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Team:Freiburg/Content/Results/Modeling
From 2014.igem.org
Modeling
The AcCELLerator is based on the combination of two systems: the light-regulated gene expression and the retroviral gene delivery.
MLV Infection
Model Formulation
In our project, gene delivery was achieved by infecting the cells with recombinant murine leukemia virus (MLV). As a typical retrovirus, its life cycle has been well characterized. Usually, this process can be divided artificially into several steps, including adsorption, internalization, integration, replication, assembly and release. However, our recombinant MLVs lacked the genes which are essentially for the replication and the virus assembly. Thus only the gene of interest (GOI) could be integrated into the genome and expressed. The process from adsorption to integration can be again subdivided into seven steps, so that each step can be described with a simple mathematical model.
Figure 1. (1) The infection is initiated by the adsorption of the virions onto the cell surface, which is covered by the specific receptor mCAT1. (2) Once the virion binds with the receptor, fusion of viral and cell membrane is triggered and the viral core is internalized into the cytoplasm. (3) Using viral RNA as template, double stranded DNA is produced by reverse transcriptase. (4) The viral DNA is then transported along the microtubuli to the microtubule organizing center near the nucleus. (5) During the transcription and transport, the viral molecules could be degraded by cellular factors. (6) During cell division, the nuclear envelope dissolves and the viral DNA is imported into the nucleus. (7) Viral DNA is integrated into the chromosome by integrase. (modified from1)
The whole infection process was described by a set of differential equations, which was adopted from a previous work1 with small modifications.
First, a viral suspension of depth h was added to a layer of adherent cells to infect them (see Fig. 2). The concentration of the virion (Vm) is a function of both time and depth. It is influenced by four different processes: diffusion, sedimentation, degradation and binding.
Figure 2. Virus suspension and cells
The diffusion of the virions follows the fick’s law of diffusion. u is the velocity of sedimentation due to gravity. Since the virions are instable at 37°C, they decay in the medium with a constant decay rate kd_vm. Thus an additional term was added to the partial differential equation (PDE).
