model

1 Delivery module

1.1 Introduction

Pharmacokinetics is the quantitative study of drug absorption, distribution and metabolism in the body. Pharmacokinetic data are indispensable for phase I clinical trials to evaluate the tissue distribution and safety of drugs. To construct a strategy for developing efficient and safe in vivo RNAi therapy systems, pharmacokinetics at whole body, organ, cellular and sub-cellular levels need to be considered [1].

In our laboratory study (GFP experiment), we obtained a qualitative description of in vivo drug distribution after systematic administration. A computational and compartmental model was built to provide mechanistic insights into a quantitative explanation of the experimental results.

Three primary aspects were counted in this pharmacokinetic model:
i) theoretically predicting the effect of RVG modification of the targeting ability of exosomes,
ii) approximating time-series exosome (siRNA) concentration data for use in modeling RNAi kinetics in target tissue and subsequently calculating the effective dose, and
iii) determining what portion of the delivery system could be improved based on simulation data.

1.2 Model methods

The process of drug delivery in humans and mice is quite complex. Physiologically speaking, drug delivery after administration can be simplified into two separate phases:

i) circulation from a central compartment (blood) to a peripheral compartment (body tissues), and
ii) uptake and trafficking at cellular and sub-cellular levels in target tissues.
Although physiologically based pharmacokinetic (PBPK) models have been widely used in clinical trials, few described the cellular uptake behavior because most of the available drugs, at present, are chemically synthesized and have different biological properties compared with exosomes. Exosomes differ from conventional chemical drugs because of their distinct biological characteristics as microvesicles [2]. Thus, we would like to modify the current PBPK model and add details regarding cellular uptake behavior based on the biological nature of exosomes.

1.2.1 Modeling multi-compartmental transport

In our laboratory work, we measured the relative level of GFP in the brain, liver, lung and spleen after injecting anti-GFP siRNA into mouse. Thus, we examined separate compartments for the brain, liver, lung and spleen. Other tissues were merged into one compartment. Each peripheral compartment had blood exchange with the central blood circulation, during which a certain percentage of exosomes were captured into the extracellular matrix of endothelial cells in different tissues.

Figure 1. Schematic diagram of the arrangement of different tissues in the pharmacokinetic model. The blood, along with exosomes, circulates from the central compartment to five peripheral compartments.

As membrane vesicles, exosomes may rapidly shift from associating with other complexes and disassociating into a free format during blood circulation. Moreover, the ultimate fate of exosomes, similar to other microvesicles, is degradation by lysosomes after internalization via a common process discussed later. Research has shown that microvesicles, containing miRNAs or siRNAs, are stable in serum and play significant biological roles in cell communication [3]. 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 [4]. These two findings suggest that 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.

Using standard mass action kinetics, the equations below describe the change in the concentration (mass) of free exosomes over time in blood and target tissues. Here, kblooddis and kbloodbind represents the association and disassociation, respectively, of exosomes to other complexes in the blood circulation.

Notably, not all exosomes are effective or completely absorbed by tissues. Therefore, partitiontissue is included to describe the effective fraction of the dose. 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 represents the velocity of blood flowing in peripheral and central compartments, respectively.

This work is supported by model of IGEM Slovenia 2012, IGEM NJU-China 2013 and other literatures [5,6].

1.2.2 Modeling cellular uptake and intracellular trafficking

Extracellular vesicles can be internalized by cells via a variety of pathways, namely, phagocytosis, clathrin- and caveolin-mediated endocytosis and macropinocytosis [7]. We assume that receptor-mediated endocytosis is the major pathway of primary exosome internalization.

The cellular uptake pathway is summarized in Figure_2. 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. Although other pathways such as transcytosis and exocytosis following endocytosis may occur, we did not take them into account for simplification.

Figure 2. Pathways that participate in exosomes uptake by target cells. Exosomes are transported from the extracellular matrix to the cell surface and undergo intracellular trafficking after internalization. The RISC complex in exosomes is released, and exosomes are ultimately degraded.

We used several equations to describe the above pathway. RVG modification helps exosomes bind acetylcholine receptors specifically expressed in neuronal cells. Exosomes internalization is much easier provided that more exosomes bind target cells. The binding process is modeled using mass action kinetics. AR denotes the number of acetylcholine receptors 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 below using the parameters kinttissue and kelimttissue, respectively. Note that different tissues have different internalization and elimination rates.

