Difference between revisions of "Team:NTNU Trondheim/Collaborations"

Collaborations

I. Brixells modeling (University of Warwick)

Team Warwick has shown interest in our offer to help in modeling and quantitative analysis that we have posted on the iGEM Matchmaker. Team Warwick is aiming to provide precision control over spatial arrangement of cells by designing a tool that enables drawing and building with them.

Zinc finger proteins are intracellular molecules which recognize and bind unique dsDNA sequences. We have engineered these proteins to be expressed on the surface of an E. coli cell, such that dsDNA can be used as mortar to cement cells together. Team Warwick plans to demonstrate this principle by assembling fluorescent cells onto a 2D surface and producing microscopic images, with the ultimate goal being to build complex 3D structures comprised of different cell types. This level of control over cellular localisation is useful in multiple fields including research into cell-cell interactions in microbial communities, multicellularity, and the construction of 3D cell structures in tissue engineering.

The collaboration focused on two elements:

1. Calculating the probability of formation, including the probability of E. Coli bonding correctly.

2. Calculating the effect of arm length on structure changes increases. This has been motivated by the observation that the longer the arms the higher the likelihood that the e.coli cells can attach because they are less closely packed and such wouldn't get in each others way.

There are many methods to look at this kind of problems, but the most realistic may require huge computational resources. So it is necessary to find an approach that is experimentally relevant, computationally tractable, and reflecting the biophysics underlying Brixells.

We, Team NTNU Trondheim have offered ideas, modeling frameworks, software simulation, and data analysis to answer these questions, based on information theory and thermodynamics. For Problem 1, we have suggested an approach in terms of binding affinity and specificity where the information entropy is used as a measure of specificity. For Problem 2, we have suggested a thermodynamics approach using the Poisson-Boltzmann theory where the zinc fingers and E. Coli are approximated by a set of beads (one large bead for the E. Coli, small beads for each zinc finger, and a rod of beads for the DNA arm. Team Warwick has been enthusiastic about this approach since it is a stochastic method that they have not considered, and they have provided that us with data related to the geometry of E. Coli-arm formation.

I.1) Probability of bond formation

$$P=\prod _i{P}_i$$ $$P_i=\frac{S_i}{W(S_i)}$$ $$S_i=\sum _j\frac{K_{i,j}}{\sum _j{K}_{i,j}}\ln (\frac{K_{i,j}}{⟨K_{i,j}⟩})$$ $$P_{i,j}^{\mathit{bound}}=\frac{[F_i]}{[F_i]+K_{i,j}}$$ $$A_i+F_j\iff A_i{F}_j$$

I.2) Effect of arm length

$$K_{i,j}=e^{\frac{\mathrm{\Delta }{G}_{i,j}}{\mathit{RT}}}$$ $$E_{m,n}=\frac{q_m{q}_n}{8\mathrm{\pi }\mathrm{ϵ}{R}_{m,n}^2}$$ $$V_{m,n}=\frac{-A}{6}(\frac{2{\mathrm{\rho }}_m{\mathrm{\rho }}_n}{R_{m,n}^2-{({\mathrm{\rho }}_m+{\mathrm{\rho }}_n)}^2}+\frac{2{\mathrm{\rho }}_m{\mathrm{\rho }}_n}{R_{m,n}^2-{({\mathrm{\rho }}_m-{\mathrm{\rho }}_n)}^2}+\ln (\frac{R_{m,n}^2-{({\mathrm{\rho }}_m+{\mathrm{\rho }}_n)}^2}{R_{m,n}^2-{({\mathrm{\rho }}_m-{\mathrm{\rho }}_n)}^2}))$$ $$g_{m,n}=\frac{R_{m,n}}{4{\mathrm{\rho }}_m{\mathrm{\rho }}_n}$$ $$f_{m,n}=\sqrt{R_{m,n}^2+{\mathrm{\rho }}_m{\mathrm{\rho }}_n{e}^{-g_{m,n}}}$$ $$S_{m,n}=\frac{1}{8\mathrm{\pi }}(\frac{1}{{\mathrm{\epsilon }}_0}-\frac{1}{\mathrm{\epsilon }})\frac{q_m{q}_n}{f_{m,n}}$$ $$G^{\mathit{bound}}=\sum _{\begin{array}{c}m,n=1\\ n\ne m\end{array}}^{M+N}(S_{m,n}+V_{m,n}+E_{m,n})$$ $$G^{\mathit{unbound}}=\sum _{\begin{array}{c}m,n=1\\ n\ne m\end{array}}^N(S_{m,n}+V_{m,n}+E_{m,n})+\sum _{\begin{array}{c}m,n=N+1\\ n\ne m\end{array}}^{M+N}(S_{m,n}+V_{m,n}+E_{m,n})$$ $$\mathrm{\Delta }G=G^{\mathit{bound}}-G^{\mathit{unbound}}$$

I.3) Numerical evaluation

II. iGEM Matchmaker and LabSurfing (Technische Universität Darmstadt)