Fig 1.
Model of glycoprotein quality control via the chaperone binding cycle.
Pg represents the monoglucosylated proteins, Pc the unfolded chaperone-bound proteins, Pcf the folded chaperone-bound proteins, P the proteins lacking a glucose tag, Pb the background proteins, and Pcb the chaperone-bound background proteins.
Table 1.
Model protein concentrations, parameters, and performance metrics.
Fig 2.
Quality control engenders a trade-off between folding accuracy, speed, and energy.
(A) Shaded regions in the phase diagram represent all combinations of folding fraction f and total steady-state unfolded protein Punfolded that can be achieved by varying cycle parameters kc, k-c, kr, k-r, kg, k-g, and kd while keeping a fixed folding rate kf, production rate kpt, misfolded fraction mf, and background protein concentration Pb. Solid lines represent the maximal achievable folding fraction fmax. Dots represent the efficiency metric . (B) Each curve adjusts kc, k-c, kr, k-r, kg, k-g, and kd to maximize the folding fraction (Eq 2) while the total cycle energy (Eq 3) is varied and the total unfolded protein
is constrained to equal one. Each curve shows a distinct level of background proteins Pb, with fixed kpt = 0.1, kf = 0.1, and mf = 0.001 for all curves.
Fig 3.
Untagged protein binding and reversible chaperone binding can be disadvantageous.
(A) Maximal achievable folding fraction at fixed unfolded protein, Punfolded = 1, plotted versus the untagged rebinding rate k-r, as cycle parameters kc, k-c, kr, kg, k-g, and kd are free to vary. Other curves show similar behavior when folding and production rates are altered. (B) Folding efficiency is plotted as a function of unbinding rate k-c. Cycle parameters kc, kr, kg, k-g, and kd are free to vary. Folding rate kf and production rate kpt are held constant as indicated. The misfolding fraction is set to mf = 0.001.
Fig 4.
Physiological model for glycoprotein quality control outperforms other models.
(A) Schematic of cyclic and non-cyclic models. The physiological model corresponds to the consensus description of the glycoprotein quality control pathway. (B) Ratios of folding efficiency comparing performance of all models to the physiological model. Curve color indicates the model being compared, with solid lines for mf = 0.001 and dashed lines for mf = 0.4. For all curves, kf = 1.
Fig 5.
Optimal performance and corresponding parameters.
Maximum folding fraction fmax at Punfolded = 1, (blue curves, left blue vertical axis), and corresponding optimal rate constants, ki (red curves with markers, right red vertical axis) as cycle conditions are varied for the physiological model. (A) varies protein production rate kpt for fixed mf = 10−3 and kf = 1, (B) varies protein folding rate constant kf for fixed mf = 10−3 and kpt = 0.9, and (C) varies misfolded fraction mf for fixed kpt = 0.7 and kf = 1.
Fig 6.
Robustness of quality control cycle to changing production rates.
(A) The folding fraction achieved with fixed rate constants is plotted as a fraction of the maximum achievable folding fraction fmax for Punfolded = 1 as the protein production rate kpt is varied. Fixed rate constants kc, kg, k-g, and kd are those that achieve fmax with mf = 0.001 at various protein production levels: kpt = 0.1 (red curves and star), kpt = 1 (green), and kpt = 10 (blue). (B) The Punfolded corresponding to the folding fractions in (A). (C) Analogous plot to (A), with rate constants fixed at the optimal values for specific kpt values, except that the degradation rate constant kd adjusts to maintain Punfolded = 1. If kd adjustment cannot achieve Punfolded = 1, then kd adjustment minimizes the difference from Punfolded = 1. (D) The Punfolded corresponding to the folding fractions in (C).