# Team:MIT MAHE/Model

Model | iGEM MIT_MAHE

# Introduction

Biological systems are like poetry — mesmerizingly complex yet marvelously simple. Proteins are the words of this poem, giving it a structure and function. The core components of our project are these molecules, enabling us to bring to life our problem statement. In order to use them effectively, understanding their complexity is necessary. To do the same we have visualized and simulated our proteins, dividing them to their core aspects: structure and function.

# Structural Analysis

"Visual molecular dynamics" is a molecular visualization program used for display, animation, and analysis of large biomolecular systems using 3-D graphics and built-in scripting Visual molecular dynamics - TCg. We have used this software to visualize our dual enzyme system MerA and MerB. A CHARMM force-field with additional entries in the topology and parameter files was used for the mercury ion and cysteine (sulphur) interactions.

### Alkylmercury Lyase

Alkylmercury lyase is encoded by the MerB gene and breaks the carbon mercury bond in the organometallic compound and transfers the resulting mercury ion (Hg2+) to mercury (II) reductase (MerA)Lafrance-Vanasse, J. et al, 2009Parks et al., 2009.

Figure 1: Alkylmercury lyase without organic mercury. New cartoons representation with residues highlighted in CPK.

The active site of this protein is CYS-95 and CYS-158. Here we show only one chain of the dimer of the MerB complex. Searches for PDB files of MerB with an organometallic ligand were futile, therefore a carbon atom was inserted into the PDB file manually after calculating the distance between mercury and carbon in methylmercury compound.

Video 1: Alkylmercury Lyase with organic mercury. New cartoons representation with residues highlighted in CPK.
Video 2: Alkylmercury Lyase with organic mercury - video shows conformational changes of the enzyme when it is working.

### Mercuric reductase

Figure 2: Mercuric reductase without mercury. New cartoons representation with residues highlighted in CPK.

Mercuric reductase, as the name implies, reduces the Mercuric ion (Hg2+) to elemental mercury (Hg). The binding site for this protein is CYS-10 and CYS-13 Ledwidge, R. et al, 2005 Mathema et al., 2011.

Video 3: Mercuric reductase with mercuric ion. New cartoons representation with residues highlighted in CPK.

Our aim was to show the stability of our enzyme by determining Root Mean Square Deviation of the protein-ligand system. We failed to do so due to the uncertainty about mercuric ion properties. The results we obtained at the time of submission were too unsatisfactory for us to proceed with the analysis.

# Functional Analysis

Functional analysis was modelled using MATLAB - SimBiology.

### Model 1

In order to assess the order of concentration of enzymes required for optimal conversion, we have designed an experiment (refer to iGEM MIT_MAHE Composite Bio-Brick 1 handbook for complete protocol). This experiment would provide three graphs

• Graph of mercury concentration vs time is obtained for constant concentration of enzyme
• Graph of enzyme concentration vs activity is obtained.
• Graph of no of cells vs enzyme concentration graph is obtained.

Using the graphs, estimation about the optimal enzyme concentration to enable optimum activity must be determined. Thus, the optimum CFU/mL to be used can be estimated.

To provide a range of concentration of enzymes that can be used in order to attain the first graph, we have designed a MATLAB model.

We have used Michaelis Menten Kinetics to simulate the kinetics of our two enzymes alkylmercury lyase and mercuric reductase.

Figure 3: Michaelis Menten kinetics-based enzyme reaction mechanism.

Assumptions to be considered:

1. ES formation is much faster than E + P formation i.e. k1, k-1 >>> k2
2. Steady state condition (ES concentration is constant).

Ordinary differential equations (ODEs) used: $$[\frac{dCH_3Hg}{dt}=\frac{(-(V_{m1}.[CH_3Hg])}{(K_{m1}+[CH_3Hg])}]$$ $$[\frac{d[Hg^{2+}]}{dt}=\frac{(V_{m1}.[CH_3Hg]}{(K_{m1}+[CH_3Hg])}-\frac{(V_{m2}.[Hg^{2+}])}{(K_{m2}+[Hg^{2+}])}]$$

We have considered the optimal time range to be 6-7 hours for complete conversion as the retention time of food in the small intestine is about the same.

