Valorization of Glycerol into Polyhydroxyalkanoates ...

doi 10.1515/cppm-2014-0011

Chemical Product and Process Modeling 2014; 9(2): 117–131

Research Article Mohd Zafar, Shashi Kumar, Surendra Kumar*, Jay Agrawal and Amit K. Dhiman

Valorization of Glycerol into Polyhydroxyalkanoates by Sludge Isolated Bacillus sp. RER002: Experimental and Modeling Studies Abstract: In this study, the feasibility of glycerol valorization into homo- and hetero-polymers of polyhydroxyalkanoates by a sludge isolated Bacillus sp. RER002 in a 3 L bioreactor was investigated. A mathematical model including logistic, Luedeking–Piret, and Luedeking–Piret-like equations that simulated the active residual biomass growth, P(3HB) synthesis, and glycerol consumption, respectively, was developed. In order to describe the dynamics of batch P(3HB) production, the model kinetic parameters viz., µmax, K1, K2, α, β, and KN were optimized using the stochastic searchbased genetic algorithm. The synthesis of P(3HB) was observed to be highly growth associated and partially non-growth associated as reflected in a significant higher values of K1 (0.2435–0.5477) than K2 (2.2 10−6 to 9.1 10−3) within the glycerol concentration range of 10–40 g/L. Besides, the maximum 3.2 g/L of copolymer [P(3HAscl-co-3HAmcl)] was observed at 30 g/L of glycerol concentration in synthetic crude glycerol medium with a yield coefficient (YP/S) of 0.16 g/g. Furthermore, the analyses of chemical and thermal properties of copolymer P(3HAsclco-3HAmcl) revealed its enhanced material properties which make it suitable for various applications. Keywords: valorization, glycerol, P(HAscl-co-HAmcl), modeling, genetic algorithm

*Corresponding author: Surendra Kumar, Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India, E-mail: [email protected] Mohd Zafar, Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India; Department of Biological Engineering, Shobhit University, Meerut 250 110, Uttar Pradesh, India, E-mail: [email protected]

Shashi Kumar: E-mail: [email protected], Jay Agrawal: E-mail: [email protected], Amit K. Dhiman: E-mail: [email protected], Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee 247 667, Uttarakhand, India

1 Introduction Polyhydroxyalkanoates (PHAs) are a group of biopolymers originated from bacterial source and considered as an excellent substitute for non-degradable petroleum-based polymers due to its biodegradable and/or biocompatible properties [1]. Both the Gram-positive and the Gram-negative bacterial species have been reported for the accumulation of PHAs (chain of homo- and/or hetero-polymers including more than 150 monomers) having distinct properties [2]. The well-known Gram-negative PHAs producing bacterial strains as reported in the open literature are: Azohydromonas lata [3–5], Cupriavidus nector [6–8], some species of Pseudomonas [1, 9], and Azotobacter beijerinckii [10, 11]. It is noteworthy that the PHAs accumulated by Gram-negative bacterial strains contain the outer membrane of lipopolysaccharide (LPS), i.e. a pyrogen having a strong immunogenic reaction in the human body [2]. In contrast, PHAs accumulated by some species of Gram-positive bacteria including Bacillus, Clostridium, Corynebacterium, Nocardia, and Staphylococcus lack with LPS. Owing to this property, it is compatible with human system and suitable for various biomedical applications viz., wound-management, orthopedic-applications, bone-tissue engineering, and cardiovascular and drug-delivery systems [1, 2]. The production of microbial biopolymers is currently not cost effective due to the associated substrate cost (i.e. accounts up to 50% of the production cost) and complex downstream processing [9, 12]. Therefore, the potential of

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M. Zafar et al.: Valorization of Glycerol into Polyhydroxyalkanoates by Bacillus

