Team:XMU-China/Model
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Introduction
Secretion of recombinant protein from engineered bacteria ties to two components: one is the secretion machinery of engineered bacteria, the other is the signal peptide or signal sequence1. The sequence of recombinant protein is obtained by fusing the sequence of protein of interest (POI) with the signal peptide, in most cases, at the N-terminal of POI. The type of signal peptide is accordance with the specific secretion pathway. In prokaryotic cells, for many application systems, there are three common secretion pathways of recombinant proteins: Sec (or SecB) pathway, SRP (signal recognition particle) pathway and Tat (twin-arginine translocation) pathway, which all belong to the T2SS secretion mechanism of bacteria2. The signal peptide we used in our project was Aly013, LMT and PelB4 and the secretion mechanisms of which are classified to Sec pathway, Tat pathway and Sec pathway, respectively. Inspired by the Tat pathway-dependent protein secretion model in Vibrio natriegens which was constructed by 2019 Aalto-Helsinki iGEM Team and according to the real conditions of our project, we decided to study and model the protein secretion model in Vibrio natriegens.
The original intention of this model was to mathematically describe the relationship between the amount of secreted recombinant protein from Vibrio natriegens (VnDx) and time, and thus to explore the secretion efficiency of different signal peptides that we used. Such modelling process was of great significance for us to implement SALVAGE and part collection. Before starting modelling, we first learned the detailed mechanisms of the three different pathways:
Fig. 1. Recombinant protein was secreted via Sec pathway, SRP pathway and Tat pathway in engineered bacteria.
i. For Sec pathway, a soluble molecular chaperone protein named SecB binds to the recombinant protein’s signal peptide or other features of its incompletely folded structure. The bound protein is then delivered to SecA, a protein acts as both a receptor and a translocating ATPase that is associated with the cytoplasm membrane. The Sec-recombinant protein complex forms a translocation complex with SecY/SecE/SecG (SecYEG). The protein is conducted by the energy released from ATP hydrolysis and PMF (proton motive force). The SecDF complex (YajC is an accessory protein) plays the role as the signal peptidase (SPase) to cleave the signal peptide in the final stage of translocation. (middle in Fig. 1)
ii. For SRP pathway, recognition of signal peptide by signal recognition particle (SRP) begins in the tunnel of ribosomes or directly after the emergence of a nascent polypeptide chain of the recombinant protein on the ribosome. While the FtsY in the cytoplasm membrane binds to the SRP-polypeptide complex as a receptor and then the complex is targeted to the same translocon in Sec pathway. (left in Fig. 1)
iii. The Tat pathway is commonly used for those proteins that contain two consecutive and highly conserved arginine residues in their leader peptides. On the Tat pathway, the protein is fully synthesized and folds in the cytoplasm where it can bind specific cofactors. The signal peptide is then recognized by TatC in the TatBC complex. Signal peptide binding promotes association of the complex with TatA oligomers at the expense of PMF. Protein translocation occurs through a channel formed by TatA and possibly TatE oligomers. (right in Fig. 1)
There are many ways for the recombinant protein being secreted into the culture medium after it is translocated into the periplasmic space2, 5. Considering the strain we used (VnDx) was not modified specifically for secretion expression, so we only took the extracellular secretion mechanism of the strain itself in to account. Under this circumstance, the recombinant protein can reach the culture medium due to the nonspecific periplasmic leakiness or via the secreton in the outer membrane. Besides, a part of recombinant protein may enter the culture medium by T1SS mechanism.
In general, the secretion of recombinant protein from cytoplasm to culture medium needs complicated binding and translocating processes. Actually, because of the secretion events’ complexity, some teams preferred to use empirical formula to describe the process (https://2017.igem.org/Team:Stuttgart/Model, https://2018.igem.org/Team:IIT_Kanpur/Model). However, we finally did not adopt it because we thought the empirical formula was too simple and it was easy to cause misunderstanding as the physical quantities were not clearly referred to. In consideration of the complexity of translocation and the relative stability of the strain’s secretion machinery, we regarded that the translocation of recombinant protein from cytoplasm to periplasm was an intact process while the extracellular secretion from periplasm to culture medium was another intact process. Therefore, the recombinant protein will undergo the several following processes from its expression to finally reaching the culture medium: transcription, translation, translocation (cytoplasm → periplasm) and extracellular secretion (periplasm → culture medium). Although the amount of transcript is affected by the copy number of plasmid, the promoter strength and the degradation rate of mRNA6, we just began with the translation stage rather than the transcription stage due to the fact that the process we focused on is a post-translational process. It is worth mentioning that we used the amount of molecules per unit volume of reactor to replace the concentration of molecules in order to avoid discussing the physical quantity of volume due to the changes in space during secretion7.
