Gel optics modelling RNA organelle modelling Logic circuit modelling

Gel Optics Modelling

Characterizing the light signal inside the gel medium in which our bacteria grow is necessary to predict the performance of our optic control system.

We developed a strategy to measure the light intensity landscape created by a laser going through a gel (See Gel Optics page ) . We described this intensity landscape by fitting its absorption and scattering. Since the scattering observed was low, we tested whether we could predict the intensity landscape in a given gel (0.5% Gelrite with LB media) based on a simple cuvette absorbance reading.

The absorbance readings were used to find [ε*C], the parameter which governs the logarithmic decrease of the laser (see Table 2 on Gel Optics page).
We assumed the light scattering in 0.5% Gelrite to be the same as in 1% Gelrite. This is an oversimplification but predicting the scattering of a gel based on its concentration would make it necessary to acquire light diffusion data for a range of gel concentrations which was outside the scope of our model development.

We observed that our predicted light profiles were close to the fit of the intensity data recorded. This suggest that the intensity profile of a laser in the gel can be characterize from a single absorbance reading.

Fig:

Laser Beam Shape Modelling

To predict and visualize the volume of gel in which the immobilized bacteria would be activated, we modelled the 3D shapes of the laser in the different gels. We assumed that bacteria would be sharply activated in an ON/OFF manner when light reached an intensity threshold equal to 80% the intensity used in the optogenetic work of Fernandez-Rodriguez et al. This allowed us to predict the volume activated by our two intersecting laser at any point within the three gel characterized.

At 6cm depth, the activating volume was of the order of a few mm² for the 1% gels. This is very promising as it suggests that a sub-mm² resolution could be obtained with lasers having a smaller beam diameter in less concentrated gels.

RNA

Introduction

Creating a microenvironment in a chassis is a groundbreaking way to allow the implementation of foreign introduced pathway to another species. Previous studies have observed that liquid phase separation occurs in mammalian cells, under the production of mutated RNA sequences with tri-nucleotide repeats - such as CAG. These RNA strands agglomerate to form a membrane-less organelle.

Therefore Medusa aimed at reproducing this phenomenon in a chosen chassis cell by designing synthetic RNA sequences made up of CAG repeats to different lengths. In our model, we characterised the organelle formation and kinetics, which in turn influenced our experimental design.

Liquid phase Separation - Flory Huggins

We wanted to first characterise the RNA organelles under different repeat lengths to ensure liquid phase separation. This was done through applying the Flory Huggins solution theory, which is a mathematical model of the thermodynamics involved in polymer-solvent solutions, in our case- water and RNA (Brangwynne et al. 2015).

Where n1, and n2 define the concentration and Φ1 and Φ2 define the volume fraction of the water and the RNA ‘polymer’ respectively. The parameter χ12 is the interaction parameter defined as such:

Where z is the lattice space interaction, k is the Boltzmann constant and T is the temperature. The interaction parameters are defined as: w12 solvent-polymer, w11 solvent-solvent, w22 polymer polymer.

The interaction parameter in the Flory-Huggins Solution specifies whether phase separation occurs in the mixture.

Therefore we tested this with various different length of RNA repeats, whose interaction parameters calculated through structural modelling of the RNA folding and cofolding using NuPack and cross referenced with SimRNA data (which was tested with the help of the IONIS iGEM team.)

This structural modelling demonstrated that the longer the repeat, the stronger the monomer- monomer interaction, which would be favourable for RNa organelle formation.

The χ12 was then calculated for each of the lengths to see what length of RNA showed agglomeration formation. It was shown that all lengths tested were able to form agglomerations, as all the χ12 values are positive. This included strands starting from 5 repeats ranging to 70 repeats.

With this information, we did not only focus on creating synthetic RNA strands with very large numbers of repeats but relied on a more random method to give us a larger variation in repeat lengths starting from smaller sizes.

Strand	χ12
5xCAG	1.25E+21
15xCAG	9.06E+20
20xCAG	8.43E+20
24xCAG	7.55E+20
40xCAG	7.76E+20
45xCAG	7.7E+20
50xCAG	7.62E+20
70xCAG	9.68E+20

See more in pdf

Logic circuit modeling

Recent work on transcription elements showed that assembling insulated synthetic operator upstream and downstream of a insulated T7 promoter core allowed for a more diverse control of gene expression and a more specific response time (Zong et al., 2017).
More importantly, the expression of a gene regulated by such repressible promoters can be well-described by a simple equation:

α, β , η_A, K_A are respectively the maximal and basal promoter activity, the Hill coefficient and the dissociation constant of the transcriptional activator-promoter core pair. η_R and Κ_R represent the Hill coefficient and dissociation constant of the binding of a repressor to its cognate operator. δ_R represents the relaxation time, the expected time in which an operator is not bound to any repressor.

Making the assumption that the elements are insulated, we can easily combine them to create not single but dually repressible promoters, and predict their performance by generalising equation 1. In Equation (2), the fact that more than one repressor type binding to the promoter was taken into account and changes to relaxation time and the number of total microstates in the equilibrium were made accordingly.

Figure 1:

Using the experimental data acquired from single repressible promoters, we were able to simulate the behavior of corresponding dually repressible promoters. The experimental data was obtained by testing the impact of different configurations of operators (Figure 1) on gene expression. Results from the data obtained in configuration A and B were combined in silico to create a large number of promoters. Indeed, we worked with 11 different repressors, leading to a total of 110 promoters. The results obtained for the entirety of this library are available here. We will focus for now on three repressors with interesting behaviors:

Figure 2: Modeling results for an in silico dually repressible promoter.

These three candidates were chosen for further testing depending on parameter values: the dissociation constant of repressor-operator binding had to be reasonably low and the Hill coefficient η needed to allow for a cooperative behavior. They are also easily available on the iGEM registry and are very commonly used in research. Each promoter was designed to contain two out of the three chosen repressors - TetR, P22c2, HKcI. For each couple of repressors, four different arrangements of the operators were characterized experimentally under different input combinations. More information on the experimental part of this project can be found here.

References

Brangwynne, C.P., Tompa, P. and Pappu, R.V., 2015. Polymer physics of intracellular phase transitions. Nature Physics, 11(11), pp.899-904.

Zong, Y., Zhang, H., Lyu, C., Ji, X., Hou, J., Guo, X., Ouyang, Q. and Lou, C. (2017). Insulated transcriptional elements enable precise design of genetic circuits. Nature Communications, 8(1).

Centre for Research and Interdisciplinarity (CRI)
Faculty of Medicine Cochin Port-Royal, South wing, 2nd floor
Paris Descartes University
24, rue du Faubourg Saint Jacques
75014 Paris, France

bettencourt.igem2017@gmail.com

Team:Paris Bettencourt/Model