inexpensive and renewable raw materials as a carbon source is to be explored for the cost-effective sustainable production of biopolymer. Biodiesel is an alternative biomass-based renewable fuel that has received the increasing attention in the recent past [13]. During the production of biodiesel, crude glycerol (CG) is generated as a byproduct at the rate of 10% (w/w) of the substrate. This CG has very low value (sometime negative value) due to the presence of various impurities such as methanol, free fatty acids, heavy metals, and salts [14]. Therefore, it is essential to valorize the low-grade CG into value-added products such as bioenergy, biofuels, and biochemicals in order to improve the economics of biodiesel production in the competitive global market [15, 16]. In the recent years, CG has been utilized as a biological feedstock for the production of 1,3-propanediol, organic (citric, lactic, succinic) acids, ethanol, and butanol [17]. Some researchers have also utilized the CG as a renewable carbon substrate for the synthesis of P(3HB) and copolymer of PHAs in the batch process [7, 9, 18–20] and for high-density cultivation in fed-batch process [7, 21, 22]. These promising studies have opened a new domain of value-added valorization of pure/crude glycerol into microbial biopolymer (PHAs) that can enhance the economics of biodiesel production through the integrated biorefinery system. In this study, the feasibility of valorization of glycerol into PHAs by a sludge isolated Bacillus sp. RER002 was investigated. The dynamics of biomass growth and PHA synthesis on glycerol was examined and quantitatively described by a mathematical model using the advanced optimized technique, genetic algorithm (GA). Despite the fact that the glycerol is a potential carbon source, to the best of our knowledge, the modeling of microbial growth and PHAs synthesis using glycerol as a substrate has not been investigated. Besides, the valorization of synthetic CG medium into copolymer of small (scl) and medium (mcl) chain length PHA [P(3HAscl-co-3HAmcl)] was examined in a 3 L bioreactor. The chemical and thermal properties of synthesized copolymer were investigated using appropriate analytical techniques.

2 Materials and methods 2.1 Isolation and acclimatization of PHAs accumulating bacteria Activated sludge sample was collected from the aeration tank of a municipal sewage treatment plant located at Hardwar, India (latitude, 29° 58′ N and longitude, 78° 13′

E). Collected sludge sample was kept for 2 days under the condition of starvation, i.e. limited supply of carbon and oxygen to initiate the sporulation process [23]. Further, mixed microbial populations of sludge (1 L) were subjected to heat-shock treatment in a water-bath at 85°C for 10 min to kill all non-spore forming bacteria followed by centrifugation at 5,000 g for 10 min. In order to acclimatize and enrich the PHAs accumulating microbial population, cell pellets were resuspended in a sequencing batch reactor (SBR) being fed with glycerol (1% w/v) as carbon source in a modified E2 mineral medium [24]. E2 medium consisted of reduced (NH4)2SO4 concentration, 0.4 g/L; K2HPO4, 5.0 g/L; KH2PO4, 3.48 g/L; MgSO4·7H2O, 0.4 g/L; CaCl2·2H2O, 0.2 g/L; TE solution, 3 mL/L (working volume, 1 L; temperature, 30°C). The mineral trace microelement solution (TE) contained (per liter): FeSO4·7H2O, 2.78 g; MnCl2·4H2O, 1.98 g; CoSO4·7H2O, 2.81 g; CaCl2·2H2O, 1.67 g; CuCl2·2H2O, 0.117 g; ZnSO4·7H2O, 0.29 g. Medium was sterilized at 121°C and 15 lbs pressure for 15 min in an autoclave. In order to avoid the precipitation of salts in medium, K2HPO4 and KH2PO4 were sterilized separately and after cooling, mixed with other nutrients solution. The 24 h cycles of SBR were consisted of four phases: filling (10 min); microaerophilic– aerobic process (23 h); settling (40 min); and withdrawn (10 min). A little amount of oxygen was introduced into the reactor with the rate of 1 vvm for about 3 h during the process. The hydraulic retention time was kept at 2 days with the replacement of 500 mL of E2-mineral medium daily. The sludge retention time was maintained at 10 days with a purging of 100 mL of mixed liquor daily. The sludge was acclimatized over a period of 6 months to enriched the PHAs accumulating bacteria under microaerophilic–aerobic condition in SBR. Isolation of pure bacterial strains were carried out by serial dilution of enriched mixed microbial culture of sludge in 0.85% w/v sterile saline solution followed by plating of the samples on a modified agar E2 medium [25]. After incubation of 24 h at 30°C, two to five bacterial colonies were randomly picked from each plate with the help of sterile tooth picks and transferred onto a fresh secondary plate. The viable single colony appeared on secondary plates was examined for PHA accumulation potential in a 250 mL Erlenmeyer flask containing 50 mL of glycerol-based modified E2 medium under 30°C temperature and agitation speed of 180 rpm for 24 h.

