Reliable determination of the growth and hydrogen production parameters of the photosynthetic bacterium Rhodobacter capsulatus in fed batch culture using a combination of the Gompertz function and the Luedeking-Piret model

Abstract

In this study, experimental results of hydrogen producing process based on anaerobic photosynthesis using the purple non-sulfur bacterium Rhodobacter capsulatus are scrutinized. The bacterial culture was carried out in a photo-bioreactor operated in a quasi-continuous mode, using lactate as a carbon source. The method is based on the continuous stirred tank reactors (CSTR) technique to access kinetic parameters. The dynamic evolution of hydrogen production as a function of time was accurately simulated using Luedeking-Piret model and the growth of R. capsulatus was computed using Gompertz model. The combination of both models was successfully applied to determine the relevant parameters (λ, μ_max, α and β) for two R. capsulatus strains studied: the wild-type strain B10 and the H₂ over-producing mutant IR3. The mathematical description indicates that the photofermentation is more promising than dark fermentation for the conversion of organic substrates into biogas.

Photofermentation modeling, hydrogen production; Rhodobacter capsulatus; quasi-continuous fermentation

1. Introduction

Economic development over the last few decades has been strongly dependent on fossil fuels as sources of energy. These resources are not unlimited in the long term, and environmental concerns have led to the search for clean, renewable energy sources. Urban/agro-industrial/agricultural wastes appear as relevant energetic resources in a sustainable energy mix. Biogas results from the anaerobic digestion of organic matter that, is the main constituent of these wastes. Indeed, the production of methane or hydrogen from the biomass follows the principle of the fermentation. Hydrogen is considered as the more sustainable energy carrier due to the high efficient end-use technologies such as the fuel cells [1, 2]. Clean-hydrogen gas can be produced either by electrolysis [3], steam biomethane reforming [4], biomass gasification [5], or biological synthesis [6, 7].

Biohydrogen production processes, are divided into two groups according to the dependency on light: dark and photo fermentations [8, 9]. Under dark anaerobic conditions, the organic substrates and waste waters are metabolized to form hydrogen and lower molecular weight organic acids. Photofermentative hydrogen production, issued from oxidation of organic compounds, occurs under anaerobic, nitrogen-limited conditions, utilizing light as energy source. A wide range of photosynthetic bacteria has been reported to produce hydrogen, including Rhodobacter capsulatus, Rhodobacter sphaeroïdes, Rhodopseudomonas palustris, and Rhodospirillum rubrum [10, 11]. Among them, Rhodobacter capsulatus is a favorable candidate for large-scale production due to its high energy and substrate conversion efficiencies and its ability to utilize a wide variety of substrates for growth and hydrogen production [12, 13].

The rate and yield of hydrogen production is greatly dependent on the carbon source used, physiological growth conditions, such as light intensity [14, 15], and bacterial growth mode. Fed-batch growth mode is recognized as the most suitable operation mode for H₂ production, in comparison with batch and continuous modes [16]. In fact, studies for H₂ production during fed-batch conditions by photosynthetic bacteria have been reported for Rhodopseudomonas palustris sp. and R. palustris 42OL (on acetate and malate as carbon source, respectively) [17, 18], R. sphaeroïdes ZX-5 (on malate) [19], R. faecalis RLD-53 (on acetate) [20], and R. capsulatus DSM1710 (on acetate) [13].

Various kinetics models have been derived for biohydrogen production, as previously reviewed [21, 22]. In particular, and because of its simple initial form, the Luedeking-Piret model, developed in 1959 to describe lactic acid production and others processes [23, 24], has recently been applied to fermentative hydrogen production. In this widely used mathematical model, the rate of product formation (like hydrogen) can be related to both biomass concentration and microbial growth rate. All the studies concerned dark fermentation conditions with the exception of one devoted to the phot osynthetic bacterium, R. palustris [25].

Unfortunately, comparison between studies is quite complicated because the use of batch culture and different operating conditions makes it difficult to determine Luedeking-Piret model parameters from the published data. The estimation of not directly quantifiable compounds is essential in the development of biotechnology processes like photo-hydrogen production. However, a complex model involves several kinetics parameters and it is difficult to discuss the relevance of each one. It is also difficult to use traditional batch techniques, without complex model, to scrutinize useful parameters. This problem is theoretically overcome with continuous stirred tank reactors (CSTR) inside which the composition is uniform at any point. For a given mean residence time ($\frac{V}{Q}$) and inlet and outlet concentrations, the mass balance is very simple and it is hence easy to calculate the kinetic constants. In practice, the stirring of bioreactor is well achieved with a good mixing but the inlet flow rate must be adapted to avoid wash-out of microbial biomass.

