Team:BNU-China/Model

Overview

Beta-oxidation Enhancement

Glucose Concentration Simulation

Recombinase System

Protein Docking

Overview


Throughout our project, we have been using different types of model to refine our design, explain experimental results and predict effect of new systems based on previous data. In beta-oxidation module of our project, we used modelling to help us decide which enzymes had most potential to enhance consumption of higher fatty acids, saving us a considerable amount of work on the less valid enzymes. In glucose concentration simulation, we used modelling to simulate change in glucose concentration in the intestine after a meal, data we could neither find in literature nor measure in our project. In the recombinase system, modelling helped us to confine the interval in which we regulated synthesis and degradation rates of recombinase directionality factor (RDF). Also, a protein docking model enabled us to exclude interference in protein function when adding a tag to RDF sequence. In the end, in our final integrated system, we used the data obtained from all the individual parts to build a model that simulated the overall effect of the integrated system.

Beta-oxidation Enhancement


Introduction


To boost the fatty acids consumption of our engineered bacteria, we enhance their beta oxidation, where four key enzymes are directly involved in a prokaryote system – fatty acyl-CoA synthetase (FadD), fatty acyl-CoA dehydrogenase (FadE), fatty enoyl-CoA hydratase and fatty hydroxy acyl-CoA dehydrogenase (FadB), as well as thiolase (FadA).(Fig.1)

Fig. 1 Fatty acid beta-oxidation pathway

In order to choose the enzyme out of four candidates that most efficiently increases the rate of such a process, we combined modelling and experiment approaches. Models of each of the four enzymes are built and their fatty acids consumption rates compared.




Prediction model


1.Assumptions

We assume that the amount of fatty acids is excessive. And to satisfy the condition of Michaelis-Menten equations, we also need a steady-state hypothesis: the rate of formation and decomposition of enzyme-substrate complex is equal. In the reactions, FadD, as an ATPase, catalyzes the irreversible reaction in which fatty acids are converted to fatty acyl-CoA, while the other enzymes catalyze the reversible reactions within the cycle. The enzymatic activities are enhanced by 100 fold to simulate the effect of overexpression.

2.Symbols and Definitions

3.Parameters and Definitions

4.Models and Results

Enzymatic reaction model

★ reaction diagram and Michaelis-Menten equation

Here are the main reactions in the consumption of FA:

Using the Michaelis-Menten equation, we can get the concentration change rate of the reactants during the circular reactions:

The relationship between Vmax and kcat are given by definitions:

★ differential equations

Through integrating the equations above, we get two differential equations for the concentration change rate of acyl-CoA and Fatty Acid:

★ Solve the model

In this problem, we are interested in the consumption effects of Fatty Acid when setting one of the enzymes excessive. Using MATLAB we solved the differential equations above, and here are the concentration change curves of the FA and other reactants with respect to each situation.

Values or initial values of the parameters are as follows:





Results


Out of the four enzymes, FadD, as the enzyme that convert fatty acids into a component of beta-oxidation cycle, has the most significant enhancement in the catabolism of the latter. Whereas with the cycle, FadE is the most effective (Fig. 2).

Fig. 2 Effects of different enzymes when overexpressed

The beta-oxidation model based on credible parameters from literature saved the laborious work of testing all the four enzymes. Only the effect of the most promising enzyme FadD, and the relatively more effective enzyme within the cycle, FadE, are tested experimentally. Moreover, our later experiment results did align with the relative effect of the two tested candidates (Fig. 3)

Fig. 3 Experimental results of FadD and FadE overexpression





References


[1] Kameda K , Nunn W D . Purification and characterization of acyl coenzyme A synthetase from Escherichia coli[J]. Journal of Biological Chemistry, 1981, 256(11):5702-5707.

[2] Doulias P T , Tenopoulou M , Greene J L , et al. Nitric Oxide Regulates Mitochondrial Fatty Acid Metabolism Through Reversible Protein S-Nitrosylation[J]. Science Signaling, 2013, 6(256):rs1-rs1.

