The area of region II in Fig 3 with different <i>p</i>₁.

<p>There exists <i>P</i> ≈ 1.149 making the smallest area at <i>p</i>₁ = <i>P</i>. When <i>p</i>₁ < <i>P</i>, the area decreases with the increasing <i>p</i>₁; when <i>p</i>₁ > <i>P</i>, the area increases with the increasing <i>p</i>₁.</p

Additional file 1 of Multi-omics analysis defines 5-fluorouracil drug resistance in 3D HeLa carcinoma cell model

Additional file 1. Details of mass spectrometry-based analytical methods, supplementary figures and tables. Fig. S1. The application of 3D MTSs culture method to a variety of tumor cell types and co-culturing models. Fig. S2. The morphology and microstructure of multi-component 3D MTSs. Fig. S3. The specific growth rates of HeLa carcinoma cells cultured in 2D monolayer and 3D MTS. Fig. S4. The specific rates of extracellular (A) glucose, (B) glutamine, (C) ammonium, and (D) lactate. Fig. S5. (A) PCA analysis of proteome. (B) Heatmap of differential proteins between the control condition and 5-FU treatment. (C) The KEGG pathways involving proteome difference between the control condition and 5-FU treatment (p-value < 0.05, top 20 sorted according to the -log10 p-value). (D) KEGG map of differential proteins for 2D monolayer between the control condition and 5-FU treatment. (E) KEGG map of differential proteins between 2D monolayer and 3D MTSs before and after 5-FU treatment. The increase and decrease of proteins are marked with red and green rectangles, respectively. Fig. S6. (A) PCA analysis of metabolome. (B) Heatmap of differential metabolites between the control condition and 5-FU treatment conditions. (C) The KEGG pathways involving metabolome difference between the control condition and 5-FU treatment (p-value < 0.05, top 20 sorted according to the -log10 p-value). (D) KEGG map of differential metabolites for 2D monolayer and 3D MTS between the control condition and 5-FU treatment. (E) KEGG map of differential metabolites between 2D monolayer and 3D MTSs before and after 5-FU treatment. The increase and decrease of metabolites are marked with red and blue circles, respectively. Table S1. Primer sequences in this study. Table S2. Screening results of MTSs culture conditions. Table S3. GO enrichment results between 2D monolayer culture and 3D MTS under the control condition. Table S4. GO enrichment results between 2D monolayer culture and 3D MTS under 5-FU treatment condition

(color online) Densities of five species in Monte Carlo simulation. <i>L</i> = 200,<i>k</i>_{<i>i</i>, <i>j</i>} = 1.

<p>After about 500 time steps, the species <i>S</i>₄ and <i>S</i>₃ extinct and species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist.</p

(color online) <i>p</i> = 0.5, <i>s</i> = 1.2.

<p>Densities of species under different population sizes. (a) <i>L</i> = 100. (b) <i>L</i> = 200. (c) <i>L</i> = 400. (d) <i>L</i> = 800. (a) Species <i>S</i>₂ and <i>S</i>₃ extinct after 10000 MCS, species <i>S</i>₁, <i>S</i>₄ and <i>S</i>₅ coexist. In (b), (c) and (d), all the five species coexist, the densities fluctuation decreases with the increasing <i>L</i>.</p

(color online). The relationships of five species in the Jungle game.

<p>Arrows point from predator to prey. <i>S</i>₁ and <i>S</i>₂ can prey three species and be hunt by one species; <i>S</i>₃ can prey two species and be hunt by two species; <i>S</i>₄ and <i>S</i>₅ can prey one species and be hunt by three species.</p

(color online) Coexistence of species in example 1 using Monte Carlo simulation. <i>L</i> = 400.

<p>All five species coexist in the red region. Species <i>S</i>₁<i>S</i>₄<i>S</i>₅ coexist in the orange region. Species <i>S</i>₁<i>S</i>₂<i>S</i>₅ coexist in the light yellow region. Species <i>S</i>₁<i>S</i>₃<i>S</i>₅ coexist in the deep yellow region. Only <i>S</i>₅ remains in the green region. Only <i>S</i>₁ or <i>S</i>₂ remains in the blue region.</p

(color online) Densities of five species in Monte Carlo simulation. <i>L</i> = 200,<i>k</i>_{<i>i</i>, <i>j</i>} = 1.

<p>After about 500 time steps, the species <i>S</i>₄ and <i>S</i>₃ extinct and species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist.</p

Influence of Clay Particles on the Transport and Retention of Titanium Dioxide Nanoparticles in Quartz Sand

This study investigated the influence of two representative suspended clay particles, bentonite and kaolinite, on the transport of titanium dioxide nanoparticles (<i>n</i>TiO₂) in saturated quartz sand in both NaCl (1 and 10 mM ionic strength) and CaCl₂ solutions (0.1 and 1 mM ionic strength) at pH 7. The breakthrough curves of <i>n</i>TiO₂ with bentonite or kaolinite were higher than those without the presence of clay particles in NaCl solutions, indicating that both types of clay particles increased <i>n</i>TiO₂ transport in NaCl solutions. Moreover, the enhancement of <i>n</i>TiO₂ transport was more significant when bentonite was present in <i>n</i>TiO₂ suspensions relative to kaolinite. Similar to NaCl solutions, in CaCl₂ solutions, the breakthrough curves of <i>n</i>TiO₂ with bentonite were also higher than those without clay particles, while the breakthrough curves of <i>n</i>TiO₂ with kaolinite were lower than those without clay particles. Clearly, in CaCl₂ solutions, the presence of bentonite in suspensions increased <i>n</i>TiO₂ transport, whereas, kaolinite decreased <i>n</i>TiO₂ transport in quartz sand. The attachment of <i>n</i>TiO₂ onto clay particles (both bentonite and kaolinite) were observed under all experimental conditions. The increased transport of <i>n</i>TiO₂ in most experimental conditions (except for kaolinite in CaCl₂ solutions) was attributed mainly to the clay-facilitated <i>n</i>TiO₂ transport. The straining of larger <i>n</i>TiO₂-kaolinite clusters yet contributed to the decreased transport (enhanced retention) of <i>n</i>TiO₂ in divalent CaCl₂ solutions when kaolinite particles were copresent in suspensions

The biodiversity of the Jungle game in the first example.

<p>Species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist in region I; all five species coexist in region II; and species <i>S</i>₁, <i>S</i>₄ and <i>S</i>₅ coexist in region III.</p

The biodiversity of the Jungle game in the second example.

<p>(a) <i>p</i>₁ ≤ 1; (b) ; (c) . Species <i>S</i>₁, <i>S</i>₂ and <i>S</i>₅ coexist in region I (green); all five species coexist in region II (white); and species <i>S</i>₁, <i>S</i>₄ and <i>S</i>₅ coexist in region III (yellow).</p