Phosphorylated PPPSPXS peptides inhibit β-catenin phosphorylation by GSK3 in vitro.

<p><i>A</i>. The HA, Phos-E, Phos-C, Phos-D and Phos-A peptides (left panel) and the HA, Phos-A, and A-mut peptides (right panel) were included in the β-catenin phosphorylation assay. Each peptide was at 10 µM final concentration. <i>B</i>. Four-fold serial dilutions of HA, Phos-A, and A-mut peptides were included in the β-catenin phosphorylation assay. <i>C</i>. Four-fold serial dilutions of Phos-A, and 14-3-3BP peptides were included in the β-catenin phosphorylation assay. <i>D</i>. Four-fold serial dilutions of HA, Phos-E, Phos-A, Phos-C, and Phos-D peptides were included in the β-catenin phosphorylation assay. <i>E</i>. The result from D was quantified via Adobe Photoshop. β-catenin phosphorylation assays were performed in the presence of Axin and CK1 as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004926#pone-0004926-g001" target="_blank">Figure 1C</a>. Each peptide was at 10 µM, 2.5 µM, 0.63 µM, and 0.16 µM (four-fold serial dilutions) final concentration. The phosphorylation reaction products were analyzed by western blotting using an anti-phospho-Ser33/Ser37/Thr41 β-catenin antibody and an anti-β-catenin antibody.</p

Data_Sheet_5_Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown.PDF

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.</p

Data_Sheet_4_Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown.PDF

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.</p

Image_1_Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown.JPEG

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.</p

Image_3_Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown.JPEG

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.</p

A working model for LRP6 inhibition of β-catenin phosphorylation by the Axin-GSK3 complex.

<p>While one of the five phosphorylated PPPSPXS motifs of LRP6 physically interacts with Axin, other phosphorylated PPPSPXS motifs may directly inhibit GSK3 phosphorylation of β-catenin in the Axin complex. Axin-binding to motif C is drawn arbitrarily. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004926#s3" target="_blank">Discussion</a> for details.</p

The inhibition of β-catenin phosphorylation by phosphorylated PPPSPXS peptides is specific for GSK3 and independent of Axin function.

<p><i>A</i>. Different Axin constructs used in this study, the full length Axin (amino acid 1–863), AxinΔDix (1-773), and Axin(351-701) are shown. <i>B</i>. Purification of the full length Axin, AxinΔDix, and Axin(351-701) proteins. These Flagged tagged Axin and Axin fragments were expressed in HEK293T cells, purified via M2 agarose (Sigma) resin, and eluted by 0.2 mg/ml Flag peptides. <i>C</i> and <i>D</i>. The Phos-A peptide inhibited GSK3 phosphorylation of β-catenin in the presence of the full length Axin, or AxinΔDIX (C), or Axin(351-701) (D). Four-fold serial dilutions of the Phos-A peptide were tested as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004926#pone-0004926-g003" target="_blank">Figure 3</a>. The A-mut peptide was added at the concentration equivalent to that of Phos-A without dilution (10 µM). The phosphorylation reaction products were analyzed using an anti-phospho-Ser33/Ser37/Thr41 β-catenin antibody. <i>E</i>. Inhibition of GSK3 phosphorylation of β-catenin by Phos-A was independent of Axin. Four-fold serial dilutions of the Phos-A peptide (10 µM, 2.5 µM, and 0.63 µM) were included in the β-catenin phosphorylation assay in the absence or presence of Axin. The A-mut peptide was added at the concentration equivalent to that of Phos-A without dilution (10 µM). The phosphorylation reaction products were analyzed using an anti-phospho-Ser33/Ser37/Thr41 β-catenin antibody. Note that in order to achieve and visualize β-catenin phosphorylation by GSK3 in the absence of Axin (lanes 1–5), 5-fold excess amount of GSK3 (2.2 µM) was employed compared to that in the presence of Axin (lanes 6–10), and the film was overexposed. <i>F</i>. β-catenin Ser45 phosphorylation by CK1 was not affected by Phos-A, used at 10 µM and 2.5 µM. A-mut was at 10 µM. The phosphorylation reaction products were analyzed using an anti-phospho-Ser33/Ser37/Thr41 β-catenin antibody and an anti-phospho-Ser45 β-catenin antibody.</p

In vitro reconstitution of Axin-dependent and CK1 priming-dependent β-catenin phosphorylation by GSK3.

<p><i>A</i>. Recombinant GST-β-catenin, Flag-CK1, MBP-Axin, and His-GSK3 proteins were expressed in bacteria or insect cells and purified by glutathione agarose, anti-Flag M2 agarose, amylose resin, or Ni-NTA resin, respectively. In the case of β-catenin, GST was cleaved via thrombin and purified away from β-catenin. * indicates each recombinant protein. <i>B</i>. β-catenin phosphorylation by CK1 was reconstituted in vitro using purified proteins. The phosphorylation reaction products were analyzed by western blotting using an anti-phospho-Ser45 β-catenin antibody. <i>C</i>. Axin-dependent phosphorylation by GSK3 was reconstituted in vitro using purified proteins. For Axin-dependent β-catenin phosphorylation in this and other figures, 0.43 µM of GSK3, 0.54 µM of CK1α, 0.21 µM of Axin, and 0.73 µM of β-catenin were used in each assay. The phosphorylation reaction products were analyzed by western blotting using an anti-phospho-Ser45 β-catenin antibody and an anti-phospho-Ser33/Ser37/Thr41 β-catenin antibody.</p

Image_2_Mathematical appraisal of SARS-CoV-2 Omicron epidemic outbreak in unprecedented Shanghai lockdown.JPEG

The SARS-CoV-2 Omicron outbreak is ongoing in Shanghai, home to 25 million population. Here, we presented a novel mathematical model to evaluate the Omicron spread and Zero-COVID strategy. Our model provided important parameters, the average quarantine ratio, the detection interval from being infected to being tested positive, and the spreading coefficient to understand the epidemic progression better. Moreover, we found that the key to a relatively accurate long-term forecast was to take the variation/relaxation of the parameters into consideration based on the flexible execution of the quarantine policy. This allowed us to propose the criteria for estimating the parameters and outcome for the ending stage that is likely to take place in late May. Altogether, this model helped to give a correct mathematical appraisal of the SARS-CoV-2 Omicron outbreak under the strict Zero-COVID policy in China.</p

Peptide design according to the PPPSPXS motifs in human LRP6.

<p><i>A</i>. Sequence alignment of the five PPPSPXS motifs in human LRP6 and LRP5 by the Cluster V program. The PPPSPXS motifs are highlighted in color and boxed. <i>B</i>. The sequences of synthetic peptides are shown. The PPPSPXS motifs in the peptides are underlined, and phosphorylated Ser/Thr residues are shown in italics. The C or K residue in the parenthesis at the amino terminus of peptides A, C, D, and E was introduced for protein conjugation purposes (during immunization for antibody production) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004926#pone.0004926-Tamai2" target="_blank">[34]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004926#pone.0004926-MacDonald1" target="_blank">[37]</a>.</p