From the very beginning, based on conservation of materials, we have the following equation (1):
$$ P_{T}=P_{M}+(P_{C}+P_{P})X $$
where X is the cell density, PT is the total amount of recombinant protein per unit volume of reactor, PM is the amount of the recombinant protein in the medium compartment in unit volume, while PC and PP is the amount of recombinant protein in cytoplasm and periplasm of an average bacterium, respectively.
In cytoplasm, the protein balance per unit volume of reactor can be expressed as the following equation (2):
$$ \frac{d(P_{C}X)}{dt}=f_{p}X-\alpha P_{C}X-\beta P_{C}X $$
where fp represents the translation rate of a secretory recombinant protein in an average bacterium, α and β represents the translocation rate constant from cytoplasm to periplasm and degradation rate constant, respectively.
Similarly, in periplasm, we have the following equation (3):
$$ \frac{d(P_{P}X)}{dt} = \alpha P_{C}X - \gamma P_{p}X $$
where γ represents extracellular secretion rate constant. Given that the proteolytic process in periplasm and culture medium can be neglected, in culture medium, we have the equation(4):
$$ \frac{dP_{M}}{dt} = \gamma P_{P}X $$
Since PC and PP are unmeasurable and nonestimatable, while PT and PM or PT and PT - PM are measurable quantities, we did not hope that the PC and PP existed in the final equation. The dynamic response of PC and PP can be obtained from equations (2) and (3). By the chain rule, equation (2) becomes the equation (5):
$$ X \frac{dP_{C}}{dt} + P_{C}\frac{dX}{dt} = f_{p}X-\alpha P_{C}X-\beta P_{C}X $$
The growth of engineered bacteria can be deascribed by equation (6) :
$$ \frac{dX}{dt} = \mu _{X}X $$
where μ_X represents the specific growth rate of engineered bacteria. Rearranging equation (5) combining equation (6) gives equation (7)
$$ \frac{dP_{C}}{dt} = f_{p} - (\alpha + \beta +\mu_{X})P_{C} $$
Similarly, we can obtain the equation (8):
$$ \frac{dP_{P}}{dt} = \alpha P_{C} - (\gamma + \mu_{X})P_{P} $$
In consideration of the fact that the amount of secretory recombinant protein in culture medium is unavoidably less than that of the cytoplasm due to the heterogeneity of recombinant protein, we thought that in the steady state, the amount of recombinant protein in cytoplasm was relative stable. And thus, we can write the equation (9)
$$ \frac{dP_{C}}{dt} = f_{p}-(\alpha+\beta +\mu_{X})P_{C} \cong 0 $$
Elimination of PC and PP from the expression results in the following equation (10):
$$ \frac{dP_{M}}{dt}=\gamma(P_{T}-P_{M})-\gamma\frac{f_{p}}{\alpha+\beta+\mu_{X}}X $$
Hence, we deduced the dynamic model of the recombinant protein’s secretion.
During the growth of engineered bacteria, the synthesis of recombinant protein is always going on. In order to make the experimental operations more convenient, we need to find a way to bog down the synthesis of protein in the engineered bacteria. In characterization experiments, when the growth of bacteria reaches the mid- or late- log-phase, we can add chloroamphenicol or tetracycline into culture medium (our vector is KanR) to stop the protein’s synthesis. Under this circumstance, there is no more recombinant protein inflow to the cytoplasm, and the existing external pool of secretory recombinant protein will increase due to secretion as time progresses. Thus, with the addition of chloroamphenicol or tetracycline, the following relationship is established per unit volume of reactor:
equation (11):
$$ P_{T}=const $$
equation (12):
$$ f_{p}=0 $$
So we have the equation (13):,
$$ \frac{dP_{M}}{dt} = \gamma(P_{T}-P_{M}) = \gamma P_{T} - \gamma P_{M} $$
Let ∆=γPT, the equation (13) can be re-written as equation (14):
$$ \frac{dP_{M}}{dt} = \Delta -\gamma P_{M} $$
Then let u=∆-γPM, so the ordinary differential equation can be changed to equation (15):
$$ \frac{du}{dt} = -\gamma \frac{dP_{M}}{dt} = -\gamma u $$
For the shifting and integration of equation (15), we can obtain eqation (16):
$$ \int_{u_{0}}^{u_{t}} \frac{1}{u}du = \int_{0}^{t} -\gamma dt $$
i.e. equation (17)
$$ \frac{u_{t}}{u_{0}} = e^{-\gamma t} $$
To replace u, we can write the equation (18):
$$ \frac{\Delta - \gamma P_{Mt}}{\Delta - \gamma P_{M0}} = e^{-\gamma t} $$
Rearranging the equation (18) results in the following structure:
$$ P_{Mt} = \frac{\Delta}{\gamma} -(\frac{\Delta}{\gamma} - P_{M0})e^{-\gamma t} $$
After adding chloroamphenicol or tetracycline, samples will be taken out from the culture at specific time points (neglecting the decrease of culture volume caused by sampling). By measuring the amount of secretory recombinant protein in the supernatant at specific time points, whatever using Western-Blot or the interaction between FlAsH-Tag and FlAsH-EDT28-9, we can plot the relationship between the amount of secretory recombinant protein and time, and hence further check the accuracy of our model.