Glucose Concentration Simulation


Introduction


Glucose is one of our chosen indicators for digestion, and we choose promoter rpoH P5 BBa_K3036003 to sense this signal. In order to verify the validity of this part, we need data of the sensitivity of the promoter which we obtain from experiments, as well as changes in glucose concentration inside intestine. However, latter is not accessible for lack of relevant research. So, we estimated the change in intestinal glucose concentration before and after meals through mathematical modelling methods, and then combine it with experimental results.

First, by analyzing the digestion and absorption of in-taken starch, we established the ordinary differential equation (ODE) model of glucose concentration changes over time. Then, considering that the activity of amylase is related to the substrate concentration, we improved the model by the kinetics of enzyme-catalyzed reactions equation. Next, a MATLAB program is executed to solve the model using a differential method. Finally, we obtained the change of glucose concentration in the intestine over time.





Assumptions and Symbols


1.Assumptions

1. The concentration of glucose in gut before meals is 0[mg/mL]. 2. Glucose in gut is only decomposed by the starch that is eaten by meal. 3. The rate of decomposition of amylase conforms to the kinetics of enzyme-catalyzed reactions equation.

2.Symbols and Definitions





Models and Results


1.Intestinal glucose concentration model

From the literature [1], the differential equation of glucose concentration in the intestine over time is as follows:

Where P is the concentration of glucose in the gut, x is concentration of substrate (glucose, oligosaccharide, etc), u is the rate constants for glucose uptake from the gut into the blood, respectively. dx/dt means the amount of glucose produced by starch decomposition per minute, and uP means the amount of glucose uptake from the gut into the blood per minute.

The kinetics of enzyme-catalyzed reactions equation is as follows:

Where x is substrate (glucose, oligosaccharide, etc) concentration，k describes the Michaelis constant. Because x′ (t) = v, so we can write:

Then we got the differential equations:

2.Solve the Model

It is easy to know that the second equation of the equations (3) can be solved independently. Transform formula (2) as follows:

which is:

Integrate both left and right, then we get the implicit equation relationship between substrate concentration x and time t, where C is a constant.

Let t = 0:

x(0) is the initial value of substrate concentration, so the implicit equation relationship between substrate concentration x and time t is:

We can set x(0) = 64[mg/ml] according to the information that adults consume 64g of starch per meal. [1-2] Then let K = 5.189[mg/ml], v max = 1.04[mg/(mL·min)] [3]

Fig. 1 Relationship between substrate concentration x and time t

Using MATLAB to solve the implicit function (4), we can get the following figure (1): Discretize the ODE (1) into a difference equation:

Here is the result:

Fig. 2 Relationship between P and t





Conclusion


According to our measurement, the glucose regulatory threshold of rpoH P5 promoter is between 0.01% and 0.05%, calculated to be 5.6mmol/L. As is shown in the glucose concentration simulation model, it is validated that the rpoH P5 promoter respond to slight changes in gut glucose as expected. In conclusion, we can put our bilateral switch under the control of rpoH P5 promoter as a digestion sensor.





References


[1] Grabitske, HA; Slavin, JL(2009). Gastrointestinal effects of low-digestible carbohydrates. Critical Reviews in Food Science and Nutrition. 49 (4):327–360. doi:10.1080 / 10408390802067126. PMID 19234944.

[2] Like Y. Hasek,Robert J. Phillips,Genyi Zhang,Kimberly P. Kinzig,Choon Young Kim,Terry L. Powley,Bruce R. Hamaker. Dietary Slowly Digestible Starch Triggers the Gut–Brain Axis in Obese Rats with Accompanied Reduced Food Intake[J]. Molecular Nutrition & Food Research,2018,62(5).

[3] Dickson J, Signal M, Harris D, et al. Modelling Intestinal Glucose Absorption using Continuous Glucose Monitor Data[J]. Ifac Papersonline, 2015, 48(20):118-123.

Recombinase System


Introduction


The recombinase system in our project aims to validate a bilateral switch by flipping the sequence of a constitutive promoter between two pathways and thus determine the expression state of the two pathways.

We choose the integrase and its recombination directionality factor (RDF) derived from mycobacterial phage Bxb1 to perform this function. But different from many previous iGEM project involving such a system, we express integrase at a constant level and put RDF gene under control of an inducible promoter, thus determine the directionality of the system by tuning the ratio between integrase and its RDF. Consequently, it is of great importance that the level of RDF rises and falls in a rapid manner. Also, it is essential that RDF and integrase, when coexpressed, reaches a ratio high enough so that the integrase shows only its excisionase activity and not its integrase activity.

