Difference between revisions of "Team:NJU-China/Modeling"

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<h2> Modeling</h2>
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>
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<body class="index" data-view="index">
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<p>
 
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Here are a few examples from previous teams:
 
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<ul>
 
<ul>
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<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">ETH Zurich 2014</a></li>
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<li><a href="aknow.html" style="font-weight:bold;font-family:Microsoft YaHei">acknowledgement</a></li>
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<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">Waterloo 2014</a></li>
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<li><a href="human-practice.html" style="font-weight:bold;font-family:Microsoft YaHei">humanpractice</a></li>
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<li><a href="project.html" style="font-weight:bold;font-family:Microsoft YaHei">project</a></li>
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<li><a href="notebook.html" style="font-weight:bold;font-family:Microsoft YaHei">notebook</a></li>
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<li><a href="safty.html" style="font-weight:bold;font-family:Microsoft YaHei">safty</a></li>
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        <ul>
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            <li><a href="model.html#deliverymodel" style="font-weight:bold;font-family:幼圆;font-size:20px;color:black">Delivery model</a></li>
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            <li><a href="model.html#RNAimodel" style="font-weight:bold;font-family:幼圆;font-size:20px;color:black">RNAi model</a></li>
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<li style="line-height:250%"><a href="aknow.html" style="font-weight:bold;font-family:幼圆;font-size:25px;color:black">Acknowledgement</a></li>
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<h2 align="center">Delivery Module</h2>
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<h3>Introduction:</h3></br>
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Pharmacokinetics is the quantitative study of drug absorption, distribution and metabolism in the body. We created pharmacokinetic model to simulate the time-dependent tissue distribution of exosomes. To construct a strategy for developing efficient and safe in vivo RNAi therapy systems, pharmacokinetics at whole body, organ, cellular and sub-cellular level need to be considered.</br></br>
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In our preliminary wet lab study(GFP experiment), we obtain qualitative description of in vivo drug distribution after systematic administration. A computational and compartmental model can be built to give mechanistic insights into quantitative explanation of the experiment results.</br></br>
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There are three main aspects we take into account in this pharmacokinetic model:</br></br>
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Theoretically predicting the effect of RVG-modification of exosome on its target ability</br></br>
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Approximating time-series exosome(siRNA) concentration data for use in modeling RNAi kinetics in target tissue and subsequently calculating the effective dose</br></br>
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Finding out part of delivery system that could be improved based on simulation data</br></br></br>
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<h3>Model Methods:</h3> </br>
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The process of drug delivery in human and mouse is quite complex. Physiologically speaking, drug delivery after administration can be simplified into two separate phases: </br>
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1) circulation from central compartment(blood) to peripheral compartment(body tissues)  </br>
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2)  uptake and trafficking at cellular and sub-cellular level in target tissues. </br></br></br>
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<h3>Modeling Multi-compartmental Transport:</h3></br>
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In our lab work, we measured relatve level of GFP in brain, liver, lung and spleen after injecting anti-GFP siRNA into mouse. Thus, we decided to follow our lab work and separate compartments for brain, liver, lung and spleen. Other tissues are merged into one compartment. Each peripheral compartment has blood exchange with the central blood circulation, during which certain percentage of exosomes were captured into extracellular matrix of endothelial cells in different tissues.</br></br>
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<img src="model1.png" height="500" style="padding-left:170px;padding-right:170px" /></br>
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<p style="padding-left:80px;padding-right:80px;">Figure1. Schematic diagram of the arrangement of the different tissues in the pharmacokinetic model. The blood, along with exosomes, circulates from central compartment to five peripheral compartments.</p></br></br>
 +
Exosomes differ from conventional chemical drugs for its distinct biological characteristics as microvesicles(1).As membrane vesicles, exosomes may rapidly shift from associating with other complex and disassociating into free format during blood circulation. Besides, 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(2).Furthermore, the elimination of exosomes occurs mainly in specific tissues rather than during blood circulation, albeit that the half life of exosomes during blood circulation is much shorter(3).These two findings suggest the elimination rate of exosomes during blood circulation is negligible compared with that in target tissues and may not be considered in this part of pharmacokinetic model.</br></br>
