Our goal this year will be to better understand how a metabolic network responds to evolutionary pressure. The parts that make up a metabolic network are highly interdependent. The activity of an enzyme depends on the concentrations of its substrates and products, which in turn depend on the activities of the other enzymes in the metabolic network. The cell adds another level of complexity in that enzymes must share a fixed volume, collection of ribosomes, supply of ATP, NADH, etc. Mutations that change any component will necessarily affect the entire system in ways that are likely to be detrimental. Our aim will be to explore what effects these inter-dependencies can have on the course of evolution:

Given the unavoidably tangled interactions between the targets of mutations, how does a metabolic network ever manage to evolve? Do populations accumulate small mutations slowly, always adjusting for their side-effects, or can they find paths around these negative interactions? If we can predict these interactions (and we think we can) can we also predict how these populations will evolve?

Throughout, our approach to these questions will be both quantitative and experimental. Statistical computations and non-linear dynamics are just as important to understanding complex adaptive systems as are experimental manipulations and measurement.

Classical evolutionary theory focuses on the fate of mutations whose
contribution to fitness is predetermined. Yet the reasons behind
*why* a mutation is adaptive, and *how* a series of these mutations
leads to adaptation are extremely important. And in order to
understand these *why*’s and *how*’s, we need to treat organisms as
complex systems. Mutations cannot be dealt with simply by their
effects on fitness, we also need to understand *epistasis*: how
mutations change the system, and thereby change the effects of all
other potential mutations.

This semester we will work with a mathematical model of the inter-dependencies between several kinds mutations, then test its predictions by

- evolving populations of our model organism in the lab,
- and manipulating the physiology of our model organism to simulate the effects of possible mutations.

We will focus our attention on the the bacterium *Methylobacterium
extorquens*. This bug is famous for its lovely pink color and for
having a set of enzymes (figure 1) that allow it to get *all* of its
carbon and energy from methanol molecules! This is a rare ability,
and seems to show up in unexpected leaves of the tree of life.
*M. extorquens* is our model for understanding how methanol metabolism
works and how it evolves.

This network is small because we are treating most of the cell as one reaction, “Everything else”. We focus on the enzymes that handle methanol and its immediate derivatives because this is where the selective pressure is greatest. (In fact, we’ll be working with a mutant that the professor made which should further focus natural selection on these enzymes. Instead of its native enzymes, the mutant has 3 enzymes from a completely different bacterium which happen to do the same thing.) This huge reduction of complexity does two things: it reduces the number of targets for genetic screening and manipulations, and it lets us capture the system in a tractable mathematical model.

We will model system level effects of possible mutations.

We’ve been working with a kinetic model of the

*M. extorquens*network (figure 1). The rate of each enzyme catalyzed reaction is modeled by an ordinary differential equation which corresponds to the enzyme’s reaction mechanism. For example, this equation models the mechanism of formate dehydrogenase (FDH in figure 1):([FDH]*k*_{cat}([NAD^{ + }][CHOOH])/(*K*_{M1}*K*_{M2}))/(1 + ([ NAD^{ + }])/(*K*_{M1}) + ([ CHOOH])/(*K*_{M2}))You will use the model to generate predictions about what might happen when you change the expression of different enzymes in the metabolic network. Once you have chosen enzymes with interesting predictions, you’ll actually manipulate their expression experimentally! Then the challenge will be to use the data from your experiments to improve the model.

When taken together, the equations of the model define an adaptive landscape: a multidimensional space with one axis corresponding to a measure of fitness and the rest corresponding to the possible values of enzyme kinetic parameters. This is the structure that we are after.

**The fitness landscape captures the evolutionary consequences of the interdpendencies between different parts our our living system.**

We will mutate, then evolve populations of

*M. extorquens*to determine whether the predictions of model hold true.Replacing an enzyme’s native promoter with a weak constitutive promoter will result in under expression of the enzyme and reduced growth rate. This mutation is permanent and not directly reversible.

We will use the model to chose mutations that are likely to result in informative evolutionary trajectories and then make them and evolve them.

We will characterize the entire range of dependencies between the expression of different enzymes in our metabolic network.

We have a strain of

*M. extorquens*which expresses two transcriptional repressors. By adding operator sequences to the promoters of genes coding for the enzymes in the network, and varying inducer concentration across a range of levels, three-dimensional adaptive landscapes like the one in figure 1 can be constructed.This approach complements that of the evolutionary trajectories. It reveals a comparatively huge swath of the adaptive landscape and thus can be used to check the model and even fit kinetic parameters. It should also let us see what an adaptive landscape looks like when it is far from the optimum, to estimate the relative space of neutral variation, and to characterize the smoothness or roughness of the landscape.

[Dykhuizen1987] | Metabolic flux and fitness. DE Dykhuizen, AM
Dean, DL Hartl. Genetics. 1987 January; 115(1): 25–31. |