequence of the
unique evolutionary history of each population. This is an interesting hypothesis that
deserves further experimental tests. An interesting finding of this study is that within
populations, genetic variation in rate and yield can be maintained over long time scales
(Figure 3c).
Figure 3: Long-term evolution of rate and yield in experimental populations of E. coli. Plotted points show
the rate (panel a) and yield (panel b) of glucose metabolism in 12 populations of E. coli that were selected
in glucose-limited batch cultures over a period of 20,000 generations. In (a) and (b) dashed lines show the
regression of rate or yield against time, after accounting for the rapid initial increase in both rate and yield
in the first 1000 generations of selection and error bars represent standard errors. Plotted points in panel c
show the rate and yield of individual clones sampled from one population after 20 000 generations of
selection and the dashed line shows a linear regression of rate against yield. Similar results were found in
other populations. Figure taken from Novak et al. (2006).
They also explain that the ancestor or parent strain follows diverse pathways of
adaptation toward a hypothetical trade-off line. When a population is placed in a new
environment where faster growth is selectively favoured, it may initially be far from the
hypothesized trade-off curve. Figure 4 illustrates several different hypothetical scenarios
for the evolutionary approach to a trade-off between growth rate and yield (Novak et al.,
2006).
Figure 4:
A, over evolutionary time, increases in growth rate could be associated with
decreases in yield (path 1). On the other hand, if the population starts with a growth yield
that is below the eventually attained yield on the trade-off line, then yield and rate may
both increase over evolutionary time (path 2). B, Independently evolving populations. A
trade-off between the traits measured in independently evolving populations may be
observed if all of them eventually achieve states that are either on or sufficiently close to
the trade-off line. C, Shape of the trade-off function. The trade-off between growth rate
and yield is not necessarily a linear relation (solid line). As shown previously
(Bonhoeffer; Pfeiffer 2002), the thermodynamic trade-off implies a concave shape with a
maximal rate (dashed line). Once the phenotype has achieved this rate, it cannot further
increase the rate at the cost of yield. The presence of pathways with opposing properties
in rate and yield (such as complete oxidation of glucose vs. degradation into acetate)
implies a convex shape (dotted line). Here, to observe the trade-off might be difficult
because, given a sufficiently high initial rate, any increase in rate may have only small
costs in yield. D, Mechanistic constraints. The biochemical mechanisms of ATP
production may further influence the simultaneous evolution of growth rate and yield
(dashed lines). As a consequence, replicate populations may evolve different biochemical
solutions that adapt them to the same experimental environment. Thus, they may evolve
toward different fitness peaks, so that each population then faces somewhat different
mechanistic constraints. Similarly a case study was done by MacLean and Gudelj where
they have used only Respiratory and respire-fermentative strain of Yeast. Figure and
legend from (Novak et al., 2006).
Their results indicate that, at least for the populations they studied, an analysis of the
within-population diversity might be the most sensitive test for the existence of a tradeoff. Because the observation of a trade-off within, but not between, populations suggests
that the populations evolved different genetic solutions for growth in the selective
environment, which in turn led to different physiological constraints (Novak et al. 2006).
Yield-rate trade-off in multicellular organisms
Another possible example of yield-rate trade-off was observed by Guo et al (1991) in
eukaryotes. They have performed an experiment where the theories of density dependent
natural selection predict that evolution should favor those genotypes with the highest per
capita rates of population growth under the given density conditions. They have also
mentioned that these theories were not able to describe the exact mechanisms that may
give rise to these increases in density dependent growth rates. They have observed the
evolution of six populations of Drosophila melanogaster placed in crowded
environments after nearly 200 generations at low population density in the laboratory.
After 25 generations in those crowded cultures all six populations showed the predicted
increase in population growth rates at high-population density with the concomitant
decrease in their growth rates at low densities. They concluded the study by saying that
the detailed understanding of the mechanisms by which populations evolve under
density-dependent natural selection will provide a framework for understanding the
nature of trade-offs in life history evolution (Guo et al., 1991).
Schuetz et al (2012) propose that overflow metabolism (and metabolic regulation) in
general tries to maximize combinations of different objectives e.g. maximal yield,
maximal ATP production, including the ability to be able to adapt quickly from one
environmental condition to another. Therefore, metabolic regulation as it is a compromise
between these different goals.
Apart from experimental limitations, an additional problem we face in showing a
convincing experimental evidence for the existence of yield-rate trade-off is that we have
a limited time for evolutionary experiments in the lab and also we do not know that
during the timeline of an experiment when we will reach that hypothetical trade-off line.
Convergence of evolved strains (showed in Novak et al 2006) to a yield-rate trade-off
line would indicate that the trade-off exists; however, it is difficult to impose specific
selection factors for either yield or rate, or something in between.
.
