Team:Macquarie Australia/Model


To be able to prove the validity of our project scalability for our prototype and business plan, we need to be able to study the connection between the genes that we have incorporated into Escherichia coli, and hydrogen gas output in a way that is predictable. In order to evaluate the effectiveness of our system, mathematical modeling was performed. This allows us to study both the inputs and outputs of the system, and subsequently optimise our experiments and prototype. As our end goal is maximum hydrogen output, we can follow the flow of products backwards and ensure we are providing the ideal amount of substrates. This can then be used to minimise costs while still supplying a viable source of hydrogen.

Hydrogenases work at highest efficiency when they have a reliable source of protons and electrons. We utilised ferredoxin and ferredoxin reductase (FNR) as they occur naturally in Chlamydomonas reinhardtii as a cofactor for Hyd1, where ferredoxin can mediate electron transfer by oxidising NADPH. Our source of protons can be any strong reducing agents, which in E. coli are predominantly NADPH, NADH and cytochrome c’s. We will be focusing on NADPH as it can be produced from glucose - a cheap, readily available carbon source - and interacts directly with ferredoxin and FNR. Ferredoxin could also be used as an electron carrier in other reactions in E. coli, such as production of glutamate and ammonia, which is usually performed by NADPH. NADPH is produced through the pentose phosphate pathway, and is then used as reducing power for other reactions within the cell, such as fatty acid, nucleotide and amino acid synthesis. Because NADPH has these multitude of uses, mathematical modeling is important to be able to understand how our system is functioning under conditions similar to how it would be used commercially.

Theoretical Modeling

For the theoretical model, we will be looking primarily at the flow of glucose to NADPH, and assume that all of the intermediates move through as we want them to. We will then optimise this theoretical model using our experimental results.

First glucose is to be phosphorylated into glucose-6-phosphate through glycolysis. This can then be fed into the pentose phosphate pathway. The pentose phosphate pathway produces 2 NADPH for each glucose-6-phosphate, however, byproducts can be recycled through the pentose phosphate pathway as shown below through a series of equations.

First, the conversion of 6 glucose-6-phosphate molecules to 12 NADPH through the pentose phosphate pathway occurs as follows.

6 glucose-6-phosphate + 12 NADP+ + 6 H2O → 6 ribose-5-phosphate + 12 NADPH + 6 CO2

The 6 ribose-5-phosphate can then be used to regenerate glucose-6-phosphate.

6 ribose-5-phosphate → 4 fructose-6-phosphate + 2 glyceraldehyde-3-phosphate

4 fructose-6-phosphate + 2 glyceraldehyde-3-phosphate + H2O → 5 glucose-6-phosphate + Pi

Therefore, by balancing these equations the maximum NADPH that can be produced is 12 moles of NADPH for every 1 molecule of glucose-6-phosphate.

glucose-6-phosphate + 12 NADP+ + 7 H2O → 12 NADPH + 12 H+ + 6 CO2 + Pi

After we produce the NADPH it is able to reduce ferredoxin, which gives us an efficient electron carrier for use in the hydrogenase.

2 oxidized ferredoxin + NADPH → 2 reduced ferredoxin + NADP+ + H+

The reduced ferredoxin can then be utilised in the hydrogenase through the following reaction, where the H+ is from any strong reducing agent such as another NADPH molecule.

2 H+ + 2 reduced ferredoxin → H2 + 2 oxidised ferredoxin

We can now show the relationship between the amount of glucose and hydrogen gas produced. Using molar ratios and molar masses of the relevant species, for every 1 gram of glucose, 0.134 grams of H2 are produced theoretically, which is equivalent to 1.49 L of H2 at room temperature and atmospheric pressure using Avogadro's law. These values are based only on the amount of glucose, and we need to take into the account the rate of H2 production if we are to get a more accurate picture of how close this optimistic theoretical model is to experimental results. This can be achieved in two main ways - by looking at rate values found by other researchers or by testing our system experimentally. Our hypothesis is that we will not be able to produce as much hydrogen as this, as NADPH is also used in many other cellular processes.

Due to the simplicity of the structure of the C. reinhardtii hydrogenase it has been widely used in active site maturation (Peters et. al., 2015) and rate of gas production studies (Mus et. al., 2007). Many studies on gas production, however, have contradicting results and the activity of hydrogenases have not yet been reliably explained (́Ősz et. al., 2005). The simple enzyme was thought to function through fermentation of carbohydrates, but photosynthetic H2 production was recently demonstrated under fully aerobic conditions in the alga C. vulgaris (Hwang et. al, 2014).

One study by Mus et. al. (2007) on the rate of hydrogen and oxygen production anaerobically in C. reinhardtii found the rate of hydrogen production to be the values found in Table 1.

