Fig. 5: Two-dimensional model system to illustrate the HMR criterion and the application of the additive construction scheme for optimal enzyme arrangements.
From: Optimal spatial allocation of enzymes as an investment problem
The system has an absorbing outer boundary and three inner compartments that act as substrate sources (dashed rectangles). a Optimal enzyme density e(x, y) (grayscale) at two different total enzyme amounts (ET = 40 and 400), calculated using the construction scheme. The colored squares indicate positions at which e(x, y) is analyzed in b, c as a function of ET, to illustrate the HMR criterion. b Optimal enzyme densities and c ratios of marginal returns at the positions indicated by colored squares in a. When a ratio of marginal returns reaches one, a new position becomes occupied with enzymes (correspondence marked by dashed lines). d The flux gain of the optimized enzyme arrangement (flux Jopt) relative to a uniform arrangement (Juniform, orange) and a fully bound arrangement (Jbound, cyan), as a function of ET. The flux Juniform is produced by uniformly distributing the enzymes in the whole system, whereas Jbound is for all enzymes evenly distributed over the boundaries of the substrate sources. e Percentage of extra enzymes, ΔET/ET, required in the uniform (orange) and bound (cyan) configuration to obtain the same flux as the optimal enzyme arrangement, as a function of ET.
