Model of Liposome Gene Delivery

Background

Liposomes or plasmids may become lost and not able to reach the nucleus due to degradation in cells during transmission. This loss, among many, brings difficulties to the development and clinical application of gene drugs. Quantitative study of plasmid loss and transfection efficiency during lipofection is of great significance for the delivery of gene drugs. Therefore, we simulated the transfection and plasmid loss of a liposome gene delivery system in silico. In our model, we used queuing network and memoryless Markov process to describe the transmission of liposomes and plasmids.

Model description

There are ten states and nine transmission processes during the lipofection. The first step of liposome gene delivery is endocytosis, a process that liposomes in the surrounding are delivered to the cell in the form of endosomes (from ① to ②). The second step is endosomal escape. In this step, some of the liposomes in endosome could escape（from ② to ④） but some others are degraded by lysosome（from ② to ③）. What happens next is that the liposomes are tagged with a nuclear locus signal (NLS)（from ④ to ⑦） or ruptured to release the naked plasmid（from ④ to ⑤）. The naked plasmids in the cytoplasm then could also be added with a nuclear locus signal（from ⑤ to ⑧） or degraded（from ⑤ to ⑥）. Eventually, liposomes or naked plasmids with a nuclear locus signal are successfully delivered into the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）(Figure.1). These plasmids in the nucleus are then transcribed to do their job. Plasmids that degrade at any point during the whole process are unavoidably lost.

Figure.1 Primary transmission chain between cell membrane and nucleus

In our model, we assumed that there were 90000 plasmids packed in 9000 liposomes and all the liposomes enter the cells in the form of endosome. Then we generate 9000 random numbers following exponential distribution to describe the internalization time.

For those transmission step that have two probable routes(A and B), Figure.2 shows the algorithm of what happened in a millisecond. All of the steps that have two proper routes act like this, including endosome escape or degradation (from ② to ③ or ④), liposome adding NLS or degradation(from ④ to ⑤ or ⑦) and plasmid adding NLS or degradation (from ⑤ to ⑥ or ⑧).

Figure.2 Algorithm of transmission that have two probable routes

For those transmission step that only have one probable route, Figure.3 shows the algorithm of what happened in a millisecond. Liposomes or naked plasmids that successfully enter the nucleus （from ⑦ to ⑨ and from ⑧ to ⑩）act like this.

Figure.3 Algorithm of transmission that have one probable routes

In summary, we generated 9000 exponentially distributed numbers to describe the moment of each liposome internalization and then took a millisecond as a time interval. During every millisecond, we checked the number of liposomes/plasmids in every queue and calculated the transfer probability according to our algorithm. We then generate random numbers subject to normal distribution and compared it with the transfer probability, then conclude where it should go. What happens in such a millisecond have been actually repeated for 64800000 times in 18 hours after liposomes are added to the cell.

Significance

It is reported that the saturation number of plasmids that can be delivered to one cancer cell is 90000. By conducting our Model of Liposome Gene Delivery, we find that an injection of 90000 plasmids can lead to 44270 of which (49.19%) been transported into the nucleus successfully, what’s more, this result is promising since it enables us to predict the minimum transfection amount to guarantee enough number of of plasmids in nucleus during our experiments. Furthermore, we are able to calculate the amount of the plasmids we need to administrate in order to obtain therapeutic efficiency which is very instructional for our further application in vivo.

Click here to get the parameter, formula, results and reference.

Click here to get the code.

Cost-effectiveness analysis model

Background

Hepatocellular carcinoma (HCC) has a huge impact on human health and remains a huge burden to people all over the world. Intense research has been and will be made against this disease, so the number of available medical treatments should be expected to continue growing. For researchers and investors, the current market and competition tend to be obscured by ever-new attractions and tendencies.

In this cases, there are two main questions:

1. How to determine if a new therapy is interesting for practical application?

2. How to balance the pay and gain of the patients? How to set up a reasonable price for the patients?

To solve these problems, mathematical modeling would come in handy as it helps to explain and to study the effects of different factors, and to make predictions about new products. Therefore, efforts have been made by us to set up a model that estimates the efficiency and cost of these medical treatments.

Model description

During the clinical trials, researchers can’t really follow and record the patients until they die. However, in this model, we can define several states of the patients in advance. After every month’s medical intervention and collection of the data, we can put patients into the corresponding states and calculate the transfer probabilities (Figure.1). By running the program that we have written based on this model, we can predict the survival curve of each medical treatment.

Figure.1 The state space and the transfer relationship in our model

Then the utility can be estimated by doing some questionnaire survey and lab tests in specific disease contexts. As we mentioned before, with the life span and the utility, the quality-adjusted life years then can be calculated.

Since we can get the efficacy of different medical intervention in the model, the next step is to estimate a reasonable price (Figure.2). Companies can calculate the ICER of their products with their prospect price and compare it to other drugs of the same type contemporarily on the market.

Figure2. Schematic of how to set up a reasonable price for the patients through CUA.

Significance

Based on clinical data, we can learn the efficacy of different drugs through our Cost-effectiveness analysis model, then further estimate a reasonable price (Figure.2). This model enables us to predict the price of our system when it comes to a drug in future which contributes to our business plan and the realizable analyze of our project. Furthermore, we are proud to notice that not only our team but also the whole iGEM community and public can also benefit from this model. Since they can understand the efficacy as well as calculate the ICER of their products to know their prospect price, then compare it to other drugs of the same type contemporarily on the market to test products’ practicability.

Click here to get the parameter, formula result and reference.

Click here to get the code.