Our project aim was to express and secrete human growth hormone (hGH) effectively through bacterial twin-arginine translocation (Tat) pathway in Vibrio natriegens. To allow us to examine this secretion route in silico, a mathematical model of the protein flux in the cell was built. Our model focuses on the secretion of our protein of interest, and how increasing the Tat complexes in the inner membrane affects the cell’s secretion capability and the accumulation of the target protein in the periplasm. The model is built using GFP as our target protein, as measuring and detection is more convenient. GFP also folds too rapidly to be secreted through the more used type II secretion Sec pathway. Simulations were computed for two V. natriegensstrains with different protein production and secretion capabilities. The goal was to demonstrate the secretion potential of overexpressed TatABC strain but also to demonstrate how much room for improvement remains with our strain engineering. The model can be further extended to take more accurately into consideration the TatABC complex formation in order to examine the formation rates of each Tat protein, and to take into account the outer membrane leakiness. With a more complex model, the sensitivity analysis of possible bottlenecks and limiting factors in the target protein secretion through the Tat system could also be utilized.


In our bacterium of choice, Vibrio natriegens’ Tat pathway resembles the one of the more well-known gram-negative bacterium, Escherichia coli’s, Tat pathway. The inner membrane translocase consists of three distinct proteins TatA, TatB, and TatC proteins. The three proteins are coded by two different operons in V. natriegens, where tatA and tatB genes are expressed from one operon and tatC gene from another (Solovyev & Salamov, 2011). TatA protein is the most abundant one of the Tat translocase components and it is expressed approximately 20-fold in the cell in comparison to the TatB and TatC proteins. TatA proteins form the actual translocation pore in the inner membrane. The TatB and TatC proteins interact with a 1:1 stoichiometry to form a functional complex. The complex recognizes the signal peptide and guides the passing protein through the translocation pore formed by the TatA proteins, and cuts the signal peptide.

Our model considers the TatABC as a single protein at the inner membrane recognition site, as the TatBC complex is in any case the limiting factor of the translocation speed and efficiency. Naturally the Tat pathway is scarce in bacteria, which creates a bottleneck for periplasmic protein secretion. With overexpression the pathway components it is possible to create far more effective secretion strain (Lee et al., 2006).

The GFP protein sequence is combined with a Trimethylamine N-oxide reductase signal peptide (TorA), which directs the GFP to the Tat pathway in the cytoplasm. In this model as in our lab, our VibXPresso expression construct is expressed in a plasmid vector pC203 that includes an inducible promoter for the GFP gene and it is inducible by L–rhamnose.

Figure 1. Protein kinetics in Vibrio natriegens.


The simulation was performed in MATLAB’s SimBiology App. Version R2019a was used both in calculation and visualization.

Secretion dynamics

In order for us to simulate the TorA-GFP production and secretion in the cells, the following ODEs were built to describe the protein secretion from transcription into diffusion through the outer membrane.

The model does not take into account any alternative transport mechanisms that are present in nature, such as active secretion into the media or other pathways that transport proteins through the inner membrane. In our model, we are using a plasmid-based protein expression system, similarly to our engineered strain in the lab. The generated messenger RNA amount of our target protein depends strongly on the promoter strength P and the plasmid copy number Cn. As the mRNA is simultaneously produced with a rate of CnP, it is translated into TorA-GFP in the cytoplasm with a rate of GFPtranslation and degraded with a rate of mRNAdegradation. These cytoplasmic dynamics are described with the equations following equations.

\begin{equation} Transcription\:rate = C_n * P \end{equation} \begin{equation} \frac{d[mRNA]}{dt} = \frac{1}{V(cytoplasm)} * (Transcription - [mRNA degradation] - Translation) \end{equation}

Once the protein is folded, the cells proteases in the cytoplasm begin to degrade the TorA-GFP protein with a rate of GFPdegradation. The TatABC complex on the inner cell membrane recognizes the TorA signal peptide and binds into the GFP with a rate of [GFP + TAT]binding, cleaves the signal peptide off, and transfers the GFP into the periplasm. The protein accumulates into the periplasm, but a minuscule percentage of it diffuses through the outer membrane with a rate of GFPleaking into the culture media (Albiniak et al., 2013). These dynamics are described with the following equations.

\begin{equation} \frac{d[GFP_{cytoplasm}]}{dt} = \frac{1}{V(cytoplasm)} * (Translation - [GFP +TAT]_{binding} - GFP_{degradation}) \end{equation} \begin{equation} \frac{d[GFP_{periplasm}]}{dt} = \frac{1}{V(periplasm)} * ([GFP+TAT]_{binding} - GFP_{leaking}) \end{equation} \begin{equation} \frac{d[GFP_{media}]}{dt} = \frac{1}{V(media)} * GFP_{leaking} \end{equation}