2.2 Molecular characterization of isolated bacterial strains Genomic DNA of RER 002 bacterial strain was isolated by CTAB method [26] and subjected to the amplification of



16S rDNA gene using the primers; fD1 (5′-AGA GTT TGA TCC TGG CTC AG-3′) and rP2 (5′-ACG GCT ACC TTG TTA CGA CTT-3′) [26]. PCR reaction mixture (50 µL) contained 2 µL template DNA (50–70 ng µL−1), 2 µL of each primer (10 µM), 1 µL of 10 mM dNTPs, 5 µL of Taq buffer (10 ), 1 µL of Taq DNA polymerase (3U µL−1), and 12.0 µL of Millipore water. The temperature program for PCR amplification was: initial reaction temperature at 94°C for 5 min, 33 cycles of denaturation reaction at 94°C for 30 s, annealing reaction at 50–53°C for 30 s followed by extension reaction at 60°C for 4 min. PCR products were analyzed by 1.5% agarose gel electrophoresis and visualized by observing fluorescence using gel documentation system. The purified 16S rDNA gene was sequenced by primer walking using four different internal primers (16SEQ3F, INS16SREV, 16SEQ4F, and 16SEQ4R) designed for conserved region on 16S rDNA sequence [27]. Sequenced gene was compared to the conserved 16S rDNA database of GenBank database of the National Center for Biotechnology Information (NCBI, http:// www.ncbi.nlm.nih.gov) using BLAST (Basic Local Alignment Search Tools) program to identify the most similar 16S rDNA gene sequence.

2.3 Inoculum preparation, growth, and PHAs production in batch process Microbial growth and PHA synthesis were carried out using modified E2 medium as given in Section 2.1. Modified E2 medium contained carbon source (glucose or glycerol) and reduced amount of nitrogen source ((NH4)2SO4), i.e. essential for biomass growth and expression of enzymes participated in PHA synthesis. The inoculum of isolated Bacillus sp. RER002 was prepared by using 50 mL of modified E2 medium containing glucose (1.0 g/L) in 250 mL capacity conical flask kept at 30° C and 180 rpm for 24 h in an orbital shaking incubator. Experiments were conducted in 3 L bioreactor equipped with ez-control (Applikon, Schiedam, The Netherlands), which contained 2 L of modified E2 medium with glycerol in the range of 10–40 g/L. All the experiments were conducted at pH 6.8, temperature 30°C, and agitation rate of 180 rpm with a constant aeration of 1 vvm. The biomass growth, P(3HB) production, and residual glycerol concentrations were determined by taking samples at various time intervals. In addition, production of copolymer of P(3HAscl-co-3HAmcl) was carried out using the synthetic CG medium supplemented with reduced amount of (NH4)2SO4 in 3 L bioreactor with a working volume of 2 L. The operating conditions were set at:

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temperature, 30°C; pH, 6.8; agitation speed, 250 rpm; and air flow rate, 1.0 vvm. Synthetic CG medium consisted (weight%) of: methanol, 32.59; glycerol, 60.05; NaOCH3, 2.62; fat, 1.94 [28]. Fat consisted of the most abundance fatty acids of different oils such as octanoic (C8:0), palmitic (C16:0), stearic (C18:0), and oleic (C18:1) acids in a random molar ratio of 40:40:10:10. CG1 medium contained high glycerol (60.05%) and methanol (32.59%), which was diluted in CG2 medium to reduce their toxic effects on biomass growth and synthesis of copolymer of P(HAscl-co-HAmcl).

2.4 Analytical procedure The biomass concentration was estimated turbidimetrically at 600 nm using UV–VIS Spectrophotometer (Lambda 35, Perkin Elmer, MA, USA). The quantification of copolymer of P(3HAscl-co-3HAmcl) was carried out by the propanolysis method with little modification using gas chromatograph (Thermo, USA) [29]. The analyses of glycerol and methanol were carried out by high-performance liquid chromatography apparatus (Waters, USA), equipped with Sugar-Pak column (6.5 250 mm length, Waters, USA) and refractive index detector (model 24140, Waters). The deionizedwater at 90°C was used as eluent with a flow rate of 0.5 mL/min. The cell free supernatant was analyzed for residual NH4 þ ion concentration by phenol-hypochloride method [30].

2.5 Extraction and recovery of PHA Extraction and recovery of PHA was carried out using organic solvents as per the method given by Hahn et al. [31] with a little modification. About 100 mL of culture broth was taken at the end of process and centrifuged at 5,000 g for 10 min. The supernatant was discarded and the recovered cell pellet (~0.5 g dry weight) was treated with 100 mL of sodium hydrochloride (20% v/v) at 30°C for 2 h. After incubation, the mixture was centrifuged at 5,000 g for 10 min, and the cell pellets were washed with distilled water and acetone. After washing, the cell pellets were suspended in 100 mL of boiling chloroform in soxhlet extractor (twice) for 12 h to extract the intra-cellular PHA granules. The mixture was filtered and treated with 4 volume of cold methanol to precipitate the PHA granules. The precipitates were filtered off and dried at room temperature to get the powder of PHA [32].


