Part:BBa_K5129002

L-lactate inducible production of anticancer peptide PNC27 (ALPaGA promoter)

The present composite part consists of the ALPaGA modified lactate inducible promoter, sp3 spacer K370000, RBS B0033, NSP4 - PNC-27 and B1006 terminator. The composite parts release the NSP4 - PNC-27 in response to the high lactate concentration, which is then exported and targeted to the cancer cells, inducing their death via necrosis [1].

Aiming to address the problem of complications presented due to conventional breast adenocarcinoma therapy methods, we are proposing an innovative solution - bacteriotherapy, using non-pathogenic chassis E.coli to synthesize anticancer peptide. Bacteria will serve the synthesis purpose, therefore cannot directly interact with cancer cells. That is why the E.coli will be enclosed in the hydrogel network. The specificity of the treatment is ensured by using lactate sensor and peptide specificity itself. In order to prevent spreading out of the bacteria inside the body, the kill switch was designed.

Anticancer peptide

PNC-27 is a 32-residue peptide composed of an HDM2 binding domain of p53 (residues 12–26) and CPP leader sequence. The peptide is synthetic in nature, meaning that it was initially produced through protein engineering methods.

Penetratin sequence

CPP leader sequence represents part essential for binding and entrance into target cells. The fragment is also known as Penetratin. It was essentially derived from a leader sequence of the antennapedia protein [1]. Penetratin contains a high density of positively charged residues that stabilize an α-helix when present on its carboxyl terminal end [1]. Because of this property, aside from the main function Penetratin is essential for proper folding of PNC-27.

HDM2 binding domain

PNC-27 has been shown to eradicate cancer cells with higher specificity due to the nature of its binding partner, indicating that normal cells are typically not affected by it [2,3]. Human Double Minute Homolog 2 or HDM-2, is known to be overexpressed in cancerous cells [3]. Through binding to HDM2, PNC-27 becomes cytotoxic for cancer cells as this interaction leads to the formation of pores on cell membranes [4]. Direct binding to HDM-2 is conducted via α-helical conformation of the protein [1]. HDM-2 is overexpressed in the membranes of both solid and non-solid tissue tumors [3]. The experimental results suggest that early developing tumor cells exhibit high concentrations of HDM-2 in their membranes [5,6]. In addition, HDM-2 was reported to be a marker of rapidly growing tumors. Its elevated levels correlate with metastatic properties of primary tumor cell cultures obtained from breast cancer patients [7]. Cancer cells obtain these motility properties due to co-localization of peptide with E-cadherin in the cancer cells plasma membranes, which leads to the ubiquitination and degradation of the latter.

Treatment efficiency

PNC-27 demonstrated its efficiency in a wide variety of cancer cell lines. For instance, PNC-27 induced rapid total cell necrosis (within 1 hr) of several breast cancer cell lines [7]. The results of another study show that PNC-27 is cytotoxic to cells from long-established and chemotherapy-resistant human ovarian cancer cell lines [8]. Necrosis of cells was confirmed as elevated concentrations of lactate dehydrogenase (LDH) were released from the samples treated with the peptide [2]. IC50 values of the peptide range from 75 ug/ml (18.6 uM) to 200 ug/ml (50 uM) [2]. Notably, the studies reported that PNC-27 induced pores in the membranes of cancer cells, but cell membrane lysis was not observed after treatment of untransformed cells [6, 9, 10]. Lastly, for the in vivo experiments, PNC-27 was tested on human pancreatic cancer cells (MIA-PaCa-2) and a melanoma cell line (A2058) in nude mice. While efficient tumor eradication was observed, no evidence of toxic side effects was documented [2]. The proposed mechanism of treatment is visualized in Figure 1. PNC-27 binds to HDM-2 creating complexes that coalesce to form transmembrane pores.

PNC-27 Workpath — ***Figure 1.*** Proposed model for pore formation based on PNC-27-HDM-2 complexes.

