Our mathematical models contain two aspects: a pharmacokinetic model and RNA inference model. You can get our source code here .
Delivery module: the tissue-distribution of exosomes through the experimental results.
RNAi module: simulate the kinetics of downregulation about BCL2 protein in response to anti-BCL2 siRNA.



We built this part to help our experiment, this pharmacokinetic contains the three aspects:
1) Predicting the effect of the targeting ability about tPep modification of exosomes
2) Use in modeling RNAi kinetics in target tissue and subsequently calculating the effective dose through approximating time-series exosome (siRNA) concentration data.
3) Determining we could improve what portion of the delivery system based on simulation data.

Model methods

The diffusion of drug in humans and mice is a quite complex process. We Physiologically simplified it into two separate phases:
1) Circulation from a central compartment (blood) to a peripheral compartment (body tissues), 2) Uptake and trafficking at cellular and sub-cellular levels in target tissues.
Exosomes are different from conventional chemical drugs because of their distinct biological characteristics. So, based on the biological nature of exosomes, we would like to modify the current PBPK (physiologically based pharmacokinetic) model.

Modeling multi-compartmental transport

Research has shown that micro-vesicles containing miRNAs or siRNAs, are stable in serum and play significant biological roles in cell communication [1]. Furthermore, the elimination of exosomes occurs primarily in specific tissues rather than in blood circulation, albeit that the half-life of exosomes in blood circulation is much shorter [2].
Thus the elimination rate of exosomes in blood circulation is negligible compared with that in target tissues and does not need to be considered in this portion of the pharmacokinetic model. the equations below describe the change in the concentration (mass) of free exosomes over time in blood and target tissues through standard mass action kinetics.
Here, kblooddis and kbloodbind represents the disassociation and association, respectively, of exosomes to other complexes in the blood circulation.

Notably, exosomes aren’t totally effective or completely absorbed by tissues. Thus, to describe the effective fraction of the dose, the partition-tissue is needed. Additionally, Et represents the quantity of exosomes captured by the extracellular matrix of cells in tissues, but does not represent the final quantity of exosomes in tissues, which will be discussed in the next portion of the model.
Qtissue and Qc respectively represents the velocity of blood flowing in peripheral and central compartments.

Modeling cellular uptake and intracellular trafficking

The cellular uptake pathway is summarized in Figure 1.

Figure 1. Exosomes bind to the membranes of target cells after being captured by the extracellular matrix and then internalized through endocytosis. The receptor-ligand interaction may facilitate this process. After internalization, the RISC complex may escape from endosomes, and endosomes may be ultimately eliminated by lysosomes.
The equations below are used to describe the above pathway. tPep modification helps exosomes bind prohibitin specifically expressed in adipocytes. The larger the number of exosomes binding targeted cells is, the easier exosomes internalization gets.
The binding process is modeled using mass action kinetics. AR denotes the number of prohibitin on target cells, and km represents the specific binding constant. Non-receptor-ligand interaction--mediated binding is summarized using kbindtissue.
The internalization and elimination of exosomes: are formulated by the parameters kinttissue and kelimttissue below, respectively. Different tissues have different internalization and elimination rates.
The quantity of the endosomal RISC complex and escape behavior :
The concentration of siRNA in exosomes is determined by real-time RT-PCR in the literature [4] and represented by kc. kescendvec represents the escape rate of the RISC complex from exosomes (endosomes) to the cytosol.

Parameter finding and adjustment

As our work is similar to the model of IGEM NJU-China 2015, we used some parameter from them. You can access the description of model variables and parameters here . The determination of the parameters is also described in the list.


With increasing the partitionadipocyte to 4-fold, we finally obtained optimized simulation results which is accord with our experiment. The biological meaning of this parameter adjustment is that tPep modification helps exosomes bind prohibitin.

Figure 2. Effect of tPep modification on the tissue distribution of exosomes. The results are simulated with partitionadipocyte increased by 4-fold. A-B: Control study of the time course of the tissue-distribution of exosomes without tPep modification. C-D: Case study of the time course of the tissue-distribution of exosomes with RVG modification and BCL2-siRNA as cargo.