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2.6 Physico-chemical characterization of isolated copolymer In order to detect the infrared (IR) spectrum of copolymer of PHA, about 1 mg of sample was mixed with moisture free KBr (IR grade) to prepare the pellets. The spectrum was recorded using a Nicolet 6700 Fourier transform IR spectrometer (FTIR, Thermo Scientific, USA) by scanning at a resolution between 4,000 and 500 cm−1. 1H NMR spectrum was recorded at 500 MHz by nuclear magnetic resonance (NMR) spectrometer model Av 500 MHz (Bruker Inc., USA) using deuterated chloroform (CDCl3) as solvent. Thermal characteristics of the samples were measured by Pyris Diamond Thermogravimetric Analyser (Perkin Elmer Inc., Wellesley, MA, USA) with simultaneous recording of differential thermal analysis (DTA), thermogravimetry (TG), and derivatives thermogravimetry curves. Approximately 10 mg of samples were used to prepare about 0.1 mm thick film samples, which were placed in platinum crucibles. The analysis was carried out in an inert gas atmosphere of nitrogen at a flow rate of 100 mL/min in the temperature range from 25 to 350°C with a heating rate of 10°/min. The temperatures of melting and decomposition were determined as the temperature of corresponding endothermic maxima [32].

2.7 Development of kinetic and mathematical models The batch production of P(3HB) by a newly sludge isolated bacterial strain Bacillus sp. RER002 was carried out in a 3 L bioreactor using pure glycerol in the defined E2 medium. The experimental data at different initial concentrations of glycerol (10–40 g/L) were used for the development of mathematical model representing the active residual biomass growth, P(3HB) synthesis, and substrates (glycerol and (NH4)2SO4) consumption profiles. Microbial growth has been described by various structured and unstructured kinetic models such as Monod, logistic, modified-logistic, Tessier, and Mosser models [6, 33–41]. Bacterial biomass growth which shows the sigmoidal pattern and independent of substrate concentration has been described by logistic-model [34, 38]. Since the sigmoidal growth pattern of Bacillus sp. was observed in this study, the logistic equation was used to describe the growth pattern with time. The following assumptions were made during the development of mathematical models of growth, P(3HB) synthesis, and substrate consumption.

1.

The biomass (X) of bacterial cell is composed of two components: (i). The catalytically active residual biomass (R) consisting of various proteins including enzymes, and nucleic acids which are responsible for various metabolic activities of the microbial cell; (ii). P(3HB) is accumulated in the form of inert component, i.e. inclusion body as a result of various metabolic activities. 2. The biomass growth of Bacillus sp. RER002 is independent of substrate and sigmoidal in nature, therefore, is represented by logistic equation. 3. Glycerol is consumed as carbon substrate in terms of catalytically active biomass growth (R), P(3HB) synthesis (P), and maintenance-energy expenditure. 4. Nitrogen source is consumed for the growth of catalytically active biomass (R) and maintenance-energy requirement rather than for P(3HB) synthesis. 5. The accumulation of P(3HB) by Bacillus sp. is growth related as reported in the open literature [2, 42]. However, some amount of P(3HB) synthesis is also reported during the stationary phase. 6. The consumption of accumulated P(3HB) was reported during the process of sporulation, i.e. the characteristic feature of Bacillus spp. [42]. Hence, the culture should be harvested before the starting of sporulation process.

The logistic equation representing the specific growth rate was described as: R μ ¼ μmax 1 ð1Þ Rm Subsequently, the rate of active residual biomass formation was described as: dR ¼ μR dt

ð2Þ

where R is the concentration of residual active biomass at any time t. The residual active residual biomass can be defined as: R ¼ X – P, where X is the total biomass concentration and P is product [P(3HB)] concentration. Using eqs (1) and (2), dR R ¼ μmax 1 R ð3Þ dt Rm where µmax is the maximum specific growth rate and Rm is the maximum concentration of catalytically active residual biomass (R).



