Accurate prediction of cellular co-translational folding indicates proteins can switch from post- to co-translational folding

Abstract

The rates at which domains fold and codons are translated are important factors in determining whether a nascent protein will co-translationally fold and function or misfold and malfunction. Here we develop a chemical kinetic model that calculates a protein domain's co-translational folding curve during synthesis using only the domain's bulk folding and unfolding rates and codon translation rates. We show that this model accurately predicts the course of co-translational folding measured in vivo for four different protein molecules. We then make predictions for a number of different proteins in yeast and find that synonymous codon substitutions, which change translation-elongation rates, can switch some protein domains from folding post-translationally to folding co-translationally--a result consistent with previous experimental studies. Our approach explains essential features of co-translational folding curves and predicts how varying the translation rate at different codon positions along a transcript's coding sequence affects this self-assembly process.

Figure 1. Illustration of the pulse-chase experiment.

(a) A schematic representation of the relevant protein segments of WT SFVP. Residues 1–267 correspond to the segment known as C protein. The other three protein domains are collectively referred to as p97. (b) The crystal structures of the three protein segments for which co-translational folding curves were predicted in this study. In each case, the co-translational folding domain whose behaviour is predicted is coloured blue. Top left, C protein of SFVP. Bottom left, the FRB domain. Right, HA1 (ref. 65), for which the co-translational folding of residues 53–275 was experimentally monitored. (c) Pulse-chase experiments proceed in a step-wise manner as described in the main text. Ribosomes (grey circles) engaged in the translation of an mRNA (light green line) incorporate radiolabelled (red dots) and unlabelled (blue dots) amino acids into nascent proteins. Only those nascent chains that contain labelled amino acids (red segments) can be experimentally observed.

Figure 2. The co- and post-translational protein folding reaction scheme that equation (2) solves.

Initiation of translation of a transcript occurs at a rate k_int. At each codon position i the probability that the nascent chain segment of interest folds depends on the rates of folding, unfolding and codon translation. At short nascent chain lengths a domain within the nascent chain is not sterically permitted to fold due to the confining environment of the ribosome exit tunnel, and therefore at these lengths the rates of folding and unfolding are defined to be zero. When the domain has emerged from the exit tunnel it can fold and unfold with rates k_F,i and k_U,i. Once the nascent chain has been released from the ribsome it will fold and unfold post-translationally with the bulk folding and unfolding rates k_F and k_U. Note well that this picture does not convey that equation (2) accounts for the time-dependent fraction of radiolabelled nascent chains at codon i.

Figure 3. Comparison between the predicted and experimentally measured SFVP co-translational folding curves.

Probabilities of co-translational folding calculated using equation (2) (red triangles) and experimentally measured using pulse-chase labelling (open blue squares) for the WT (a) and ΔC mutant (b) of SFVP. Error bars for the experimental results were not reported, and so error bars were estimated as the average s.d. from the mean from three independent pulse-chase experiments carried out under similar experimental conditions (see Methods section). To match the convention used in the experiment, the predicted co-translational folding curve was shifted such that the start of the chase is at t=0. WT: R²=0.96, P=0.0001; ΔC mutant: R²=0.99 P=1 × 10⁻⁶.

Figure 4. Comparison between the predicted and experimentally-measured FRB and HA1 co-translational folding curves.

(a) The co-translational folding probability calculated with Supplementary equation (1) (black line) and the experimentally-measured fraction folded using FactSeq (blue circles) for (a) FRB, HA1 using antibody binding epitope (b) H28-E23 and (c) Y8-10C2 are shown. Regions I, II and III, as described in the main text, are indicated, respectively, by the shaded regions in green, blue and red. (d) The median values of the FactSeq-measured P_F,B(i) in Regions I, II and III are shown with bootstrapped error bars for FRB, H28-E23 and Y8-10C2.The statistical significance of the P_F,B(i) values was determined using the Mann–Whitney U-Test. Region I versus Region II: FRB: P=0.078, H28-E23: P=0.1933 and Y8-10C2: P=0.4471. Region III versus Region I: FRB: P=5.04 × 10⁻¹¹, H28-E23: P=2.56 × 10⁻¹¹ and Y8-10C2: P=9.11 × 10⁻⁸. Region III versus Region II FRB: P=3.2 × 10⁻⁹, H28-E23: P=2.75 × 10⁻¹⁵ and Y8-10C2: P=8.98 × 10⁻¹¹. Hence, the experimental data from FactSeq are consistent with the predicted co-translational folding curves in panels a, b, and c of this figure.

Figure 5. Sensitivity analysis of the predicted co-translational folding curve of ΔC SFVP to changes in the number of residues that fit inside the ribosome, k_A,i, k_F,i and k_U,i

(a) Co-translational folding curves calculated using k_F,i values of 0.02, 2, 20 or 200 s⁻¹ in equation (2) are plotted alongside the experimental time course (blue squares, panels a, b, c, and d. (b) Co-translational folding curves calculated using k_U,i values of 43.0, 4.34 × 10⁻⁴, 4.34 × 10⁻⁵ and 4.34 × 10⁻⁶ s⁻¹. (c) Co-translational folding curves for the cases of the ribosome exit tunnel including 20 (green triangles), 30 (red squares) or 40 (blue diamonds) amino acids. (d) Co-translational folding curves calculated using global codon translation rates of 7.6 (purple diamonds), 3.9 (red triangles) or 1.9 AA per second (green circles).

Figure 6. Effects of variable codon translation rates on the predicted co-translational folding curve for ΔC SFVP.

The predictions made using equation (2) with translation rates measured by Gardin et al. for yeast (green squares), Stadler and Fire for yeast (purple diamonds), Dana and Tuller for yeast (light blue triangles), Dana and Tuller for C. elegans (gold circles), and predicted by the Fluitt–Viljoen model for yeast (red circles) are displayed alongside the experimental (open blue squares) values with their associated error bars (see Fig. 3 and Methods section). The various translation-rate sets used are listed in Supplementary Table 1.

Figure 7. Synonymous codon substitutions can switch some yeast protein domains from post- to co-translational folding according to equation (2).

(a) Top panel. The probability of folding as a function of the chase time for domain 1 of DHOM predicted using equation (2). Calculations were performed for both the WT transcript (red solid line) and the transcript in which all codon positions were substituted with their slowest-translating synonymous codon (solid blue line). In the same panel is plotted the time-dependent fraction of full-length protein (see Methods section) synthesized from the WT (red dashed line) or the slow-translating (blue dashed line) transcript. (a) Bottom panel. The fraction of DHOM molecules whose first domain folds co-translationally when synthesized from the WT (red) or slowest-translating (blue) transcript. (b) Same as a but for domain 1 of SBA1. (c) Additional probabilities of co-translational folding for domain 6 of EF2 (top) and domain 2 of DPP3 (bottom) for their WT and slowest-translating transcripts. Dashed grey lines separate the co- and post-translational folding classes.