The present study describes a mathematical approach to determine reliable kinetic parameters of hydrogen production by the photosynthetic bacterium, R. capsulatus, in a quasi-continuous photobioreactor. The developed mathematical/experimental approach is simple enough in terms of mathematical complexity and experimental procedure to be further used to attain reliable parameter values (α, β) of Luedeking-Piret model or maximum growth rate (μ_max) and lag time (λ). The present work combines Luedeking-Piret model and Gompertz model using the main assumptions of continuous stirred-tank reactor (CSTR) operation.

2. Material and methods

2.1. Bacteria and culture medium

Rhodobacter capsulatus strains B10 and IR3 [26] were grown anaerobically at pH 6.8 and 30 °C in modified RCV medium. The modified medium RCV, derived from [27], contained Na-lactate (35 mM), Na-Glutamate (7 mM), phosphate buffer (K₂HPO₄/KH₂PO₄, 5.17 and 4.41, mM), and a solution of salts containing different salts as oligoelements such as Mo (1.5μmol) and Fe (42 μmol).

2.2. Photo-bioreactor

Hydrogen producing experiments were carried out in a laboratory-made, rectangular-shaped 1 L bioreactor operated in the fed batch mode [28]. Anaerobic conditions were obtained by initially purging the bioreactor with sterile argon gas. Temperature and pH values were acquired by two pH and temperature probes connected to a computer via an acquisition card (Measurement Computing SA, PMD1208 LS). The pH was controlled with a pH regulator and pumps, by automatic addition of sodium hydroxide (2 M). The hydrogen flow rate was measured by a mass flow meter (Mac Millan, model 50D, 0–20 ml H₂ h⁻¹) linked to the data acquisition card. Hydrogen volume was obtained by time-integrating the hydrogen flow rate furnished by the flow-meter.

The substrate flow during fed-batch culture was controlled by a single pump functioning in both directions and electro-valves (Sirai, Type Z130A, V12). The entry flow was identical to the output flow in order to maintain a constant culture volume. The pump and electro-valves were controlled using the digital channels of the acquisition card, interfaced with a lab-made software based on Visual Studio.

The bioreactor was illuminated from one side by a sodium-vapor lamp (OSRAM, Plantastar, 600 W). The light intensity at the surface of the reactor was varied by changing the distance between the light source and the illuminated surface. The light intensity was measured with a digital lux meter (Meter, RO 1332).

The dynamics of the bacterial population and the hydrogen production were measured in quasi-continuous mode. The culture was started in batch mode, then when a constant bacterial protein concentration was reached ca. 0.45 g/l for B10 and ca. 0,36 g/l for IR3. As soon as the bacterial concentration was reached, the quasi-continuous conditions were applied. During continuous operation, the culture was fed with RCV growth medium containing 35.7 mM (4 g/L) sodium lactate and 5 mm sodium glutamate at a rate of 1 ml min⁻¹ and bacterial culture was withdrawn at the same rate over a 30–50 h period. The withdrawal and feeding were then interrupted and the culture operated in batch mode for 6 h. These quasi -continuous conditions were repeated 3–5 times period of 100–200 h for both R. capsulatus strains. In the case of strain IR3, the final batch mode was prolonged until stationary phase was achieved.

2.3. Analytical methods

Samples were regularly withdrawn for determining the concentrations of biomass and substrate. The bacterial cell concentration was estimated by measuring the optical density at 660 nm according the relation OD 0.8 corresponded to 0.37 mg dry weight L⁻¹ and 0.16 mg protein L⁻¹. Lactate concentration was measured by HPLC (Agilent 1260, column Hi Plex H 8μm) using a Refractive Index Detector G1362A – Agilent. Sample was firstly centrifuged (16,060 g, 5 min) and the supernatant was diluted 10 times and finally filtered (0.2 μm porosity) before analysis. The mobile phase for HPLC was a solution of sulfuric acid 2.3 mM (0.4 ml min⁻¹). Calibration curves were generated using standards of ultrapure lactic acid.