 +
 +
Using standard mass action kinetics, the equations below describe the change of concentration(mass) of free exosomes over time in blood and target tissues.</br></br>
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 +
 +
 +
 +
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We would like to note that not all portion of exosomes is effective and totally absorbed by tissues. Therefore, paritiontissue is included to describe effective fraction of dose. Also, Et represents quantity of exosomes captured by extracellular matrix of cells in tissues. It does not represent the final quantity of exosomes in tissues, which will be discussed in next part of the model.</br>
 +
This work is supported by model of IGEM Slovenia 2012, IGEM NJU-China 2013 and other literatures(4,5).</br></br></br>
 +
<h3>Modeling Cellular Uptake and Intracellular Trafficking:</h3></br>
 +
There are variety of pathways for extracellular vesicles to be internalized by cells, namely phagocytosis, clathrin and caveolin-mediated endocytosis and macropinocytosis(6).We assume that receptor-mediated endocytosis is the major pathway of primary exosome internalization. </br></br>
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 +
The cellular uptake pathway can be summarized as depicted in Figure2. Exosomes bind to membrane of target cells after being captured by extracellular matrix and then internalized through endocytosis. The receptor-ligand interaction may facilitate this process. After internalization, RISC complex may escape from endosomes and endosomes may be ultimately eliminated by lysosomes. Although other pathways such as transcytosis and exocytosis following endocytosis might happen, we do not take them into account for simplification.</br></br>
 +
<img src="model2.png" height="600" style="padding-left:120px;padding-right:120px" /></br>
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<p style="padding-left:80px;padding-right:80px;">Figure2. Pathways shown to participate in exosomes uptake by target cells. Exosomes transport from extracellular matrix to cell surface and undergo intracellular trafficking after internalization. The RISC complex in exosomes is released and exosomes are ultimately degraded.</p></br>
 +
We can now define equations to describe above pathway. RVG modification helps exosomes bind to acetylcholine receptors specifically expressed in neuronal cells. Much easier are exosomes to be internalized provided that more exosomes bind to target cells. The binding process is modeled using mass action kinetics. AR denotes to number of acetylcholine receptors on target cells and km represents specific binding constant. Non receptor-ligand interaction mediated binding is summarized using kbindtissue.</br></br>
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 +
 +
 +
The internalization and elimination of exosomes are formulated below. Note that different tissues have different internalization and elimination rate. </br></br></br>
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 +
 +
 +
The quantity of endosomal RISC complex and escape behavior is modeled using following equation. The concentration of siRNA in exosome is determined by Real Time RT-PCR and represented by kc.</br></br></br>
 +
 +
 +
 +
This part of work is based on literature(4).</br></br></br>
 +
 +
<h3>Model Variables</h3>
 +
<table>
 +
<tr><td style="width:100px">Name</td>      <td style="width:200px">Model Compartment      <td style="width:500px">Description(Units)</tr>
 +
 +
<tr><td>Bcf</td>  <td>Plasma</td>   <td>Free exosomes in circulation(ug)</td> </tr>
 +
 +
<tr><td>Bcb</td> <td> Plasma</td>   <td>Bound exosomes in circulation(ug)</td> </tr>
 +
 +
<tr><td>Et</td>        <td>Extracellular</td>        <td>Free exosomes in extracellular matrix of cells in tissues(ug)</td> </tr>
 +
 +
<tr><td>Tb</td>        <td> Tissue</td>                  <td> Bound exosomes to cells in tissues(ug)</td> </tr>
 +
 +
<tr><td>brain</td>   <td>Brain cytoplasm</td> <td>Free exosomes in brain(ug)*</td> </tr>
 +
 +
<tr><td>liver</td>      <td>Liver cytoplasm</td>       <td> Free exosomes in liver(ug) *</td> </tr>
 +
 +
<tr><td>lung</td>      <td>Lung cytoplasm</td>      <td>Free exosomes in lung(ug) *</td> </tr>
 +
 +
<tr><td>spleen</td>    <td>Spleen cytoplasm</td>   <td>Free exosomes in spleen(ug) *</td> </tr>
 +
 +
<tr><td>other</td>      <td>Other tissues cytoplasm </td>      <td>Free exosomes in other tissues(ug) *</td> </tr>
 +
 +
<tr><td>Enc</td>      <td>Brain cytoplasm</td> <td>Free endosomal RISC complex in exosomes(ug) *</td> </tr>
 +
</table>
 +
 +
*: Exosomes become endosomes after interanalization. Here we still use term exosomes for clear illustration.</br></br>
 +
 +
<h3>Parameter Finding and Adjusting</h3>
 +
The most challenging part of modeling work is finding and adjusting parameters. After literature review, we are unfortunate to find that few of parameters have been measured or reported directly. The original paper written by Bartlett and Davis uses synthetic polyplexes as carrier to deliver siRNA(4). The stability and target ability of synthetic polyplexes diverge considerably from exosomes due to its chemical and biological nature. It is not appropriate if we just use all the parameters in the original paper without adjustment regardless of different biological nature and consequences. </br></br>
 +
 +
Parameter adjustment is not unusual in modeling biological process. This is a somewhat uncertain endeavor and lack of convincingness. 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(7).Following this doctrine, we run our simulation and try to fit the result to the experimental and literature data.</br></br>
 +
<table>
 +
<tr><td>Model Parameters</td>  <td>Decription(units)</td>      <td>Determination</td>        <td>Value</td></tr>
 +
 +
<tr><td>kblooddis</td>    <td> Exosomes dissociation from blood components(min-1)</td>    <td>Literature(4)</td>      <td> 1.7×10-4</td></tr>
 +
 