In fact, the equation (19) can be rewritten as equation (20) by replacing ∆/γ:
$$ P_{Mt} = P_{T} - (P_{T}-P_{M0})e^{-\gamma t} $$
That is to say, via fitting, we can obtain the value of PT as well. The equation can be changed to the form which is accessible by measuring the amount of recombinant protein in bacteria cell (including the cytoplasm and periplasm).
Implementation
1. Inoculated VnDx in 1% to 100 mL Kan+ LBv2 medium then the culture was incubated in 37 °C, 200 rpm for 12.5 hours in order to get as much cells as possible.
2. Prepared the NaN3 stock solution (20 M, 1000×) with v2 salts so as to stop secretion (i.e. quench) and maintain Na+ in a high level to prevent VnDx from lysis. Before use, the stock solution should be diluted into 10×solution for convenient operation.
3. After 12.5 hours of culturing, chloramphenicol was added to the 100 mL medium for a final concentration of 12.5 μg/mL. Then the bacterial culture was incubated in 30 °C, 200 rpm for the following culturing and sampling.
4. Samples were taken at time 0, 6, 12, 18, 24, 30, 40 and 55 min after the addition of chloramphenicol, and to quench further secretion after sampling, they were immediately added to chilled tubes of 20 mM NaN3 (final concentration). Mixed 900 μL from the medium and 100 μL of 10×NaN3 solution, after which placed the medium back to the shaker as soon as possible. 100 μL was aspirated from the 1 mL sampling mixture to investigate whether protein synthesis is completely inhibited or not. The remaining 900 μL of the sampling mixture was centrifuged at 6000 rpm for 3 min, the supernatant was filtered with 0.22-μm filters and stored, in preparation of detecting the amount of protein secretion at each sampling time point.
5. See our Experiment page for more details about using Western-Blot and FlAsH-EDT2 for determining the amount of secreted protein.
Results and Simulation
As time progressed, the concentration of the secreted protein in supernatant showed an increasing tendency (Fig. 2A). Besides, after adding chloramphenicol to the medium, the amount of total protein maintained in a relative stable level during the whole sampling process (Fig. 2B), which indicated that the chloramphenicol stopped the protein synthesis in deed. Subsequently, we simulated the data via the derived equations.
Fig. 2. Wester-Blot (anti-GFP) implemented for determining the amount of protein: (A) Supernatant groups; (B) Total groups.
Here we take the circuit LMT-His-GFP as an example, the experimental data collected in Vibrio natriegens using the Western-Blot has been used for parameter fitting. Using the equation (20) as the goal, the result been shown in Fig. 3.
Fig. 3. LMT-His-GFP in Vibrio natriegens.
Our model is also suitable for different species with different measurement method:
The same signal peptide was test in E. coli using the FlAsH technology and the result is shown in Fig. 4.
Fig. 4. LMT-His-HutH-FT-tag in E. coli.
The other signal peptide, Aly01, was test in Vibrio natriegens using Western-Blot and the result is shown in Fig. 5.
Fig. 5. Aly01-His-GFP in Vibrio natriegens.
Discussion
It is worth noting that the slowly-folding protein is in favor of Sec pathway while the rapidly-folding protein prefers Tat pathway1, 5. So, actually, it is necessary for us to explore the influence of the recombinant protein’s folding rate due to the dependency of Sec pathway for Aly01 and PelB peptides, despite LMT was predicted to be classified to Tat pathway (see our Resultpage). In addition, in view of few studies about implementing Vibrio natriegens to secrete recombinant protein up to date, we have neglected the possibilities that the recombinant proteins are secreted through other pathways which we did not discussed or even not be identified. The model will be further completed if the studies about the recombinant proteins' secretion are implemented more specifically and systematically.
Notwithstanding the subsequent reactions triggered by the functional recombinant protein outside the bacteria cell really count, we have just focused on the secretion process which has been rarely modelled. Hopefully, our model will contribute to the iGEM community and inspire other teams of using protein secretion as a strategy to solve the real issues in their projects.
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