2.4. Mathematical approach

The Gompertz function, available since 1825, can be used as exponential model to take into account the slowing down of the observed growth of the batch reactor culture of any microorganism. The Gompertz function can describe the dynamics of any living form without limitation of resources. Consequently, the Gompertz function [29] is well adapted to biological reactors with efficient substrate renewal.

The Gompertz equation is given by:

$$ln\left(\frac{X}{X_0}\right)=a{e}^{-e^{\left(b-ct\right)}}$$ (1)

We call this relationship $f\left(t\right)$ and the associated equation is

$$g\left(t\right)=X_0{e}^{a{e}^{-e^{\left(b-ct\right)}}}$$ (2)

where X is the bacterial density or protein concentration and X₀ is the initial bacterial density or initial protein concentration. First and second derivatives of $f\left(t\right)$ are given by the equation (3) and equation (4):

$$f^{\prime }\left(t\right)=ac{e}^{\left(b-ct\right)-e^{\left(b-ct\right)}}$$ (3)

$$f^{″}\left(t\right)=a{c}^2{e}^{\left(b-ct\right)-e^{\left(b-ct\right)}}\left(e^{\left(b-ct\right)}-1\right)$$ (4)

Gibson et al. [29] have coupled logistic models and the Gompertz function; however the Gompertz function is not directly interpretable. To solve this problem, Zwietering et al. [30] simplified the two models by incorporating the classic parameters of maximum concentration, latency time and maximum growth rate. However, it is also possible to determine these parameters using the nonphysical parameters (raw parameters) of the Gompertz function (a, b, c) using the undermentioned equations. The time of inflexion point is the solution of the following equation:

$$f^{″}\left(t_i\right)=0$$ (5)

Which involves:

$$t_i=\frac{b}{c}$$ (6)

And the maximum growth (${\mu }_{max})$ rate is given by:

$${\mu }_{max}=f^{\prime }\left(t_i\right)$$ (7)

The lag time (λ) is the intercept with x-axis of the tangent line:

$$f^{\prime }\left(t_i\right)t+y_{\left(t=0\right)}=0$$ (8)

And the maximum concentration is the asymptote of Gompertz function:

$$\overline{X}=\underset{t\to \infty }{\lim }{X}_0{e}^{a{e}^{-e^{\left(b-ct\right)}}}=X_0{e}^a$$ (9)

Overall techniques are well known, but few experimental cultures correspond to the simple sigmoid function (Gompertz function). In other hand, Luedeking-Piret model can well describes the fermentative process; this classical model considers the relationship of cell growth to product formation as follow:

$$\frac{dP}{dt}=\alpha \frac{dX}{dt}+\beta X$$ (10)

In the present study, we have coupled the Luedeking-Piret model and the Gompertz function. However, some assumptions were required to this combine:

• •there is no limitation by the substrate [20].
• •the decrease in bacterial density (wash-out of microorganisms during the continuous process (CSTR technic only) affects weakly the Gompertz description (asymptote value only).

All the assumption are validated by as smooth quasi-continuous feed [31] and the simple automation such as presented above. These assumptions are validated in the section 3.1. Therefore the Eq. (1) and their derivative expression, as follow:

$$\frac{dP}{dt}=\alpha f^{\prime }\left(t\right)g\left(t\right)+\beta g\left(t\right)$$ (11)

And the integration of this equation is given by:

$$P\left(t\right)=\alpha X_0\left(e^{a{e}^{-e^{\left(b-ct\right)}}}\right)+\beta X_0\underset{0}{\overset{t}{\int }}{e}^{a{e}^{-e^{\left(b-cx\right)}}}dx$$ (12)

In addition, it is possible analyze the mathematical function (12) and to observe for the time tr ≅ 3. ti (where more of 95% of maximum concentration (asymptote of Gompertz function) is obtained) that the dynamic hydrogen production could be described by a linear evolution for t >> tr as follow:

$$P\left(t\right)\cong \beta \overline{Xt}$$ (13)

3. Results and discussion

3.1. Experimental measurements of bacterial growth and substrate consumption

Kinetics of bacterial production and substrate consumption for the wild type R. capsulatus B10 and the H₂ over-producing strain IR3 were shown in Figures 1A-1B, respectively.

Figure 1.

