Team:Edinburgh/Modelling

Modelling

One way of assessing the feasibility of the synergistic approach to biorefineries is to use computer ("in silico") modelling. In particular, we would like to confirm that synergistic use of enzymes can make the process of cellulose degradation more efficient.

Some other models, calculations, and tools were also developed by the team.

Cellulase models

Approaches

As it happens, our team includes:

1. Two engineers experienced in using MATLAB.
2. An informatician who quickly learned the Kappa modelling language.
3. A biologist who, for no good reason, knows the C programming language.

This led to three different attempts to model cellulase action.

Results

• C model — a simple model that showed a difference between synergistic and non-synergistic systems
• Kappa model — a more complex model that also showed a difference
• MATLAB model — the most complex model, only worked well for the non-synergistic system

Comparison of different modelling tools

Within the reactor tasked with degrading cellulose into glucose in the biorefinery, temperature, enzyme concentration, substrate reactivity as well as xylose, cellobiose and glucose inhibition all govern the amount of glucose product. Deterministic modelling using a set of ordinary differential equations highlights the essential kinetic relationship among the enzymes, exo/endo-glucanase and β-glucosidase. By solving these governing equations using the numerical tool MATLAB the level of degradation is qualitatively predicted.

However, we found that the equations we used for the deterministic modelling only gave sensible answers when the model parameters remained within certain limits. Outside those limits, results could be physically impossible; e.g. producing negative amounts of cellobiose therefore breaking the law of conservation of mass. The deterministic model always had reactants available, i.e cellulose able for every reaction, ensuing it would never reach zero. A 'stress test' was carried out simulating the model over one hundred thousand hours confirming this. Therefore, within the limits of differential equation based modelling, it will unlikely reach a mathematical steady state. But from an engineers persepective, usually 99% of the initial condition, cellulose will reach a steady state in 8000 hours. As can be seen from Figure 3, the 'stress test' revealed neither a mathematical nor engineering steady state will be reached for cellobiose and glucose.

As an alternative, stochastic models were created using the Kappa language tool. These incorporate indeterminacy in the evolution of the state of the system. Rules are defined which describe how the model moves from one state to the next.

Other models and calculations

Energy efficiency

Consider this: for a bacteria to produce phage or INP requires energy. This energy could have been spent producing extra copies of the cellulases. In order for the phage and cell display projects to make sense, the benefits of synergy must outweigh the cost of producing all these extra proteins.

This question can probably be investigated using simple maths and back-of-envelope calculations...

Evolutionary analysis of cell-display vs. secretion

One potential benefit of attaching enzymes to the cell surface rather than secreting them into the media is that any mutations that increase enzyme efficiency will specifically benefit the cell with the mutation, as the increased sugar yield will be physically present at the cell. The mutation will thus confer a fitness advantage, potentially allowing it to take over the culture.

By contrast, if a cell produces a secreted protein that is of higher efficiency, it will disperse and benefit random cells in the culture.

Phage replication

The phage display system requires infected E. coli to dominate the system and not be outcompeted by uninfected E. coli. Our phage replication model verifies that this is indeed the expected outcome.

Genetic Stability Tool

Our projects involve having multiple fusion proteins expressed, each of which uses a genetically identical carrier protein (e.g. ice-nucleation protein or the M13 pVIII gene). The presence of repeated sequences in DNA (i.e. the same sequence in multiple locations) can lead to genetic instability.

However, it ought to be possible to design and synthesise different versions of the genes that code for the same amino acids but use different codons and so are as distinct as possible.

To prove this, we made our Genetic Stability Tool.

References

• Van Zyl WH, Lynd LR, Den Haan R, McBride EJ (2007) [http://www.springerlink.com/content/4l4m28lp06120253/ Consolidated bioprocessing for bioethanol production using Saccharomyces cerevisiae]. Advances in Biochemical Engineering/Biotechnology 108: 205-235 (doi: 10.1007/10_2007_061).