Correction for Kirby et al., Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity

Biophysics and Computational Biology Correction for “Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity,” by Duncan Kirby and Anton Zilman, which published May 16, 2023; 10.1073/pnas.2212795120 (Proc. Natl. Acad. Sci. U.S.A. 120, e2212795120).

The authors note that Figs. 2B and 4C appeared incorrectly:

Fig. 2.

Proofreading does not improve the SNR or specificity. (A) The SNR 〈n〉/σ_n for a KPR receptor as a function of the number of proofreading steps N and proofreading strength g = k_off,₁/k_f, with k_onc/k_p = 1, k_f/k_p = 1, k_pt = 100, and k_off,2 = 0.1 k_off,1. (B) The noisy signal (units of molecules per receptor) in response to two different ligands, 〈n〉 ± σ_n, as a function of the number of proofreading steps. Here, we have set k_onc/k_p = 1, k_f/k_p = 1, k_pt = 100, k_off,1/k_p = 3 and k_off,2/k_p = 1.5. Our choice of parameters emphasizes the point that noise in the signals grows faster (with N) than the mean signals separate. (C) The specificity as a function of proofreading strength g and number of proofreading steps N, using the same parameters as (A).

Fig. 4.

Classification performance is best for a small number of weakly proofread steps. (A) The fold-change in resolution achieved by KPR as a function of the number of proofreading steps, N, but for the alternative KPR schemes discussed in Section 1F: the burst type output model (red) and the burst model with fixed residence time, τ = 1/k_off, in the final receptor state (yellow). For the fixed residence time model, resolution is shown at proofreading strengths g_weak = 3 (dashed) and g_weak = 10 (solid). The burst size is 10, k_off,1/k_off,2 = 0.1, k_f/k_onc = 2(6.7) for the strong (weak) proofreading, and k_onct = 500. (B) The ligand resolution measured as ${\eta }_{\text{FLD},\mathrm{n}}={(\langle n\rangle \left(k_{\text{off},1}\right)-\langle n\rangle \left(k_{\text{off},2}\right))}^2/({\sigma }_{n,1}^2+{\sigma }_{n,2}^2)$ of the fully stochastic KPR receptor model at short times. The HN resolution is provided for reference (black). The resolution increases at longer times because receptor output accumulates and thereby reduces shot noise that otherwise obscures ligand resolution. However, the resolution enhancement decreases for N > 1 (more than one proofreading step), the same trend as was observed at long times (Fig. 3C). (C) The probability of erroneous activation relative to the total probability of activation, as a function of the number of proofreading steps N, for proofreading strength g = 10 (purple) versus g = 3 (green) for one receptor. Parameters: k_pt = 100, k_onc/k_p = 1, k_off,1/k_p = 1, k_off,2/k_p = 0.3 (0.5), and k_f/k_p = 0.1 (0.33) for the stronger (weaker) proofreading strength. Probabilities have been estimated via Gillespie stochastic simulation.

“In Fig. 2B, due to a plotting error, the boundaries of the SD regions are shown to be narrower than should be for the parameters in the figure.

Inadvertently, the image in Fig. 4C corresponded to the condition P(n(k_off,weak, c) > n*) = 0.1 rather than P(n(k_off,strong, c) > n*) = 0.1 as stated in the text. This corresponds to a scenario where the cell is interested in maximizing the fraction of the true positives (sensitivity) while keeping the false positives at a certain threshold, which was not discussed in the paper. It also contained numerical inaccuracies. The correct version of Fig. 4C, corresponding to the condition described in the text, is illustrated in the corrected Fig. 4C below, with the threshold P(n(k_off,strong, c) > n*) = 0.2.

Accordingly, the sentence on page 8, left column, fourth full paragraph: ‘The threshold is set to a value such that the probability of activation by the strongly binding ligand is 10%: P(n(k_off,strong, c) > n*) = 0.1 (the results are robust with respect to the specific choice of this value).’ has been replaced with: ‘The threshold is set to a value such that the probability of activation by the strongly binding ligand is 20%: P(n(k_off,strong, c) > n*) = 0.2 (the results are robust with respect to the specific choice of this value).’

These corrections do not affect the main results and conclusions of the paper that intrinsic noise severely limits the effectiveness of KPR for accurate ligand discrimination.

The authors thank Vahe Galstyan and Fangzhou Xiao for alerting us to the mismatch between Figs. 2B and 4C and their description in the text.”

The corrected figures and their legends appear below. The online versions have been corrected. The corrected code has been uploaded to the GitHub repository.