- University Park, Pennsylvania, United States
Ali Demirci
Penn State University, Agricultural and Biological Engineering, Faculty Member
- Professor of Agricultural and Biological Engineering at The Pennsylvania State University. Currently serving Profess... moreProfessor of Agricultural and Biological Engineering at The Pennsylvania State University. Currently serving Professor-in-Charge of the CSL Behring Fermentation Facility at Penn State.edit
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It is essential to increase microbial population during the fermentation processes. Polypropylene was modified through reactive blending for it to have anhydride groups able to covalently bind with the polycation chitosan and for it to... more
It is essential to increase microbial population during the fermentation processes. Polypropylene was modified through reactive blending for it to have anhydride groups able to covalently bind with the polycation chitosan and for it to harbor Lactococcus lactis biofilms to produce the antimicrobial peptide nisin. Biofilm development was conducted for 5 cycles of fermentation in rich and minimal media. After 5 batch cycles of fermentation for biofilm growth in rich media, the chitosan-modified polypropylene contained 6.4 ± 0.4 log(CFU/cm 2 ), whereas the polypropylene support without chitosan contained 5.9 ± 0.4 log(CFU/cm 2 ). Infrared spectroscopy and electron and atomic force microscopy analyses confirmed higher nutrient and biomass deposition on the chitosan-modified polypropylene. After 24 h of fermentation in rich media, the L. lactis biofilms grown over the chitosan-modified polypropylene support produced a maximum nisin concentration of 523.5 ± 256.7 IU/mL, while cells in suspension produced 240.6 ± 5.1 IU/mL at the same period. L. lactis biofilms grown in minimal media over the chitosan-modified polypropylene support produced a maximum nisin concentration after 24 h of incubation in rich medium of 8.5 ± 3.9 IU/mL. Through reactive blending, it is possible to prepare supports that can harbor biofilms able to significantly increase the production of metabolites during fermentations.
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Polypropylene was modified to contain chitosan and evaluate its ability to generate Lactobacillus casei biofilms and their lactic acid production. Biofilm formation was carried out in either rich or minimal media. The chitosan-modified... more
Polypropylene was modified to contain chitosan and evaluate its ability to generate Lactobacillus casei biofilms and their lactic acid production. Biofilm formation was carried out in either rich or minimal media. The chitosan-modified polypropylene harbored ~ 37% more cells than the control polypropylene. The biofilms from the chitosan-modified polypropylene grown in rich medium produced ~ 2 times more lactic acid after 72 h of incubation than the control suspended cells. There was no significant difference in the production of lactic acid after 72 h by L. casei biofilms on the chitosan-modified polypropylene grown in minimal media as compared with cells in suspension after 48 h and 72 h of incubation. Infrared spectroscopy confirmed higher deposition of nutrients and biomass on the chitosan-modified polypropylene as compared to the chitosan-free polypropylene. Electron and atomic force microscopy confirmed thicker biofilms when rich media were used to grow them as compared to minimal medium.
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Honey has naturally low levels of microorganisms due to its low water content and high concentration of sugars. However, it has been known to contain the spores of yeast, mold, and bacteria resulting in spoilage of the product.... more
Honey has naturally low levels of microorganisms due to its low water content and high concentration of sugars. However, it has been known to contain the spores of yeast, mold, and bacteria resulting in spoilage of the product. Clostridium botulinum, is associated with honey and is known to cause a disease called botulism. Heat pasteurization, pressure treatment, and irradiation have all been studied as methods of killing the spores, but have been found lacking. Pulsed Ultraviolet (UV)-Light Sterilization is a novel processing method used for microbial inactivation. For the experimentation, spores of C. sporogenes were prepared from cooked meat medium cultures grown in an anaerobic jar for 7 days at 37oC. Honey was inoculated with 0.1 ml of C. sporogenes spore suspension per 20 g honey, and mixed well. Pulsed light was applied to the inoculated honey using the SteriPulse XL® 3000 Pulsed Light Sterilization System provided by NASA Commercial Food Technology Center. The following para...
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Distillers’ dried grains with solubles (DDGS) is a by-product of dry-mill corn ethanol production comprising a high nutritional value due to residual fiber, protein, and lipid contents. The fiber content of DDGS is high enough to be... more
Distillers’ dried grains with solubles (DDGS) is a by-product of dry-mill corn ethanol production comprising a high nutritional value due to residual fiber, protein, and lipid contents. The fiber content of DDGS is high enough to be considered a valuable source for the production of hydrolytic enzymes, such as cellulase and xylanases, which can be used for hydrolysis of lignocellulosic feedstock during ethanol production. The DDGS-based medium prepared after acid hydrolysis provides adequate sugars for enzyme production, while additional macronutrients, such as salts and nitrogen sources, can enhance the enzyme production. Therefore, this study was undertaken to evaluate the effect of salts (KH2PO4, CaCl2·2H2O, MgSO4·7H2O, FeSO4·7H2O, CoCl2·6H2O, and MnSO4·H2O), peptone, and yeast extract on enzyme secretion by four different Aspergillus niger strains and to optimize the nitrogen source for maximum enzyme production. Yeast extract improved the cellulase production (0.38 IU/ml) for A. niger (NRRL 1956) as compared to peptone (0.29 IU/ml). However, maximum cellulase productions of 0.42 IU/ml and 0.45 IU/ml were obtained by A. niger (NRRL 330) and A. niger (NRRL 567), respectively, in presence of ammonium sulfate. The optimized nitrogen amounts resulted in a significant increase in the cellulase production from 0.174 to 0.63 IU/ml on day 9 of the fermentation with A. niger (NRRL 330). The composite model improved both cellulase and xylanase production. In conclusion, the optimization of all three nitrogen sources improved both cellulase and xylanase production in the DDGS-based media.