Signalling peptide

To reach the cancer cell membranes, the peptide must escape the bacteria cell. This can be accomplished by using signaling peptides, connected to the main peptide, PNC-27. Signaling peptides should guide the molecule to the membrane of E.coli and export it outside of the cell. For this project, we chose NSP4 as the signaling peptide and fused it to PNC-27. Essentially, unfolded precursors composed of the chimeric proteins get translocated across the cytoplasmic membrane of bacteria, which is followed by cleavage of the signal peptide by specific signal peptidase. As a result, the peptide gets folded into the native structure and gets exported from the periplasmic space of bacteria.

Regarding the structure, signaling peptides are composed of 3 structural domains, each having a distinct function [29]. The amino terminal part (n-region) has a positive charge. It’s typically followed by a hydrophobic h-region. The C-region contains a protein recognition sequence, which is the site through which the signaling peptide gets separated from the rest of the protein.

The following properties were considered for selection of the signaling peptide:

Must be native for E. coli to ensure proper cleavage and release of the native PNC27.
E. coli K-12 in the UniProtKB database indicates that the median signal sequence length in E. coli is 22 amino acids, with a minimum of 15–16 amino acids.

NSP4, derived from DsbAss native to E.coli, was chosen because it suits the above-described requirements and due to the following reasons [30]:

Section of the peptide is mediated via the secretory (Sec) pathway.
- The peptide gets recognized by signal recognition particles (SRP) via the fifty-four homolog (Ffh) region of SRP. Subsequently, SRP guides proteins for export into the periplasmic space [31, 32].
Other works reported higher secretion efficiency compared to other similar sequences. For instance, NSP4 improved secretion of ATH35L by Escherichia coli by four times compared to conventional DsbAss signaling peptide [30]. Induction time was also reduced.
Signaling peptidase performs very precise cleavage on the recognition site.

Below is the sequence of NSP4, with the recognition site for signaling peptidase highlighted in red: MKKITAAAGLLLLAAQPAMA

Lactate sensing system

ALPaGA - lactate sensitive promoter

The main goal of novel targeted bacterial therapy is recognizing tumor sites, specifically breast cancer cells, which is feasible by sensing signals in tumor microenvironment (TME) through the usage of genetic operons. According to “Warburg effect” that takes place during tumor proliferation, the high demand and uptake of glucose increases concentration of lactate which is followed by creation of anoxic environment as abnormal cells proliferate rapidly outpacing blood supply [34]. The wild-type LldPRD promoter was taken as a basis for construction of a lactate biosensor since the LldR operator, which orchestrates this system, works as either activator or repressor depending on L-lactate concentration [35]. However, according to previous findings, the LldPRD promoter does not function under both anoxic and glucose-rich environment, which are the main characteristics of solid breast cancer [36].

ALPaGA (A Lactate Promoter Operating in Glucose and Anoxia) -  regulated promoter for targeted gene transcription induced upon high concentration of L-lactate [37]. Applying the use of lactate biosensors, which can recognize anoxic and glucose-rich reach environments, can improve precise cancer detection for further treatments. This promoter had been reconstructed from the backbone of existing LldPRD due to it having three significant genes, but designed to operate in glucose environment and absence of oxygen [37]. Three essential genes are lldD gene encoding dehydrogenase protein for anaerobic respiration, lldP gene encoding permease for L-lactate transportation across cell membrane, and lldR gene encoding regulatory protein functioning dually as either activator or inhibitor of the pathway [35], [38]. If lactate is not present in environment then translation of lldR gene leads to binding of encoded regulatory protein to O1 and O2 operators causing looping with further inhibition of transcription by ALPaGA promoter. If high lactate concentration is sensed in hypoxic and glucose-rich environment, then binding of L-lactate to lldR changes its conformation so that it can’t bind operators and looping will not appear. This allows downstream transcription of gene of interest (GOI) by ALPaGA promoter.

Comparing PLldPRD and ALPaGA: In an experiment conducted to compare activities of two promoters (2021) it has been reported that ALPaGA biosensor detects L-lactate not only in the presence of oxygen, but also in its deprivation. Measurement was conducted through Relative Promoter Unit (RPU) where the promoter J23101 was taken as a reference. According to this method the activity of chosen promoter is measured relative to this reference and relative transcription rate of two promoters in different contexts can be calculated. While data derived from both experiments on DH5α and E.coli indicated that PLldPRD and ALPaGA function did not have significant differences in glucose rich environment, these numbers noticeably varied for both oxygen-rich and anoxic environments. The leakage RPU for PLldPRD in both environments at DH5α was 0.2 ± 0.0 which is 4 times lower the RPU of ALPaGA in glucose-rich and anoxic environment being 0.9 ± 0.0 and 0.8 ± 0.1, respectively [37]. Working principles of both wild type PLldPRD and ALPaGA working pathway diagram was illustrated on Figure 2.