Here R0 represents the active residual biomass concentration at the beginning of fermentation process. The integration of eq. (3) with boundary condition (t ¼ 0, R ¼ R0) gives R0 Rm eμmax t R¼ Rm R0 þ R0 eμmax t

Since the yield coefficients (YR=S1 and YP=S1 ) and maintenance-energy coefficient (mS1 ) are constant, eq. (9) can be reduced to

ð4Þ

ð5Þ

where K1 and K2 are growth- and non-growth-related kinetic constants, respectively, representing the P(3HB) synthesis. According to Gaden-classification [43] of product formation, the product formation may be connected with the microbial growth (K1 ≠ 0; K2 ¼ 0; Type I), partially connected to growth (K1 ≠ 0; K2 ≠ 0; Type II), and not related to bacterial growth (K1 ¼ 0; K2 ≠ 0; Type III) [43]. By combining eqs (2) and (5), the specific P(3HB) synthesis rate (qP) can be defined as: qP ¼

1 dP ¼ K1 μ þ K2 R dt

ð6Þ

By substituting the dR=dt from eqs (3)–(5), and integrating from P0 to P, R0 to R, and t0 to t, the following expression for P(3HB) synthesis is obtained. K2 Rm Rm R0 þ R0 eμmax t ln P ¼ P0 þ K1 ðR R0 Þ þ μmax Rm ð7Þ The substrate (glycerol) consumption for residual biomass growth and P(3HB) synthesis is modeled by Luedeking–Piret model [38, 41]. The glycerol consumption rate is related to the active residual biomass (R) growth, P(3HB) synthesis, and maintenance-energy expenditure. It can be mathematically expressed as: dS1 1 dR 1 dP þ þ ms1 R ð8Þ ¼ YR=S1 dt YP=S 1 dt dt where YR=S 1 is the yield coefficient of active residual biomass (R), and YP=S 1 is the yield coefficient of P(3HB) with respect to glycerol (S1) consumption. On applying eq. (5), eq. (8) is restated as: ! ! dS1 1 K1 dR K2 þ ¼ ð9Þ þ þ ms1 R YR=S1 YP=S 1 dt dt YP=S 1

dS1 dR þ βR ¼α dt dt

ð10Þ

1 K1 þ YR=S1 YP=S1

ð11Þ

K2 þ mS1 YP=S1

ð12Þ

where

In the previous studies, the accumulation of P(3HB) has reported as both growth and non-growth (stationary) associated [2, 42]. Thus, Luedeking–Piret model has been used to describe the P(3HB) synthesis incorporating both growth- and non-growth-associated components as given by eq. (5). dP dR ¼ K1 þ K2 R dt dt

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α¼

β¼

The specific glycerol consumption rate (qS1 ) is represented as: 1 dS1 ¼ ðαμ þ βÞ ð13Þ qS1 ¼ R dt Eqs (3) and (10) are solved simultaneously using boundary conditions (t ¼ 0, S ¼ S0, R ¼ R0) to get S1 as a function of time (t). R0 Rm eμmax t þ αR0 S1 ¼ S0 α Rm R0 þ R0 eμmax t ð14Þ Rm β Rm R0 þ R0 eμmax t ln μmax Rm Similarly, the nitrogen (S2) is consumed for catalytically active residual biomass (R) growth and for maintenanceenergy expenditure of the Bacillus sp. The rate of nitrogen consumption is represented by eq. (15) as:

dS2 dR ¼ KN dt dt

ð15Þ

where KN is specific consumption rate of nitrogen. The integration of this equation with boundary condition (at t ¼ 0 and S2 ¼ S20) gives " # ðeμmax t 1ÞðRm R0 Þ S2 ¼ S20 KN ð16Þ Rm μmax t 1Þ R0 þ ðe

2.8 Estimation of model parameters by optimization technique The set of model equations described in Table 1 represents the rates of active residual biomass growth, P (3HB) synthesis, glycerol consumption, and (NH4)2SO4 consumption. The unknown kinetic constants of these equations were determined by GA-based optimization technique, where the sum of squares of deviation between the model predictions and experimental


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0P 1 n ðYi;e Yi;p Þ2 Bi¼1 C C R2 ¼ 1 B n @P 2A ðYi;e Y e Þ

Table 1 Model equations to describe the time profiles of active biomass growth, P(3HB) production, and substrate consumption Model equations