Kinetics of the lactate consumption (S, ◊) and the bacterial production (X, ▲) during a quasi-continuous culture of R. capsulatus B10 (A) and IR3 (B). the arrows indicate the application of continuous flow.

For the wild type B10 strain, the first feeding procedure started at the beginning of the batch stationary phase (Figure 1A), when lactate was almost completely metabolized (concentration close to 0 g L⁻¹⁾. The application of continuous flow conditions led to an increase in lactate concentration to 0.7 g L⁻¹, concomitant with a decrease in bacterial protein concentration from 0.54 to 0.44 g L⁻¹. Interruption of continuous flow followed by batch culture then led to a stabilization at 0.7–0.8 g lactate L⁻¹ and 0.44–0.48 g protein L⁻¹. This was repeated over 3 cycles of quasi-continuous operation.

For the H₂ over-producing strain IR3, the feeding procedure started at the end of the exponential growth phase, after the consumption of 90% of lactate (residual concentration of 0.4 g L⁻¹). The feeding of growth medium led to an increase in lactate concentration to 1 g L⁻¹ and a decrease in bacterial protein concentration from 0.4 g L⁻¹ to 0.35 g L⁻¹. Alternation of continuous and batch modes led to a stabilization at 0.34–0.38 g protein L⁻¹ and 0.75–0.95 g lactate L⁻¹, and this was repeated over 5 cycles of quasi-continuous operation. The final, prolonged batch phase led to complete consumption of lactate and a final bacterial concentration of 0.45 g L⁻¹.

In both case the decrease in bacterial concentration due to wash-out during the continuous mode operation was computed to be close to 20 mg of proteins per hour for an average flow rate < 1 ml min⁻¹. This is small compared to the potential range of biomass production in the reactor of 100–350 mg protein per hour. Taken together with the lack of substrate limitation (stabilization at 0.7–0.95 g lactate L⁻¹), these results validate the assumptions of the Gompertz model.

3.2. Fitting procedure and parametric values

The aim of the “data fitting” is to determine and compare parameter values of the model that describes the process. On the other hand, the parametric optimization is also a useful tool for validating the model. Nevertheless, the fitting procedure requires an appropriate attention to achieve relevant results. The Gradient methods are generally more efficient when the objective function is continuous in its first derivative. Gradient methods use information about the slope of the function to dictate a direction of search where the minimum is thought to lie. The simplest of these is the method of steepest descent in which a search is performed in an opposite direction of gradient of the objective function. This method is available with numerous commercial software. Gompertz function and (Eq. 1) coupled Luedeking-Piret model and Gompertz function (Eq. 12) are expedient mathematical functions to achieve the conventional numerical optimizations.

Bacterial growth was modeled using the Gompertz function; and Figure 2 shows good agreement between the model and experimental values of biomass concentration. Table 1 compares the a, b and c values for the R. capsulatus strains. However, no direct interpretation is possible as these are raw parameters, and the Eqs. (5), (6), (7), and (8) must be used in order to obtain meaningful physical parameters, such as μ_max, λ, and Y_xS.

Figure 2.

Bacterial growths in quasi-continuous culture of wild strain B10 (●) and over-producer strain IR3 (○): experimental data and Gompertz simulation.

Table 1.

Gompertz function parameters.

	B10	IR3
a [-]	3.03	2.66
b [-]	1.77	2.18
c [h−1]	0.174	0.1581
R2	0,9924	0.9968

In this context, λ is the intercept with x-axis of the tangent line as expressed in the Eq. (7), μ_max is given by the derivative function of Gompertz model (Eq. (7)) and Y_xS is directly obtained from Eq. (9) and the initial substrate concentration.

The growth-associated product coefficient, α, and the non-growth-associated product coefficient, β, were the determined by numerical optimization from experimental data and the Luedeking-Piret model Eq. (12) (i.e. data fitting). Experimental data for H₂ production were correctly modelled for both strains B10 and IR3, as shown in Figure 3, and the fitted parameters are summarized in Table 2.

Figure 3.

Simulated Luedeking–Piret's model coupled Gompertz equation to and H₂-production by Rhodobacter capsulatus B10 (A) and IR3 (B) (35 mM lactate, 30,000 Lx).

Table 2.

Fitted parameters of Luedeking–Piret's model and associated growth parameters.

