All reagents used for chemical synthesis not explicitly mentioned were purchased from FUJIFILM Wako Pure Chemical Corporation (Osaka, Japan), Tokyo Chemical Industry Co. (Tokyo, Japan), Nacalai Tesque (Kyoto, Japan), and Sigma-Aldrich Co. (St. Louis, MO, USA). (±)-Naringenin was purchased from Cayman Chemical Ltd and dissolved in dimethyl sulfoxide (DMSO) as a stock solution (50 mg/mL). Meanwhile, (±)-8-prenylnaringenin (8-PN) was synthesized from (±)-naringenin in a four-step process with a 24% overall yield according to a previously reported procedure  and as detailed in the supplementary methods. In the current study, (±)-naringenin was used instead of (S)-naringenin, considering the cost.
Cells and viruses
MDCK cells were grown in EMEM (FUJIFILM Wako Pure Chemical Corporation, Osaka, Japan) containing 7% FBS. In the current study, we used influenza A H1N1 strains A/PR/8/34, A/Suita/114/2011, A/Osaka/2024/2009, and A/Osaka/71/2011; H3N2 strains A/Sydney/5/97, and A/Aich/2/68; and B strains B/Shanghai/261/2002 and B/Nagasaki/1/87. Treatment of the cells against viral infections was according to the method by Morimoto et al. 
Metabolomic data analysis
The metabolomic data was obtained via LTQ ORBITRAP XL analysis (Thermo fisher scientific) using the Power Get software (http://www.kazusa.or.jp/komics/ja/tool-ja/48-powerget.html) originally developed by the Kazusa DNA Research Institute . Chromatographic separation was performed at 40 °C using a TSK gel ODS-100V column (3mm×50mm, 5μm: TOSOH) on an Agilent 1200 series system. For separation, the mobile phases were optima grade water with 0.1% formic acid (A) and acetonitrile with 0.1% formic acid (B). A 25-min gradient at a ﬂow rate of 0.4 ml/min with the following conditions was used: 0–5 min, held at 1% B; 5–10 min, linear gradient from 1–3% B; 10–18 min, linear gradient from 3–40% B; 18–22 min, linear gradient from 40–80% B; 22–27 min, column cleaning at 95% B; and 27–35 min, re-equilibration with solution A. The injection volume was 5 µl, and the MS was operated in the positive ion mode (ESI) with a scan range of m/z 100–1500 using one of the top ﬁve MS/MS methods. The average accurate mass of the compound peak was collated with a public database (Flavonoid Viewer) using Kazusa DNA Research Institute development Software (MF Searcher)
LC/MS measurement (triple-quadrupole, QQQ)
LC/MS measurement was performed according to a previously described method . Analysis was carried out according to a previously described method .
Cell viability determination
Cell viability was performed according to the method by Morimoto et al.  using a Cell Proliferation Kit I (MTT) (F. Hoffmann–La Roche Ltd, Basel, Switzerland).
Antiviral assay of 8-PN
The effects of the addition of the compounds on viral yield were determined as previously described , with slight modifications. MDCK cells were cultured in 24-well plates (Thermo Fisher Scientific, Fair Lawn, NJ, USA) at 1 × 105 cells/well in 500 ml/well of EMEM containing FBS and incubated for 24 h at 37 °C. In case of adsorption inhibition, diluted viruses were allowed to infect confluent cells at an MOI of 0.01 for 1 h at 37 °C with or without 11.4 µg/ml 8-PN. After 1 h of adsorption, infected cells were rinsed once with serum-free EMEM and then cultured in DMEM containing 0.4% BSA (500 µl/well) without 8-PN. After 8 h, the infected cells as IFV samples were frozen at -80 °C and subjected to two freeze-thaw cycles prior to determining the viral yield by focus-forming assays. In the case of replication inhibition, diluted viruses were allowed to infect the cells at an MOI of 0.001 for 1 h at 37 °C. After 1 h of adsorption, the infected cells were rinsed once with serum-free EMEM and then cultured in DMEM containing 0.4% BSA (500 µl/well) with or without 11.4 µg/ml 8-PN. After 24 h, the supernatants were collected as IFV samples and subjected to focus-forming assays.
Focus-forming reduction assay (FFRA) for measuring virus titer
FFRA was performed as previously described , which is a modification of another previously described method .
We conducted a time-of-addition experiment using a previously described procedure  with slight modifications. The difference was the concentration of the inhibitor, 8-PN. DMEM containing 0.02 mg/ml of the compounds, which was approximately 80% the maximum inhibitory concentration (Fig. 1), was added at different periods of infection: during adsorption, for 1 h incubation with viruses; during replication for up to 8 h, measured every two- and four-hour intervals (Fig. 2a). The infected cells were then frozen at -80 °C 8 h after infection and subjected to two freeze-thaw cycles before determining the viral yield using the focus-forming assay.
Viral binding inhibition assayThe viral amount attached to the cells was determined by measuring the viral RNA encoding the HA protein (HA) using SYBR green and a pair of primers, HA-F: 5′-TTGCTAAAACCCGGAGACAC and HA-R: 5′-CCTGACGTATTTGGGCACT. Viral RNA bound to cells was extracted, and cDNA was synthesized; viral RNA was quantified as described previously . As a normalization gene for real-time PCR based on influenza virus-infected cells, 18S rRNA was quantified as described previously .