Boundary conditions

dR dt ¼ μR; μ¼fðR;S1 ;S2 Þ dP dt ¼ qP R dS1 dt ¼ qS1 R dS2 dt ¼ KN μR

At t ¼ 0, R ¼ R0, P ¼ P0, S1 ¼ S0, and S2 ¼ S20

i¼1

qP ¼ K1 μ þ K2 qS1 ¼ αμ þ β K1 1 þ YP=S α ¼ YR=S 1

RMSE ¼

MPEð%Þ ¼

1

K2 β ¼ YP=S þ mS1 1

values was minimized using the following objective function: Q¼

n X

S1i;pred S1i;exp

2

þ

i¼1

þ

n X

Ri;pred Ri;exp

2

n X

S2i;pred S2i;exp

i¼1 n X

þ

i¼1

Pi;pred Pi;exp

ð18Þ

2 2

ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn 2 ðY Y Þ =n i;e i;p i¼1 n 100 X Yi;e Yi;p =Yi;p n i¼1

ð19Þ

ð20Þ

Pn Bf ¼ 10ð i¼1 logðYi;p =Yi;e Þ=nÞ

ð21Þ

Pn Af ¼ 10ð i¼1 j logðYi;p =Yi;e Þj=nÞ

ð22Þ

where Yi,e is the experimental value of ith experiment, Yi,p is the corresponding predicted value by model of ith experiment, Y e is the mean value of experimental data of active residual biomass growth, P(3HB) synthesis, and glycerol concentrations, and n is the number of the experiments.

i¼1

ð17Þ pffiffiffiffi The minimum of root mean square error (RMSE), Q can be obtained by various gradients/initial guess methods, and non-linear regression analysis. Moreover, the gradient methods often fail to converge to the global minima and stick to local minima [44]. GA is an effective stochastic global search algorithm which is inspired by the evolutionary features of biological systems [45–47]. For the general case, where µ can be represented by any kinetic model, the model equations mentioned in Table 1 were solved by ode45 solver in MATLAB 7.8.1. The GA (ga tool) toolbox of MATLAB was used for the direct search of the minimum of the multivariate objective function described in eq. (17). The model parameters were estimated by solving the given set of model equations (Table 1) using ode45 solver and GA toolbox simultaneously in MATLAB 7.8.1. The computations were performed for 1,500 generations with the function and non-linear constraint tolerances of 1e–20.

2.9 Statistical validation In order to evaluate the fitting and prediction accuracy of proposed mathematical models, correlation coefficient (R2), RMSE, and model predictive error (MPE) were employed along with the Bias (Bf) and Accuracy (Af) factors [5].

3 Results and discussion 3.1 Molecular characterization and phylogenic analysis of sludge isolate Two pure strains were isolated from the activated sludge acclimatized on glycerol in a SBR over a period of 6 months. Upon serial dilution and incubation on agar plate (over 7 days), two distinct colonies appeared as white in color and as slimy-round growth were picked up and designated as strain RER 001 and strain RER 002. Further, strain RER 002 was identified as superior (on the basis of growth and PHAs synthesis) and further screened out for its 16S rDNA-based molecular characterization. On the basis of sequence similarity of PCR amplified gene with known gene sequences of NCBI-BLAST database (>90%), strain was identified as Bacillus sp. and designated as Bacillus sp. RER002.

3.2 Kinetic study and mathematical modeling of P(3HB) production Biomass growth and P(3HB) synthesis by Bacillus sp. RER002 were described by a set of mathematical equations (given in Section 2.7) representing the consumption



of glycerol and (NH4)2SO4. The kinetic parameters related to active residual biomass growth (µmax), P(3HB) synthesis (K1 and K2), and substrate consumption (α, β, and KN) at various initial glycerol concentrations were evaluated by GA-based optimization technique using eqs (4), (7), (14), and (15), respectively. The profile of experimental and model simulated residual biomass growth, P(3HB) synthesis, and substrate consumption rates are illustrated in Fig. 1(A)–(D). The estimated kinetic parameters and its statistical validation report are represented in Tables 2 and 3, respectively. A typical sigmoidal biomass growth pattern with a short lag phase (about 2 h) following a slow exponential and stationary phases was observed. It is noteworthy that some of the Bacillus species accumulated the growth linked PHAs, i.e. further can be used as a source of carbon during the sporulation process [2, 34, 38]. The specific growth rate (µmax) of Bacillus sp. was observed to increase from 0.105 to 0.219 h−1 with the increase of initial glycerol concentration (S0) from 10 to 40 g/L. Rao et al. [38] have developed a similar

