model

2. RNAi module

2.1 Introduction

RNA interference (RNAi) is a major tool for transiently suppressing the expression of genes. Many mathematical models have been constructed to elucidate the mechanism of RNA interference and provide accurate predictions. Nevertheless, most of the current models focus merely on RNAi and fail to consider the delivery process. We modeled the delivery process and the input variant in this module should be the output result of the delivery module.

A challenge for the successful clinical application of RNAi-based drugs is determining the dosing schedule required for efficacy. Patients may ask the following questions: How soon will RNAi-based drugs take to exert efficacy after injection? How long will the efficacy last? What is the dose I need to take, and will it be too costly? How soon will the level of Mu opioid receptor (MOR) protein recover? Is RNAi therapy safe enough? Mathematical modeling using simple kinetic equations for each step in the RNAi process can shed light on many of these questions.

2.2 Model methods

This model is inspired by the paper written by Bartlett and Davis [1]. The system uses the presence of the RISC complex, which is formed in exosomes and escaped from endosome, as a stable source to provide silencing power. Then, the RISC units are targeted to mRNA having the same sequence as the siRNA that triggers this process, binding with mRNA to form an activated RISC-mRNA complex. Once bound to complementary mRNA, activated RISC may induce the degradation of mRNA and further silence protein expression.

Figure 5. Schematic diagram of RNA interference pathway. Degradation of the RISC complex, siRNA, mRNA and protein is not shown here for clear illustration. However, these processes are included in the model equations.

Applying the usual mass action to the reaction network, we can easily obtain the following model equations:

The RISC complex, derived from endosomal escape, may disassociate into free RISC and siRNA, form an activated mRNA-RISC complex or be degraded, as represented by kdisRISC, kformRISCm and kdegRISC, respectively. The free RISC and siRNA may again form a RISC complex, which is represented by kformRISC. The amount of free RISC proteins available for the formation of activated complex is rtot (free RISC protein) – R – C – kdisRISC*R (disassociated RISC protein derived from endosomes). Thus, the total numbers of siRNA- RISC complexes can be modeled using the equations below.

The number of free siRNA in the cytosol is governed by the equation below.

Activated RISC complex bound to mRNA induces the cleavage of target mRNA (kcleavage). Additionally, activated RISC complex may undergo degradation (kdegRISC) or disassociation (kdisRISCm).

The balance of formation (kformmRNA) and degradation (kdegmRNA) of mRNA and protein (kformprot kdegprot) is interrupted by RISC-induced cleavage of mRNA.

The variables and parameters of this model can be accessed here. All the parameters we used in this module are reported in the literature [1].

2.3 Results

The simulation results demonstrate the effect of siRNA on MOR knockdown in vivo.

Figure 6. Effect of siRNA on MOR mRNA (B) and protein (A) knockdown in vivo. The quantity of total exosomes injected is 300 μg which contains 3 nmol siRNA.

As depicted in the figure, the expression level of MOR protein exhibits a rapid exponential decay and reaches lowest level 12 hours after exosome injection, following a similar pattern observed with the relative level of MOR mRNA.

Figure 7. Effect of dose on MOR mRNA (A) and protein (B) knockdown in vivo. The initial quantity of total exosome injected was set at 50 μg, 100 μg, 200 μg, 400μg and 600 μg, containing 0.5 nmol, 1 nmol, 2 nmol, 4 nmol and 6 nmol siRNA, respectively.

To explore the dose effect on MOR knockdown, we set different initial conditions and ran simulations. The result shows that the concentrations of exosomes and siRNA have significant impact on knockdown efficiency and recovery time. A high dosing schedule leads to more complete knockdown of MOR protein and takes longer for MOR protein levels to recover.

To optimize the dosing schedule, the lasting times for efficiency and recovery needs to be considered. Elongating the lasting time of drug efficiency while shortening the recovery time seems paradoxical based on the simulation data. The literature has reported that 3 nmol of siRNA is adequate for repressing reward effects after 7 days of injection with the relative level of MOR protein reaching approxiamately 80%. If we assume that the threshold of relative level of MOR protein below which opioid reward effects are repressed, is 80% [2], then injecting 400 μg exosome (4 nmol siRNA) might be the best choice. The efficacy of the drug could last for about one week, and another week would be required for MOR protein levels to absolutely recover. Increasing the frequency of dosing may also help to lengthen the drug efficacy time.

2.4 Model Variables

2.5 Model Parameters