(A) The titrimetric chemical reaction model of miRNA-induced repression upon single target RNA species. (B) MiRNAs regulate multiple RNA species. The target RNAs could be mRNA, non-coding RNA (long and short ones), pseudogene, and circular RNA. The dots on the RNAs represent MREs. (C) High miRNA binding strength sharpens the threshold-behavior of miRNA-induced repression (M=1, and N=1) [50]. (D) MiRNA level shifts the threshold of miRNA-induced repression (M=1, and N=1) [50]. (E) Simulated relationship between free ceRNA1 level and ceRNA1 transcriptional level with ceRNA2 containing MREs under conditions of low, middle, and high level miRNA under the condition that the transcriptional level of ceRNA2 is proportional to that of ceRNA1. Here M=1, and N=1 (red curve) or 2 (blue curve). Right panel shows the fold change of free ceRNA1 between with ceRNA2 and without ceRNA2. (F) Simulated relationship between free ceRNA1 level and ceRNA1 transcriptional level with ceRNA2 containing MREs with the low, middle, and high binding strength under the condition that the transcriptional level of ceRNA2 is proportional to that of ceRNA1 (M=1, and N=1 or 2). MiRNA expression level is equal in each panel. Right panel shows the fold change of free ceRNA1 between the case with ceRNA2 (blue line) and the case without ceRNA2 (red line). (G) Simulated relationship between free ceRNA1 and miRNA transcriptional level with ceRNA2 containing MREs of no, low, high expression level (M=1, and N=1 or 2). The fold changes of miRNA level needed to cause a ten-fold change of free ceRNA1 are marked. (E), (F) and (G) were modified from our previous work [31].

(A) Schematic diagram of model-guided quantitative analysis of a special ceRNA system (RNAi). CeRNA2 complementary perfectly to miRNA mimics RNAi target, while ceRNA1 complementary imperfectly to miRNA mimics off-target. (B) Binding strength between target RNA and miRNA impacts the on-target-off-target repression curve. The x-axis and y-axis are the logarithm of free ratio of the two targets respectively. (C) Expression level of off-target has no impact on the on-target-off-target repression curve. The parameters of (B) and (C) were set as follow: kR1={5,10,15}×10-3,gR1=1×10-5,g1=8×10-5,a1=0.5,k1-=5×10-5,k1+={5,10,15}×10-5; kR2=5×10-3,gR2=1×10-5,g2=8×10-5,a2=0.1,k2-=5×10-5,k2+=100×10-5; gs=1×105,ks=105~10-1.

(A) Schematic diagram of the strategy of measuring the ceRNA regulation in the minimal ceRNA regulation model. We increase the transcriptional rate of mRNA1, and measure the levels of mRNA2, including the free mRNA2 that is proportional to protein level, the complex2 containing mRNA2 and miRNA and the whole mRNA2 equaling free mRNA2 plus complex2. (B) Steady-state concentrations as function of kR1changes under the condition that gR2<g2. (C) Steady-state concentrations as function of kR1 changes under the condition that gR2>g2. (B) and (C), the left panel shows the steady-state concentrations of mRNA1 and miRNA. The right panel shows the steady-state concentrations of mRNA2. The fold changes of mRNAs concentrations caused by a ten-fold change of kR1 are marked. The parameters of (B) were set: kR1=10-5~10-1,gR1=1×10-5,g1=8×10-5,α1=0.5,k1-=5×10-5, k1+=10×10-5; kR2=5×10-3,gR2=1×10-5,g2=8×10-5,α2=0.5,k2-=5×10-5,k2+=10×10-5; gS=1×10-5,kS=4×10-3. The parameters of (C) were set the same as these of (B) with an exception that g2=0.5×10-5.

(A) One miRNA species represses three ceRNA species. (B) An indirect ceRNA regulation through ceRNA3, from ceRNA1 upon ceRNA2 is introduced. (C) Steady-state concentration as a function of kR1 of the network in (A) under the condition that gR2_<g2. (D) Steady-state concentration as a function of kR1 of the network in (B) under the condition that gR2_<g2. (C) and (D), the fold changes of concentrations of ceRNA2 caused by a ten-fold change of kR1 are marked on the plots. The parameters of (C) were set: kR1=10-5~10-1,gR1=1×10-5,g11=8×10-5,α11=0.5,k11-=5×10-5,k11+=10×10-5; kR2=5×10-3,gR2=1×10-5,g21=8×10-5,α21=0.5,k21-=5×10-5,k21+=10×10-5; kR3=5×10-3,gR3=1×10-5,g31=8×10-5,α31=0.5,k31-=5×10-5,k31+=10×10-5; kS1=4×10-3,gS1=1×10-5. The parameters of (D) were set: kR1=10-5~10-1,gR1=1×10-5,g11=8×10-5,α11=0.5,k11-=5×10-5,k11+=10×10-5 ; g13=8×10-5,α13=0.5,k13-=5×10-5,k13+=10×10-5 ; kR2=5×10-3,gR2=1×10-5,g21=8×10-5,α21=0.5,k21-=5×10-5,k21+=10×10-5; g22=8×10-5,α22=0.5,k22-=5×10-5,k22+=100×10-5;kR3=2×10-3,gR3=1×10-5,g32=8×10-5,α32=0.5,k32-=5×10-5,k32+=100×10-5; g33=8×10-5,α33=0.5,k33-=5×10-5,k33+=100×10-5; kS1=4×10-3,gS1=1×10-5,kS2=2×10-3,gs2=1×10-5,ks3=2×10-3,gs3=1×10-5

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