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mathematical model that fitted the experimental data for biomass growth and protease production by Bacillus circulans. They have reported the decrease in μmax from 1.314 h−1 to 0.956 h−1 with an increase in sucrose concentration from 10 to 40 g/L possibly due to the extra-cellular nature of product (protease) rather than intra-cellular nature of P(3HB). Thus, almost similar growth metabolic behavior of Bacillus was observed in both the cases. At initial glycerol concentration of 30 g/L, maximum P(3HB) concentration of 2.57 g/L corresponding to maximum active residual biomass concentration of 4.70 g/L was observed. Further, P(3HB) concentration of 2.39, 1.91, and 1.22 g/L corresponding to active residual biomass concentration of 5.1, 4.95, and 1.9 g/L, respectively, were observed at initial glycerol concentration of 40, 20, and 10 g/L, respectively. Accordingly, 82, 79, 66, and 40 of glycerol consumption were observed at initial glycerol concentration of 10, 20, 30, and 40 g/L, respectively. Upon incorporation of optimized specific growth constant (µmax) into eq. (4), the following empirical

Figure 1 (A) Comparison of experimental data and simulated values of active residual biomass (R), P(3HB) production, glycerol consumption, and (NH4)2SO4 consumption by Bacillus sp. at initial glycerol concentration of 10 g/L [experimental (symbols); simulated (lines)]. (B) Comparison of experimental data and simulated values of active residual biomass (R), P(3HB) production, glycerol consumption, and (NH4)2SO4 consumption by Bacillus sp. at initial glycerol concentration of 20 g/L [experimental (symbols); simulated (lines)]. (C) Comparison of experimental data and simulated values of active residual biomass (R), P(3HB) production, glycerol consumption, and (NH4)2SO4 consumption by Bacillus sp. at initial glycerol concentration of 30 g/L [experimental (symbols); simulated (lines)]. (D) Comparison of experimental data and simulated values of active residual biomass (R), P(3HB) production, glycerol consumption, and (NH4)2SO4 consumption by Bacillus sp. at initial glycerol concentration of 40 g/L [experimental (symbols); simulated (lines)]


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Figure 1 (Continued)



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Figure 1 (Continued)

Table 2 Estimated values of kinetic parameters used in the model equations representing active residual biomass, P(3HB), and substrate consumption Kinetic parameters

Glycerol concentration (g/L) S0 ¼ 10

S0 ¼ 20

S0 ¼ 30

S0 ¼ 40

Residual biomass R0 (g/g) Rm (g/g) µmax (h−1) P(3HB) Pmax (g/L) K1 (g/g) K2 (g/g h)

0.396 1.900 0.105

0.396 4.950 0.158

0.396 4.700 0.171

0.396 5.100 0.219

1.219 0.548 8.5 10−3

1.913 0.410 2.2 10−6

2.571 0.418 6.8 10−3

2.398 0.243 9.1 10−3

Substrates Sf (g/L) S2(0) (g/L) α (g/g) β (g/g h) KN

1.80 0.40 3.493 0.088 0.263

4.20 0.40 2.399 0.055 0.090

10.20 0.40 3.678 0.042 0.087

24.00 0.40 1.544 0.075 0.071

associations were obtained which describe the active residual biomass growth of Bacillus sp. with time: Rð10Þ ¼

Rð20Þ

0:75e0:105t 1:50 þ 0:396e0:105t

1:96e0:158t ¼ 4:55 þ 0:396e0:158t

ð23Þ

ð24Þ

1:86e0:171t 4:30 þ 0:396e0:171t

ð25Þ

2:01e0:219t 4:70 þ 0:396e0:0:219t

ð26Þ

Rð30Þ ¼

Rð40Þ ¼

where R(10), R(20), R(30), and R(40) are active residual biomass concentration (g/L) with time at initial concentration of glycerol 10, 20, 30, and 40 g/L, respectively.


