Team:Nottingham/Model



Structural & Dynamic


Modelling


“All models are wrong, but some are useful.”

George E. P. Box

Structural and Dynamic
Modelling

Please Note . . .

The following report is an abridged version of our full modelling paper. This is available for download here, along with several accompanying files.

Highlights

  • A new structural model of Clostridium sporogenes is presented.
  • Acetone is produced in the optimal FBA solution if acid production is blocked (mimicking acid stress).
  • Adding acetate to the media significantly reduces non-acetone producing modes in the solution space.
  • Ethanol is co-produced in one of the highest ATP yielding elementary modes, which may cause problems for the nose detector.
  • We constructed a kinetic model, based on the ABE fermentation pathway in C. sporogenes.
  • Sensitivity analysis suggested that the thiolase enzyme is not a bottleneck in the ABE pathway, contrary to the popular hypothesis in the literature.
  • Modelling results based on Henry’s law predicted that the acetone concentration exceeds the ethanol concentration in the headspace, and therefore will not impact the electronic nose detection.

Introduction

In this project, our aim was to develop a new approach for detecting neurotoxin production in Clostridium botulinum that could be used in challenge testing in the food industry.


Our new approach involves replacing the toxin genes with genes of a volatile reporter, such as acetone, to allow quick detection via an electron nose. As proof-of-concept we have tested this approach using Clostridium sporogenes - a safe and non-toxic surrogate of Clostridium botulinum.


To assist the experimental efforts we wanted to consider different modelling approaches with the following objectives in mind:


Structural Model

  • Determine whether C. Sporogenes has any metabolic pathways capable of producing acetone. If not, the model will assist in the engineering of C. sporogenes to produce acetone.
  • Identify the best pathway to add, namely the most thermodynamically feasible.
  • Assess the feasibility the network with acetone production included. In other words, ensure that a steady-state solution exists.
  • Identify the optimal elementary modes with regards to ATP production.
  • Identify which co-products are produced and how this may impact the data collected by the electronic nose (acetone-detection sensor).

Dynamic Model

  • Inform the experimentalists about the minimum concentration of acetone needed for the nose to detect its presence.
  • Determine whether the thiolase enzyme would be a bottle neck in our C. sporogenes mutant.

During this project, we have developed a new structural model of C. sporogenes based on a previously published model.[1] This has been made available and could be used in future work involving C. sporogenes.

Constructing the Metabolic Core Model

We compared the sequencegenes with known function, to the entire genome sequence of C. sporogenes. If a gene was considered present in the genome, we added the associated metabolic reaction to the model. The core network generated is presented in Figure 2. Note that no acetone-producing pathways were identified in the genome.


Figure 1. Model curation method.

Acetone Metabolism in C. sporogenes

We assessed four different pathways involving acetone and identified the CtfA/B-Adc pathway, which completes the widely-studied ABE (Acetone-Butanol-Ethanol) pathway in C. sporogenes, as the most promising candidate.


Under the assumption that the missing acetone-production genes could be added to C. sporogenes, a model was created to predict whether C. sporogenes could have a complete and possibly favourable acetone-production pathway.


It is also important to ensure that the bacterium is not capable of recycling the acetone being produced via degradation pathways. If acetone was produced and then immediately reconsumed, then the electron nose would fail to detect it, and therefore incorrectly report the environment as being safe from toxic bacterial growth. We searched the genome of C. sporogenes and found no evidence to suggest acetone degradation pathways are present.

Figure 2. Mutant C. sporogenes metabolic pathway, with added adc and ctfA/B genes from C. acetobutylicum in red.

Constraint-Based Modelling

Reconstruction of a Large Metabolic Model


We have reconstructed a new metabolic network of C. sporogenes, based on a previously published model.[1] This model includes all the reactions from the core model, as well as reactions involved in producing the essential components required for biomass, as seen in Figure 3.


Figure 3. Pathways included in larger model.

Model Curation


Each reaction was curated to include protons and water, as these were missing in the previous model. The reactions were then all checked for elemental balance in terms of C, N, S, P, O and H. The biomass was checked to ensure it amounted to 1 gDCW and was corrected accordingly.


We identified all the gene-reaction associations, using the same approach described for the core model above (Figure 2). The information regarding the operons was inferred from the SBRC database for C. sporogenes, which was constructed using Pathway Tools Software. In doing so, we identified that the Bcd (Acyl-CoA dehydrogenase) reaction, which converts crotonoyl-CoA to butanoyl-CoA, should be included as the bifurcating version in the model. This is because thr bcd gene was located in an operon with etfA and etfB. The operons can be seen in Figure 4.


Figure 4. etfA/B, bcd, thIA, hbd, crt operon.

