Fig. 4: Geometrical analysis of the optimal enzyme configuration in a system with two sites.
From: Optimal spatial allocation of enzymes as an investment problem
Dashed black lines show lines of constant ET = e1 + e2, while dashed green lines show lines of constant reaction flux \({J}^{{{{{{{{\mathcal{P}}}}}}}}}\). The optimal configuration \({{{{{{{{\bf{e}}}}}}}}}^{* }=({e}_{1}^{* },{e}_{2}^{* })\) for each value of ET forms an optimal trajectory e*(ET) (orange). Green arrows show the marginal returns vector \(\frac{d{J}^{{{{{{{{\mathcal{P}}}}}}}}}}{d{{{{{{{\bf{e}}}}}}}}}\). The tangent vector \(\frac{d{{{{{{{{\bf{e}}}}}}}}}^{* }}{d{E}_{{{{{{{{\rm{T}}}}}}}}}}\) (blue arrows) shows how added enzymes should be optimally partitioned between the two sites.