***Figure 2.*** (A) - Wild type LldRPD working principle. (B) - ALPaGA working principle.

***Figure 2.*** (A) - Wild type LldRPD working principle. (B) - ALPaGA working principle.

ALPaGA - PNC-27 composite part function

Proposed new composite part ensures regulated anticancer PNC-27 production when needed, upon sensing solid tumor microenvironment (TME), which are anoxic and glucose-rich environments. To stimulate the release of anticancer peptide the L-lactate metabolite which is redundantly present in TME was taken as a basis of system. LldPRD promoter perfectly fit into that system as it encoded proteins responsible for L-lactate transportation and regulation. However, its inhibition in above-mentioned TME made it ineffective in creating live biosensor for breast cancer treatment. The engineered ALPaGA promoter from the existing PLldPRD is precise substituent for that system as it induces transcription of gene of interest even in oxygen-deprived conditions. As soon as L-lactate is actively produced in cancer cells, this metabolite binds lldR protein causing its conformational change due to which lldR loses its ability to bind O1 and O2 operon. Since it does not bind to operons and does not create DNA loop, the ALPaGA promoter readily activates the transcription of downstream GOI, which is PNC 27 in that case.

Modelling

Introduction

General introduction

In science, mathematical models are necessary for formulating hypotheses, making predictions, understanding complex systems, estimating parameters, optimizing processes, and interpreting data. Because they pose no risk, scientists can learn about potentially dangerous situations. When studies provide sample information, they aid in data analysis and preliminary data interpretation to support scientists in conclusions. Additionally, these models serve as a scientific language, facilitating discussions and knowledge advancement among a range of specialists.

Structural bioinformatics analysis for PNC-27 and NSP4-PNC-27

BLAST Protein-Protein Alignment Image 1 — ***Figure 3.*** Summary of BLAST protein-protein alignment of PNC-27 to p53.

BLAST Protein-Protein Alignment Image 2 — ***Figure 3.*** Summary of BLAST protein-protein alignment of PNC-27 to p53.

PNC-27 Visualization A — ***Figure 4.*** Color coded PyMOL visualization of PNC-27 structure.

PNC-27 Visualization B — ***Figure 4.*** Color coded PyMOL visualization of PNC-27 structure.

As PNC-27 is known to be a chimeric protein composed of two parts, the p53 HDM-2 binding domain, and cell-penetrating sequence, it was beneficial to understand which peptide fragments correspond to these parts. To do so, we obtained an amino acid sequence and PDB ID (1Q2I) of PNC-27 from UniProt. Subsequently, amino PNC-27 was analyzed through the BLAST tool by aligning the amino acid sequences of PNC-27, p53, and the cell-penetrating peptide (CPP) leader of antennapedia protein. For p53, the HDM-2 binding domain, which corresponds to residues 12−26, was utilized. The summary is illustrated on Figure 3. After alignment, the structure was visualized via PyMOL, and each of the components was color-coded on the protein: yellow corresponds to the p53 fragment, and cyan corresponds to the CPP sequence. Figure 4 demonstrates the obtained results: A - cartoon representation, B - mesh representation, C - surface representation.

Chimeric Model A — ***Figure 5.*** Color coded PyMOL visualization of chimeric peptides’ (NSP4+PNC-27) structure.

Chimeric Model B — ***Figure 5.*** Color coded PyMOL visualization of chimeric peptides’ (NSP4+PNC-27) structure.

