To determine the usability of our constructs it is important to consider the extend to which translation levels must increase by to accommodate for the increase in capsid size. Translation is the process in which ribosomes bind to the mRNA sequence to synthesise proteins from the genetic code organised into three-letter combination (codons). Translation consists of three main phases: initiation, elongation, and termination. Of these three steps, translation initiation is the key-rate limiting step whereby translation efficiency of the mRNA transcript relies heavily upon nucleotides situated within the 5’ region of the mRNA.

The two important factors that govern translation efficiency at the 5’ initiation region include:

The secondary structure of the mRNA translation initiation region, whereby the transcript dynamically transitions between folded and unfolded conformations.
The hybridization affinity of the ribosome to the ribosome-recognizing sequence(RRS), defined as a 10-nucleotide sequence containing the conventional Shine Dalgarno sequence and the 16S rRNA-binding site.

Overall, our program models estimated translation efficiencies of AAV subunit protein constructs by firstly determining the probability of regional unfolding at the ribosome-docking site, followed by calculating the hybridization energy associated with the binding of the ribosome to the RRS.

Integration of Constructs into Modelling Measurements

Figure 1. mRNA sequence of AAV subunit protein construct.

Table 1. mRNA Construct Combinations.

Promoters	RBS Site	AAV Subunit Protein Coding Sequence (CDS)
Strong (J23104)	Weak (B0031)	VP1 mRNA sequence VP2 mRNA sequence VP3 mRNA sequence
Strong (J23104)	Medium (B0032)
Medium (J233110)	Weak (B0031)
	Medium (B0032)
	Strong (B0034)

mRNA Folding Dynamics

Probability of mRNA molecule existing in a given folded conformation:

Equation 1: Calculating the overall RDS-exposure probability.

P_{e x} = \sum_{l}^{} p (S_{i}) \times p_{i}

The probability of the RDS exposure, p_i, is defined by the product of the unpairing probabilities of all nucleotides in the docking site. Nucleotide unpairing probabilities are calculated from a partition function, where the unpairing probability of nucleotides in a loop are equal to 1 (these nucleotides are free of base pairing). Whereas, nucleotides in stack structures are base paired and unpairing probabilities can be derived using equation 4.

Equation 2: Calculating the RDS-exposure probability of the given mRNA conformation.

P_{i} = \prod_{j} θ_{i, j}

Equation 3: Calculating the nucleotide unpairing probability.

θ_{i, j} = \{\frac{1}{\sqrt[L]{\frac{1}{1 + e^{(- \frac{Δ G_{i, j}}{R \times T})}}}}

Where θ is the nucleotide unpairing probability of the j-th nucleotide of the i-th mRNA conformation, L denotes the number of nucleotides in a given stack structure, and ∆G is the Gibbs free energy of a stack structure.

Values for the number and Gibbs free energies of nucleotides in stack structures were obtained from the Mfold web server.

Ribosome Binding Affinity

Determining the equilibrium constant of steady state ribosome binding.

The probability of binding of the ribosome to the mRNA transcript is occurs at steady state, in this way an equilibrium constant, (K)R, related to the association and dissociation rate constants of the ribosome bound to the mRNA. The equilibrium constant was obtained using the hybridization energy, (∆G)R, released when the nine nucleotides of the 16s rRNA cofolds and hybridizes with the mRNA subsequence at the RRS. The values for the hybridization energy were obtained from the RBS Calculator v2.1 web application created by the Salis Lab.

Equation 4: Calculating the equilibrium constant for each construct.

K_{R} = e^{(- \frac{Δ G_{R}}{R \times T})}

Once the equilibrium constant was obtained for each construct, equation 5 was used to estimate the probability of ribosome bound to mRNA, (P)c which corresponds to the translation efficiency.

Equation 5: Calculating the probability of the ribosome binding to the mRNA.

P_{c} = \frac{α - \sqrt{α^{2} - 4 \times K_{R}^{2} \times P_{e x}^{2} \times \frac{R_{T}}{S} \times T_{m R N A}}}{2 \times K_{R} \times P_{e x} \times T_{m R N A}}

α is equal to:

α = 1 + K_{R} \times P_{e x} \times \frac{R_{T}}{s} + K_{R} \times P_{e x} \times T_{m R N A}

where (R)T is the total number of ribosomes in cell (which in E.coli is 57,000), s denotes the number of ribosomes simultaneously translating a given transcript (in E.coli this is 20), andT(mRNA) is the total number of mRNA transcripts in the cell.

T(mRNA) values for the each of the constructs was estimated from GFP fluorescence intensity data published on the iGEM registry of biological parts webpages. The baseline value for transcript copy number was assumed to be equal to 60 subunits associated with the pre-existing values of the AAV T = 1 architecture. This was set for the construct combination of the strong promoter and the weak RBS site. The remaining T(mRNA)values were then estimated by multiplying the expression strength factor to each set of corresponding constructs by 60.

Table 2: Estimated T(mRNA) values for each mRNA construct.

Construct:	Original Factor:	Estimated TmRNA value:
Strong Promoter – Weak RBS	1	60
Strong Promoter – Medium RBS	7.9	474
Medium Promoter – Weak RBS	18.6	1116
Medium Promoter – Medium RBS	28.5	1710
Medium Promoter – Strong RBS	3.2	192

Overall, the steps and equations outlined were used to determine a list of baseline translation efficiencies for each of the subunit proteins of the AAV capsid. Determining the suitability of these constructs for the design of novel theoretical viral capsids takes into consideration the newly required amount of subunit proteins.

References

Hagan, M. F. (2014) Modeling Viral Capsid Assembly. Advances in Chemical Physics Advances in Chemical Physics: Volume 155.1–68.
Twarock, R. & Luque, A. (2019) Structural puzzles in virology solved with an overarching icosahedral design principle. Nature Communications. 10 (1).
Mannige, R. V. & Brooks, C. L. (2010) Periodic Table of Virus Capsids: Implications for Natural Selection and Design. PLoS ONE. 5 (3), .
Brandes, N. & Linial, M. (2016) Gene overlapping and size constraints in the viral world. Biology Direct. 11 (1).
Lundstrom, K. (2018) Viral Vectors in Gene Therapy. Diseases. 6 (2), 42.
Bosma, B. et al. (2018) Optimization of viral protein ratios for production of rAAV serotype 5 in the baculovirus system. Gene Therapy. [Online] 25 (6), 415–424.
Na, D. et al. (2010) Mathematical modeling of translation initiation for the estimation of its efficiency to computationally design mRNA sequences with desired expression levels in prokaryotes. BMC Systems Biology. 4 (1), 71.

Team:KCL UK/Model

Model

Background: Modelling the Translation Initiation Process