Team:Shenzhen SFLS/Drug Designing
Introduction
At first, we intended to use liposome as genetic vector. However, experiment data shows that liposome (has blank plasmid in it) has a high cytotoxic effect. When the liposome concentration is 4μg/mL, the number of cells died from cytotoxic effect is even greater than the number of survival cells (G361). Because the malignant degree of A375 is higher than G361, cytotoxic effect seems much weaker in A375.
Therefore, we planned to use lentivirus as gene vector, which is reported to have lower cytotoxic effect and higher transduction efficiency than liposome vector. Lentiviruses enter into cells when transducing, while most kinds of viruses bind to cellular membrane and inject their genetic material into cells.
As the picture shown, the lentiviruses behave two ways in vivo: Diffusion and reaction (entering cells). The concentration of drug is a function of time (since injection of drug) and position (the distance to drug injection site).
Diffusion part
we assume that lentiviruses diffusing in extracellular substance is unsteady-state diffusion, which follows Fick’s Second Law:
Cdiff is the concentration of drug which participates diffusion ,C is the concentration of drug at certain time and position. t is time, D is the diffusion coefficient, ∇C is the concentration gradient of drug in vivo.
In order to reduce the quantity of calculation, we consider the diffusion coefficient D is a constant, which does not change over time or space. Thus, the equation can be written as:
Δ is the Laplace operator.
Reaction part
We assume that at each moment, the number of lentiviruses entering into cells is proportional to the concentration of lentivirus at which time and position.
Creac is the concentration of drug which participates the reaction,C is the concentration of drug at certain time and position, k is a constant.
Combining the two terms together, we have:
The partial differential equation has the following boundary conditions:
I means that at the moment of injection, the drug has not diffused or entered into cells, so the concentration at the injection site is the initial drug concentration C0.
II means that when drug gets to the border of the dermis and subcutaneous tissue (where the distance to injection site is χc), it will be immediately taken away through the complex network of blood vessels.
Future work
Due to the limited time, we could not realize our genetic circuit into drugs. We also failed to find data from the existing articles with which the values of parameters can be perfectly determined.
After determining the parameters, we can know the concentration at any time and position, when the initial concentration is set.
Reference