	B10	IR3
YXS	0.124	0.109
λ [h]	9.8	13.9
μmax [h−1]	0.195	0.166
β [ml H2 (g L−1)−1 h−1]	17	72
α (ml (g L−1)−1)	4.5	36.6
R2	0.9980	0.9975
β [ml H2 (g L−1)−1 h−1] (linear regression)	14	75.6
R2	0.9942	0. 9969

The corresponding physical parameters, μ_max, Y_xS, λ, α, β were summarized in Table 2.

μ_max and λ parameters differed according to the basic growth observation of both bacterial strains. The value of the maximum specific growth rate, μ_max, was higher for the wild type strain B10 (0.195 h⁻¹) than the one observed for the over-producer strain IR3 (0.166 h⁻¹). In addition, the wild strain B10 grew earlier than the mutant strain IR3 with a similar substrate utilization rate, Y_XS: 0.124 and 0.109 g protein g⁻¹ lactate, respectively B10 and IR3, this was correlated with a lower lag time observed for the wild type B10 (9.8 h) compared to the mutant IR3 (13.9 h).

The Luedeking-Piret model implies that hydrogen production is associated with both non-growth and growth-associated terms. The growth-associated term indicates that hydrogen production (α) is proportional to the bacterial growth rate. On the other hand, the non-growth associated term (β) signifies that hydrogen production is linearly dependent on biomass concentration. In the case of strain IR3, both parameters were substantially higher than for the wild type strain B10 (see Table 2). It is noteworthy that the β parameter is main parameter to describe hydrogen production by photofermentation. Eq. (13) shows that it possible to model fermentation products using a linear relationship, assuming a negligible artificial mortality and biomass dilution during the continuous or quasi-continuous process:

$$P\left(t\right)=b+\beta \overline{Xt}$$ (14)

Therefore, the non-growth associated term could be attained by direct linear regression and the parameters determined by the linear procedure (equation 13) were very close to those obtained by the overall simulation of the Luedeking–Piret model. Both mathematical procedures can provide realistic β parameters, which is the most important parameter when selecting a productive strain. One cannot estimate α separately using batch culture data (Eq. (12)), except for t << tr, and concomitant α and β fitting is complicated by the necessary approximations of growth. Thus, in the case of batch cultures, realistic estimations of β and α require much additional data.

3.3. Discussion

Using the Gompertz function to model bacterial growth and the Luedeking-Piret model to describe hydrogen production by R. capsulatus during quasi-continuous culture, good agreement was observed between the experimental data and the models, with high regression coefficient values (R²) exceeding 0.99 in all cases (Table 2). The β and α parameters were lower in the wild type strain B10 than in the H₂ over-producer mutant IR3, as previously observed in batch culture [28]. The authors showed that the specific hydrogen production rate (ml h⁻¹) is proportional to the light intensity, which is the multiplying factor applied to non-growth -associated term (β) of Luedeking-Piret model. As above, in the present study, the wild type B10 exhibited a maximum specific growth rate, μ_max, higher (0.195 h⁻¹) that the over-producer strain IR3 (0.166 h⁻¹), this latter converted more efficiently the substrate (lactate) in product (H₂) that the wild-type B10 strain.

The maximum growth rate observed in indoor culture on synthetic medium with the wild-type R. capsulatus B10, on lactate-glutamate (35/5 mM as carbon and nitrogen source, is comparable with this obtained with the strain 37b4 on malate-(NH₄)₂SO₄ (16/9.5 mM), 0.195 and 0.251 h⁻¹ [32]. However, much lower maximum growth rates were observed in outdoor fed batch cultures on acetate-glutamate medium of R. capsulatus DSM1710 and the hydrogenase-deficient mutant YO3 (0.025 h⁻¹ and 0.052 h⁻¹, respectively [13, 33]. By contrast, in the present study both strains (IR3 and B10) exhibit similar values of the conversion rate of product/biomass. Hydrogen yields can be expressed according to different form like g or L hydrogen per g⁻¹ biomass, or by lactate conversion rate. The latter was based on the theoretical total conversion (100%) of 1 mol of lactate leading to the formation of 6 mol of hydrogen. For both strains, the first step of culture corresponding to batch conditions led to a weak lactate conversion, 4.5 and 18.6 % of lactate conversion for B10 and IR3, respectively. During the quasi-continuous process, B10 strain exhibited a weak lactate conversion rate compared to the over-producer strain IR3, 26.7 % and 95 %, respectively. These values were equivalent to 0.36 and 1.1 L H₂ g⁻¹ lactate, representing 27 mg and 110 mg H₂ g⁻¹ lactate, for B10 and IR3 strains, respectively.

