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Revision as of 09:27, 11 September 2015

Modeling the cellulose pathway

Introduction

Our goal in the project is to produce propane from cellulose. For modeling team this means that both propane pathway and cellulose pathway should be modeled. Being able to model the cellulose breakdown could provide us insight on whether it is fast enough for our system to function at all. If the hydrolytic enzymes don't break cellulose down to glucose fast enough, the cells cannot get enough energy to actually produce propane. In the worst case, there wouldn't be enough glucose for even the basic metabolism of the cell and the cells would not survive. If it would appear that cellulose alone isn't enough, modeling the system could further allow us to estimate how much glucose or other energy sources we would need to give to the bacteria in addition to the cellulose.

We recognized right away that modeling the cellulose breakdown would be difficult. Nevertheless, we wanted to look into the cellulose hydrolyzing enzymes and their production to understand what kinds of things need to be taken into account when modeling the system. To get a useful model of how efficiently cellulose is hydrolyzed by our bacteria, we'd need to take into account at very least the following things:

  • How much enzymes do our bacteria produce?

  • How much of the enzymes produced are actually exported outside of the cell? How efficiently do the export tags work? To what extent do the produced enzymes reach the periplasmic space? What part of enzymes reaching periplasmic space are further exported to the extracellular space?

  • What is the extracellular environment like and how does it affect our enzymes? How efficiently do our enzymes actually function there?

    • For most questions, there are no ready answers available. Thus we'd need to conduct experiments to figure out the constants and rates for each step. We recognized that within our timeframe, it was not possible to gather the necessary quantitative information about these processes to model them sufficiently. Therefore, we decided not to proceed with trying to model the pathway but instead just wrote down some ideas regarding modeling the pathway.

    --pic of cellulose pathway?--

    Our thoughts on a basic model

    Our cellulose pathway is pretty simple, consisting only of a few genes cutting the cellulose into cellobiose and then to glucose. We wanted to make a basic model to tell us if the enzymes are efficient enough to break down the cellulose for our bacteria to use it as an energy source. The challenge of this model lies instead in the properties of enzymes or rather, our limited knowledge of those. The members of our team spent many frustrating days trying to find the information we would need to model the pathway and were finally forced to give up.

    If it were possible to get the needed values, our model of cellulose pathway would have been based on [1].

    --things below need a doublecheck--

    Langmuir isotherm models adsorption (do we want to put equation here or a link to wikipedia?), and the rate equations are as follows. Inhibition of glucose and cellobiose is taken into account. \( R_s\) is substrate reactivity, \(K_{iG2}\) is inhibition constant of cellobiose, \(K_{iG}\) is inhibition constant for glucose. Cellulose to cellobiose: \[r_1 = \frac{k_{1r}[\beta\text{-glucosidase(bound)}]R_s [\text{cellulose}]}{1+\frac{[\text{cellobiose}]}{K_{iG2}} + \frac{[\text{glucose}]}{K_{iG}}}\] Cellobiose to glucose: \[r_3 = \frac{k_{3r}[\beta\text{-glucosidase}][\text{cellobiose}]}{K_{3M}\left( 1+\frac{[\text{glucose}]}{K_{3iG}}\right) + [\text{cellobiose}]}\]

    This model could have been implemented into Copasi with following reactions where the rate equations are above. \begin{align} \text{cellulose} &\rightarrow \text{cellulose} + \text{cellobiose} \\ \text{cellulose} &\rightarrow 2\cdot\text{cellobiose} \\ \text{cellobiose} &\rightarrow 2\cdot\text{glucose} \end{align} It should be implemented so, that cellulose to two cellobioses -reaction would occur about 300-1700 times less frequently than cellulose to cellulose and cellobiose [2]. This is to represent the fact that a cellobiose can be cut from a cellulose strand many times, but a cellulose strand can only be transformed into two cellobioses once, i.e. when the cellulose strand consists of two cellobiose molecules.

    Even if we would have gotten all the constants of our cellulose pathway the model would have not been perfect as discussed in previous section. We would have been forced to guess the amount of enzymes produced, as well as how much of them would travel outside of cell to cellulose. Neither do we know how the chemical conditions of the extracellular space affect the enzymes' function. Last but not least, we don't know how the produced glucose is used up in the cell and to what effect it is transported inside the cell. These holes in our knowledge make the possibility of us getting our model right seem very slim indeed.