Subsequently, as NSP4 was fused to PNC-27 on the amino-terminus, the newly obtained sequence had to be visualized via PyMOL as well. Firstly, we needed to obtain a PDB file of the structure. The SWISS-MODEL tool was used for structure prediction. However, as the tool performs modeling based on sequence homology alignment, the NSP4 component of the chimeric protein did not appear on the obtained structures. The most plausible explanation for this error is the absence of a template covering the region, meaning that the sequence similarity of proteins in the corresponding library is very low. Hence, the NSP4 part was omitted in the model. To overcome this challenge, the peptide analysis was conducted using the AlphaFold server, which was designed for protein 3D model prediction from submitted amino acid sequences. The software predicted chimeric peptides’ structure, which was then downloaded as a PDB file and visualized through PyMOL, the results of which can be accessed in Figure 5 (A - cartoon representation, B - mesh representation, C - surface representation). Yellow color corresponds to the p53 fragment, and cyan corresponds to the CPP sequence, and orange fragment corresponds to NSP4 signaling peptide. As can be seen by the images, addition of signaling peptide drastically changes the conformation of the chimeric protein, meaning that functioning of PNC-27 might be hindered by these modifications. Hence, antitumor activity can be completely lost. Therefore, it was highly beneficial to choose the signaling peptide, which gets cleaved from the native protein at specific sites with high accuracy and efficiency, which is the case for NSP4. Essentially, NSP4 will be removed by the corresponding signaling peptidase native to E.coli after translocation of the chimeric protein to periplasmic space through recognition by SRP and subsequent transport via SEC pathway. Afterwards, PNC-27 folds into its native structure, as described by structural bioinformatics moedling, which can then perform normal functions of the protein.

PNC-27 Docking Zoom Out — ***Figure 6.*** Color coded PyMOL visualization of PNC-27 docking to HDM-2.

PNC-27 Surface Docking Zoom In — ***Figure 6.*** Color coded PyMOL visualization of PNC-27 docking to HDM-2.

After visualizing the structure of PNC-27 and its chimeric counterpart, protein-protein docking indicating the binding of PNC-27 to its target, HDM-2, was performed by submitting PDB files of both proteins to the ClusPro 2.0 tool. Subsequently, several potential models for this binding were obtained, each described by their respective coefficient weight values:

Only balanced coefficients were read. Cluster 0, with a Center Weighted Score of -1174.3 and Lowest Energy of -1212.7, was chosen for further analysis. Lastly, visualization with PyMOL was repeated as described before, and the results can be accessed through Figure 6 (A- cartoon representation, B - surface representation).

As for the construction of the plasmid, the genetic sequence of PNC-27 was not available on open sources prior to our work. Therefore, the sequence had to be computed for the creation of the PNC-27 coding part. To do so, we utilized amino acid alignments of the peptide to p53 and CPP obtained for the visualization. Afterward, appropriate amino acid fragments of both components of PNC-27 were aligned to the mRNA sequences that code for these amino acids in native proteins from which the synthetic construct was made. BLAST alignment was used for this analysis as well. Then, reverse DNA sequences coding these mRNA fragments were manually computed, which was followed by codon optimization and insertion of the obtained parts into the plasmid designed for this project through SnapGene. Hence, we were able to compute a new part coding PNC-27 anticancer peptide having only its amino acid sequence.

Protein Introduction

By adjusting the model's parameters, the system can be adjusted to a PNC-27 concentration within the therapeutic window. It is possible to reduce the number of experiments and enhance the experiment configurations by adjusting the concentrations and values of sensitive parameters. These elements make the experimental work effective. This is what we do to help other researchers who are using the modified bacteria in a hydrogel system, as well as our ongoing research. In most carcinomas and melanomas, the overexpression of the HDM-2 receptor was observed in various research [28]. Therefore, PNC-27 protein can bind cancer cells with high efficiency based on the concentration of HDM-2 receptors and the concentration of PNC-27 in the tumour site, unravelling the practical specificity for protein-protein interactive binding and expanding the limitations of targeted tumour bacteriotherapy with genetically modified bacteria. Practically speaking, it was identified that PNC-27 chimeric protein and HDM-2 receptor bind in a 1:1 fashion. During the process of the complex formation, the leader sequence of PNC-27 points away from the complex, allowing for the transmembrane pores to be formed in the tumour cells, which leads to cell lysis and tumour necrosis [9]. An Ordinary Differential Equation (ODE) is used to predict the mechanism of action of PNC-27 against cancer cells. Figure 1 is an illustration of the simulation. The relationship between a function and its derivatives is explained by an ODE, a type of mathematical equation. Our goal is to gain further insight into the behaviour of the modified plasmid in the hydrogel system. Transcribing equations allows an ODE model to mimic our signalling route and predict the system's behaviour across time.