Table 1. H2 production Clarke electrode data, sourced from Mus et. al., 2007.
Time / hr Rate of H2 production / mL hr-1

We can compare these literature values to our experimental values to see how our system is functioning in comparison to similar experiments.

Experimental Modeling

To quantify the amount of hydrogen produced, we used two different approaches. A modified Clark electrode procedure measured the levels of dissolved hydrogen, and a gas measuring apparatus was used to measure the amount of hydrogen gas.

Clark Electrode

The full results for the Clark electrode are found here. To get these results, a Clark electrode was first calibrated using H2 saturated water. This was then removed and induced culture with an OD600 0.4 was then diluted with M9 media and 20 mM glucose to give a final volume of 2 mL and added to the chamber. This was then sealed off from air and the electrode was left to measure anaerobic gas production until we were able to see the maximum hydrogen peak begin to decrease or return to baseline. We used multiple controls to ensure that hydrogen production was due to our induced plasmid not due to native E. coli hydrogen production. These included an uninduced culture of our Hydrogen Gas Producing Gene Cluster in E. coli, a culture containing a plasmid with only Fer/Hyd and a negative control culture containing no biobrick constructs.

This resulted in the graph below. There is a large increase in the hydrogen production of our induced Hydrogen Gas Producing Gene Cluster (Fer/Hyd/HydEFG + or HGPGC), which confirms that the majority of the hydrogen produced is due to our BioBrick.

Figure 1. Graph of 1 replicate of the Clark electrode data, using 2 mL of culture in M9 media with 20 mM glucose and 1 mM IPTG.

We are able to find the max rate of H2 production by measuring the slope at each point in the graph, and this can then be converted into a volume per hour value using Avogadro's law. The results are found below in Table 2.

Table 2. Results of maximum rate of H2 production by measurement of the slope of 3 consecutive data points, where the concentration was found by calibration with saturated H2 water. For each sample 2 mL culture was used in M9 media containing 20 mM glucose and 1 mM IPTG, except for the sample HGPGC -, which had no IPTG added.
Culture Max rate of H2 production
/ mM hr-1
Max rate of H2 production
/ μL hr-1

We can now compare our results with literature values from studies in both C. reinhardtii and E. coli, along with our experimental gas measuring apparatus results. As these results were from only using 2 mL induced culture, further experiments to scale up would be needed as the rate is not necessarily proportional to the amount of culture used.

Gas measuring apparatus

The full methods for the gas measuring apparatus are found here and the full results are found here.
To prepare this apparatus, a large tub of water was filled, along with 4 graduated measuring cylinders. The opening of the graduated cylinder was then covered and upturned into the tub of water. Flexible tubing was then attached to a bent glass tube and fed through the cylinder. The other end of the tubing was attached to a Büchner flask with 80 mL mature culture in M9 media at approximately 0.2 OD600, supplemented with 20 mM glucose and 1 mM IPTG. The three cultures tested were: a culture of untransformed DH5α, one transformed with Fer/Hyd and one with an induced Hydrogen Gas Producing Gene Cluster. All cylinders were equalised to a gas volume of 15 mL.

The flask was stirred constantly and volume readings for each cylinder were taken at regular intervals. In this apparatus, any gas produced by the cultures displaced water in the cylinder. Theoretically, if this apparatus is completely airtight, the gas produced in the cylinder should contain only CO2 and H2, except for the 88 mL of gas in the headspace above the culture and in the cylinder, which is regular air, containing 80% N2 and 20% O2. We can then work out the concentration of H2 in a few ways – by assuming that the O2 is consumed and replaced by CO2 and H2, our gas mixture after reaction should be composed of CO2, H2 and N2. As we can weigh a sample of the same volume of air, and the same volume of H2, we can then weigh the gas sample after removal of CO2 to help us elucidate the concentration of H2. We can also precipitate out the CO2 and weigh it to confirm our results and assumptions. We have estimated the volume of the flask headspace and tube leading to the cylinder to be 88 mL so this can also act as a confirmation. Table 3 and Figure 2 show the results found over 2 replicates. It can be seen that for replicate 2 (Figure 2), HGPGC did not produce as much gas. Both replicates used the same original mature culture. The culture had been kept refrigerated for approximately three weeks when data was collected for replicate 2, which indicates optimal production may be found with a fresh culture. This information is valuable feeding into our prototype and commercial model which provides at home hydrogen production.