### Observations

We recorded the following observations.

#### Enzyme Concentration 10-4

Figure 4: 2.9 µM

Figure 5: 1.55 µM

Figure 6: 0.0358 nM

Graphs for the activity for MerA and MerB at [CH3Hg] =2.9 µM, 1.55 µM, 0.0358 nM

#### Enzyme Concentration 10-5

Figure 7: 2.9 µM

Figure 8: 1.55 µM

Figure 9: 0.0358 nM

Graphs for the activity for MerA and MerB at [CH3Hg] =2.9 µM, 1.55 µM, 0.0358 nM

#### Enzyme Concentration 10-3

Figure 10: 2.9 µM

Figure 11: 1.55 µM

Figure 12: 0.0358 nM

Graphs for the activity for MerA and MerB at [CH3Hg] =2.9 µM, 1.55 µM, 0.0358 nM

We have chosen the optimal order of enzyme concentration to be 10-4 as the conversion rate falls within our time range. However, more experiments have to be performed to see whether 10-3 concentration can be utilized.

### Model 2

Aim: To describe the activity of the transport system.

Assumptions which were considered:

• The production of the proteins has already started due to a small amount of CH3Hg having diffused inside the cell prior and bound to MerR, initiating the transcription.
• Amount of protein within the cell will remain constant.
CH3Hgout + MerC ⇔ CH3Hgin + MerC, (kf1,kr1)
CH3Hgout + MerP ⇔ MerP-CH3Hg Complex, (kf2,kr2)
MerP-CH3Hg Complex + MerT ⇔ MerT-CH3Hg Complex + MerP (kf3,kr3)
MerP-CH3Hg Complex + MerE ⇔ MerE-CH3Hg Complex + MerP (kf4,kr4)
MerT-CH3Hg Complex ⇔ CH3Hgin + MerT (kf5,kr5)
MerP-CH3Hg Complex ⇔ CH3Hgin + MerE (kf6,kr6)

#### Results

The final ordinary differential equations were obtained.

$$[CH_3Hg_{out} = ([MerP-CH_3Hg_{complex}].k_{r2} - \frac{C1.\exp(-t.([MerC].k_{f1} + [MerP].k_{f2})) + [CH_3Hg_{in}].[MerC].k_{r1})}{([MerC].k_{f1} + [MerP].k_{f2})}]$$ $$[CH_3Hg_{in} = ([MerE-CH_3Hg_{complex}].k_{f6} + [MerT-CH_3Hg_{complex}].k_{f5} - \frac{C1.\exp(-[MerC].k_{r1}.t) + [CH_3Hg_{out}].[MerC].k_{f1})}{([MerC].k_{r1})}]$$

But due to lack of information about the activities of the protein further analysis could not be performed. Kinetic modelling of these proteins could be a future prospect to enable complete understanding of Mer operon.

# Handbook

You can read the full documentation on our iGEM MIT_MAHE Model Handbook. The model handbook has complete information about our MATLAB and VMD models including challenges which we had faced.

# References

1. Visual Molecular Dynamics. Theoretical and computational biophysics group.

(October 9, 2020). Retrieved on October 11, 2020. from https://www.ks.uiuc.edu/Research/vmd/

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2. Crystal Structures of the Organomercurial Lyase MerB in Its Free and Mercury-bound Forms.

Journal of Biological Chemistry 284(2), 938-944.

3. Mechanism of Hg C Protonolysis in the Organomercurial Lyase MerB.

Journal of the American Chemical Society 131(37), 13278-13285.

4. NmerA, the Metal Binding Domain of Mercuric Ion Reductase, Removes Hg2+from Proteins, Delivers It to the Catalytic Core, and Protects Cells under Glutathione-Depleted Conditions , .

Biochemistry 44(34), 11402-11416.