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NTU@iGEM Project Introduction Methodology Team Introduction Team background Notebook Dry Lab Introduction ODEs used Modeling Constructs Parameters used Deterministic Modeling Sensitivity Analysis Stochastic Modeling Wetlab Introduction Materials and Equipment Protocols Verification of Detection & Lysis System Our New Parts Characterization Introduction Standard Promoters Characterization of pLacI-GFP pLacI-GFP images and clips Characterization of pLsrA-YFP New characterization Proposal Parameter Estimation & Correlations Acknowledgements

Contents 1 Introduction 2 System 3 ODEs used in modeling 3.1 Constant synthesis & Linear Synthesis 3.2 Linear Degradation 3.3 Simple Forward Reaction 3.4 Phosphorylation and Dephosphorylation 3.5 Regulated Transcription 4 ODE system used in model 4.1 Lactose controlled production of E7 + Imm 4.1.1 Variables 4.2 Iron and Ai2 controlled production of Lysis 4.2.1 Variables 5 Parameter Estimation 5.1 E7 prodcution system 5.2 E7 prodcution system 6 Results of Modeling 6.1 E7 prodcution system 6.2 Lysis Production system

Introduction

The use of models to describe synthetic biology has its merits. Synthetic biology investigates the use of different biological parts to put together and assemble devices that carry out specific functions. Good mathematical models to describe each part would greatly help not only in the characterization of a part but also facilitate the use of the part by other people when they choose to use the part within their devices or systems.

Simulations based on modeling can give a first insight on how the system would turn out and provide a rough guide of the system’s behaviour.

System

The system can be viewed as two parts. The first part comprises of lactose induced production of colicin E7 and the immunity protein. The second part comprises of a detection mechanism that produces the lysis protein upon the detection of both Iron ions and Ai-2 ( Autoinducer 2).

ODEs used in modeling

The following equations shows the break down of the different equations that will be used in this modeling exercise. By understanding this section, it would make the understanding of the system of ODEs used

Constant synthesis & Linear Synthesis

• Simple ode to describe constant synthesis
• Gives an explicit analytical solution
• Unique solution once a IC is posed

Linear Degradation

• Rate of degradation is proportional to how much of the molecule is present
• Gives an explicit analytical solution
• Constant half life

Simple Forward Reaction

This equation ignores the fact that dissociation of the complex occurs. We can do so if the dissociation is much slower than the formation.

• Single solvable equation for the unknown C
• Simple, unique solution available with I.C

Phosphorylation and Dephosphorylation

Assumptions:

• Linear kintic rate laws apply only if XT is much less than the Michaelis constants of both kinase and phosphotase

• Modeled after simple linear kinetics
• Gives a hyperbolic signal response curve when X plotted vs S

Regulated Transcription

ODE system used in model

Lactose controlled production of E7 + Imm

Variables

1. LacI = A
2. Lactose =B
3. E7 = C

Iron and Ai2 controlled production of Lysis

Variables

Variables

1. Ai-2 : A
2. ai-2-phos : B
3. LsrR : C
4. SupD derivatives : D
5. T7ptag : E
6. Lysis : F

Parameter Estimation

Estimation of different parameters

1. Transcription  : 70nt/s
2. Translation : 40aa/s
3. Number of Essential Genes : 297
4. Number of mRNA per cell : 4000
5. Average mRNA half life : 5min
6. Average mRNA length  : 1100

Assumptions

1. Rate of transcription is dependent on length of gene
2. Number of amino acids is 1/3 of the number of nucleotides in a gene
3. Rate of Translation is dependent on number of nucleotides
4. For each gene mRNA = 10 at steady state
5. Rate of degradation of average mRNA = 1100/ 5 min
6. Rate of degradation of protein is equivalent to time for cell division i.e. 40 min