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Table 3


Statistical indices used to validate the model accuracy for fitting the experimental data

Statistical

At glycerol

At glycerol

At glycerol

At glycerol

constants

conc. ¼ 10 g/L

conc. ¼ 20 g/L

conc. ¼ 30 g/L

conc. ¼ 40 g/L

R

P

S1

S2

R

P

S1

S2

R

P

S1

S2

R

P

S1

S2

R2

0.978

0.961

0.974

0.948

0.990

0.986

0.996

0.974

0.991

0.990

0.993

0.968

0.989

0.985

0.983

0.878

RMSE

0.076

0.108

0.572

0.043

0.188

0.104

0.453

0.031

0.171

0.115

0.694

0.033

0.185

0.121

0.184

0.060

Bf

0.981

0.904

0.991

1.278

1.063

1.168

0.992

0.947

1.047

1.175

0.995

1.324

1.013

1.169

0.996

1.232

Af

1.050

1.251

1.085

1.472

1.082

1.201

1.032

1.234

1.080

1.208

1.021

1.490

1.050

1.213

1.022

1.803

SEP

0.050

0.171

0.083

0.232

0.071

0.135

0.312

0.217

0.073

0.128

0.021

0.228

0.049

0.139

0.022

0.355

Note: R ¼ active residual biomass; P ¼ P(3HB); S1 ¼ Glycerol; S2 ¼ (NH4)2SO4.

The P(3HB) synthesis was observed to be growth associated and enhanced up to glycerol saturation level of 30 g/L and then, decreased further at high concentration of 40 g/L. The values of K1 constant were varied from 0.243 to 0.548 at varying initial glycerol concentrations of 10– 40 g/L and were much higher than K2 values ranged from 2.2 10−6 to 9.1 10−3. These kinetic constants (K1 and K2) revealed the nature of P(3HB) synthesis, i.e. both growth and non-growth associated and led to Type II product according to the Gaden-classification [43]. Kinetic constants α and β were derived upon fitting the proposed mathematical model representing glycerol consumption (eq. (14)) to experimental data. α-Coefficient is directly proportional to K1 and inversely proportional to the active residual biomass yield coefficient (YR=S1 ) and P (3HB) yield coefficient (YP=S1 ). At initial glycerol concentration of 30 g/L, a high value (3.678) of α-coefficient represented the maximum possible P(3HB) synthesis at this concentration. β-Coefficient (i.e. including K2, mS1 , and YP=S 1 ) represented the pattern of P(3HB) synthesis and maintenance-energy expenditure during the growth and P(3HB) synthesis. Almost equal values of β-coefficient (0.055 and 0.042 g/g h) at 20 and 30 g/L of initial glycerol concentration, respectively, represented their favorable range having less maintenance-energy expenditure. However, high maintenance-energy expenditure was observed at 10 and 40 g/L of glycerol represented by high β-coefficients of 0.088 and 0.075 g/g h, respectively. Besides, high consumption rate (KN ¼ 0.263) of (NH4)2SO4 was observed at low glycerol concentration of 10 g/L and followed by a decrease with the increase of initial glycerol concentration from 20 to 40 g/L (Table 1). Almost similar findings were reported by Khanna and Srivastava [6] and Faccin et al. [34] during their studies on the biomass growth and P(3HB) production by Ralstonia eutropha and Bacillus megaterium, respectively. These studies revealed that even the substrate was finished, the intermediate metabolite pools led the

continuous P(3HB) production in non-growth phase in addition to growth phase. The observed kinetic parameters were almost consistent with the finding of Faccin et al. [34] in which they have modeled the P (3HB) production by B. megaterium using similar type of model, i.e. Khanna and Srivastava model [Table 2].

3.3 Statistical validation of modeling ability The modeling ability of proposed mathematical models were assessed using some statistical and mathematical constants such as R2, RMSE, MPE, Bf, and Af (Table 3). A good agreement between experimental and model simulated values was observed for active residual biomass, P (3HB) synthesis, glycerol, and (NH4)2SO4 consumptions at all initial concentrations of glycerol ranged from 10 to 40 g/L, except at 40 g/L (R2 ¼ 0.878) for (NH4)2SO4 consumption. RMSE between experimental and model simulated values of active residual biomass, P(3HB) accumulation, glycerol, and (NH4)2SO4 consumptions was very low (≤0.5) at all initial glycerol concentration except glycerol consumption at 30 g/L (0.694). At the same glycerol concentration (30 g/L), the Bf (0.995) and Af (1.021) values were closed to unity indicating the less extent of model deviation from experimental data. Besides, these factors were also closed to unity for logistic and Leudeking–Piret-type models simulating the active residual biomass and glycerol consumption, respectively. However, the factors (Bf and Af) were slightly higher than unity for Leudeking–Piret model and for model representing the (NH4)2SO4 consumption. This result shows that the logistics and Leudeking–Pirettype models accurately predicted the active residual biomass growth and glycerol consumption, respectively, however, Leudeking–Piret model slightly over predicted the P(3HB) synthesis. Besides, the low values of SEP (