We have projected that our modified plasmid will produce PNC-27 and related proteins in response to lactate by using Matlab simbiology. It made it easier for us to estimate how much PNC-27 would be applied to the tumour site. As a result, we can effectively control the concentration to treat cancer.

Methods

Model structure

The model was created in MATLAB Simbiology Entension with the usage of Ordinary Differential Equations (ODEs) with the basic principle to modulate the level of expression of PNC-27 protein to the tumour site. Generally, the model relies on the central dogma of the molecular biology mechanisms - DNA transcription and protein translation, supplied by additional processes such as transcriptional regulation by promoter-repressor system and binding affinity of transcription factors.

Model description

The system senses the lactate in the tumor environment and in response activates the PNC- 27 expression. After the transcription, PNC-27 mRNA is translated into PNC-27 protein, which is further transported outside the bacterial cells. As soon as PNC-27 is exported, it binds to the HDM-2 receptor on the surface of cancer cells and includes pore formation in the cancer cell membrane, leading to cell lysis and apoptosis. 100% of the cancer cells undergo apoptosis within 90 minutes of induction with PNC-27. Visually, model was summarized in Figure 7.

PNC-27 Synthesis Mechanism — ***Figure 7.*** Mechanism of PNC-27 synthesis.

Model construction methods

ODE15s is the solver type used in the system, with the reactions being mostly Mass-Action kinetics and a few being set to Unknown laws as an exception for more accurate results. All the concentrations and values in the system of the PNC-27 synthesis are identified per 1 transformed bacterial cell. In total, the model contains 10 reactions for PNC-27 synthesis

The model is comprised of three main components:

Tumor site - applying the average volume of cancer, this compartment is responsible for identifying the PNC-27 binding to HDM-2.
Environment (hydrogel) - this compartment is responsible for identifying the overall volume of the system, in which PNC-27 is exported.
E.coli BL21(DE3) - the main compartment of the system, in which the synthesis of PNC-27 is regulated.

Assumptions and Limitations

The concentration of lactate. The literature states that the concentration of lactate in the tumour varies from 10 mM to 30 mM.[11] Taking the average value, we assume that the lactate concentration equals 20 mM in our system.
The copy number of plasmid in the E.coli BL21 (DE3) cell. To construct the plasmid, a pET9a, defined as a low-copy plasmid, the copy number is approximately 10 per cell.
The model contains several reactions, the rate for which was neither found in the literature nor studied yet in vitro. In such cases, the values for the reaction rates were either calculated manually by combining different sources and simple algebraic equations or were assumed to equal 1 if no data were available in the literature. All the values for compartment properties and parameters are represented in Table 1 and Table 2, respectively.
The major part of the equations in the model works on the Mass Action kinetics, which is not the most precise equation type for modelling biomolecular synthesis processes. Although some values for Michaelis-Menten kinetics for receptor-ligand binding are present in the literature, they are not enough to fully convert the system into another type of kinetics.
PNC-27 is not a native protein for either E.coli BL21 (DE3) or any other living organism. Additionally, no one tried to synthesize it in vivo using transformed bacteria or transfected cells. Based on this, the behaviour of the PNC-27 production in E.coli BL21 (DE3) cells is hardly predictable.

