Toolbox model of evolution of metabolic pathways on networks of arbitrary topology

In prokaryotic genomes the number of transcriptional regulators is known to quadratically scale with the total number of protein-coding genes. Toolbox model was recently proposed to explain this scaling for metabolic enzymes and their regulators. According to its rules the metabolic network of an organism evolves by horizontal transfer of pathways from other species. These pathways are part of a larger "universal" network formed by the union of all species-specific networks. It remained to be understood, however, how the topological properties of this universal network influence the scaling law of functional content of genomes. In this study we answer this question by first analyzing the scaling properties of the toolbox model on arbitrary tree-like universal networks. We mathematically prove that the critical branching topology, in which the average number of upstream neighbors of a node is equal to one, is both necessary and sufficient for the quadratic scaling. Conversely, the toolbox model on trees with exponentially expanding, supercritical topology is characterized by the linear scaling with logarithmic corrections. We further generalize our model to include reactions with multiple substrates/products as well as branched or cyclic metabolic pathways. Unlike the original model the new version employs evolutionary optimized pathways with the smallest number of reactions necessary to achieve their metabolic tasks. Numerical simulations of this most realistic model on the universal network from the KEGG database again produced approximately quadratic scaling. Our results demonstrate why, in spite of their "small-world" topology, real-life metabolic networks are characterized by a broad distribution of pathway lengths and sizes of metabolic regulons in regulatory networks.Comment: 34 pages, 9 figures, 2 table

Neratinib after trastuzumab-based adjuvant therapy in HER2-positive breast cancer (ExteNET): 5-year analysis of a randomised, double-blind, placebo-controlled, phase 3 trial

Background: ExteNET showed that 1 year of neratinib, an irreversible pan-HER tyrosine kinase inhibitor, significantly improves 2-year invasive disease-free survival after trastuzumab-based adjuvant therapy in women with HER2-positive breast cancer. We report updated efficacy outcomes from a protocol-defined 5-year follow-up sensitivity analysis and long-term toxicity findings. Methods: In this ongoing randomised, double-blind, placebo-controlled, phase 3 trial, eligible women aged 18 years or older (≥20 years in Japan) with stage 1–3c (modified to stage 2–3c in February, 2010) operable breast cancer, who had completed neoadjuvant and adjuvant chemotherapy plus trastuzumab with no evidence of disease recurrence or metastatic disease at study entry. Patients who were eligible patients were randomly assigned (1:1) via permuted blocks stratified according to hormone receptor status (hormone receptor-positive vs hormone receptor-negative), nodal status (0 vs 1–3 vs or ≥4 positive nodes), and trastuzumab adjuvant regimen (given sequentially vs concurrently with chemotherapy), then implemented centrally via an interactive voice and web-response system, to receive 1 year of oral neratinib 240 mg/day or matching placebo. Treatment was given continuously for 1 year, unless disease recurrence or new breast cancer, intolerable adverse events, or consent withdrawal occurred. Patients, investigators, and trial funder were masked to treatment allocation. The predefined endpoint of the 5-year analysis was invasive disease-free survival, analysed by intention to treat. ExteNET is registered with ClinicalTrials.gov, number NCT00878709, and is closed to new participants. Findings: Between July 9, 2009, and Oct 24, 2011, 2840 eligible women with early HER2-positive breast cancer were recruited from community-based and academic institutions in 40 countries and randomly assigned to receive neratinib (n=1420) or placebo (n=1420). After a median follow-up of 5·2 years (IQR 2·1–5·3), patients in the neratinib group had significantly fewer invasive disease-free survival events than those in the placebo group (116 vs 163 events; stratified hazard ratio 0·73, 95% CI 0·57–0·92, p=0·0083). The 5-year invasive disease-free survival was 90·2% (95% CI 88·3–91·8) in the neratinib group and 87·7% (85·7–89·4) in the placebo group. Without diarrhoea prophylaxis, the most common grade 3–4 adverse events in the neratinib group, compared with the placebo group, were diarrhoea (561 [40%] grade 3 and one [<1%] grade 4 with neratinib vs 23 [2%] grade 3 with placebo), vomiting (grade 3: 47 [3%] vs five [<1%]), and nausea (grade 3: 26 [2%] vs two [<1%]). Treatment-emergent serious adverse events occurred in 103 (7%) women in the neratinib group and 85 (6%) women in the placebo group. No evidence of increased risk of long-term toxicity or long-term adverse consequences of neratinib-associated diarrhoea were identified with neratinib compared with placebo. Interpretation: At the 5-year follow-up, 1 year of extended adjuvant therapy with neratinib, administered after chemotherapy and trastuzumab, significantly reduced the proportion of clinically relevant breast cancer relapses—ie, those that might lead to death, such as distant and locoregional relapses outside the preserved breast—without increasing the risk of long-term toxicity. An analysis of overall survival is planned after 248 events