E7 prodcution system

Type	Parameter	Values	Comments
Transcription Rate of Lac I gene	k1A	21	Made using Earlier assumptions
Transcription Rate of E7 + Imm gene	k1C	2.470588	Made using Earlier assumptions
Degradation Rate of Lac I mRNA	d1A	0.76246	Made using Earlier assumptions
Transcription Rate of E7 + Imm mRNA	d1C	0.0897	Made using Earlier assumptions
Translation Rate of Lac I mRNA	k2A	36	Made using Earlier assumptions
Translation Rate of E7 + Imm mRNA	k2C	4.23539	Made using Earlier assumptions
Protein Degradation Rate	d2A,d2C	0.03465	Made using Earlier assumptions
Hill coefficeint for E7 + Imm	nC	1	This is obtained on the assumption that one Repressor Protein binds to one Lactose molecule complex
Dissociation Constant for E7 + Imm	KC	0.8	[3]
Constitutive Portion for E7 + Imm	aC	0.5	Estimate since a is between 0 and 1 Implication that Lactose may not be a very strongly Regulated Promoter
Complex Formation Rate Between Lac I Repressor and Lactose	k3AB	1	Estimate

E7 prodcution system

Type	Parameter	Values	Comments
Phosphorylation Rate of Ai-2	kPF	1	Estimate
Dephosphorylation Rate of Ai-2	kPB	1	Estimate
Transcription Rate of LsrR gene	k1C	4.402517	Made using Earlier assumptions
Transcription Rate of SupD gene	k1D	46.667	Made using Earlier assumptions
Transcription Rate of t7pTag gene	k1E	1.5556	Made using Earlier assumptions
Transcription Rate of Lysis gene	k1F	28	Made using Earlier assumptions
Degradation Rate of LsrR mRNA	d1C	0.159845	Made using Earlier assumptions
Degradation Rate of SupD mRNA	d1D	1.694359	Made using Earlier assumptions
Degradation Rate of t7pTag mRNA	d1E	0.056478	Made using Earlier assumptions
Degradation Rate of Lysis mRNA	d1F	1.0166	Made using Earlier assumptions
Translation Rate of LsrR Protein	k2C	7.54716	Made using Earlier assumptions
Translation Rate of t7 pTag Protein	k2E	2.6667	Made using Earlier assumptions
Translation Rate of Lysis Protein	k2F	48	Made using Earlier assumptions
Protein Degradation Rate	d2C,d2E,d2F	0.03465	Made using Earlier assumptions
Hill coefficeint for SupD	nD	50	Trial And Error
Hill coefficeint for t7 pTag	nE	1	Trial And Error
Hill coefficeint for Lysis	nF	1	Estimate
Dissociation Constant for SupD	KD	15	[5]
Dissociation Constant for t7 pTag	KE	1	Estimate
Dissociation Constant for Lysis	KF	0.8	Estimate
Constitutive Portion for SupD	aD	0.01	Estimate
Constitutive Portion for t7 pTag	aE	0.01	Estimate
Constitutive Portion for Lysis	aF	0.0001	Estimate
Complex Formation Rate Between LsrR Repressor and Ai-2-Phosphorylated	k3BC	0.01	Estimate
Complex Formation Rate Between SupD tRNA and t7 pTag mRNA	k3DE	0.000000001	Estimate
Amount of Protein Kinase	S	28.747	From Earlier Assumptions

Results of Modeling

E7 prodcution system

Modeling of the System shows that Lactose induction is essential to produce E7 and a variation of Lactose input can result in different yeilds of E7

Lysis Production system

Here we define 1 as a certain threshold e.g. (<250 µM) that when the lysis protein reaches it, lysis in the cell definitely occurs. Although we wish for an absolute AND gate, where 0 will have no lysis production at all, simulation on biological systems shows that such results are impossible. Both addition Fe ions and Ai-2 alone would induce a certain level of lysis production. However when both are available, the lysis protein production would be higher.

In the presence of Ai-2 alone, Lysis will most likely still occur albeit at a slower rate compared to situation when both Fe and Ai-2 are present.

With the addition of iron and Ai-2 together the rate of lysis production is still significantly much higher compared to Ai-2 alone.

Therefore, by giving the logical output ‘1’ as a suitable threshold value of Lysis protein production higher than that of Ai-2 induction alone, we would still be able to obtain an AND gate based on our definition.