The Model


The final version of the model, Cspo216:adc:ctfA/B with acetone-production genes, consists of 216 reactions (including the new acetone genes), 157 metabolites and 156 gene associations. Using FBA we tested that the model was capable of simulating growth and could produce acetate, butyrate, ethanol and butanol, which was in agreement with our experimental data. The mutant can also produce acetone, as a result of the addition of adc, ctfA and ctfB genes from C. acetobutylicum.


Results


Using FBA, we were able to confirm that a steady state solution existed that produces acetone whilst supporting growth. In the optimal solution, acetate is the main product. However, when acid excretion is blocked in the model to mimic the effect of decreasing pH, acetone becomes the optimal product. This is known to occur in C. acetobutylicum and supports the idea of using acetone as a reporter.


Elementary Modes Analysis


For growth on glucose, 34% of the elementary modes produced acetone. Unsurprisingly, the modes with the highest ATP yield (an indicator for growth) produced acetate (Figure 5).


We added acetate to the media to mimic acetate reassimilation that occurs at low pH levels (known to occur in C. acetobutylicum). As a result, the number of modes producing acetone increased and acetone became a favourable product.


Figure 5. Highest-Ranking Elementary Mode and Highest-Ranking, Acetone-Producing Elementary Mode respectively.

However, ethanol was also produced in some high-ranking modes. Whilst co-products are generally not problematic for this application, production of ethanol may interfere with acetone detection. The sensor used in the detector is a ‘Figaro TGS 822 Organic Solvents Vapours Sensor’; this is sensitive to ethanol as well as acetone. Both produce a similar voltage when read in their respective concentrations so differentiating between them is challenging.

Dynamic Modelling

Dynamic modelling allows us to make predictions across the lifespan of the bacteria and not just at fixed time points.


Kinetic Model


We constructed a kinetic model based on the core metabolic network described above. Rate laws for each of the 19 enzymatic reactions were defined using Michaelis-Menten-like equations. The rate of change for each of the 16 metabolites was then represented by a set of coupled differential equations. The parameters were taken from the C. acetobutylicum model, since the data are not available for C. sporogenes and deriving these values in the lab was infeasible for this project. We used robust non-linear regression, however, to fit curves to our experimental data, in order to determine the parameter for the maximum biomass value.


Adjustments to the parameters for glucose uptake and product formation were carried out to determine the parameters which best fit the experimental data. Due to time limitation we could not get the experimental data for the mutant but, if considered in future work, would improve the predictive capability of the model.


Predicting of Acetone Formation


A switch function can be used to simulate the turning on and off of a gene and was therefore useful in mimicking the regulation of the toxin by the BotR regulator. The botR gene regulates the neurotoxin production in C. botulinum. The gene is expressed in late exponential phase and early stationary phase but ceases in late stationary phase. However, it is not well understood which factors activate toxin production. A hypothesis is that it might depend on population density and a declining growth rate, but further research is required in order to make any conclusions. We found that acetone production followed a similar pattern as the activation of the botR gene, such that the acetone production significantly increased and then subsequently stopped and remained constant.


Sensitivity Analysis for Thiolase


The thiolase in C. sporogenes, which is part of the ABE pathway, is hypothesised as being a bottleneck. We used sensitivity analysis to assess how acetone concentration changes whilst making small changes to the kinetic parameters of the thiolase enzyme. We found that the acetone concentration was only affected during the stationary phase of the bacterial growth. However, we know from previous research carried out by Prof. Mike Pike at the Quadram Institute Bioscience (QIB), that the neurotoxin is produced during the late exponential phase and switches off when the stationary phase is reached. This information combined with our result suggests that the thiolase enzyme is not a bottleneck in the pathway. The model, however, does not consider the effect that additional regulation, such as product inhibition, may have on the enzyme’s activity.


Predicting Maximum Growth Rate


We used non-linear regression to try and fit a growth curve to SBRC derived experimental data. We considered the following three different growth equations:

  • Logistic equation
  • Gompetz equation
  • Richard’s equation

Non-linear regression, however, is extremely sensitive to outliers. Robust regression was therefore used to alleviate this issue. In Figures X and Y we show how the robust regression significantly improves the fitting.


Figure 6.

Figure 7.

Using robust regression, we determined which of the three growth equations gave the best fit to the experimental data, and subsequently determined the maximum growth rate. The maximum growth rate was used as a parameter in the kinetic model of C. sporogenes. Calculating the maximum growth rate is also useful for validating structural models.


Electronic Nose

As mentioned previously, the electronic nose is sensitive to ethanol concentration. Importantly, we used Henry’s law defined below,


C = H · p,


Where C is the soluble concentration, H is Henry’s constant and p is the partial pressure. This equation allows us to link the concentration in the atmosphere (headspace) to the concentration in the medium. We are then able to compare the concentration of acetone and ethanol, to determine whether ethanol would be a problem in the headspace. We found that, due to the higher volatility of acetone, ethanol production would not be a problem to the detection system.

References

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