4. Consequences of a trade-off
We presume that as a consequences of yield-rate trade-off in organisms we see overflow
metabolism in organisms. The name overflow metabolism itself describes that choosing
the fast and inefficient pathways to produce ATP instead of choosing slow but efficient
way to produce more ATP wastes energy. A few examples of overflow metabolism:
a. Acetate production in E.coli
b. Ethanol production in Yeast
c. Lactate production in lactic acid bacteria (LAB)
d. Warburg effect in cancer cells
Tragedy of the commons
Early studies suggest that under competition for a common resource, the strain with high
rate of ATP production always displaces the prudent strain with high yield of ATP
production. This reveals the potential for metabolic trade-offs to generate a tragedy of
commons. A cell using a pathway with high yield and low rate can produce more ATP
(and thus more offspring) from a given amount of resource. However, this advantage
disappears when the cell is in resource competition with cells that produce ATP at a
higher rate but a lower yield. While only those cells that consume the resource more
rapidly benefit from the higher rate of ATP production, all competitors exploiting the
resource share the consequences of the more rapid resource exhaustion (Beardmore et al.,
2011). Whenever individuals (microorganisms) have access to a common resource that
can be consumed either rapidly (fast growth rate) or efficiently (high growth yield) an
evolutionary dilemma is created: average fitness in a population is highest if all
individuals use common resources efficiently, but individual reproductive rate is
maximized by consuming common resources at the highest possible rate (MacLean,
2008). In an interesting paper, (Hardin, 1968) mentioned that this conflict selects for
increasingly selfish resource use, because the benefit an individual gains from increasing
its resource exploitation rate is much less than the cost it pays in terms of reduced
available resources, a scenario that he termed the ‘tragedy of the commons’. The logic of
the tragedy of the commons predicts that individual good will be maximized with
disastrous consequences for the population. In an extreme scenario, this social conflict
between the interest of individuals and the group could conceivably result in extinction of
some of the variants of the species. For example, in a heterogeneous population of a
species where one variant has a higher growth rate but uses the resources inefficiently
and the other variant has higher growth yield but slower growth rate, the former variant
will lose the competition for the common resource and they will disappear from the
population (MacLean, 2008). Similar example was showed experimentally by Bachmann
et al (2011) where he reports that the expression of an extracellular protease by the lactic
acid bacterium Lactococcus lactis, which degrades milk proteins into free utilizable
peptides that are essential to allow growth to high cell densities in milk. Cheating,
protease-negative strains can invade the population and drive the protease-positive strain
to extinction. By using multiple experimental approaches, as well as modeling population
dynamics, they demonstrate that the persistence of the proteolytic trait is determined by
the fraction of the generated peptides that can be captured by the cell before diffusing
away from it (Bachmann, Molenaar, Kleerebezem, & van Hylckama Vlieg, 2011).
5. Conclusion and future perspective
The metabolic rate-yield trade-off appears to be a universal feature of metabolic
pathways that creates a profound social conflict in microbial populations. Considerable
progress toward understanding how this conflict is resolved has been made by developing
mathematical models that integrate theoretical aspects of biochemistry with ecological
principles and testing these models using microbial selection experiments.
Furthermore, all the discussed mechanisms above, leading to a trade-off between rate and
yield, imply that organisms selected under different regimes will occupy different
positions on the yield trade-off line. In an extreme case one should be able to select for
either growth rate or growth yield and obtain completely different organisms. The growth
yield selected organism is called a cooperator by Pfeiffer et al (2001) for obvious reasons
that it benefits the population as a whole (maximal number of offspring).
Molenaar et al (2009) showed how the shift in metabolic efficiency originates from a
trade-off between investments in enzyme synthesis and metabolic yields for alternative
catabolic pathways. His model elucidates how the optimization of growth by natural
selection shapes growth strategies. From his study it is also clear that apart from the
thermodynamic constrains there are other constraints that provide an alternative
explanation for the existence of a yield-rate trade-off in microbial populations.
There has been a lot of simulation studies and experiments performed in order to give
convincing evidence on whether the yield rate trade off exists in living organism or not.
In addition, it may be difficult to conclude which constraints impose such a yield-rate
trade-off. As explained above that most living organisms operate far from
thermodynamic equilibrium, therefore, this fundamental thermodynamic constraint may
not be relevant for microorganisms and other constraints like metabolism is responsible
for such a yield-rate trade-off. Additionally, there are number of theoretical explanations
given for this phenomenon where they say that the yield maximization is very difficult
and need special environment to grow them. However, until now, convincing
experimental evidence has not been shown as it is very difficult to impose a single
selection regime in evolutionary experiments. Hence, pure selection on growth yield or
growth rate are difficult to implement. This could be achieved if we can
compartmentalize the cells individually and then perform an evolutionary experiment
with selective pressure for long enough to evolve strain that can be either high yield and
slow growing or high yield as well as fast growing. However, this type of
compartmentalization is difficult to obtain as multiple selection pressure can act on the
population.
There have been some extensive efforts made on developing such a yield-selection
protocol at the VU university Amsterdam (figure 4) to evolve a strain on the basis of high
yield selection by growing them in separate compartments isolated from other cells by oil
phase. The results obtained with such an experimental setup should help in obtaining
convincing evidence to clarify the existence and understanding of the yield-rate trade-off.
Figure 4: Schematics of Serial propagation performed in the laboratory. Serial propagation for strain
improvement is usually done in suspension and leads to the selection of spontaneous mutants that are fast
but metabolically inefficient (panel a). In panel a and panel b the top parts show cultures directly after
inoculation. The bottom parts show the same cultures after they are fully grown. During laboratory
evolution, cultures will be diluted and used for the inoculation of the next step. If droplets in emulsions are
initially occupied (inoculated) with a single cell and the incubation times are long enough, metabolically
efficient but slow growing mutants will be able to grow to a higher cell density in the droplet as the wild
type strain. If the emulsion is subsequently broken, diluted and used to inoculate a new emulsion one can
enrich for metabolically efficient strains (panel b) Figure taken from Bachmann et al (2011).
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