| NU_Kazakhstan - iGEM 2023

HA Concentration	Molecular Weight Between Cross-Links (kg/mol)
1%	4.047
2%	2.210
3%	1.028

HA Concentration	Mesh size, m
1%	1.570*10^-8
2%	1.224*10^-8
3%	0.835* 10^-8

Protein

Model structure

The model was composed in MATLAB Simbiology extension, using Ordinary Differential Equations (ODEs) as the basis for the modulation of processes of Colicin E1 synthesis at tumor sites. The model is mainly built on the synthesis of colicin E1 in response to the presence of lactate in the environment, which is a main product of tumor cell metabolism due to the Warburg effect.

Model description

Figure 4. The schemal review of Colicin E1 synthesis in response to cancer synthesized lactate.

The visual illustration of the model process at tumor sites is depicted in Figure 4. As lactate enters bacteria cells (1), it acts as a stimulator of colicin E1 mRNA transcription via dissociation of hairpin formed by the LldR protein encoded in our plasmid (2). This allows the T7 RNA Polymerase to bind the P11 promoter of the plasmid (3) and proceed to the transcription phase (4). Following that, the colicin E1 mRNA is translated into colicin E1 protein (5), and it escapes the bacteria cell (6) and leads to the apoptosis of cancer cells (7). This leads to a decrease in lactate in the environment (8) and colicin E1 synthesis.

LldR is commonly known as a lactate-responsive transcription factor that regulates the transcription of genes in response to the presence of lactate in the environment [22]. In our plasmid, LldR regulates the transcription of the colicin E1 through binding to O1 and O2 binding sites, opening up the P11 promoter.

As colicin E1 accumulates at the tumor site and reaches its effective concentration, it affects the cancer cells and could decrease their population by up to 43% in 24 hours [23]. Cancer cell depletion has an effect on lactate concentration in the environment. Thus, it downregulates the synthesis of colicin E1, creating a loop.

Model construction methods:

The solver type used in the simulation is ode15s, and reactions are primarily Mass-Action, with several exceptions being set at Unknown. Besides ODEs, the model also has repeated assignments. The model comprises 5 ODEs and 2 repeated assignments, demonstrating rates of synthesis and degradation of colicin E1, its effects on tumor site depletion and a negative feedback loop of DNA replication regulation produced by the effect of Colicin E1 on decreasing lactate production.

As stated above, most reactions use Mass-Action models, and some use repeated assignments. Repeated assignments are dedicated to the control and change of the molecules in time, which do not participate in the reactions explicitly nor are consumed during the reactions.

The reactions used in the model were defined from scratch, based on the ODEs engineering webinar series from iGEM. The values used in the model for equations were derived from the literature or manually due to the need for concrete information on specific constants.

The model consists of three compartments representing:
a. Tumor site - given the average volume of cancer, the bacteria will target in a hydrogel we plan to inject.
b. Environment - which consists of the bacteria and hydrogel. It shows the volume in which the toxin will spread.
c. Bacteria (in our case, E.coli BL21 (DE3)) - the volume of bacteria that will be encapsulated in hydrogel to inject further and synthesize colicin E1.
The limiting factor of colicin E1 synthesis in our model is considered to be lactate. The initial lactate value in the environment was assumed to be 20 mM, referring to the available literature [23].

Assumptions

The model our team proposes has three major assumptions we had to take to make our model realistic:

1. The lactate concentration. It is stated through the literature that lactate concentration varies in tumor sites from 10 mM to 30 mM [23], and given that we have this data, it was assumed that the lactate concentration in tumor sites, on average, is 20 mM.
2. The number of plasmid copies transformed in E.coli BL21 (DE3). Since our plasmid is based on pET9a plasmid, defined as low-copy, we assume the copy number in bacteria to be 5 [24]
3. The amount of bacteria in the simulated model.

The value for bacteria number is assumed to be constant since the strain used in the simulation is mainly oriented on transcription and not replication[25]; furthermore, the hydrogel possesses a little toxicity to bacterial cells due to hyaluronic acid in the structure [26].

Initial Conditions

Abbreviation	Full name	Value	Units	Source
Environment	Tumor site Environment	965	uL	-
E.coli	E.coli BL21 (DE3)	5	uL	-
Tumor	Tumor cells	524	uL	-
ColE1_env	Colicin E1 in Environment	0	M	-
Lactate_IN	Lactate inside E.coli BL21 (DE3)	20	mM	[23]
LldR	LldR protein in E.coli BL21 (DE3)	4.4 x 10^-9	M	Calculated
P11	P11 promoter	4.4 x 10^-9	M	Calculated
ColE1mRNA	Colicin E1 mRNA	0	M	-
T7	T7 polymerase	4.98 x 10^-6	M	-
ColE1	Colicin E1 in E.coli BL21 (DE3)	0	M	-

Parameters

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Abbreviation	Full name	Value	Units	Source
k_1	LldR and lactate affinity value	0.8	uL	-
k_2	P11 promoter release rate from LldR	1	-	Assumption
kf_0	Colicin E1 mRNA degradation rate	0.0078	1/s	[27]
kf_1	Colicin E1 translation rate	0.0383	1/s	[28]
kf_2	Colicin E1 degradation rate	0.069	1/s	[29]
kf_3	Colicin E1 escape rate from bacteria	1	1/s	Assumption
kf_4	Colicin E1 mRNA transcription rate	0.1147	1/(M/s)	[28]
kf_5	Rate of lactate decrease	0.0238	1/hour	[19]
k_ColE1_threshold	Efficient anti-tumor concentration of Colicin E1	2.19 x 10^-8	M	[19]

Reaction equations

ODEs:

Modeling

Introduction

Conclusion

Hydrogel

Protein

Hydrogel

Protein