 +
 +
<tr><td>kbloodbind</td>  <td> Exosomes binding to blood components(min-1)</td>   <td>Literature(4)</td>   <td>1.7×10-6</td></tr>
 +
 
 +
 +
<tr><td>ktransblood</td>  <td>Exosomestransport from plasma to  extracellular fluid(min-1)</td>  <td> Literature(3,4)</td>    <td> 0.4</td></tr>
 +
 +
 +
<tr><td>Qc</td>        <td> Cardiac Output(L/min)</td>            <td>IGEM Slovenia 2012</td>  <td>5.6</td></tr>
 +
 +
<tr><td>Qbrain</td> <td> blood flowing through brain(L/min)</td>   <td>Literature(5)</td>    <td>7.8×10-1</td></tr>
 +
 +
<tr><td>Qlung</td> <td>blood flowing through lung(L/min)</td> <td>IGEM Slovenia 2012</td>  <td>5.6</td></tr>
 +
 +
<tr><td>Qliver</td>   <td>blood flowing through liver(L/min)</td>     <td>IGEM Slovenia 2012</td>  <td>1.4</td></tr>
 +
 +
<tr><td>Qspleen</td>   <td>blood flowing through spleen (L/min)</td>    <td>Estimated?</td> <td> 0.6</td></tr>
 +
 +
<tr><td>Qother</td>   <td>blood flowing through other tissues(L/min)</td>    <td>Determined logically</td>    <td> 2.8</td></tr>
 +
     
 +
<tr><td>parititionbrain</td>  <td>Effective fraction of dose available to brain</td>   <td>Estimated from literature(3,4,8,9)</td>    <td>1×10-1</td></tr>
 +
 +
  <tr><td>parititionlung</td>  <td>Effective fraction of dose available to lung</td> <td>Estimated from literature(3,4,8,9)</td>    <td>1.8×10-2</td></tr>
 +
 
 +
  <tr><td>parititionliver</td>  <td>Effective fraction of dose available to liver</td>  <td>Estimated from literature(3,4,8,9)</td>  <td>3.5×10-1</td></tr>
 +
 
 +
  <tr><td>parititionspleen</td>  <td>Effective fraction of dose available to spleen</td> <td>Estimated from literature(3,4,8,9)</td>  <td>2×10-1</td></tr>
 +
             
