Fig. 1.
Overview of the design algorithm. (a) Fractional occupancy shows a sigmoidal dependence on ∆G, the equilibrium free-energy change [Eq. (4)]. ∆Goffset is the free-energy offset at which the target state, for example, the bound receptor, is half occupied. The plot illustrates three regimes: left, high occupancy (95–100%) and low sensitivity, where the fractional occupancy remains largely unaffected by mutations that induce moderate changes in ∆G; middle, medium occupancy (5–95%) and high sensitivity, where there is significant change in the fractional occupancy due to changes in ∆G; and right, low occupancy (0–5%) and low sensitivity, where the fractional occupancy is negligible and remains thus despite moderate improvements in ∆G. (b) Venn diagram graphically demonstrates the Boolean operators AND, OR, and NOT. AND and OR gates act on two states X and Y, whereas the NOT gate acts on one state, X. All states are drawn as circles and the selected area is marked in stripes. (c) Boolean operators (NOT, AND, and OR) are used to integrate the variables into an optimization objective function. By defining the three fundamental logical operators, we can formulate arguments encoding combinations of physical properties, including where properties tradeoff with one another. (d) The design flow chart exemplified for designing for stability and ligand binding, in four steps: first, the relevant properties of the system (stability of individual components and affinities between components) are defined. Second, for each property, the steepness and offset are defined and the sigmoidal function is set [Eq. (6)]. Third, the objective function is calculated by integrating the sigmoidal functions using Boolean operators. Fourth, the objective function is used by simulated annealing Monte Carlo sequence optimization. (e) Fitness is a complex function of biomolecular properties (such as binding, stability, etc.) exemplified here as a function of sequence exchanges at two positions only; in reality, fitness is a function in n-dimensional space, where n is the number of mutable protein or RNA residues. The landscape's ruggedness is the outcome of the nonadditive fitness effects of mutations, the limited choice of natural amino acids, and of tradeoffs between different molecular properties.