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Modeling

What are we modeling?

The aim of our project is to genetically modify a bacteria that can break down the polymer chains in expanded polystyrene (EPS). The result is a solution of monomer chains that can be extracted and used in the synthesis of other useful chemicals, for instance Lactic Acid (C₃H₆O₃). The computational model is going to be used to aid in calculations predicting how much substrate (polymer chains) will be needed, how much product will be required to sustain the bacterial colony and how much product will be left over for other uses.

Why are we modeling?

By creating a computational model of a biological system, theoretical and experimental biologists are able to predict the outcomes and behaviour of a system for a set of input parameters. The results of the simulation can provide guidance to the success of the experiment for the tested input parameters before undertaking it physically in the lab. The model built in our project will help determine the next steps in the project, for example to attempt to change the amount of enzyme produced by the bacteria, or to modify how the enzyme behaves. The major advantages of developing and using a model in the project are that it can save time exploring ideas that might have a high probability of failure, and simultaneously save resources.

Enzyme Kenetics

Enzyme Kinetics is the processes by which chemical reactions are catalysed by enzymes. When we say that we aim to "genetically modify a bacteria that can degrade expanded polystyrene" what we really mean is that we aim to "create a chemical reaction catalysed by enzymes that can break down polystyrene polymer chains". The polymer chains in expanded polystyrene can be broken into monomers by industrial processes, however this involves the use of toxic chemicals.

The method adopted by bacteria to modify their environment, in order to obtain useful products, is the use of enzymes. Enzymes are biological molecules that have the ability to act as a catalyst in chemical reactions. In other words they increase the rate of reaction. Enzymes have an active site that fits the substrate, like a "lock and key"and once connected the enzyme performs the reaction. The Psuedmonas bacteria in our project secrete enzymes that break the polystyrene polymer in order to extract the carbon.

Above is a diagram illustrating an example of how a substrate can be manipulated by the enzyme. The substrate collides with the active site of the enzyme to form a complex, the products are later released by the enzyme.

The transformation of substrate to product via the use of enzymes can be described in the following expression:

Where:
E is the number of enzymes
S is the substrate concentration
ES is the enzyme-substrate complex
P is the product
k₁ is the forward rate constant for enzyme-substrate formation
k_-1 is the reverse rate constant for enzyme-substrate formation (the enzyme "drops" the substrate)
k₂ is the forward rate constant for production formation from the enzyme-substrate complex and is assumed irreversible

The substrate concentration uses the units of molarity. A single monomer chain of polystyrene, known as styrene, has a molecular weight of 104.1 g/mol. In order to get one molarity solution, we would need 104.1 grams in 1Litre of solvent. The average chain molecular weight is approximately 9.7685 x 10⁶ g/mol, that's around 93, 838 styrene monomers per average chain. The active sites of the enzymes secreted by the bacteria can only fit the free ends of the polystyrene chain, so out of a 93, 838 long chain of styrene monomers, only 0.002% of the chain is available to the enzyme.

Also, we considered the method the enzyme will use to find the end of the chain. It could either collide with the polymer chain suspended in solution, and at part of the chain hold on and shuffle along to the end - similar to restriction enzymes. The other method, with a chain suspended in solution, specifies that the enzyme can only start catalysing the reaction when it collides with a free end only; a much more lengthly, although possibly more realistic, senerio.

Michaelis-Menton equation

The Michaelis-Menton equation is a model for single-substrate reaction is used as a base for our model.

Where:
V₀ is the initial veliocity of the reaction
V_max is the rate of reaction when substrate is saturated
S is the substrate concentration
K_m is the substrate concentration when the reaction rate is half the maximum and can be calculated using: k_-1 + k₂/k₁

Resulting model

This model simulates enzymes that are released by the bacteria into the solution:

This model is not an exact representation of the Psuedomonas behaviour. This is largely due to the values for the M-M equation where gathered from a paper regarding Tyrosinase since there was no available data for Psuedomonas using Polystyrene. Further, it has been noted that Pseudomonas do not use free enzymes, instead they rely on the end of a polystyrene chain colliding with the active site on the bacteria.

