Team:Peking R/Project/RBSAutomatedDesign

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Thermodynamics-based RBS Calculator

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Introduction
Through fine-tuning the tranlation of core genes using the genetic rheostat, we can easily modulate the behavior of genetic devices and complex gene circuits with ligands at various concentrations and finally configure an automated-designed RBS to meet the corresponding translation strength, thus optimal performance of gene circuits.

To achieve such a goal, we employed two sets of tools to rationalize the process of genetic devices/gene circuit modulation–genetic rheostats(ligand-responsive RNA elements) to quantitatively modulate translation process, and the RBS Calculator to predict the rate of translation initiation and automatically design a synthetic RBS sequence that meets the needed relative translation rate determined by the genetic rheostat. A critical step, therefore, is to map the translation strength of a particular sequence to that of a genetic rheostat-modulated messenger RNA (mRNA). Since the genetic rheostat tunes translation by decreasing or increasing the probability of RBS exposure, which is proportional to translation strength, we can achieve the mapping process merely by determining the translation strength of the fully exposed RBS.

Conventionally, trl. str. was calibrated with a library of RBS mutants. But this approach is not truly reliable, because the strength of RBS strongly depends on the surrounding sequence, for instance the coding sequence, as is shown in Figure 2. Salis and Voigt have derived a model for RBS str. prediction that takes sequence context into consideration.

According to the model, the bridging factor between the strength of translation and a particular RBS sequence is Gibbs free energy change for translation initiation determined by RBS Calculator.A schematic representation of our modeling for the platform is shown in the diagram below.

 

	Figure 1 Schematic representation of genetic soft-coding approach and the role of RBS calculator.In a two-step strategy (green boxes connected by curved arrows) to engineer biological systems, a ligand-responsive RNA controller("genetic rheostat") is used to easily determine an appropriate translation strength from varying concentrations of the ligand, followed by replacement of the genetic rheostat(together with its native RBS) with a fixed synthetic RBS that meets the previously determined translation strength. The role of the RBS Calculator, therefore, is to map a value of translation strength (expressed in terms of △G) to a specific RBS sequence.

Overview of Components of the Prokaryotic Ribosome

	Figure 3 Components of a prokaryotic ribosome.(Alberts et al., 2008).

It can be seen from Figure 3 that ribosome in prokaryotes consists of two subunits, one larger with a Svedberg sedimentation coefficient of 50, and a smaller subunit with a Svedberg sedimentation coefficient of 301. Both subunits consist of several proteins and several strands of ribosomal RNA (rRNA) in different lengths. In the process of translation initiation, the 30S subunit first binds to ribosome binding site (RBS) of the messenger RNA (mRNA), in which the 16S rRNA of the 30S subunit has a critical role of recognizing and binding to RBS in mRNA. After recognizing and binding to the RBS, the 30S subunit then recognizes the start codon and recruits the transfer RNA(tRNA)that carries a fMet residue corresponding to the start codon, followed by the 50S large subunit. The formation of a complete ribosome-mRNA complex then “fires off” from the start codon and starts translation.

	Figure 4 The postulated process of translation initiation. (a) Single-chain mRNA in its native folded form, with RBS and start codon indicated in yellow and red respectively. (b) Binding of the 30S ribosomal subunit to the RBS (yellow ribbon), excluding secondary structures in a region surrounding it. The last nine nucleotides of the 16S rRNA in the 30S subunit are given. (c) Binding of the 30S subunit to the start codon (red ribbon) and recruitment of the first tRNA and 50S subunit to start translation.