The concentration of the bacteria in our hydrogel system is presumed to be constant since the strain, E.coli BL21 (DE3), is focused on the transcription and translation processes rather than the replication process.[33]

**Table 1. Initial conditions in the modelled system**
Abbreviation	Full name	Value	Units	Source
E.coli	E.coli BL21 (DE3)	0.001	mL	[12]
Tumor	Tumor environment	0.0042	mL	[16]
Hydrogel	Hydrogel environment	0.0018	mL	Derived from hydrogel modelling
TF	Transcription factors	75,000	molecules	[13]
RNAP	RNA polymerase	4,600	molecules	[14]
Ribosomes	Ribosomes	26,100	molecules	[12]
P9 promoter	P9 promoter	10	molecules	*(plasmid copy number)
ALPaGA promoter	ALPaGA promoter	10	molecules	*(plasmid copy number)

Parameters

The following parameters are included in the system to model the expression of PNC-27 protein in a single bacterial cell. The values that were not found are assumed to equal 1, with the prescription “assumption” in the source column. Additionally, some of the values were manually calculated from the combinations of different sources via using simple mathematical operations such as multiplication and division; in the table, those values are labelled as “manually calculated”.

**Table 2. Parameters for expression model of PNC-27**
Abbreviation	Full name	Value	Units	Source
Translation per mRNA	The average number of translations per 1 mRNA molecule	40	dimensionless	[17]
P9-TF binding	The rate of the transcription factor binding to the P9 promoter	1	1/(molecule*second)	assumption
LldR transcription	The rate of the LldR gene transcription under the P9 promoter	0.0644	1/(molecule*second)	[16,17] manually calculated
LldR translation rate	The rate of the LldR mRNA translation	0.0581	1/(molecule*second)	[19] manually calculated
kf	The rate of LldR mRNA degradation	0.0022	1/second	[20] manually calculated
ALPaGA-LldR-Lactate association rate	The affinity of the LldR unbinding from the ALPaGA promoter in the presence of lactate	1	1/(second*molecule)	assumption
LldR degradation rate	The rate of the LldR protein degradation	0.0010	1/second	[20] manually calculated
PNC-27 transcription rate	The rate of PNC-27 gene transcription	3.180	1/(second*molecule)	[18] manually calculated
PNC-27 mRNA degradation rate	The rate of PNC-27 mRNA degradation	0.0033	1/second	[21] manually calculated
PNC-27 translation rate	The rate of PNC-27 mRNA translation	0.2885	1/(second*molecule)	[19] manually calculated
PNC-27 degradation rate	The rate of PNC-27 protein degradation	5.56×10^(-4)	1/second	[22] manually calculated

ODEs

PNC-27 Model Image — ***Figure 8.*** PNC-27 Peptide and Hydrogel Model Simulation represented in the Ordinary Differential Equations (ODEs). This model predicts the concentration of PNC-27 for targeted breast adenocarcinoma treatment.

Results

Model Validation

The modelling of the PNC-27 and MazF proteins was conducted using an ode15s solver type system in MATLAB Simbiology extension. As it was mentioned earlier, we decided to model the system on the scale of a single bacterial cell to minimize the miscalculations in the model related to the transcription and translation. The following plots were obtained: LldR protein concentration, PNC-27 mRNA concentration, and the concentration of PNC-27 against time. Additionally, cancer vitality is modelled after the concentration of PNC-27 is over the threshold value.

LldR Protein Concentration Image — ***Figure 9.*** The concentration of the LldR protein.

Figure 9 clearly shows the rate of production of the LldR regulatory protein in the system. As it is expressed in very high concentrations, it completely blocks the expression of the PNC-27 protein due to the binding of the LldR protein to the ALPaGA operon region. Furtherly, as the lactate from tumor tissues enters the bacterial cell, it binds the LldR protein and the protein changes its conformation, not being able to bind the ALPaGA operon anymore, which would induce the production of the PNC-27 construct.

PNC-27 mRNA Production Image — ***Figure 10.*** The rate of PNC-27 mRNA production.

In Figure 10, the concentration change of the PNC-27 mRNA after the exposure of the bacteria to lactate can be observed. The initial concentration change rate of PNC-27 mRNA is relatively high, which can be explained by the nature of the E.coli BL21 (DE3) strain, possessing T7 RNA Polymerase activity. As can be seen from the plot, the production rate of PNC-27 mRNA achieves its equilibrium state at the concentration of approximately 2.25 * 10^8 molecules per cell. Afterwards, the PNC-27 mRNA is used to synthesize the PNC-27 protein, which would provoke apoptosis in cancerous cells.

PNC-27 Protein Production Image — ***Figure 11.*** The production rate of PNC-27 protein.