The quantity of the endosomal RISC complex and escape behavior is modeled using the following equation. The concentration of siRNA in exosomes is determined by real-time RT-PCR in the literature [8] and represented by kc. kescendvec represents the escape rate of the RISC complex from exosomes (endosomes) to the cytosol.

This part of work is based on literature [5].

1.3 Parameter finding and adjustment

The most challenging part of modeling is finding and adjusting parameters. After reviewing the literature, we unfortunately found that few of the parameters have been measured or reported directly. The original paper written by Bartlett and Davis uses synthetic polyplexes as carriers to deliver siRNA [5]. The stability and targeting ability of synthetic polyplexes diverge considerably from exosomes due to their different biochemical nature. Using all the parameters in the original paper without adjustment would not be appropriate because of different biochemical natures and consequences of these delivery systems.

Parameter adjustment is not unusual in modeling biological processes. This endeavor is a somewhat uncertain endeavor and lacks specific procedures. In an iterative process, each set of parameters must be run through the model and modified to bring the output of the model into better and better agreement with observed experiment and literature results [9]. Following this doctrine, we ran our simulation and attempted to fit the results to the experimental and literature data.

You can access the description of model variables and parameters here . The determination of the parameters is also described in the list. When one parameter was reported in the literature, we cited the literature directly; when the parameter was not accessible but could be estimated and fitted to the literature or experimental results, we used the terms “estimated from literature and experimental results”.

1.4 Results

We simulated the pharmacokinetic model and obtained initial results. Unfortunately, the results showed that the model was not accurate. Distinguishing the effects of RVG modification on the tissue distribution of exosomes was difficult, as shown in the figure below.

Figure 3. Effect of RVG modification on the tissue distribution of exosomes. A: Without RVG modification; B: With RVG modification. The initial results are simulated with partitionbrain set at 1×10^-1.

Why did we obtain unrealistic simulation results? The answer simply lies in the parameter set we chose. After performing parameter sensitivity analysis, we were surprised to find that exosome bindings to the neuronal cell surface does not determine the internalization rate. In contrast, paritionbrain is more sensitive, indicating that the rate limiting step for exosome internalization is its effective dose fraction to targeted cells.

We next carefully investigated the presence of BBB and the effect of RGV modification on paritionbrain. The blood brain barrier is formed by endothelial cells at the level of cerebral capillaries [10]. The cerebral endothelial cells may form complex tight junctions that interfere with permeability. The binding of RVG to acetylcholine receptors, which are present in high density at the neuromuscular junction, would provide a mechanism whereby exosomes could be locally concentrated at sites in proximity to peripheral nerves, facilitating subsequent uptake and transfer to the central nervous system [11]. The local concentrating of exosomes at proximal sites may significantly increase the effective dose fraction available to targeted cells, resulting in a greater number of exosomes passing through the BBB and captured by the extracellular matrix of target cells. To our knowledge, this mechanism is why exosomes may pass through the BBB much more easily after RVG modification. Thus, we hypothesized that partitionbrain may also be influenced by RVG modification.

With partitionbrain increased by 6-fold, we finally obtained optimized simulation results. The biological meaning of this parameter adjustment is that RVG modification helps exosomes bind acetyl-choline receptors, not only facilitating internalization into target cells but also increasing the ability of exosomes to pass though the BBB by at least 6-fold.

Figure 4. Effect of RVG modification on the tissue distribution of exosomes. The results are simulated with partitionbrain increased by 6-fold. A-B: Control study of the time course of the tissue-distribution of exosomes without RVG modification. C-D: Case study of the time course of the tissue-distribution of exosomes with RVG modification and MOR-siRNA as cargo. E: In situ simulation of the tissue-distribution of exosomes.

We now better understand our delivery device using computational simulation data. The half-life of exosomes in blood is short, which is consistent with findings with the literature [12]. The tissue distribution pattern of exosomes with or without RVG modifications is also consistent with findings in the literature [13] and our GFP experiment.

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.

1.5 Conclusion and Remarks

In this module, we created a pharmacokinetic model to simulate the time-dependent tissue distribution of exosomes at whole organ and cellular levels. We theoretically tested the effect of RVG modification on the capability of exosomes to pass through the BBB. The simulation results are consistent with experimental measurements, and provide clues regarding improvements to the delivery device.

1.6 Model Variables

*: Exosomes become endosomes after interanalization. Here we still use term exosomes for clear illustration.

1.7 Model Parameters

?: We are very uncertain about these parameters. However, the parameter sensitivity analysis showed these parameters were not notable for the accuracy of the result.

***: Details and Reasons of this adjustment for RVG modification are discussed in the text.

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