Table 3. Results of rate of gas production (RGP) for the gas measuring apparatus, where the 80 mL culture used contained an induced Hydrogen Gas Producing Gene Cluster (HGPGC), an induced Fer/Hyd or was DH5α with no insert.
Gas measuring apparatus Replicate 1
Time elapsed / hr
HGPGC / mL hr-1
Fer/Hyd / mL hr-1
DH5α / mL hr-1
6.25 6.08 0 0
21.75 3.98 0.235 0.653
29.75 2.14 0.114 1.04
31 1.43 0.683 0.690
46.5 1.36 0.0590 0.656
49.5 4.75 0.910 1.23
51.25 2.17 1.56 1.05
67.2 2.15 0.286 1.39
74.2 1.90 0.130 0.920
Average rate 2.77 0.233 0.856
Gas measuring apparatus Replicate 2
Time elapsed / hr
HGPGC / mL hr-1
Fer/Hyd / mL hr-1
DH5α / mL hr-1
2 1.43 1.37 0
4 2.85 1.82 0
7 1.27 1.21 0
22 1.90 1.21 0.675
26 0.950 0.683 0.92
30 0.950 0.683 0.46
34 0.475 0.455 0.46
48.25 0.800 0.511 0.387
51 1.38 0.331 0.335
54.5 0.543 0.52 0.263
57 0.760 0 0.368
77 0.855 0.410 0.184
79 0.475 0.455 0
Average rate 1.11 0691 0.373

Figure 2. Graph of volume gas produced over time in the gas measuring apparatus, where 80 mL of OD600 0.2 culture in M9 media with 20 mM glucose and 1 mM IPTG was tested by use of a gas measuring apparatus.

To test for the percent hydrogen gas in each headspace, a 20 mL gas sample was taken from each culture using a syringe and weighed. A sealed tube with 20 mL barium hydroxide was then put under negative pressure and the gas sample was injected and shaken for 10 minutes to remove CO2 in the form of barium carbonate, a stable precipitate.

The remaining gas was extracted back into the same syringe and the volume recorded and again weighed. The same volume of air was then weighed in the syringe, followed by the same volume of pure hydrogen gas. We found that the gas mixture contained only 7% H2, which indicates that some air must have leaked into the system during this experiment or during the measurement. As explained in the demonstrate section, a more elaborate set up that is completely gas tight or a hydrogen sensor would be used in future experiments to get more accurate results.


Through our experiments, we have been able to confirm a higher rate of H2 production when E. coli is transformed with our BioBrick when compared to a negative control culture and a culture with an induced plasmid containing only Fer/Hyd. We found a maximum rate of 2.37 mL/H2/hr/L for 2 mL of culture in the Clark electrode data for induced HGPGC, and a maximum rate of 7.0 mL/H2/hr/L for 80 mL of culture in the gas measuring apparatus. In comparison, the literature values in C. reinhardtii showed a maximum rate of only 4.0 mL/H2/hr/L. A summary is shown in Table 4.

Table 4. Comparison of rate values from both of our experiments, plus a literature value from Gordon and Seckbach 2012, scaled up to a 1 L culture to directly compare the rate values.
Clark electrode 2.37 mL H2/hr
Gas measuring 7.0 mL H2/hr
Literature (Mus et. al. 2007) 4.0 mL H2/hr

We found in the Clark electrode experiment we had a 32 fold increase in hydrogen concentration when comparing the maximum hydrogen concentration in our induced hydrogen gas producing gene cluster with the maximum hydrogen concentration in our negative control culture. When scaled up in the gas measuring apparatus, there was 3 fold increase, which indicates that when the culture is scaled up, more hydrogen gas is produced. Overall we were able to qualitatively confirm a higher rate of hydrogen production with the insertion of our HGPGC and further quantitation is necessary to be able to form a better idea of how well the scalability of our project will work in use of our prototype.


Peters, J.W., Schut, G.J., Boyd, E.S., Mulder, D.W., Shepard, E.M., Broderick, J.B., King, P.W. and Adams, M.W., 2015. [FeFe]-and [NiFe]-hydrogenase diversity, mechanism, and maturation. Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, 1853(6), pp.1350-1369.

Mus, F., Dubini, A., Seibert, M., Posewitz, M.C. and Grossman, A.R., 2007. Anaerobic acclimation in Chlamydomonas reinhardtii anoxic gene expression, hydrogenase induction, and metabolic pathways. Journal of Biological Chemistry, 282(35), pp.25475-25486.

Hwang, J.H., Kim, H.C., Choi, J.A., Abou-Shanab, R.A.I., Dempsey, B.A., Regan, J.M., Kim, J.R., Song, H., Nam, I.H., Kim, S.N. and Lee, W., 2014. Photoautotrophic hydrogen production by eukaryotic microalgae under aerobic conditions. Nature communications, 5, p.3234.

Ősz, J., Bodó, G., Branca, R.M.M. and Bagyinka, C., 2005. Theoretical calculations on hydrogenase kinetics: explanation of the lag phase and the enzyme concentration dependence of the activity of hydrogenase uptake. Biophysical journal, 89(3), pp.1957-1964.

Gordon, R. and Seckbach, J. 2012. The science of algal fuels. JBC, 282(35).




Faculty of Science and Engineering,
Macquarie University
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