Team:Wageningen UR/Modeling

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== Modelling ==
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=== Introduction ===
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= Modeling =
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In our [[Team:Wageningen_UR/Project|project]] there are multiple aspects that we can model. Starting at the modelling of the formation of VLPs under different conditions, continuing at a dispersion model for when VLPs are injected into a human body and ending at marcro-models for degredation of VLPs in the environment.
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Formation of modified Virus-Like Particles is key to the success of our project. Therefore we first [[Team:Wageningen_UR/InSilico|predict the structure of the subunits]] after which we use a [[Team:Wageningen_UR/FormationModel|model describing the formation of the whole VLPs]].
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We chose to model VLP formation and aggregate formation.
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=== VLP Formation ===
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Finally, we wanted to know the applicability of our device. Therefore, we used a human body model which is based on the model made by the [[Team:Slovenia/ModelingPK|Slovenia 2012 iGEM team]]. We extensively modifyed this model to make it applicable for VLPs, their affinity with diseased tissue, the speed of excretion and degradation and finally, the drug delivery at the targeted tissue.
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A VLP has a certain number of subunits or monomers. In the case of CCMV, there are 180 subunits which go on to form capsomeres in the form of pentamers or hexamers and self-assemble according to the triangulation number, T=7 to form a capsid approximately 28nm in diameter. The CCMV capsid consists of 12 pentameric capsomeres and 20 hexagonal ones. But for the sake of modelling, we take an average of it forming 36 pentameric capsomeres.
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*[https://2012.igem.org/Team:Wageningen_UR/HumanBody Human Body Model]
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*[https://2012.igem.org/Team:Wageningen_UR/InSilico Tertiary Structure Modeling]
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For modelling our VLPs we needed to find a model which could fit the assembly of our entire virus like particles, namely, CCMV, HBV and PLRV. Presently, assembly of virus particles is not fully understood and different idealized models and theories are present which try to explain the assembly process. One such theory is the classical nucleation theory, where the self-association reaction begins with a nucleation event followed by elongation through sequential addition of free subunits, one at a time, to nuclei and partially assembled intermediates, until a closed icosahedral VLP is formed. Nucleus formation is regarded as the rate-limiting step.
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*[https://2012.igem.org/Team:Wageningen_UR/FormationModel VLP Assembly Model]
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The effective concentration of capsomeres participating in
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self-association, C, is defined as:
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(1) C = C<sub>total</sub> – C<sub>critical</sub>
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C<sub>total</sub> is the total capsomere concentration and C<sub>critical</sub> is the critical capsomere concentration. The critical concentration is defined as the concentration below which VLP formation will not take place.
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It is considered that a dimer is the first species (nucleus) formed in the reaction, and is subsequently consumed to form higher-order intermediates by the addition of free subunits.
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(2) dC<sub>2</sub>/d<sub>t</sub> = (1/2) * k<sub>v,critical</sub> * C<sub>2</sub> – k<sub>v</sub> * C * C<sub>2</sub>
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where C<sub>2</sub> is the dimer (nucleus) concentration, k<sub>V,crit</sub> (M<sup>-1</sup> s<sup>-1</sup>) the nucleation rate constant and k<sub>V</sub> (M<sup>-1</sup> s<sup>-1</sup>) the elongation rate constant.  
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The aggregation of  the viral protein is modelled by a second-order reaction describing the agglomeration of two capsomeres:
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(3) dA/dt = (1/2) * k<sub>A</sub> * C<sub>2</sub>
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where A is the aggregate concentration and k<sub>A</sub> (M<sup>-1</sup> s<sup>-1</sup>)  the aggregation rate constant.
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The competing reactions of VLP assembly and aggregation can thus be described by the following set of equations:
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(4) dC/dt = k<sub>V,critical</sub> * C<sub>2</sub> - k<sub>V</sub> * C * ∑_(i=2)^(s-1) C<sub>i</sub>  - k<sub>A</sub> * C<sub>2</sub>
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(5) dC<sub>i</sub>/dt = k<sub>V</sub> *C * (C<sub>i-1</sub> - C<sub>i</sub>); i= 3; 4; . . . ; s-1
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(6) dV/dt = k<sub>V</sub> * C * C<sub>s-1</sub>
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where V is the VLP concentration, s is the number of subunits in a correctly formed VLP (36 in the case of CCMV), and i is the number of subunits in a given intermediate. The initial conditions at t=0 were set as C=C<sub>0</sub> and C<sub>2</sub> = C<sub>3</sub> =...... = C<sub>35</sub>= V=A=0.
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Parameters to be determined were C<sub>critical</sub>, K<sub>v</sub>, K<sub>v,critical</sub> and k<sub>A</sub>
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Latest revision as of 19:12, 26 October 2012

Modeling

Formation of modified Virus-Like Particles is key to the success of our project. Therefore we first predict the structure of the subunits after which we use a model describing the formation of the whole VLPs.

Finally, we wanted to know the applicability of our device. Therefore, we used a human body model which is based on the model made by the Slovenia 2012 iGEM team. We extensively modifyed this model to make it applicable for VLPs, their affinity with diseased tissue, the speed of excretion and degradation and finally, the drug delivery at the targeted tissue.

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