 +
  <tr><td>parititionother </td> <td>Effective fraction of dose available to other tissues</td> <td>Estimated from literature(3,4,8,9)</td>  <td>1×10-3</td></tr>
 +
 
 +
  <tr><td>kbindbrain</td>    <td>exosomes binding to extracellular matrix of endothelial cells in brain(min-1)</td>    <td>Estimated from literature(3,8,9) </td>    <td>1</td></tr>
 +
 +
<tr><td>kbindlung</td>    <td>exosomes binding to extracellular matrix of endothelial cells in lung(min-1) </td>    <td>Estimated from literature(3,8,9) </td>  <td>2×10-1</td></tr>
 +
 +
<tr><td>kbindliver</td>    <td>exosomes binding to extracellular matrix of endothelial cells in lung (min-1)</td>  <td>Estimated from literature(3,8,9)</td>  <td>1×102</td></tr>
 +
 +
<tr><td>kbindspleen </td>    <td>exosomes binding to extracellular matrix of endothelial cells in spleen(min-1)</td>  <td>Estimated from literature(3,8,9)</td>      <td>1</td></tr>
 +
 +
<tr><td>kbindother</td>    <td>exosomes binding to extracellular matrix of brain endothelial cells in other tissues(min-1)</td>    <td>Estimated from literature(3,8,9)</td>  <td>1×10-1</td></tr>
 +
 +
<tr><td>kintbrain</td>    <td>exosomes internalizing into brain(min-1)</td>  <td>Estimated from literature(4,10)</td>  <td>1×101</td></tr>
 +
   
 +
<tr><td>kintlung </td>  <td>exosomes internalizing into lung(min-1)</td>  <td>Estimated from literature(4,10,11)</td>  <td>1×102</td></tr>
 +
   
 +
<tr><td>kintliver</td>    <td>exosomes internalizing into liver(min-1)</td>  <td>Estimated from literature(4,10,11)</td>  <td>3×10-2</td></tr>
 +
   
 +
<tr><td>kintspleen </td>    <td>exosomes internalizing into spleen(min-1)</td>  <td>Estimated from literature(4,10,11)</td> <td>1×102</td></tr>
 +
   
 +
<tr><td>kintother</td>    <td>exosomes internalizing into brain(min-1)</td>  <td>Estimated from literature(4,10,11)</td>  <td>2×10-2</td></tr>
 +
   
 +
<tr><td>kelimtbrain</td>  <td>exosomes degradation in brain(min-1)</td>    <td>Estimated from literature(4,10,11)</td>  <td>6×10-2</td></tr>
 +
 +
<tr><td>kelimtlung </td> <td>exosomes degradation in lung (min-1)</td>  <td>Estimated from literature</td>  <td>2×10-2</td></tr>
 +
 +
<tr><td>kelimtliver</td>  <td>exosomes degradation in liver (min-1)</td>    <td>Estimated from literature</td>  <td>6×10-1</td></tr>
 +
 +
<tr><td>kelimtspleen</td> <td>exosomes degradation in spleen(min-1)</td>    <td>Estimated from literature</td>  <td> 4×10-3</td></tr>
 +
 +
<tr><td>kelimtother</td> <td>exosomes degradation in other tissue(min-1)</td> <td>Estimated from literature </td>  <td>5×10-3</td></tr>
 +
 +
<tr><td>AR</td>   <td>Number of acetylcholine receptors in brain(#)</td>  <td>Estimated? </td>     <td>1×1010</td></tr>
 +
 +
<tr><td>km</td>      <td>binding rates of RVG peptides to acetylcholine Estimated? </td>  <td>1×10-8</td>   <td>receptors(#-1min-1)</td> </tr>
 +
<tr><td>kescendvec</td>  <td>endosomal escape for RISC complex(min-1)</td> <td>Literature(4) </td>  <td>1.7×10-4</td></tr>
 +
 