Figure 11 represents the translation process of the PNC-27 mRNA and shows the concentration of the protein produced. As PNC-27 is being produced, it is exported outside of the bacterial cell due to the NSP-4 signal, which is attached to the PNC-27 protein on the N-terminus and marks the protein for extracellular export. We can see that the production of the PNC-27 protein is hyperbolic and achieves its equilibrium concentration at about 13 * 10^8 molecules per cell. In the upcoming section, the actual concentration of the PNC-27 protein will be calculated concerning the concentration of bacterial cells in the system.

PNC-27 molar concentration calculation

To identify the molar concentration of the PNC-27 protein produced by our system, we needed to know the concentration of bacteria in a particular volume of the medium. To address this problem, we decided to use the concentration of the bacteria, in which the Optical Density (OD) of the medium equals 1. In the literature, it is stated that the concentration of E.coli, at which the OD reaches 1, is 7 * 10^8 cells/mL [23]. Let’s assume that we use 1mL of the medium with the transformed bacteria to mix it with the hydrogel and inject it into the cancer site of the patient. To further recalculate the concentration of the PNC-27 protein we need some additional values, represented in Table 3.

**Table 3. Constants and values used for stoichiometric calculations.**
Constant	Value	Units	Source
Avogadro Number	6.02 * 10^23	molecules/mole	[24]
The concentration of E.coli at the OD=0.7	7 * 10^8	cells/mL	[23]
The molecular mass (MW or MM) of the PNC-27 protein	4031.72	Da (g/mol)	[25]

Using simple stoichiometric formulae and calculations, we obtain the concentration of the PNC-27 equal to 6094 ug/mL, produced by 1 mL of the transformed bacteria with an OD of 0.7. Since this concentration does not consider the volumes of the cancerous tissue and the hydrogel, we need to identify the average volume of the breast cancer. In the literature, it is stated that the average diameter of the newly identified breast cancer is 20 mm^3 [26]. Using simple calculations, we derive that the volume of such a tumor would be 4.186 mL. Implying that volume into the system, we obtain the concentration of the PNC-27 to be 1175 ug/mL, whereas the required inhibitory concentration of the PNC-27 is 50 ug/mL [27]. Once again, by using simple mathematical calculations, we identify that the volume of the injected transformed bacteria should be around 0.05 mL or 50 uL. All the calculations are presented below.

Conclusively, we need to inject 0.05 mL of the transformed bacteria into the tumour site with a volume of 4.186 mL to obtain the required inhibitory concentration of 72 ug/mL. The difference between the required inhibitory and the calculated concentration is because the system will also include the hydrogel and the extracellular matrix of the human tissue, so a 44% increase in the concentration will be sufficient to outweigh the factors that were not included and all the approximations that were made during the modelling of the system.

Tumor Vitality Image — ***Figure 12.*** The vitality of the cancer cells with PNC-27.

Figure 12 represents the vitality of the cancerous tissue after the required inhibitory concentration of PNC-27 of 50 ug/mL is reached in the tissues. As it can be seen from the plot, the first 70% of the cells die within 2 hours of treatment and almost 100% of the cells die within approximately 9 hours of treatment.

Improvements

It is yet possible to expand the scope of the model to different scales by implementing a lactate feedback loop, in which the concentration of lactate would change as the production of the PNC-27 protein is started. This would allow us to obtain more precise and credible results. Apart from that, different compositions of the plasmid backbone and regulator sequences could be used to tune the production of the protein of interest within the system. In addition, MATLAB Simbiology possesses several restrictive rules to the system; e.g. we know that in real biological systems, all the processes of metabolic pathways as well as the processes including the central dogma of molecular biology intercept with each other and are interconnected. Yet, within the software we utilized, each molecule species or compartment could be affected by a limited number of reaction rates or simultaneous reactions are conducted as if they occur in order. To get rid of such miscalculational errors, more advanced software could have been utilized.

Conclusion

The model of the protein synthesis satisfies the expected outcomes of the PNC-27 controlled production in the E.coli BL21 (DE3) strain. The central dogma of molecular biology was preserved along the whole process of modelling the system. We have successfully received the results that prove the viability of our system and its ability to be used as an innovative method for personalized cancer treatment.