Previous research has revealed the demand of excess RDF when the conversion from LR to BP state takes place[1]. By modelling we compare the difference in reaction rate and final conversion ratio when RDF is put under control of promoters of different strengths. Otherwise, to degrade the high-level RDF with high efficiency when expression stops, it can be beneficial to promote degradation rate of RDF. However, the side effect of such a promotion is that it lowers the maximum concentration of RDF. Again, we use models to find balance between these factors.





Prediction model


1.Assumptions and Symbols

In our model, we name each state of target sequence by recognition sites flanking it, that is, BP and LR, respectively. The total amount of BP and LR is 500, the copy number of pUC19 in a bacterium. The conversion between BP and LR states are conducted by integrase dimers (I2) and integrase-RDF tetramers (I2X2) respectively. Integrase concentration is maintained at a constant level, whereas level of RDF depends on its dynamically changing expression and degradation rates. RDF is expressed at a constant rate when induced and is not expressed when uninduced, and its degradation is proportional to its concentration in the cell.

2.Parameters and Definitions

3.Models and Results

★ BP and LR

The conversion relationships between BP and LR is as follows:

The chemical reactions are as follows：

According to the definition of chemical equilibrium constant, we know that:

There are other quantitative relationships in this reaction system:

According to the program [1], we learned that the differential equation of the concentration of LR and LRI4X4 yLRtot over time is as follows:

So the equation can be written as:

★ Integrase and RDF

From the program[1], the concentration of RDF and Integrase are defined as:

where α1 is the transcription rate of input set, αI is the maximal transcription rate of integrase, γI is the degradation rate of integrase, α2 is the transcription rate of input reset, αX is the maximal transcription rate of RDF, γX is the degradation rate of RDF.

★ Solve the Model

From the problem background,the promoter that regulates the production of RDF begins to express when eating and stops to express after meal, therefore we solve the model separately in the case of eating and stopping eating.

(1) Upon induction

When induced, the values of the parameters and initial values are as follows:

Then use the matlab command ode23 to solve the differential equations composed of equations (1), (2) and (3). The results are as follows:

blue–LR, red–BP

(2) Upon removal of inducer

When inducer is removed, RDF stops being expressed and is degraded only, so we can let α2 = 0. Through the previous calculation, we know that the stable value of yLRtot is 10, so in this case we can set the initial value yLRtot = 10. The remaining parameters and initial values are the same as the previous ones. And the results are as follows:

4.Tuning Expression and Degradation Rates of RDF

It is presumed that the excisionase activity of integrase depends on its ratio to RDF, so we try to tune up the expression rate of the latter to achieve a high RDF-integrase ratio. As can be seen below, the enhance of RDF expression notably raises the turn-over rate from LR to BP state.

However, the additional amount of RDF calls for more time to be degraded, causing trouble for the conversion from BP to LR state. To solve the problem, we propose to promote degradation of RDF. From the chart, we can see that after this alteration, although the proportion of LR-BP conversion slightly declines, there is a significant improvement in BP-LR conversion rate.





Conclusion


From this model we can conclude that it would be beneficial to put RDF gene under control of a promoter much stronger than that of integrase and to enhance degradation rate of RDF at the same time.





References


[1]Dı́az-López, T., Lages-Gonzalo, M., Serrano-López, A., Alfonso, C., Rivas, G., Dı́az-Orejas, R., and Giraldo, R. (2003) Structural changes in RepA, a plasmid replication initiator, upon binding to origin DNA. J. Biol. Chem. 278, 18606−18616.

Protein Docking


Antitoxin-toxin system


1.Introduction

In our cold-triggered kill switch, the downstream relE (BBa_K185000) gene encodes for a constantly expressed stable toxin and the upstream relB (BBa_K185048) gene encodes for a labile antitoxin under the control of the RNA thermometer (BBa_K115002). When the engineered microbe escape from human body, leading to temperature dropping, the antitoxin RelB stops to counteracting RelE and thereby causes death of the microbe.