It is essential to point out the assessments of Luedeking-Piret parameters in the literature in order to understand the values obtained in this study. Table 3 summarizes the H₂ production processes, based either on dark or light fermentation, and modeled by the Luedeking-Piret model. The modeling of dark fermentation processes only implied the hydrogen production associated to the biomass growth; β value was equal to zero. At the opposite, the H₂-producing process based on photosynthetic biomass involved both a non-growth and a growth-associated hydrogen production. Our results are the first study devoted to the robust estimation of λ, μ_max, α and β parameter. It shows that β parameter is main parameter to describe kinetic of gas production by photofermentation, therefore dark anaerobic conditions present lower potential of volatile fatty acid conversion into hydrogen than light anaerobic conditions. In addition, the production rates of hydrogen by R. capsulatus with respect to light intensity irrespective of cell concentration have been previously described by Obeid et al [28] and Androga et al [34]. Authors showed that the specific hydrogen production rate (ml h⁻¹) is proportional to the light intensity, which is the multiplying factor applied to non-growth -associated term (β) of Luedeking-Piret model.

Table 3.

H₂-producing processes described by the original or modified forms of the Luedeking-Piret (LP) model.

Biomass	α value (ml g−1 VSSa)	β value (ml H2 g−1 dw h−1)	Reactor type	substrate	Fermentation/LP model	Ref.
R. palustris	6.85b	0.41b	batch	glycerol	Light/modified	[25]
R. capsulatus B10 IR3	4.5c 36.6c	17c 72c	Quasi-continuous	Lactate	Light/modified	This study
Mangrove sediments	11.04	0	batch	glucose	Dark/original	[35]
Local sewage sludge	224	0	continuous	sucrose	Dark/e rH2 = DαX	[36]
Anaerobic sludge	759	0	batch	glucose	Dark/original	[37]
Anaerobic sludge	793	0	batch	glucose	Dark/original	[38]
Enterobacter cloacae	166d	0	batch	glucose	Dark/original	[39]
Clostridium pasteuranium	918 876	0 0	batch	xylose sucrose	Dark/dP/dt = α(1/X.dX/dt)	[40]

^aVolatile Suspended Solids.

^bundefined.

^cα = 1/Y_XP expressed in ml H₂ g protein L⁻¹ and β in ml H₂ (g L⁻¹)⁻¹h⁻¹.

^dml H₂ g⁻¹ cell mass.

^eD = liquid phase dilution rate, X = biomass concentration.

Since the first study [44] devoted to the outdoor H₂ production during a fed-batch culture of Rhodopseudomonas sphaeroïdes, many studies with PNS (purple-non-sulfur) bacteria have been carried out in different culture modes including fed-batch, repeated conditions or semi and continuous condition. They were summarized by Argun and Kargi [20], Androga et al. [41], Sagnak and Kargi [42], Basak et al. [10], and Uyar et al. [43]. Table 4 incorporates these and more recent data based on fed-batch and semi-continuous H₂ production processes using either pure PNS cultures or co-cultures with dark fermentative bacteria. Indoor conditions represented the majority of previous fed-batch studies, using different light source and intensity as tungsten, halogen, fluorescent, incandescent, and Na vapor light. Nature and use of different unities of illumination increased the difficulty to compare experimental conditions. Recently many outdoor operating system for H₂ production by R. capsulatus were carried out according to reactor design, effluent nature, bacterial strains, and feeding strategy conditions (Table 5), principally with Rhodobacter capsulatus.

Table 4.

H₂-producing processes based on fed-batch regime. These processes have been previously summarized by Argun and Kargi 20], Androga et al. [41], Sagnak and Kargi [42], Basak et al. [16], and Uyar et al. [43].