 +
<tr><td>kc</td>  <td>concentration of RISC complex(#/ug)</td> <td>Literature(12)</td> <td>6.02×1012</td></tr>
 +
</table>
 +
</br>
 +
?: We are very uncertain about these parameters. However, we determine the magnitude of AR*km is about 102.</br></br>
 +
<h3>Results:</h3>
 +
We simulate the pharmacokinetic model and get initial results. Unfortunately, the results show that the model is not accurate. It is hard to distinguish the effects of RVG modification on tissue distribution of exosomes based on the figure below.</br>
 +
<table>
 +
</br>
 +
</br>
 +
<tr>
 +
<td>
 +
<p style="padding-left:80px;padding-right:80px;">Tissue distribution of exosomes without RVG modification</p>
 +
<img src="model3.png" height="300" style="padding-left:0px" /></td>
 +
<td>
 +
<p style="padding-left:80px;padding-right:80px;">Tissue distribution of exosomes with RVG modification</p>
 +
<img src="model4.png" height="300" style="padding-right:0px" /></td>
 +
</tr>
 +
</table>
 +
</br>
 +
<p style="padding-left:80px;padding-right:80px;">Figure3. Effect of RVG modification on tissue distribution of exosomes. A: Without RVG modification; B: With RVG modification. The initial results are simulated using the exact parameter set described above.</p></br>
 +
Why do we get unrealistic simulation results? The answer simply lies in the parameter set we choose. After performing parameter sensitivity analysis, we are surprised to find that it is not binding of exosomes to neuronal cell surface that determines the internalization rate. In contrast, the rate limiting step for exosome internalization is its capacity of being captured by extracellular matrix of endothelial cells.</br></br>
 +
 +
The blood brain barrier is formed by endothelial cells at the level of cerebral capillaries(13). The cerebral endothelial cells may form complex tight junctions that interfere the 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 concentrate at sites in proximity to peripheral nerves facilitating subsequent uptake and transfer to the central nervous system(14). The local concentrating of exosomes at proximal sites may significantly increase the effective fraction of dose available to target cells, resulting in more exosomes captured by extracellular matrix. Thus, we hypothesized that partitionbrain may also be influenced by RVG modification.</br>
 +
 +
With partitionbrain increased by 6 fold, we finally obtain optimized simulation results. </br></br>
 +
<table>
 +
</br>
 +
</br>
 +
<tr>
 +
<td>
 +
<img src="model5.png" height="300" style="padding-left:0px" /></td>
 +
<td>
 +
<img src="model6.png" height="300" style="padding-right:0px" /></td>
 +
</tr>
 +
<tr>
 +
<td>
 +
<img src="model7.png" height="300" style="padding-left:0px" /></td>
 +
<td>
 +
<img src="model8.png" height="300" style="padding-right:0px" /></td>
 +
</tr>
 +
</table>
 +
<p style="padding-left:80px;padding-right:80px;">Figure4. Effect of RVG modification on tissue distribution of exosomes. The results are simulated with partitionbrain increased by 6 fold. A-B: time course of distribution of exosomes without RVG modification. C-D: time course of distribution of exosomes with RVG modification. </p></br>
 +
We now understand our delivery device better using computational simulation data. The half life of exosome in blood is short, which agrees with literature findings(9).The pattern of tissue distribution of exosome with or without RVG modification is also consistent with literature(11) and our GFP experiment. Furthermore, the simulation data provides a new perspective for improving delivery device—modification of exosome is recommended to inhibit its internalization in non-interested tissues.</br></br>
 +
References:</br>
 +
<table>
 +
<tr>
 +
<td valign="top">1.</td> <td>El Andaloussi, S., Lakhal, S., Mager, I. and Wood, M.J. (2013) Exosomes for targeted siRNA delivery across biological barriers. Adv Drug Deliv Rev, 65, 391-397.</td>
 +
</tr>
 +
<tr>
 +
<td valign="top">2.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">3.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">4.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td  valign="top">5.</td> <td>Levitt, D.G. and Schoemaker, R.C. (2006) Human physiologically based pharmacokinetic model for ACE inhibitors: ramipril and ramiprilat. BMC clinical pharmacology, 6, 1.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">6.</td><td> Mulcahy, L.A., Pink, R.C. and Carter, D.R. (2014) Routes and mechanisms of extracellular vesicle uptake. J Extracell Vesicles, 3.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">7.</td> <td>Sible, J.C. and Tyson, J.J. (2007) Mathematical modeling as a tool for investigating cell cycle control networks. Methods (San Diego, Calif.), 41, 238-247.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">8.</td><td> 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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">9.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">10.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">11.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">12.</td> <td>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.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">13.</td> <td>Cecchelli, R., Berezowski, V., Lundquist, S., Culot, M., Renftel, M., Dehouck, M.P. and Fenart, L. (2007) Modelling of the blood-brain barrier in drug discovery and development. Nat Rev Drug Discov, 6, 650-661.</br></td>
 +
</tr>
 +
<tr>
 +
<td valign="top">14.</td> <td>Lentz, T.L., Burrage, T.G., Smith, A.L., Crick, J. and Tignor, G.H. (1982) Is the acetylcholine receptor a rabies virus receptor? Science, 215, 182-184.</br></td>
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</tr>
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</table>
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</TD>
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Revision as of 11:26, 13 September 2015

