Fig 1.
Two pathways, Ras-Raf-MEK-ERK and PI3K-AKT lead to the cell proliferation.
Sharp arrows indicate activation/enhancement and blocked arrows indicate inhibition.
Fig 2.
Abbreviated version of Fig 1 depicting the roles of miR-21, miR-205 and miR-155.
MAPK represents the Ras-Raf-MEK-ERK signaling pathway and AKT represents the PI3K-AKT signaling pathway. (a) MiR-21 blocks TKI; miR-21 and miR-205 block PTEN. (b) MiR-155 blocks Apaf-1+caspase 9. Sharp arrows indicate activation/enhancement and blocked arrows indicate inhibition.
Table 1.
List of variables in unit of g/cm3.
Table 2.
Summary of parameter values.
Table 3.
Summary of parameter values (continued).
Fig 3.
Invasion of cancer cells with density C(x, t).
The parameters are as in Tables 2 and 3, and χ = 3 × 10−2 cm5g−1day−1. (a) The first row: The control case; a mutation in EGFR where λE is increased by 1.3-fold; a mutation in MAPK where λM is increased by 1.6-fold; a mutation in AKT where λE is increased by 1.8-fold. (b) The second row: Using anti-miR-21, where λm1 is reduced by a factor 2 compared to the first row. (c) The third row: Using both anti-miR-21 and anti-miR-155, where λm1 and λm2 are reduced by a factor 2 compared to the first row. The time is in unit of day, and x is in unit of cm.
Fig 4.
Total linear mass of cancer cells.
The mutations and anti-miRs are the same as in Fig 3, and all parameters are the same as in Fig 3. In the legend, anti-m1 indicates anti-miR-21, and anti-m1&m2 indicates the combination of anti-miR-21 and anti-miR-155. The time is in unit of day, and the mass is in unit of g.
Fig 5.
Invasion of cancer cells with density C(x, t).
The parameters are as in Tables 2 and 3, and χ = 3 × 10−2 cm5g−1day−1. (a) Mutations in both EGFR and MAPK, where λE and λM are increased by 1.15-fold and 1.3-fold, respectively; mutations in both EGFR and AKT, where λE and λA are increased by 1.15-fold and 1.4-fold, respectively; mutations in both MAPK and AKT, where λM and λA are increased by 1.3-fold and 1.4-fold, respectively. (b) Using both anti-miR-21 and anti-miR-155, where both λm1 and λm2 are reduced by a factor 2 compared to the panels in (a). The time is in unit of days, and x is in unit of cm.
Fig 6.
(a) The distance that the invasion front traveled by day 60 (Rχ, in unit of cm). (b) The total linear mass of cancer cells at day 60 (Mχ, in unit of g). χ ranges from 3 × 10−4 to 3 × 10−2 cm5g−1day−1. All other parameter values are the same as in the EGFR-mutation case of Fig 3.
Fig 7.
(a) The efficacy (ϕR) of anti-miR drugs in reducing the distance traveled by the tumor front at day 60. (b) The efficacy (ϕM) of anti-miR drugs in reducing the total linear mass of cancer cells at day 60. χ varies from 3 × 10−4 to 3 × 10−2 cm5g−1day−1. The anti-miR drugs reduce both λm1 and λm2 by a factor 2. All other parameter values are the same as Fig 6.
Fig 8.
Growth of invasion distance as a function of the total mass of m1 and total mass of m2.
(a) The invasion distance of cancer cells in the control case as a function of the total mass of miR-21 and miR-205. (b) The invasion distance of cancer cells as a function of the total mass of miR-155. All the parameter values are the same as the control case in Fig 3.
Fig 9.
Average densities/concentrations of all the variables in the model.
λC1 and λC2 are increased by a factor 1.4. θ = 0.6 g/cm3, C0 = 0.46 g/cm3 and N0 = 0.14 g/cm3. All other parameter values are the same as in Tables 2 and 3.
Fig 10.
The growth of tumor radius R(t), tumor volume, total mass of m1 and total mass of m2 for the first 60 days.
λC1 and λC2 are increased by a factor 1.4. θ is taken to be 0.6 g/cm3. All other parameter values are the same as in Tables 2 and 3.
Fig 11.
Volume of tumor as a function of the total mass of miR-21 and that of miR-155.
(a) The volume of tumor as a function of the total mass of miR-21 after the first 60 days. (b) The volume of tumor as a function of the total mass of miR-155 after the first 60 days. All the parameter values are the same as Fig 10.
Fig 12.
Tumor growth under different drugs. EGFR mutation is accounted for by increasing λE by factor 3.
(a) Paclitaxel inhibits the division of cells, where λCi are reduced from 1.4λCi to 1.3λCi (i = 1, 2); anti-miR-21 is accounted for by reducing λm1 to λm1/2. (b) Both anti-miR-21 and the gefitinib, a drug that inhibits the EGFR, reduce the growth of tumor; anti-miR-21 is accounted for by reducing λm1 to λm1/2, and EGFR-inhibitor gefitinib is accounted for by decreasing 3λE to 1.5λE. (c) Anti-miR-155 is accounted for by reducing λm2 to λm2/1.2 and cisplatin, a drug that induces cancer cell apoptosis, is accounted for by increasing dC and dD by factor 1.1.
Fig 13.
Statistically significant PRCC values (p-value < 0.01) for R(t) at day 60.