Integrated modeling and analysis of intracellular and intercellular mechanisms in shaping the interferon response to viral infection

Abstract

The interferons (IFNs) responses to viral infection are heterogeneous, while the underlying mechanisms for variability among cells are still not clear. In this study, we developed a hybrid model to systematically identify the sources of IFN induction heterogeneity. The experiment-integrated simulation demonstrated that the viral dose/type, the diversity in transcriptional factors activation and the intercellular paracrine signaling could strikingly shape the heterogeneity of IFN expression. We further determined that the IFNβ and IFNλ1 induced diverse dynamics of IFN-stimulated genes (ISGs) production. Collectively, our findings revealed the intracellular and intercellular mechanisms contributing to cell-to-cell variation in IFN induction, and further demonstrated the significant effects of IFN heterogeneity on antagonizing viruses.

Fig 1. Mathematical model of IFN heterocellular induction by RNA viral infection.

(A) Schematic representation of multi-cellular IFN response induced by RNA virus infection. (B) Detailed diagram of signaling pathways involved in IFNβ/λ1 response triggered by viral ssRNA. The variables with superscript M denoted its mRNA level. (C) Model simulations (red lines) fitted well with experimental data (blue dots) measured in A549 cells by VSV infection (MOI = 0.05). The gray lines denote 100 simulations randomly selected from 10,000 cells, and the red lines represent average level of 10,000 simulations. The data of both experiment and simulation are mean ± SD. The mean squared error (MSE) between the simulation and experimental data is 0.0112. (D) Local sensitivity analysis of IFNβ and IFNλ1 mRNA induction with respect to each kinetic parameter. The blue and red bars represent the sensitivity coefficients of IFNβ^M and IFNλ1^M respectively.

Fig 2. Viral properties affect the variation of IFNs early induction.

(A-B) The early IFNβ/λ1^M induction with varying fold of viral dose treatment. (A) Each column includes 1,000 cells selected stochastically from 10,000 simulations (t = 18h). The red circle, blue square and green triangle denotes 0.3, 1.0 and 3.0 fold of initial viral dose respectively. (B) Each bar includes 10,000 simulations (t = 24h). The gray, red and blue bars denote 0.3, 1.0 and 3.0 fold of viral dose respectively. Results are mean ± SEM. The standard deviation (SD) indicates the variation of IFNβ^M or IFNλ1^M induction among multicellular population. “Sim.” represents simulations by model. (C) Experimentally measured IFNβ/λ1 responses in A549 cells with VSV at a MOI of 0.3 (gray), 1.0 (red) or 3.0 (blue) fold of 0.05 (t = 24h). “Exp.” represents experimental data. The data are mean ± SD, n = 3. (D-E) Temporal variation in cellular IFNβ/λ1^M induction. The viral replication (parameter k₁, left panel in D and E) and its ability to initiate anti-viral signal (parameter k₂, right panel in D and E) significantly shapes the IFNs^M onset. (D) Virus affects temporal variability of early IFNs induction. The gray, red and blue module indicates the time interval in which the cellular IFNβ^M or IFNλ1^M expression onset occurs. (E) Viral properties control onset times of IFNβ^M (blue) and IFNλ1^M (red). Data are mean ± SEM, n = 10,000. (F-G) Viral properties modulate the variation of IFNs early induction. The gray, red and blue bars indicate 0.8, 1.0 and 1.2 fold of k₁ respectively (F) or 0.2, 1.0 and 5.0 fold of k₂ respectively (G). The results are mean ± SEM, n = 10,000, t = 18h. (H) Various types of viruses induce distinct IFNβ/λ1^M expression measured by q-PCR assay. The red and blue bars represent SeV and VSV respectively. The data are mean ± SD, n = 3.

Fig 3. The variety among TFs activation significantly affects the variation and magnitude of IFNs response.

(A, C, E and G) Distributions of IFNβ^M and IFNλ1^M levels. The knockdown (KD, red bars) of initial levels of NF-κB (A), JNK1 (C), IRF3 (E) and IRF1 (G) have significant effects on cell-to-cell variation of IFNs expression compared to wild type (WT, blue bars), where the yellow bars indicate the overlap between WT and KD. (B, D, F and H) The knockdown (KD, red bars) of initial levels of NF-κB (B), JNK1 (D), IRF3 (F) and IRF1 (H) reduce the expressions of IFNβ/λ1^M through simulations (left panel) and experiments (right panel), compared to WT (blue bars). (I) Local sensitivity analysis of integrated output of IFNβ^M and IFNλ1^M induction with respect to kinetic parameters involved in TFs activation. The blue and red bars denote IFNβ^M and IFNλ1^M respectively. (J) The change of IRF1 activation rate (k₁₁) more greatly impacts IFNλ1^M than IFNβ^M. The blue circle and red square indicate fold changes of IFNβ^M and IFNλ1^M respectively. (K-L) The change of K_{11_12} or K_{11_13} affects the difference between IFNβ^M and IFNλ1^M in (K) onset-time (Δt), and (L) integrated values (Ri). (M) The ratio between K_{11_12} and K_{11_13} affects the variety between temporal dynamics of IFNβ^M and IFNλ1^M. The blue and red lines denote IFNβ^M and IFNλ1^M respectively. These two sets of K_{11_12} and K_{11_13} values were referred to green stars in (K) and (L) respectively. The data are mean ± SEM, n = 10,000.

Fig 4. The paracrine of IFNs impacts the viral replication and cellular variation of IFN responses at late phase of viral infection.

(A) The function of IFN paracrine signaling on IFNs response and viral replication (n = 10,000, t = 27h). The red, blue and gray bars denote simulated levels of IFNβ^M, IFNλ1^M and ssRNA, respectively. The data are mean ± SEM. (B) The paracrine secretion of IFNs influences the temporal onset of IFNβ^M and IFNλ1^M response during late phase of viral infection (n = 9,500). The red, blue and yellow bars indicate the wild-type, paracrine blockage and overlap. (C) Paracrine blockage has significant effects on cell-to-cell variation of IFN expression. Each column includes 100 cells selected stochastically from 9,500 simulations infected at late phase. Data are shown as mean ± SEM, t = 27h. (D) The dispersion of IFNs might dramatically increase in paracrine blockage (right panel, blue squares) compared to that under wild-type condition (left panel, WT, red circles) (n = 9,500, t = 27h).

Fig 5. The IFNβ and IFNλ1 induce diverse temporal patterns of ISGs to antagonize virus.

(A) Scatter plot of the distribution of IFNβ and IFNλ1 mRNA in early infected cells (n = 500, t = 18h). (B) Time courses of differential expressions of IFNβ^M and IFNλ1^M. The blue and red lines denote IFNβ^M and IFNλ1^M respectively. The data are mean ± SEM, n = 3. (C-D) Induction of antiviral genes stimulated by IFNβ (C) and IFNλ1 (D). The red and blue bars represent gene expression after 6 and 24 hours of stimulation respectively. Data in these figures were presented as the mean ± SD of three independent experiments or 10,000 simulations. (E) The differential influences of IFNβ^M (left) and IFNλ1^M (right) on temporal pattern of ISG56^M by scatter analysis in early infected cells (n = 500, t = 18h). The squares of the Pearson correlation coefficients between ISG56^M and IFNβ/λ1^M (r²) are 0.40 and 0.16, respectively. The P values of two panels are less than 0.0001.