Strains	Carbon and nitrogen sources	Photobioreactor characteristics and operating conditions	Fed batch, semi continuous conditions	Maximal H2 productivitya (mM H2 L−1 medium h−1)	Substrate conversion efficiency (mol H2 mol−1 carbon source)	Ref.
R. sphaeroïdes B6 (thermostable)	Lactate (25 mM) Na Glutamate (5 mM)	6-L plate polyacrylate outdoor	15 % dilution/4 days	1.07–1.56 (fine weather) 0.61–1 (cloudy weather) 0.09–0.56 (rainy weather)	3.51a	[44]
Rhodopseudomonas capsulata	Glucose DFEb: acetate (8.5 mM) propionate (1.7 mM) butyrate (13.6 mM) Na Glutamate (3 mM)	1.5-L indoor	HRTc: 72 h	0.65	1.6 (acetate) 2.8 (propionate) 4 (butyrate)	[45]
	acetate (30.5 mM) propionate (2 mM) butyrate (9 mM) Na Glutamate (3 mM)	1.5-L indoor	HRTc: 72 h	0.8	ND
	acetate (11.5 mM) propionate (3 mM) Na Glutamate (3 mM)	1.5-L indoor	HRTc: 72 h	0.94	ND
Rhodopseudomonas palustris 42OL	Malic acid (24.3 mM) Glutamic acid (5.6 mM)	1.07 L cylindric glass pH 6.8 320 W m2 408-h duration	ND small concentrated stock solution volume replacing sampling volume	0.49	ND	[46]
Rhodopseudomonas palustris sp.	Acetate (66.7 mM) Glutamic acid (5.6 mM)	Cylindric glass (0.22 L) pH 6.8–7.2 4 W m2 indoor	10% withdraw (experimental condition SCd 240h)	0.39	1.6	[17]
Clostridium acetobutylicum DSM792 + R. sphaeroïdes O.U.O O 1	Non pretreated wheat starch from corn (C source)/yeast extract (0.5)e and peptone (1)e	cylindrical reactor (0.25 L/0.12 L)f controlled pH 7 192 W/m2 Light/Dark ratiog = 2	OLRh 1.5 g starch L−1 d−1 2.5 % volume of medium replaced every day 0.375 g OLR L−1 d−1	1.03	2.62 (average on 33 days)	[47]
Clostridium butirycum N1VLB-B-3060 + R. sphaeroïdes VKM-3050	Starch (4.5)c/yeast extract (0.04)c, Na Glutamate (0.9)c	Hungate tube (16 ml/8 ml)d Microaerobic conditions pH7.5 30 W/m2 Light/Dark ratiog = 2.28	95–96 % volume of medium replaced	ND	5.2	[48]

^acalculated from data.

^bDark Fermentation Effluent.

^cHydraulic Retention Time.

^dSemi continuous, culture volume withdraw.

^eexpressed in g L⁻¹.

^fworking volume/total volume of reactor.

^gLight fermentative biomass/Dark fermentative biomass concentration ratio.

^hOrganic Loading Rates.

Table 5.

Comparison of the H₂ productivity and substrate conversion ratio obtained by Rhodobacter capsulatus strains under fed-batch, continuous and semi-continuous conditions.

Carbon sources	Photo-bioreactor	Growth mode	Location	Studied biomasses	Maximal H2 productivity (mL H2 L−1 medium h−1)	Substrate conversion efficiency (mol H2 mol−1 carbon source)	Ref.
Lactate (35 mM) Na Glutamate (5 mM)	1-L PMMA panel	semi-continuous	Indoor	B10, wild-type	0.26	0.24	This study
				IR3, H2 over producer	0.41	0.75	This study
Acetate (40 mM) Na Glutamate (2 mM)	4L–8L PMMA panel	fed-batch (10 L daily feeding)	outdoor	YO3, hup− mutant	0.51	0.53	[51]
	80-L PMMA tubular	fed-batch (10 L daily feeding)	outdoor	DSM1710, wildt type	0.31	0.60	[32]
				YO3, hup− mutant	0.40	0.35	[13]
Lactate (4 mM) Acetate (23 mM) Na Glutamate (1.37 mM)	65-L PMMA panel	continuous (daily replacement of 20 % volume reactor)	outdoor	DSM155, wild-type	0.36	ND	[52]
	4 ∗ 25-L PMMA tubular	continuous (daily replacement of 20 % volume reactor)	outdoor	DSM155, wild-type	0.15	ND	[16]
Sugar beet thick juice DFEa (Acetate 42 mM, NH4+ 2.2 mM, Total nitrogen 3.3 mM)b	4-L PMMA panel	fed-batch (10% daily feeding v:v)	outdoor	YO3, hup− mutant	1.12	0.77	[49]
Sugar beet thick juice DFEa (Acetate 31 mM, NH4+ 2 mM, Total nitrogen 7 mM)c	4-L PMMA panel	continuous (daily replacement of 10% v:v)	indoor	YO3, hup− mutant	1.01	0.48	[43]
	4-L PMMA panel	continuous (daily replacement of 10% v:v)	indoor	DSM1710, wild type	1.05	0.46
Molasse DFEa (Acetate 32.5 mM, lactate 2.5 mM, Formiate 2.5 mM)b	4-L PMMA panel	fed-batch (10% daily feeding v:v)	outdoor	DSM1710, wildt type	0.5	0.5	[50]
				YO3, hup− mutant	0.67	0.78