model

Delivery Module

Introduction:


Pharmacokinetics is the quantitative study of drug absorption, distribution and metabolism in the body. We created pharmacokinetic model to simulate the time-dependent tissue distribution of exosomes. To construct a strategy for developing efficient and safe in vivo RNAi therapy systems, pharmacokinetics at whole body, organ, cellular and sub-cellular level need to be considered.

In our preliminary wet lab study(GFP experiment), we obtain qualitative description of in vivo drug distribution after systematic administration. A computational and compartmental model can be built to give mechanistic insights into quantitative explanation of the experiment results.

There are three main aspects we take into account in this pharmacokinetic model:

Theoretically predicting the effect of RVG-modification of exosome on its target ability

Approximating time-series exosome(siRNA) concentration data for use in modeling RNAi kinetics in target tissue and subsequently calculating the effective dose

Finding out part of delivery system that could be improved based on simulation data


Model Methods:


The process of drug delivery in human and mouse is quite complex. Physiologically speaking, drug delivery after administration can be simplified into two separate phases:
1) circulation from central compartment(blood) to peripheral compartment(body tissues)
2) uptake and trafficking at cellular and sub-cellular level in target tissues.


Modeling Multi-compartmental Transport:


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


Figure1. Schematic diagram of the arrangement of the different tissues in the pharmacokinetic model. The blood, along with exosomes, circulates from central compartment to five peripheral compartments.



Exosomes differ from conventional chemical drugs for its distinct biological characteristics as microvesicles(1).As membrane vesicles, exosomes may rapidly shift from associating with other complex and disassociating into free format during blood circulation. Besides, 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(2).Furthermore, the elimination of exosomes occurs mainly in specific tissues rather than during blood circulation, albeit that the half life of exosomes during blood circulation is much shorter(3).These two findings suggest the elimination rate of exosomes during blood circulation is negligible compared with that in target tissues and may not be considered in this part of pharmacokinetic model.

Using standard mass action kinetics, the equations below describe the change of concentration(mass) of free exosomes over time in blood and target tissues.

We would like to note that not all portion of exosomes is effective and totally absorbed by tissues. Therefore, paritiontissue is included to describe effective fraction of dose. Also, Et represents quantity of exosomes captured by extracellular matrix of cells in tissues. It does not represent the final quantity of exosomes in tissues, which will be discussed in next part of the model.
This work is supported by model of IGEM Slovenia 2012, IGEM NJU-China 2013 and other literatures(4,5).


Modeling Cellular Uptake and Intracellular Trafficking:


There are variety of pathways for extracellular vesicles to be internalized by cells, namely phagocytosis, clathrin and caveolin-mediated endocytosis and macropinocytosis(6).We assume that receptor-mediated endocytosis is the major pathway of primary exosome internalization.

