Fig. 3.

Uneven allocation of dissipation maximizes flux in a three-state FL cycle. Dissipation allocations $\mathrm{\Delta }{\omega }_{12}^{\ast }$ (solid curves), $\mathrm{\Delta }{\omega }_{23}^{\ast }$ (dashed), and $\mathrm{\Delta }{\omega }_{31}^{\ast }$ (dotted) for the three transitions in Fig. 1B that maximize the flux. Dissipations are expressed as differences $\mathrm{\Delta }{\omega }_{ij}^{\ast }\equiv {\omega }_{ij}^{\ast }-\frac{1}{3}{\omega }_{\text{tot}}$ from the naive allocation of equal dissipation $\frac{1}{3}{\omega }_{\text{tot}}$ to each transition. $k_{23}^0=k_{31}^0=1$ is fixed, and $k_{12}^0$ varies with color. When $k_{12}^0=1$ (black), an even allocation of dissipation to each transition maximizes flux, and therefore, $\mathrm{\Delta }{\omega }_{ij}^{\ast }=0$ for all ${\omega }_{\text{tot}}$. As $k_{12}^0$ increases (black $\to$ red $\to$ blue $\to$ green), the flux-maximizing allocation increasingly deviates from an even allocation as shown by the increasing magnitude of $\mathrm{\Delta }{\omega }_{ij}^{\ast }$. Allocations at limiting ${\omega }_{\text{tot}}$ are shown by circles [low ${\omega }_{\text{tot}}$ plotted at ${\omega }_{\text{tot}}=0$ (Eq. 11); high ${\omega }_{\text{tot}}$ at ${\omega }_{\text{tot}}=\mathrm{\infty }$ (Eq. 13)]. The vertical dotted orange line at ${\omega }_{\text{tot}}=20$ represents the ATP hydrolysis free energy under physiological conditions.