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Additional file 1.

Additional file 1. Section 1: Equations and codes for the multiple-route AuNPs PBPK model. Section 2: Methods on preliminary model calibration. Section 3: Methods on estimation of posterior parameter within Bayesian framework. Section 4: Model calibration results. Section 5. Sensitivity analysis methods. Table S1: Physicochemical characteristics of gold nanoparticles and dosing information of pharmacokinetic studies used in the PBPK model. Table S2: Physiological parameters used in the multi-route PBPK model for gold nanoparticles in rats. Table S3: Gold nanoparticle-specific parameters used in the PBPK model after various routes of administration in rats. Table S4: Posterior uncertainty distributions for the population mean (µ) and variance ( $${\Sigma }^{2}$$ Σ 2 ) of the PBPK model parameters following oral administration. Table S5: Posterior uncertainty distributions for the population mean (µ) and variance ( $${\Sigma }^{2}$$ Σ 2 ) of the PBPK model parameters following intravenous administration. Table S6: Posterior uncertainty distributions for the population mean (µ) and variance ( $${\Sigma }^{2}$$ Σ 2 ) of the PBPK model parameters following intratracheal instillation. Table S7: Posterior uncertainty distributions for the population mean (µ) and variance ( $${\Sigma }^{2}$$ Σ 2 ) of the PBPK model parameters following endotracheal inhalation for 23 nm AuNPs. Table S8: Normalized sensitivity coefficients (NSCs) of highly influential parameters after oral administration to 5 nm AuNPs. Table S9: Normalized sensitivity coefficients (NSCs) of highly influential parameters after intravenous (IV) administration to 5 nm AuNPs. Table S10: Normalized sensitivity coefficients (NSCs) of highly influential parameters after intratracheal instillation to 5 nm AuNPs. Table S11: Normalized sensitivity coefficients (NSCs) of highly influential parameters after inhalation administration to 23 nm AuNPs. Table S12: Final multivariate linear regression models describing relationships between the physicochemical properties of AuNPs and biodistribution parameters following oral gavage. Table S13: Final multivariate linear regression models describing relationships between the physicochemical properties of AuNPs and biodistribution parameters following intratracheal instillation. Table S14: Main physicochemical characteristics of the AuNPs in the selected pharmacokinetic studies used for model evaluation in this study. Table S15: Model-predicted and measured amount of AuNPs in blood, GI, Kidneys, Liver, Lungs and spleen. Figure S1: Schematic diagram of the multi-route physiologically based pharmacokinetic (PBPK) model for 1.4, 5, 18, 23, 80, and 200 nm gold nanoparticles (AuNPs) in adult rats. Figure S2: PBPK model simulation results compared with 24-h IV-based pharmacokinetic data of 1.4, 5, 18, 80, and 200 nm AuNPs in healthy rats. Figure S3: PBPK model simulation results compared with 24-h pharmacokinetic data of 5, 18, 80, and 200 nm AuNPs in rats following oral gavage. Figure S4: PBPK model simulation results compared with 24-h pharmacokinetic data of 5, 18, 80, and 200 nm AuNPs in rats following oral gavage. Figure S5: PBPK model calibration with 28-d pharmacokinetic data in rats after inhalation of 23 nm aerosolized AuNPs via endotracheal tube for 2 h. Figure S6: PBPK model calibration results with pharmacokinetic data of 1.4, 5, 18, 80 and 200 nm AuNPs in rats after intravenous injection. Figure S7: PBPK model calibration results with pharmacokinetic data of 5, 18, 80 and 200 nm AuNPs in rats after oral administration. Figure S8: PBPK model calibration results with pharmacokinetic data of 1.4, 5, 18, 80 and 200 nm AuNPs in rats after intratracheal instillation. Figure S9: Heat map plot of the normalized sensitivity coefficient (NSC) for comparative sensitivity analyses for 18, 80 and 200 nm AuNPs at 24 h and 672 h following oral administration, IV injection, and IT instillation. Figure S10: Comparisons of model prediction (x-axis) with observed data (y-axis) for the validation datasets. Section 8: Tutorial for Nano-iPBPK interface. Section 9: Supplementary references.

In Fig. 3h of this Article, along the bottom row labelled ‘IL-2’, the third lane (above the ‘WT’ bracket) should be a plus and not a minus symbol, and the fourth lane (above the ‘Aim2-/-’ bracket) should be a minus and not a plus; from left to right, the symbols for the ‘IL-2’ row should therefore be: ‘- - + - - +’. In Extended Data Fig. 2k, the first label should be ‘IL-17A-IFN?+’ rather than ‘IL-17A+IFN?–’, and the third label should be ‘IL-17A+IFN?-’ rather than ‘IL-17A–IFN?+’. In addition, in the final sentence of the Fig. 4 legend, the text should be ‘two-sided t-test (a–c, e right, m right)’ and not ‘two-sided t-test (a–c, e right)’. The original Article has been corrected online.

Yi-Hsien Cheng,1 Shu-Han You,2 Yi-Jun Lin,3 Szu-Chieh Chen,4,5 Wei-Yu Chen,6 Wei-Chun Chou,2 Nan-Hung Hsieh,7 Chung-Min Liao3 1Institute of Computational Comparative Medicine (ICCM), Department of Anatomy and Physiology, College of Veterinary Medicine, Kansas State University, Manhattan, KS, USA; 2National Institute of Environmental Health Sciences, National Health Research Institutes, Zhunan, 3Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, 4Department of Public Health, 5Department of Family and Community Medicine, Chung Shan Medical University Hospital, Taichung, 6Department of Biomedical Science and Environmental Biology, Kaohsiung Medical University, Kaohsiung, Taiwan; 7Department of Veterinary Integrative Biosciences, College of Veterinary Medicine and Biomedical Sciences, Texas A&M University, College Station,TX, USA Background: The interaction between influenza and pneumococcus is important for understanding how coinfection may exacerbate pneumonia. Secondary pneumococcal pneumonia associated with influenza infection is more likely to increase respiratory morbidity and mortality. This study aimed to assess exacerbated inflammatory effects posed by secondary pneumococcal pneumonia, given prior influenza infection. Materials and methods: A well-derived mathematical within-host dynamic model of coinfection with influenza A virus and Streptococcus pneumoniae (SP) integrated with dose–response relationships composed of previously published mouse experimental data and clinical studies was implemented to study potentially exacerbated inflammatory responses in pneumonia based on a probabilistic approach. Results: We found that TNFα is likely to be the most sensitive biomarker reflecting inflammatory response during coinfection among three explored cytokines. We showed that the worst inflammatory effects would occur at day 7 SP coinfection, with risk probability of 50% (likely) to develop severe inflammatory responses. Our model also showed that the day of secondary SP infection had much more impact on the severity of inflammatory responses in pneumonia compared to the effects caused by initial virus titers and bacteria loads. Conclusion: People and healthcare workers should be wary of secondary SP infection on day 7 post-influenza infection for prompt and proper control-measure implementation. Our quantitative risk-assessment framework can provide new insights into improvements in respiratory health especially, predominantly due to chronic obstructive pulmonary disease (COPD). Keywords: chronic obstructive pulmonary disease, pneumonia, influenza, coinfection, modeling, risk assessment