The cellular uptake pathway can be summarized as depicted in Figure2. Exosomes bind to membrane of target cells after being captured by extracellular matrix and then internalized through endocytosis. The receptor-ligand interaction may facilitate this process. After internalization, RISC complex may escape from endosomes and endosomes may be ultimately eliminated by lysosomes. Although other pathways such as transcytosis and exocytosis following endocytosis might happen, we do not take them into account for simplification.


Figure2. Pathways shown to participate in exosomes uptake by target cells. Exosomes transport from extracellular matrix to cell surface and undergo intracellular trafficking after internalization. The RISC complex in exosomes is released and exosomes are ultimately degraded.


We can now define equations to describe above pathway. RVG modification helps exosomes bind to acetylcholine receptors specifically expressed in neuronal cells. Much easier are exosomes to be internalized provided that more exosomes bind to target cells. The binding process is modeled using mass action kinetics. AR denotes to number of acetylcholine receptors on target cells and km represents specific binding constant. Non receptor-ligand interaction mediated binding is summarized using kbindtissue.

The internalization and elimination of exosomes are formulated below. Note that different tissues have different internalization and elimination rate.


The quantity of endosomal RISC complex and escape behavior is modeled using following equation. The concentration of siRNA in exosome is determined by Real Time RT-PCR and represented by kc.


This part of work is based on literature(4).


Model Variables

Name Model Compartment Description(Units)
Bcf Plasma Free exosomes in circulation(ug)
Bcb Plasma Bound exosomes in circulation(ug)
Et Extracellular Free exosomes in extracellular matrix of cells in tissues(ug)
Tb Tissue Bound exosomes to cells in tissues(ug)
brain Brain cytoplasm Free exosomes in brain(ug)*
liver Liver cytoplasm Free exosomes in liver(ug) *
lung Lung cytoplasm Free exosomes in lung(ug) *
spleen Spleen cytoplasm Free exosomes in spleen(ug) *
other Other tissues cytoplasm Free exosomes in other tissues(ug) *
Enc Brain cytoplasm Free endosomal RISC complex in exosomes(ug) *
*: Exosomes become endosomes after interanalization. Here we still use term exosomes for clear illustration.

Parameter Finding and Adjusting

The most challenging part of modeling work is finding and adjusting parameters. After literature review, we are unfortunate to find that few of parameters have been measured or reported directly. The original paper written by Bartlett and Davis uses synthetic polyplexes as carrier to deliver siRNA(4). The stability and target ability of synthetic polyplexes diverge considerably from exosomes due to its chemical and biological nature. It is not appropriate if we just use all the parameters in the original paper without adjustment regardless of different biological nature and consequences.

Parameter adjustment is not unusual in modeling biological process. This is a somewhat uncertain endeavor and lack of convincingness. 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(7).Following this doctrine, we run our simulation and try to fit the result to the experimental and literature data.

