Design constraints on a synthetic metabolism

Abstract

A metabolism is a complex network of chemical reactions that converts sources of energy and chemical elements into biomass and other molecules. To design a metabolism from scratch and to implement it in a synthetic genome is almost within technological reach. Ideally, a synthetic metabolism should be able to synthesize a desired spectrum of molecules at a high rate, from multiple different nutrients, while using few chemical reactions, and producing little or no waste. Not all of these properties are achievable simultaneously. We here use a recently developed technique to create random metabolic networks with pre-specified properties to quantify trade-offs between these and other properties. We find that for every additional molecule to be synthesized a network needs on average three additional reactions. For every additional carbon source to be utilized, it needs on average two additional reactions. Networks able to synthesize 20 biomass molecules from each of 20 alternative sole carbon sources need to have at least 260 reactions. This number increases to 518 reactions for networks that can synthesize more than 60 molecules from each of 80 carbon sources. The maximally achievable rate of biosynthesis decreases by approximately 5 percent for every additional molecule to be synthesized. Biochemically related molecules can be synthesized at higher rates, because their synthesis produces less waste. Overall, the variables we study can explain 87 percent of variation in network size and 84 percent of the variation in synthesis rate. The constraints we identify prescribe broad boundary conditions that can help to guide synthetic metabolism design.

Figure 1. The number of required reactions increases with nutrient flexibility and biosynthetic ability.

The vertical axis shows the number of reactions in minimal networks as a function of a) nutrient flexibility and b) biosynthetic ability. Dots and length of error bars correspond to means and one standard deviation based on a sample of n = 50 minimal networks. Solid lines indicate linear regression lines for different values of B in a) and N in b). Numerical estimates of regression coefficients with 95% confidence intervals are given in the inset, in the format y = (a±e)x+b, where a is the regression coefficient, e the confidence interval, and b is the intercept of the regression line with the vertical axis.

Figure 2. Biosynthetic flux decreases with biosynthetic ability and increases with nutrient flexibility.

The vertical axis shows biosynthetic flux in mmoles per g DW per hour in random networks as a function of a) biosynthetic ability and b) nutrient flexibility. Dots and lengths of error bars correspond to means and one standard deviations based on a sample of n = 1000 minimal networks. Solid lines indicate linear regression lines for different values of B. Numerical estimates of regression coefficients with 95% confidence intervals are given in the inset, in the format y = (a±e)x+b, where a is the regression coefficient, e the confidence interval, and b is the intercept of the regression line with the vertical axis.

Figure 3. Waste production decreases with nutrient flexibility.

The vertical axis shows waste that is excreted carbon in mmoles per g DW hour in random networks as a function of nutrient flexibility. Dots and lengths of error bars correspond to means and one standard deviation based on a sample of n = 1000 minimal networks. Solid lines indicate linear regression lines for different values of B. Numerical estimates of regression coefficients with 95% confidence intervals are given in the inset.

Figure 4. Synthesis of biochemically related compounds require less reactions, achieve higher biosynthetic flux with less waste.

Box-plot of a) number of reactions, b) biosynthetic flux in mmoles per g DW hour, and c) waste in mmoles per g DW per hour in minimal networks synthesizing twenty amino acids (left panel) and synthesizing twenty random biomass molecules (right panel). Horizontal lines in the middle of each box mark the median. The edges of the boxes correspond to the 25th and 75th percentiles. Data is based on a sample of n = 80 for each box.

Figure 5. Exploration of a metabolic network space.

Metabolic networks can be viewed as subsets of enzyme-catalyzed metabolic reactions in a global reaction set. Formally, they can be represented as binary vectors listing the reactions catalyzed by enzymes in an organism, as indicated for two hypothetical metabolic networks (N1, N2) in the figure. Metabolic phenotypes are computed from metabolic networks using FBA. They can be represented as binary vectors indicating the carbon sources (i.e.: alanine, glucose, melibiose,…) on which a network is viable, that is, on which it can synthesize a given set of (biomass) molecules. Neighboring networks (blue circles linked by edges) differ by a single reaction swap (edges between circles) that leaves the metabolic phenotype unchanged. A reaction swap consists of two changes: one random reaction addition (R4 in the example) and one random reaction deletion (R3 in the example). A series of successful reaction swaps is called a random walk (indicated by red arrows). The Markov Chain Monte Carlo (MCMC) technique allows one to randomly sample networks with a given phenotype by generating long random walks through genotype space, where each step in a walk consists of a reaction swap. The advantage of using reaction swaps is that they leave the number of reactions constant.