Combinatorics of feedback in cellular uptake and metabolism of small molecules

Abstract

We analyze the connection between structure and function for regulatory motifs associated with cellular uptake and usage of small molecules. Based on the boolean logic of the feedback we suggest four classes: the socialist, consumer, fashion, and collector motifs. We find that the socialist motif is good for homeostasis of a useful but potentially poisonous molecule, whereas the consumer motif is optimal for nutrition molecules. Accordingly, examples of these motifs are found in, respectively, the iron homeostasis system in various organisms and in the uptake of sugar molecules in bacteria. The remaining two motifs have no obvious analogs in small molecule regulation, but we illustrate their behavior using analogies to fashion and obesity. These extreme motifs could inspire construction of synthetic systems that exhibit bistable, history-dependent states, and homeostasis of flux (rather than concentration).

Fig. 1.

Behavior of four entangled feedback loop motifs. Plots show the steady state values of s (middle column) and influx (σT = γEs + s, Right) as a function of σ. In all plots, the black curve shows the behavior for standard parameter values (see Materials and Methods). The red curve shows the behavior when only the transport loop is active, i.e., E = 1. The blue curve is produced by keeping T = 1, i.e., only the metabolism loop is active. The plots were made by two sweeps of the value of σ, the first from 0.1 to 1,000, and the second from 1,000 back to 0.1. At each σ value, we start E, T, and s concentrations at the previous steady-state values, and then integrate the equations until a new steady state is reached. Thus, for each σ, the plots contain information from two simulations, one starting from a lower value of s, the other from a higher. For systems where there is no bistability, the s and flux vs. σ curves for the two sweeps are identical. However, where there is some bistability, the two curves differ, i.e., they show hysterisis.

Fig. 2.

Schematic illustration of the consumer (+ − a) motif. This motif is found in the regulation of uptake and metabolism of, for example, maltose and arabinose (19, 20). σ and s denote, respectively, extra- and intracellular concentrations of the small molecule. The molecule binds to the regulator, R, forming the complex {Rs}, which activates production of transport proteins, T, and metabolic enzymes, E. γ is a parameter controlling the metabolic rate per enzyme (see Materials and Methods).

Fig. 3.

The main features of single and double loops. The figure lists first all four single loop motifs, followed by the four two-loop motifs of Fig. 1, along with the main characteristics of their steady state behavior. Those features of the two-loop motifs that are significantly different from a simple sum of the single loop behaviors are highlighted in yellow.