In order to accelerate the speed of suicide for maximum safety, we proposed to add a degradation-promoting tag RepA to antitoxin RelB, which makes antitoxin disabled to detoxify rapidly. So, we built a protein docking model of RelB and RelE to identify which terminal of RelB is more suitable for adding a tag without affecting the recombination between antitoxin and toxin.

2.Protein structure model

We used Swiss-Model [1-4] to predict the structure of RelB and RelE, which is universally used to perform alignment and build 3D protein models, and select the best matched of known protein models according to submitted amino acid sequence. The 3D model was displayed in Chimera.

The template of antitoxin RelB is 4fxe.1.B, and the template of toxin RelE is 4v7k.1.U.

Fig. 1 Predicted protein docking model of toxin and antitoxin

As is shown in Fig. 1, N-terminal of RelB is dissociative, but the C-terminal is close to the binding surface. Hence, the N-terminal of RelB is a better choice.

3.Conclusion

After confirmed that N-terminal of RelB preferably applies to add the tag RepA, we improved the performance of antitoxin RelB in a remarkable way, which is a key element of a more efficient kill switch. As is shown in Figure 2, under same nonpermissive conditions, the bacteria containing the kill switch with improved RelB die at a notably higher rate than those with unimproved RelB, verifying the effect of the improvement.

Fig.2 Comparison between kill switches before and after improvement.





Recombinase system


1.Introduction

In order to raise the efficiency of bilateral switch, we designed a degradation tag (RepA) attached to recombination direct factor (RDF). However, RDF needs to combine with integrase (BBa_K907000) to convert the DNA sequence flanked by attB and attP sites. Hence, the added tag is supposed not to influence the recombination, so that we built a prediction model to display the position of C and N terminals, from which we chose one to add RepA.

2.Protein structure model

We used NCBI blast and Swiss-Model to perform homologous modeling and chose the best matched one of all results. The template of integrase is 3UJ3_X, and the template of RDF is 4yke.1 (click the name to learn more). Pymol [5-7] was used to divide them into monomers, and Chimera [8] was used to build and display protein docking model.

Fig. 2 Predicted protein docking model of integrase and RDF

As is shown in Fig. 2, N and C terminals are both away from the binding surface of proteins, so adding tag to either of them would influence formation of the dimer.

3.Conclusion

After confirmed that N and C terminals both apply to manipulate, we chose the N-terminal of RDF to add RepA, so that there would be less chance for tag loss by nonsense mutation.





References


[1] Waterhouse, A., Bertoni, M., Bienert, S., Studer, G., Tauriello, G., Gumienny, R., Heer, F.T., de Beer, T.A.P., Rempfer, C., Bordoli, L., Lepore, R., Schwede, T. SWISS-MODEL: homology modelling of protein structures and complexes. Nucleic Acids Res. 46(W1), W296-W303 (2018).

[2] Bienert, S., Waterhouse, A., de Beer, T.A.P., Tauriello, G., Studer, G., Bordoli, L., Schwede, T. The SWISS-MODEL Repository - new features and functionality. Nucleic Acids Res. 45, D313-D319 (2017).

[3] Guex, N., Peitsch, M.C., Schwede, T. Automated comparative protein structure modeling with SWISS-MODEL and Swiss-PdbViewer: A historical perspective. Electrophoresis 30, S162-S173 (2009).

[4] Benkert, P., Biasini, M., Schwede, T. Toward the estimation of the absolute quality of individual protein structure models. Bioinformatics 27, 343-350 (2011).

[5] DeLano, W. L. (2002). PyMOL. DeLano Scientific, San Carlos, CA, 700.

[6] DeLano, W. L. (2009). The PyMOL Molecular Graphics System; DeLano Scientific: San Carlos, CA, 2002. There is no corresponding record for this reference.

[7] DeLano, W. L. (2002). Pymol: An open-source molecular graphics tool. CCP4 Newsletter On Protein Crystallography, 40, 82-92.

[8] UCSF Chimera--a visualization system for exploratory research and analysis. Pettersen EF, Goddard TD, Huang CC, Couch GS, Greenblatt DM, Meng EC, Ferrin TE. J Comput Chem. 2004 Oct;25(13):1605-12.

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