What this model can tell use, however, is the pattern of behaviour expected if Psuedomonas was modified to use free enzymes. This can be compared to results gained by observing the Psuedomonas at work, sadly this data is still currently unavailable to us.

Enzyme modification

Programs, such as Pymol [INSERT URL], allow one to manipulate the tertiary/quaternary structure of enzymes and other proteins, that have already had their structure determined by X-ray diffraction and/or NMR after they have been successfully crystallised. Whereas programs such as RASWIN [ISNSERT URL] only allow you to display these structures (in many different ways), Pymol takes this one stage further by giving one the power to manipulate individual residues to change the rotamer (direction/position the atoms in the residue) or even the residue itself (a kind of In silico mutagenesis). This means you can modify enzymes to such an extent that you may be able to fit any substrate you want into a particular enzyme's active site. However, in reality, the modified protein may adopt a completely different tertiary/quaternary structure which may cause it not to actually work as expected.

Polystyrene doesn't have its own degradation pathway due to the short time polystyrene has actually been in any great quantity in the world. Also, polystyrene is extremely unreactive, due to stable phenyl side chains present. Styrene, its monomer, has a degradation pathway as, being a much smaller molecule, it can diffuse into bacterial cells, and could cause toxicity is it is not degraded down to safer products. The environment of the cell allows much more flexibility with proteins, as the highly reducing environment allows unstable complexes more stability (such as iron-sulphur complexes).

Firstly, we identified a possible pathway that could be modified to accept polystyrene as a substrate. There were 2 potential pathways we could use: the styrene degradation pathway, and the toluene degrading pathway. Both have several different degradation pathways depending on the bacterial species/strain, but we ended up choosing the aerobic toluene degradation pathway from Pseudomonas putida, as the active sites of the pathway could remove/break the unreactive phenyl groups from the polystyrene chain.

The toluene degradation pathway. TDO is the enzyme we modified in silico using Pymol, and is Toluene 2,3-dioxygenase, which is made up of an alpha and beta subunit (TodC1 and TodC2) in a hexamer, with TodA and TodB acting as electron shuttles for the reaction from NADH to the enzyme. TodD is cis-1,2-dihydrobenzene-1,2-diol dehydrogenase which forms 3-methyl catechol. The other enzymes weren't focused on very much, though it was later found that there was no TodD crystal structure available online to modify. (George et. al, 2011)

Toluene 2,3-dioxygenase is the first enzyme of the pathway, and crystal structures are available online on the RCSB Protein Data bank. It was found that there was a gap directly into the active site, that if widened, could potentially fit polystyrene:

Toluene 2,3-dioxygenase made up of alpha and beta subunits. The sticks show each non-hydrogen atom, and the dots show the area each atom takes up. The pink residues indicate the active site residues, and the orange molecule is toluene. As can be seen, there is only a small gap when the enzyme has toluene bound that links the active site to the external environment (from 3EN1). A interactive version of 3EN1 is available Here

However, there are only a few residues that actually causes this gap to be this small, which we modified to smaller, but still hydrophobic residues to widen the gap to potentially allow polystyrene into the active site. The residues we modified were Met220→Ala220 (which when the Toluene 2,3-dioxygenase was blast searched, came up as a natural variation in some dioxygenases), Val421→Ala421, Tyr422→Leu422 and Tyr266→Val266, which created a bigger gap, which when the polystyrene structure was added to the active site and was sculpted, barely changed the active site structure as can be seen below:

Whether or not the relatively large change in the positioning/angle of the polystyrene aromatic ring in the active site would hinder the reaction or not needs to be studied. Because there are also 2 proteins involved in transporting electrons to the enzyme, as few of the modified residues, if any are on the surface, so shouldn't affect binding. A future project could actually get this synthesised and assayed to see whether the modifications could allow polystyrene to bind in the active site, and cause hydroxylation of the side chain.