Intracellular fluxes
$$P = Promoter\:strength$$ $$C_n = Plasmid\:copy\:number$$ $$mRNA_{degradation} = mRNA_{degradation} * mRNA * V(cytoplasm)$$ $$GFP_{Translation} = k_{translation} * mRNA * V(cytoplasm)$$ $$GFP_{degradation} = k_{degradation} * GFP_{cytoplasm} * V(cytoplasm)$$ $$[GFP + TAT]_{binding} = k_{passing^{TAT}} * GFP_{cytoplasm} * TAT * V(cytoplasm)$$ $$GFP_{leaking} = GFP_{leakiness}*GFP_{periplasm} * V(periplasm)$$ The secretion model was run to simulate two different V. natriegens strains, our own VibXPresso 1.0 and an “ideal” VibXPresso 2.0, that has more optimal characteristics for a secretion strain. The major differences between the strains are VibXPresso 2.0’s 5-fold TatABC concentration, protease deletions which lowers the GFPDegradation into about half of the original and increase the GFP yield. The 2.0 strain also has high copy number plasmid with a strong promoter. As the majority of the literature covers E. coli ’s and other more well known and characterized microbes, for V. natriegens there exists only very few, if none, standardized literature values concerning e.g. promoters and protease deletion effects. Therefore, most of the presented estimates are crude and they base on similar values and magnitudes that have been reported for E. coli and other bacteria.

Strain differences in simulation:

Table 1. Differences between the two strains.

Used Constants:

Table 2. Constants used in solving the secretion model.

Used constants explained more detailded in the Simbiology sbproj files.

Download Kinetics Simulations (MatLab) here


With the Simbiology’s Simulation tool the systems ODEs were solved using a ODE15 solver, resulting the two different plots in Figure 2. We see that that the GFP concentrations of the VibXPresso 2.0 strain are approximately 100-fold in comparison to VibXPresso 1.0. Another notable factor is the more rapid GFP accumulation in the periplasm with the increase in TatABC complexes.

Figure 2. Comparison between concentrations of mRNA, cytoplasmic GFP, periplasmic GFP and GFP in media over 8 hour simulation.

Growth rate

In order to prove a faster protein production with VibXPresso, we used the OD600 data collected from measurements and analyzed the OD600 graphs to get the growth rate of VibXPresso. We followed the methods used in article by Ram et al. (2019). Based on all of the data collected from the OD600 measurement in V. natriegens, we decided to use OD600 in 25 mM induction concentration to increase the protein yield. As a result, we got an initial growth graph.

Using Matlab we fitted the third power polynomial graph, which gave us a polynomial equation. From this equation we found the maximum of the derivative, which gave us the time for maximum growth rate. This time was used to fit a linear function at + b = y into the log of initial growth curve.
Figure 3. VibXPresso growth curve.

Figure 4. VibXPresso growth curve determination.

The parameter a of the linear function is interpreted as the growth rate (Ram et al., 2019).
The comparison between Wild Type V. natriegens and VibXPresso modelled data was performed and the results indicate a faster doubling time and bigger growth rate in VibXPresso, which, as a conclusion, can predict faster protein production, and thus bigger protein yield in the same amount of time.

Table 3. Differences between WT V. natriegens and VibXPresso 1.0.

Growth rate explained more detailded in the Matlab files.

Download Growth rates calculations (MatLab) here


Albiniak, A. M., Matos, C. F. R. O., Branston, S. D., Freedman, R. B., Keshavarz-moore, E., & Robinson, C. (2013). High-level secretion of a recombinant protein to the culture medium with a Bacillus subtilis twin-arginine translocation system in Escherichia coli, 280, 3810–3821.

Lee, P., Tullman-Ercek, D., & Georgiou, G. (2006). The Bacterial Twin-Arginine Translocation Pathway. Annual Review of Microbiology, 60, 373–395.

Morello, E., Nouaille, S., Cortes-Perez, N. G., Blugeon, S., Medina, L. F. C., Azevedo, V., … Langella, P. (2012). Inactivation of the ybdD Gene in Lactococcus lactis Increases the Amounts of Exported Proteins. Applied and Environmental Microbiology, 78(19), 7148 LP-7151.

Ram, Y., Dellus-Gur, E., Bibi, M., Karkare, K., Obolski, U., Feldman, M. W., Cooper, T. F., Berman, J., Hadany, L. (2019). Predicting microbial growth in a mixed culture from growth curve data. PNAS, 116(29), 14698-14707.

Solovyev, V., Salamov, A., (2011) Automatic Annotation of Microbial Genomes and Metagenomic Sequences. In Metagenomics and its Applications in Agriculture, Biomedicine and Environmental Studies (Ed. R.W. Li), Nova Science Publishers, p.61-78. (pp. 61–78).

Tschirhart, T., Shukla, V., Kelly, E. E., Schultzhaus, Z., Newringeisen, E., Erickson, S., … Vora, G. J. (2019). Synthetic Biology Tools for the Fast-Growing Marine Bacterium Vibrio natriegens.