Model Parameters Decription(units) Determination Value
kblooddis Exosomes dissociation from blood components(min-1) Literature(4) 1.7×10-4
kbloodbind Exosomes binding to blood components(min-1) Literature(4) 1.7×10-6
ktransblood Exosomestransport from plasma to extracellular fluid(min-1) Literature(3,4) 0.4
Qc Cardiac Output(L/min) IGEM Slovenia 2012 5.6
Qbrain blood flowing through brain(L/min) Literature(5) 7.8×10-1
Qlung blood flowing through lung(L/min) IGEM Slovenia 2012 5.6
Qliver blood flowing through liver(L/min) IGEM Slovenia 2012 1.4
Qspleen blood flowing through spleen (L/min) Estimated? 0.6
Qother blood flowing through other tissues(L/min) Determined logically 2.8
parititionbrain Effective fraction of dose available to brain Estimated from literature(3,4,8,9) 1×10-1
parititionlung Effective fraction of dose available to lung Estimated from literature(3,4,8,9) 1.8×10-2
parititionliver Effective fraction of dose available to liver Estimated from literature(3,4,8,9) 3.5×10-1
parititionspleen Effective fraction of dose available to spleen Estimated from literature(3,4,8,9) 2×10-1
parititionother Effective fraction of dose available to other tissues Estimated from literature(3,4,8,9) 1×10-3
kbindbrain exosomes binding to extracellular matrix of endothelial cells in brain(min-1) Estimated from literature(3,8,9) 1
kbindlung exosomes binding to extracellular matrix of endothelial cells in lung(min-1) Estimated from literature(3,8,9) 2×10-1
kbindliver exosomes binding to extracellular matrix of endothelial cells in lung (min-1) Estimated from literature(3,8,9) 1×102
kbindspleen exosomes binding to extracellular matrix of endothelial cells in spleen(min-1) Estimated from literature(3,8,9) 1
kbindother exosomes binding to extracellular matrix of brain endothelial cells in other tissues(min-1) Estimated from literature(3,8,9) 1×10-1
kintbrain exosomes internalizing into brain(min-1) Estimated from literature(4,10) 1×101
kintlung exosomes internalizing into lung(min-1) Estimated from literature(4,10,11) 1×102
kintliver exosomes internalizing into liver(min-1) Estimated from literature(4,10,11) 3×10-2
kintspleen exosomes internalizing into spleen(min-1) Estimated from literature(4,10,11) 1×102
kintother exosomes internalizing into brain(min-1) Estimated from literature(4,10,11) 2×10-2
kelimtbrain exosomes degradation in brain(min-1) Estimated from literature(4,10,11) 6×10-2
kelimtlung exosomes degradation in lung (min-1) Estimated from literature 2×10-2
kelimtliver exosomes degradation in liver (min-1) Estimated from literature 6×10-1
kelimtspleen exosomes degradation in spleen(min-1) Estimated from literature 4×10-3
kelimtother exosomes degradation in other tissue(min-1) Estimated from literature 5×10-3
AR Number of acetylcholine receptors in brain(#) Estimated? 1×1010
km binding rates of RVG peptides to acetylcholine Estimated? 1×10-8 receptors(#-1min-1)
kescendvec endosomal escape for RISC complex(min-1) Literature(4) 1.7×10-4
kc concentration of RISC complex(#/ug) Literature(12) 6.02×1012

?: We are very uncertain about these parameters. However, we determine the magnitude of AR*km is about 102.

Results:

We simulate the pharmacokinetic model and get initial results. Unfortunately, the results show that the model is not accurate. It is hard to distinguish the effects of RVG modification on tissue distribution of exosomes based on the figure below.


Tissue distribution of exosomes without RVG modification

Tissue distribution of exosomes with RVG modification

Figure3. Effect of RVG modification on tissue distribution of exosomes. A: Without RVG modification; B: With RVG modification. The initial results are simulated using the exact parameter set described above.


Why do we get unrealistic simulation results? The answer simply lies in the parameter set we choose. After performing parameter sensitivity analysis, we are surprised to find that it is not binding of exosomes to neuronal cell surface that determines the internalization rate. In contrast, the rate limiting step for exosome internalization is its capacity of being captured by extracellular matrix of endothelial cells.

The blood brain barrier is formed by endothelial cells at the level of cerebral capillaries(13). The cerebral endothelial cells may form complex tight junctions that interfere the 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 concentrate at sites in proximity to peripheral nerves facilitating subsequent uptake and transfer to the central nervous system(14). The local concentrating of exosomes at proximal sites may significantly increase the effective fraction of dose available to target cells, resulting in more exosomes captured by extracellular matrix. Thus, we hypothesized that partitionbrain may also be influenced by RVG modification.
With partitionbrain increased by 6 fold, we finally obtain optimized simulation results.



Figure4. Effect of RVG modification on tissue distribution of exosomes. The results are simulated with partitionbrain increased by 6 fold. A-B: time course of distribution of exosomes without RVG modification. C-D: time course of distribution of exosomes with RVG modification.


We now understand our delivery device better using computational simulation data. The half life of exosome in blood is short, which agrees with literature findings(9).The pattern of tissue distribution of exosome with or without RVG modification is also consistent with literature(11) and our GFP experiment. Furthermore, the simulation data provides a new perspective for improving delivery device—modification of exosome is recommended to inhibit its internalization in non-interested tissues.

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