Based on the above assumptions, ∆Gtot is composed of five additive Gibbs free energy terms:
∆Gtot = ∆GmRNA:rRNA + ∆Gstart + ∆Gspacing- ∆Gstandby- ∆GmRNA
where:
∆GmRNA:rRNAis the energy change brought by binding of the 16S rRNA tail to the specific binding region in the 5' UTR of the mRNA.
∆Gstart is the free energy change that results from binding of the 16S-rRNA to the start codon(it is treated as a constant for all mRNAs with AUG as the start codon.
∆Gspacing is the free energy change brought by the spacing sequence between the RBS and the start codon, determined by the sequence length using an empirical formula derived from experimental data.
∆Gstandby is the energy needed to expose the 16S-rRNA binding site to the 16S-rRNA.
∆GmRNA is the free energy change for a free mRNA sequence in solution to spontaneously fold into a native secondary structure.
The results in the original work agree well with that derived from another probabilistic model constructed by Na et al. (2010)3.
For RBS Calculator used in our platform, we optimized parameters and algorithms in the original work by Salis et al. to produce a more general tool for predicting the translation rate of mRNAs that encode different proteins. The program showed fair performance with the green fluorescent protein (GFP) that we used, but not as satisfactory as it did with red fluorescent protein (RFP) and its fusion proteins in the original work. Therefore, we attempted to optimize the program for equal performance on different protein-coding mRNAs. Since the free energy terms to a great extent depend on a set of thermodynamic parameters used for secondary structure prediction3, the thermodynamic scoring matrix for base pairing in RNA was changed from rna1999 parameters used in the original program to rna1995. Besides, as the sequence surrounding the start codon has been shown to significantly affect the accuracy of prediction1,the cutoff value, which is the number of nucleotides up- and downstream of the start codon used for calculating free energy terms, was increased from 35 to 51, which produced a better fit with experimental measurements (see results below).

In order to evaluate the accuracy of the model, we exploited green fluorescent protein (GFP) as a reporter gene to measure relative translation initiation rates of a library of mRNAs with synthetic RBSs. The output fluorescence measured by flow cytometry and/or spectrophotometry was fitted to the corresponding prediction by RBS Calculator software package that integrates the separate calculations of the five energy terms described above into ∆Gtot and provides an arbitrary expression level using equation (1) and fitted parameters for the scaling coefficient K (~2500) and β(~0.45).Results for GFP before and after changing the parameters are shown in Fig 5a and Fig 5b respectively. It can be seen that altering the parameters used in the algorithm significantly improved the fitting results.

	(a) (b)
	Figure 5 Fitness of experimental measurements to computational predictions by RBS Calculator. Horizontal axis indicates the △Gtot determined by RBS Calculator, and vertical axis corresponds to logarithm of expression level(in terms of GFP fluorescence normalized for host bacteria growth). (a) Original parameters (rna1999, cutoff=35nt) produced unsatisfactory fitting with low square R (Pearson correlation coefficient). (b) Changing thermodynamic scoring matrix and cutoff value to rna1995 and 51nt respectively resulted in better fitting. Note that the improvement primarily occurred at the two ends – high and low △G.

After confirming the reliability of the RBS Calculator in determining translation strength, we are able to employ the computational results to predict a synthetic RBS sequence that matches the desired relative translation rate (forward engineering). The prediction curve is shown in Figure 6.

	Figure 6 Using RBS Calculator to find a sequence with desired translation strength. It can be seen that the RBS Calculator also performs well in finding the right sequence under our optimized parameter combination.

 

Finally, we can figure out the trl. str of the fully exposed RBS sequence and then convert the probabilities of RBS exposure to a range of deltaG for translation. Besides, any given deltaG for trl can be met by an RBS sequence calculated from the RBS Calc. Therefore we can convert any given TPP conc. into an RBS sequence.

	Figure 7 Mapping of ligand concentrations and fixed RBS sequences. Using the response curve of RBS exposure probability to TPP(ligand) concentration, in combination with the mapping of RBS exposure probabilities to RBS sequences through translation strengths(deltaG) determined by the RBS Calculator, we may find a corresponding RBS sequence for any given TPP concentration.

 

 

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Reference:

[1].Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P.(2008). Molecular Biology of the Cell. Garland Science, Fifth Edition, 373-376.
[2]. Salis, H.M., Mirsky, E.A., and Voigt, C.A.(2009). Automated design of synthetic ribosome binding sites to control protein expression. Nature Biotechnology 27, 946-952.
[3]. Na, D., Lee, S., and L, D.(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 4,71.