^aDark fermentation effluent.

^bSupplemented with Fe-citrate and Na2MoO4,2H20, 0.1 mM and 0.16 μm, respectively.

^cSupplemented with Fe-citrate 0.1 mM.

Efficiency of H₂ producing bioprocess based on PNS was habitually characterized by two principal parameters: the H2 productivity expressed as mM H2 produced L-1. h-1 and the substrate conversion ratio, which is the experimental H₂ yield divided by theoretical yield. H₂ productivity and substrate conversion ratio depend on experimental conditions as substrate nature, illumination, bacterial strain and feeding strategy conditions as indicated in previous summary tables extracted from recent reviews. In order to make the comparison more concise only results with Rhodobacter capsulatus strains were reported here. The production of H₂ by PNS totally depends on the enzymatic activity of nitrogenase. However, H₂ can be consumed by another enzymatic system known as uptake hydrogenase (hup). The productivity values for the wild type strain B10 and the over-producer strain IR3, extracted from Figure 3; were 0.26 and 0.41 mM H2 L-1 culture h-1, respectively. Substrate conversion ratio was calculated from oxidized lactate during semi-continuous of wild-type B10 and H₂ over-producer strain IR3. H₂ productivity value of wild-type B10 was 0.24 M M⁻¹ lactate. This value was close to that of DSM155 (0.15–0.36 M M⁻¹ carbon source), but lower that those obtained for the wild-type DSM1710 (0.5–0.78 M M⁻¹ carbon source); irrespective to experimental conditions (Table 5). The H₂ over-producer mutant IR3 exhibited a substrate conversion ratio of 0.75. This latter was larger than the wild-type B10, but close to the maximum H₂ substrate conversion ratio obtained during fed-batch culture of the hup-R. capsulatus mutant YO3 on dark fermented effluents of sugar beet thick huice [49] or molasse [50] (Table 5). Therefore, our methodology provides a robust estimation of λ, μ_max, α and β parameter in agreement with literature results (i.e. substrate conversion ratio and H₂ productivity) which achieved under fed-batch, continuous and semi-continuous conditions.

4. Conclusions

The Luedeking-Piret model was used in this study to describe the bacterial growth, substrate consumption, and hydrogen gas production by using the purple non-sulfur bacterium Rhodobacter capsulatus. Hydrogen production by R. capsulatus during a quasi-continuous culture over a 150–200 h period was successfully controlled with various key parameters as inlet flow rate, feed volume, and dilution rate of substrate supply. The R. capsulatus over-producing strain IR3 displayed a greater hydrogen production yield correlated to the non-growth associated term (β). A good agreement was obtained between the experiments and simulations with high regression coefficient values (R² > 0.99). Fitting procedure allows to relevant parameters such as the lag time (λ), the maximum growth rate μmax and both non-growth (β) and growth-associated terms (α) of Luedeking-Piret model. This parameter access will be useful for comparison between strains or/and literature data and for the automation and control of bioprocesses for the continuous fermentation process.

Declarations

Author contribution statement

Jonathan Deseure, Jean-Pierre Magnin: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Jamila Obeid: Conceived and designed the experiments; Performed the experiments.

John C. Willison: Analyzed and interpreted the data; Wrote the paper.

Funding statement

Jamila Obeid was supported by the Institute of International Education’s Scholar Rescue Fund, USA and the University Grenoble Alpes, LEPMI, France.

Data availability statement

Data will be made available on request.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.