RNA

Introduction

Liquid phase Separation - Flory Huggins lattice modeling

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.)

See more in pdf

RNA organelle preference and selectivity on specific chemical reactions over non-specific ones - Analytical solution on reaction-diffusion systems

Once we proved that the RNA repeats could assemble together and form to an synthetic "organelle" rapidly, we wants to know if the RNA organelle could fulfill our need - reduce the underground reactions and improve the efficiency of desired reactions. Given the facts that in bacteria, all the components and reactants come from the cytoplasm, not synthesized inside the organelle itself, the situation turns to be very complicated. Besides, how the natural organelles works in this situation was still unclear -- which may be very important for us to understand the initial fitness emerged in organelles and to better design and engineer synthetic organelles. In this study, we compare the composition reaction hosted by the organelles or the cytoplasm (considered as a homogeneous mixture). Using chemical reaction steady state analysis, we generated an analytical solution of the complex quadratic dynamic system for the cytoplasm behavior according to the law of mass action. For the reaction model when the organelle exists in the cell, we hybridized the model we used for the cytoplasm and a specific reaction-diffusion model to describe the specific behaviors on the surface and inside of the organelle (Figure RD 1). In our analysis, we found that the RNA organelles prefer to enhance the reactions with high reaction rate constant (constant k) -- double the production at most, but make the whole-cell production rate significantly when the reaction rate constant is low (Figure RD 2). This indicates that the organelles may serve as compartments that increases the specific experiments and remove the non-specific experiments. Guided by this results, we managed to design a testing system using proper split GFP version. To better understand the parameter sensitivity of the system, we scanned the system performance with different synthesis rate, degradation rate and reaction rate constant combinations (Figure RD 3). We found that when the synthesis rate is low, the advantages of organelle is getting smaller and disappears at the end -- also observed in our wet-lab experiments (Figure RD 3A, C). A few specific parameter constraints are needed to make the advantages of organelle occur, which are usually true in the real biological conditions -- high affinity of organelles to their targets, big enough organelles and low diffusion rate. Specifically, we predicted that larger the cells are, more likely they will benefit from the organelles, even without counting into the cost to pay for the organelle. Also, interestingly, lower the degradation and dilution rate is, it seems that the cell could benefit more from the organelle. Together, these may indicate the reasons that why bacteria lack big independent organelles. For the detailed mathematical description and proofs, welcome to see more in our article attached.

Logic circuit modeling

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: Structure of the insulated promoters used in the study by Zang et al. A - Structure of promoters with a single insulated operator B - Structure of promoters with two insulated operators

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 in pdf here and 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).