From this figure we can get that the half-life of exosomes in blood is short, which is consistent with findings with the literature. Furthermore, the simulation data shows that a small portion of exosomes may also pass into non-targeted tissues due to circulation. We could improve the targeting precision by further modifying the exosomes.

RNAi module


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.

Model methods

This model is inspired by the paper written by Bartlett and Davis [3]. The system employs the RISC complex, which takes formed in exosomes and is release 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 mRNA degrading and further hinder protein expression.

Figure 3. 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 get 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 become a RISC complex, which is demonstrated 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.
TThe number of free siRNA in the cytosol is monitored 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].


Figure 4. Effect of dose on BCL2 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 BCL2 knockdown, we set different initial conditions and ran simulations. We found that the concentrations of exosomes and siRNA have significant impact on knockdown efficiency and recovery time. A high dosing schedule leads to complete knockdown of BCL2 protein and takes longer for BCL2 protein levels to recover.

To optimize the dosing schedule, the lasting times for efficiency and recovery needs to be taken into account. Prolonging the lasting time of drug efficiency while shortening the recovery time seems paradoxical based on the simulation data. It has been reported in a literature that 3 nmol of siRNA is adequate for repressing reward effects after 7 days of injection with the relative level of BCL2 protein reaching approxiamately 80%. Suppose that the threshold of relative level of BCL2 protein below which anti-apoptosis effects are repressed, is 80% [9], 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 BCL2 protein levels to absolutely recover. Increasing the frequency of dosing may also help to lengthen the drug efficacy time.

Model Variables

Model Parameters


1. Zhang, Y., Liu, D., Chen, X., Li, J., Li, L., Bian, Z., Sun, F., Lu, J., Yin, Y., Cai, X. et al. (2010) Secreted monocytic miR-150 enhances targeted endothelial cell migration. Molecular cell, 39, 133-144.
2. Takahashi, Y., Nishikawa, M., Shinotsuka, H., Matsui, Y., Ohara, S., Imai, T. and Takakura, Y. (2013) Visualization and in vivo tracking of the exosomes of murine melanoma B16-BL6 cells in mice after intravenous injection. Journal of Biotechnology, 165, 77-84.
3. Bartlett, D.W. and Davis, M.E. (2006) Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging. Nucleic Acids Res, 34, 322-333.
4. Alvarez-Erviti, L., Seow, Y., Yin, H., Betts, C., Lakhal, S. and Wood, M.J. (2011) Delivery of siRNA to the mouse brain by systemic injection of targeted exosomes. Nature biotechnology, 29, 341-345.
5. Morishita, M., Takahashi, Y., Nishikawa, M., Sano, K., Kato, K., Yamashita, T., Imai, T., Saji, H. and Takakura, Y. (2015) Quantitative analysis of tissue distribution of the B16BL6-derived exosomes using a streptavidin-lactadherin fusion protein and iodine-125-labeled biotin derivative after intravenous injection in mice. Journal of pharmaceutical sciences, 104, 705-713.
6. Kumar, P., Wu, H., McBride, J.L., Jung, K.E., Kim, M.H., Davidson, B.L., Lee, S.K., Shankar, P. and Manjunath, N. (2007) Transvascular delivery of small interfering RNA to the central nervous system. Nature, 448, 39-43. 7. Lai, C.P., Mardini, O., Ericsson, M., Prabhakar, S., Maguire, C.A., Chen, J.W., Tannous, B.A. and Breakefield, X.O. (2014) Dynamic biodistribution of extracellular vesicles in vivo using a multimodal imaging reporter. ACS Nano, 8, 483- 494.
8. Banks, G.A., Roselli, R.J., Chen, R. and Giorgio, T.D. (2003) A model for the analysis of nonviral gene therapy. Gene Ther, 10, 1766-1775.
9.Zhang, Y., Landthaler, M., Schlussman, S.D., Yuferov, V., Ho, A., Tuschl, T. and Kreek, M.J. (2009) Mu opioid receptor knockdown in the substantia nigra/ventral tegmental area by synthetic small interfering RNA blocks the rewarding and locomotor effects of heroin. Neuroscience, 158, 474-483.



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