Basic Principle

The mechanism by which the photosystem II (PSII) reaction centre absorbs and utilises sunlight is critical to the functioning of our photosynthetic E. coli. Visible light (~400-70 nm) is the major impetus provoking release by PSII of the electrons necessary for subsequent hydrogen generation via hydrogenase enzymes.

Figure 1: Light-induced water splitting by photosystem II in photosynthesis and hydrogen production by an [FeFe] hydrogenase (Lubitz et al., 2008).

We therefore designed this three-stage model to explore efficiency of PSII action towards hydrogen production within bounds established by an initial conception of our implementation prototype.

The initial stage of our model examines the sunlight absorbance process. It calculates the capacity of chlorophyll-a, and thereby PSII, to absorb sunlight; and calculates the light intensity received by the E. coli cells as situated in our prototype. The second stage establishes the electron production rate per PSII. The model’s final stage integrates the preceding findings to predict H₂ production per mL of E. coli cells per hour.

Stage 1

The production of H₂ is ultimately driven by sunlight. The optimal functioning of our prototype in generating hydrogen thus relies upon the sunlight absorption process. The scheme shown (Figure 2) outlines the physical model we have devised, and upon which our calculations are based, to take best advantage of available light.

Figure 2: The basic implementation prototype initially designed. Our photosynthetic E. coli cells are housed between two layers of media, each backed by a one-way mirrored surface to reflect and magnify light.

Absorption of the sunlight is governed by:

• a: absorption by E. coli
• k: absorption by the solution = 0.722 (Paolin, 2012)
• r: reflexion coefficients of the mirrors = 0.95

Calculation of a first requires the concentration of PSII ([PSII]). In deriving this concentration, we have assumed firstly that PSII will be located only at the surface of E. coli cells; and secondly that they will occupy 10% of this area. This percentage is a minimum value, not taking into account the possibility of an increased occupancy by placing PSIIs within vesicles inside the E. coli cells.

These initial assumptions fed into the development of specific physical parameters for the surface areas of our initial prototype, as follows:

• Se: surface area of E. coli cells = 18.8 µm2
• Su: ‘useful’ surface area of E. coli cells = 6 µm2
• SPSII: surface area of PSII = 0.202 µm2 (Morris et al., 1997)
• Ne: number of E. coli cells (per mL) = 109 cells/mL

Figure 3: Scheme representing physical parameters of E. coli total (Se) and ‘useful’ (Su) cell surfaces as determined in accordance with our initial prototype.

These parameters provide the number of PSIIs per E. coli cell (NPSII), and consequently [PSII]:

Concentration of the antenna pigment chlorophyll-a ([chla]) is known to be eight times the [PSII] (Liu et al., 2004). Therefore:

Using ε of [chla], we can derive its absorbance A. This allowed consequent determination of a, the percentage of light absorbed by E. coli:

• ε: extinction coefficient of chla = 73300 L/mol/cm (Inskeep and Bloom, 1985)
• l: pathlength = 1 cm

Having established the cells’ capacity to absorb light relative to its intensity, we proceeded to calculate the light available for that absorbance process in the environment of our theorised implementation prototype (Figure 4).

Figure 4: A more detailed scheme of our prototype.

We have assumed for this physical model that the light is absorbed first by the media, then by the E. coli cells, and finally follows the reflection on the mirrors. From this scheme, we were able to create a discrete model deducing the absorption of sunlight:

Absorption of the media at depth z:

As the light crosses two layers of media of l length = 0.01, light intensity:

Absorption of E. coli:

Loss of intensity due to reflection:

The relationship between In+1 and In therefore becomes:

This gives us:

The above equation, solved for N iterations = 100, was used to derive cumulative intensity. Available reflected light passing through the prototype to be absorbed by our cells declined with each iteration; this decrease (e-k.2l.r.a) was relative to light intensity, and itself showed decline over time. The sum total of light intensity available per each iteration proved to be magnified from the initial light input, I0.

We have thereby concluded that the light intensity received by the E. coli cells is about 13.4 times that of the light entering the prototype. (cf “absorption” excel file)

Stage 2

The absorbance of visible light by Photosystem II causes the release of electrons, which travel via the electron transport chain to Photosystem I. Our aim is to divert these electrons, preventing them from reaching the electron transport chain, and instead utilise them in hydrogen production.

Figure 5: Electron produced by Photosystem II diverted to H₂ production instead of entering the electron transport chain.

Conversion of introduced light energy to primary product is affected by limiting factors including the low electron transfer rate between Photosystems II and I. Under full sunlight, up to 90% of captured photons may decay as heat or fluorescence (Hallenbeck and Benemann, 2002). When the electrons generated are diverted to hydrogen production, this lag between photosystems is irrelevant. The electron production rate per PSII (ETRPSII) becomes directly proportional to the amount of light introduced to Photosystem II.

Figure 6: The green curve represents electron production rate for electrons introduced into the electron transport chain; the blue line represents electron production rate for electrons used in hydrogen production.

We have taken the photosynthetic photon flux, Isun, to be 2000 umol/m²/s as previously reported (Posada et al., 2009).* Our modelling of its direct relationship with release of electrons by PSII, 2*Isun, is illustrated in Figure 6.

ETRPSII was therefore found to be 4000 é/s/PSII (Zorz et al., 2015).

[*The intensity of sunlight assumed here is the maximum value, not that which cells will receive throughout the day; daily irradiance can show significant variation.]

Stage 3

Hydrogen is generated through the action of the hydrogenase enzyme. This process utilises two diverted electrons released by PSII per H₂ molecule:

2^H+ + 2^e- ⇄ H₂.

Hydrogenase reaction rates are known to range between 10³-10⁴ turnovers per second at 30oC, sufficiently high to circumvent any potential limiting factors (Pershad et al., 1999; Lubitz et al., 2008). Our modelling has consequently used the following known parameters:

• ETR_PSII: production of electrons per PSII = 4000 é/s/PSII
• N_PSII: number of PSII per cells = 9300
• S_u: “useful” surface of E. coli cells = 6.0 µm²
• Se: surface of E. coli cells = 18.8 µm2
• Ne: number of E. coli in one mL = 109 cells/mL
• v(H2): molar volume of H2 = 22.43 mol/L

We have thereby calculated the H₂ production in mL/hour per mL of our solution:

By this model, 1 mL of our E. coli cells will give 0.8 mL of H₂ per hour.

Given that the electron production rate per PSII (ETR_PSII) is proportional to the sunlight absorbed, the coefficient linking the magnified amount of sunlight absorbed by our prototype (x13.4) can be directly introduced:

Our 1 mL of cells can therefore be predicted to produce 10.7 mL of H₂ per hour!

CONCLUSION

The models created for PSII production of (é) and of H₂ through hydrogenase have provided us with highly encouraging results. The H₂ production of 10.7 mL per mL of E. coli per hour predicted by this modelling indicates higher quantities than comparable procedures currently under investigation.

For reference, green algae had previously been calculated to yield hydrogen at about 10 moles of H₂ per m² of cell culture area per day (Melis and Happe, 2001; Melis, 2007). An engineered cyanobacterial strain has recently been shown to generate H₂ at a maximal volumetric production rate of 6.2 mL per litre per hour (Nyberg et al., 2015). Both of these fall below our own estimation, which thus represents a significant improvement in photobiological hydrogen production efficacy.

The improved understanding of the light absorption and hydrogen production processes that was provided by this modelling informed further development of our business implementation prototype.

References:

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