A mathematic model to reveal delicate cross‐regulation between MAVS/STING, inflammasome and MyD88‐dependent type I interferon signalling

Abstract Early type I interferon is essential for antagonizing against malaria infection, which remains a significant global infectious disease. After Plasmodium yoelii YM infection, the activation of MAVS‐, STING‐ and inflammasome‐IRF3‐mediated pathway could trigger the Socs1 expression to inhibit the TLR7‐MyD88‐IRF7‐induced type I interferon production. However, the dynamic regulatory mechanisms of type I interferon response to YM infection and delicate cross‐regulation of these signalling are far from clear. In current study, we established a mathematical model to systematically demonstrate that the MAVS‐, STING‐ and inflammasome‐mediated signalling pathways play distinct roles in regulating type I interferon response after YM infection; and the YM dose could significantly affect the difference of resistance to YM infection among MAVS, STING and inflammasome deficiency. Collectively, our study systematically elucidated the precise regulatory mechanisms of type I interferon signalling after YM infection and advanced the research on therapy of plasmodium infection by incorporating multiple signalling pathways at diverse time.

orchestrating effective innate immune response. However, the relative contribution of these pathways in response to malaria infection remains be further defined.
Malaria is a deadly infectious disease that affects approximately 200 million people (WHO2019), leading to about half a million deaths each year. [15][16][17] No highly effective vaccine has been a major limiting factor in preventing malaria infection, which largely arise from the incomplete understanding of the underlying mechanism of host-parasite interactions. [18][19][20][21][22] Malaria infection initiates a systemic immune response and subsequently triggers a elevated release of inflammatory cytokines, resulting in parasite elimination and/or disease. [22][23][24][25][26][27][28][29] Our previous studies showed that during P.lasmodium yoelii YM (YM for short) strain blood stage infection, several components of malaria, including haemozoin, genomic DNA (gDNA) and RNA, could simultaneously activate diverse host sensors to initiate multiple pathways activation. 30,31 Although it is conceivable that the MAVS-, STING-, and inflammasome-mediated signalling pathways converge to induce Besides, we identified that mice deficient in MAVS-, STING-or inflammasome-mediated pathways also have distinct resistance to YM infection. Interestingly, we found that the YM dose could significantly affect the difference of resistance to YM infection among MAVS, STING and Caspase1 deficiency. Our findings further revealed that the synergistic or antagonistic effect of these three pathways on Socs1 or Ifnα/β expression is also diverse for varying time and stimulus, respectively.

| Microbes
The Plasmodium yoelii YM has been previously described. 32

| Primary cells
Bone marrow cells were isolated from the tibia and femur, and cultured in RPMI1640 medium with 10% FBS, 1% penicillin-streptomycin and 200 ng/mL Flt3L for 7 days to harvest pDCs.
All animal studies were approved by the ethics committee of Qinghai University and carried out in accordance with animal management regulations of the Ministry of Health of China.

| Isolation and preparation of Plasmodium gDNA, RNA and haemozoin
Parasite-infected mice blood was collected in saline solution and filtered to deplete white blood cells. Parasites were spun down after RBC lysis buffer treatment, and lysate incubated with buffer A (150 mmol/L NaCl, 25 mmol/L EDTA, 10% SDS and protein kinase) overnight. gDNAs were isolated using phenol/chloroform, and RNAs were isolated using TRIzol reagent (Invitrogen). Haemozoin was purified as previously described. 28

| RNA extraction and quantitative polymerase chain reaction (qPCR)
Total RNA was isolated from primary cells with TRIzol reagent (Invitrogen), according to the manufacturer's instructions.
The complimentary cDNA was performed using reverse transcriptase IV (Invitrogen). Quantitative real-time PCR was performed using the ABI Prism 7000 analyser (Applied Biosystems), and using iTaq SYBR Green Supermix (BioRad) with following specific primers:

| Mathematical modelling
We developed a simplified model to describe STING-, MAVSand inflammasome-mediated Socs1 expression, which negatively regulates type I IFN response to YM challenge in pDCs.
Several components of malaria could simultaneously activate diverse host sensors to initiate immune response. 24,30 Activation of MDA5 and an unrevealed RNA sensor recruits the MAVS adaptor protein, whereas stimulation of DNA sensors (cGAS and an unrevealed DNA sensor) leads to the recruitment of STING, which both induce the phosphorylation of IRF3 (reactions 2-5, 11-12 in Table S1). 30,33,34 In addition, we have found that the gDNA-haemozoin complex could activate the AIM2 and NLRP3 inflammasomes, respectively, to initiate the IL-1β signalling to activate IRF3 in pDCs (reactions 6-10, 13 in Table S1). 31 Subsequently, the phosphorylated IRF3 induces a negative regulator Socs1 expression (reactions 14 in Table S1). As we have reported, the activation of TLR7 can trigger MyD88-dependent IRF-mediated IFNα/β response to plasmodium infection in pDC, and this process might be potently inhibited by SOCS1 (reactions 15-19 in Table S1). 30 The computational model was formulated using ordinary differential equations (ODEs) in MATLAB R2010a (MathWorks).
The corresponding ODE model is described by the following equations: The unknown parameters were estimated using non-linear least square method using genetic algorithm. 35  Local sensitivity coefficient evaluates the systematic responses to an infinitesimal disturbance in nominal model parameters. The relative change of a derived systematic quantity M with respect to a relative change (1%) of parameter p is given as follows 36 : We perform the Bliss index to quantitatively identify whether the co-administration of two parameters, such as kaMA with kILR, produces synergistic effects on Socs1 expression. The index is defined by the following equation 37 : where O 1 (x1), O 2 (x2) and O 12 (x1,x2) are the relative SOCS1 mRNA to kaMA (at a x1 fold of its initial value), kILR (at a x2 fold of its initial value) and their combination (at (x1,x2) multiplier), respectively. Therefore, CI Bliss <1, CI Bliss >1 and CI Bliss = 1 denote synergistic, antagonistic and additive combination effects, respectively.

| Statistical analysis
The results of all quantitative experiments are reported as mean ± SD of three independent experiments. Comparisons between groups for statistical significance were assessed with a two-

| Mathematical model could quantitatively reproduce the dynamics of Socs1 and Ifnα/β expression by YM treatment
According to previous studies and our experimental data, we concluded a schematic representation of the dynamic regulation of MAVS/STING, inflammasome and MyD88-IRF7-dependent type I IFN response to YM infection as shown in Figure 1A. 24 A key question is how these pathways finely regulate the dynamic response of type I interferon to YM infection. To address this issue, we isolated pDCs from WT and gene deficient whereas were more sensitive at early stage than late (eg kaMA); parameters involved in STING activation were sensitive at the early stage, but rapidly weakened (eg kaS); and parameters involved in inflammasome activation were less sensitive at the early stage than late, whereas there is sustained modest sensitivity at late stage (eg kILR) ( Figure 2B).

| The YM dose could significantly affect the difference of resistance to YM infection among MAVS, STING and inflammasome deficiency
Our previous studies have shown that the MAVS deficiency mice confer stronger inhibition of Socs1 expression, leading to higher level of Ifnα/β production, and consequently stronger resistance to YM challenging than Caspase1 deficiency. 31 To further qualitatively and quantitatively determine the resistance of MAVS, STING or Caspase1 deficiency to YM infection, we in silico-varied the YM doses and kaMA/kaS/kILR values simultaneously. Analysis of Ifns mRNA int.
phase spaces showed that at high dosage of YM treatment, the variation in kaMA value had greatest contribution to inhibit Ifns expression; and the impact of variation in kaS value on Ifns production was more significant than kILR, whereas upon low dosage YM treatment, the change of kaMA, kaS or kILR value did not substantially influence the type I IFN response to YM infection ( Figure 3A). Thus, we hypoth-

| D ISCUSS I ON
As aberrant type I interferon response may result in many autoimmune diseases, tight modulation of type I IFN signalling is critical for maintaining homoeostasis of immune system after microbial invasion. 38,39 Accumulating evidence indicates that the type I IFN signalling plays an important role in anti-malaria. 40  Thus, our findings may provide mechanistic insights into dynamic regulation of IRF7-dependent type I IFN response to YM infection, and provide impetus to orchestrate effective innate immune response to YM challenging by manipulate multiple pathways.

ACK N OWLED G EM ENT
CC was supported by the National Natural Science Foundation

CO N FLI C T S O F I NTE R E S T
The authors declare no conflict(s) of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data sets used and/or analysed during the current study are available from the corresponding author upon reasonable request.