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Plastic composite supports containing 50% agricultural products (oat hulls, soybean hulls, yeast extract, soybean flour, dried bovine erythrocytes, bovine albumin, and/or mineral salts) and 50% (wt/wt) polypropylene were produced by... more
Plastic composite supports containing 50% agricultural products (oat hulls, soybean hulls, yeast extract, soybean flour, dried bovine erythrocytes, bovine albumin, and/or mineral salts) and 50% (wt/wt) polypropylene were produced by high-temperature twin-screw extrusion. The research employed two half sets of a five-factorial fractional design (2(5 - 1)) to evaluate the effects of different agricultural components on the properties of the plastic composite supports and to select the best plastic composite support formulation for lactic acid fermentation. The biofilm population was affected by the contact angle and relative hydrophobicity of the supports (r = 0.79 to 0.82). Lactic acid was produced by the suspended cells (r = 0.96) and the biofilm on the plastic composite support discs (r = 0.85). Incorporation of yeast extract into plastic composite supports enhanced growth of free and attached cells in minimal medium (P < 0.0001). The presence of soybean hulls, yeast extract, or...
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Novel solid supports, consisting of polypropylene blended with various agricultural materials (pp composite), were evaluated as supports for pure- and mixed-culture continuous lactic acid fermentations in biofilm reactors. Streptomyces... more
Novel solid supports, consisting of polypropylene blended with various agricultural materials (pp composite), were evaluated as supports for pure- and mixed-culture continuous lactic acid fermentations in biofilm reactors. Streptomyces viridosporus T7A (ATCC 39115) was used to form a biofilm, and Lactobacillus casei subsp. rhamnosus (ATCC 11443) was used for lactic acid production. For mixed-culture fermentations, a 15-day continuous fermentation of S. viridosporus was performed initially to establish the biofilm. The culture medium was then inoculated with L. casei subsp. rhamnosus. For pure-culture fermentation, L. casei subsp. rhamnosus was inoculated directly into the reactors containing sterile pp composite chips. The biofilm reactors containing various pp composite chips were compared with a biofilm reactor containing pure polypropylene chips and with a reactor containing a suspension culture. Continuous fermentation was started, and each flow rate (0.06 to 1.92 ml/min) was he...
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Abstract. Phenylpyruvic acid (PPA) is an alpha keto acid, which has the potential to be used in monogastric animals' diets to prevent excessive nitrogen accumulation in their manure and adverse effects on the environment. PPA is also... more
Abstract. Phenylpyruvic acid (PPA) is an alpha keto acid, which has the potential to be used in monogastric animals' diets to prevent excessive nitrogen accumulation in their manure and adverse effects on the environment. PPA is also used as a flavor enhancer in the food industry and for kidney patients' diets to decrease urea accumulation in the body. However, the high production cost of PPA is limiting the use for these applications. Therefore, this project was undertaken to enhance PPA production by submerged fermentation. Firstly, microorganism selection was performed and Proteus vulgaris was determined to be the best strain for PPA production among four evaluated. Growth parameters (temperature, pH, and aeration) and concentrations of medium ingredients (glucose, yeast extract, and phenylalanine) were optimized in 2-L bioreactors by using a Box-Behnken design. The optimum temperature, pH, and aeration levels were determined to be 34.5oC, 5.12, and 0.5 vvm, respectively. Concentrations for optimizing the fermentation medium for glucose, yeast extract, and phenylalanine were 119, 3.68 , and 14.84 g/L, respectively. Under these optimum conditions, 1349 mg/L PPA was produced by Proteus vulgaris in submerged fermentation. This study demonstrated about a 3-fold improvement compared to shake flask fermentation (358 mg/L PPA).
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Carob pod has been widely used in food industry as a feed for livestock and human consumption, including sweets, biscuits and processed pekmez; a Turkish traditional carob concentrate and thus attracted the attention of producers with... more
Carob pod has been widely used in food industry as a feed for livestock and human consumption, including sweets, biscuits and processed pekmez; a Turkish traditional carob concentrate and thus attracted the attention of producers with increasing market value. With their suitable content, carob extract are known to be utilized by using fermentation methods. The effect of various fermentation parameters such as pH, media content and inoculum size were evaluated for ethanol fermentation in carob extract. Also, in order to determine economically appropriate nitrogen sources, four different nitrogen sources were evaluated. The optimum extraction condition for carob extract was determined to be 80°C, 2h in 1:4 dilution rate (fruit: water ratio) according to the result of response surface analysis (115.3 g/L). When the fermentation with pH at 5.5 was applied, the final ethanol concentration and production rates were 42.6 g/L and 3.37 g/L/h, respectively, which were higher than using an uncontrolled pH. Among inocula sizes of 1-5%, 3% was determined as the best inoculum size. The maximum production rate and final ethanol concentration were 3.48 g/L/h and 44.51%, respectively, with an alternative nitrogen source of Meat-Bone Meal. Overall, this study suggested that carob extract can be utilized for production of ethanol in order to meet the demands of renewable energy.
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Research Interests: Water, Poultry Science, Biology, Medicine, Animal Production, and 15 moreFood Microbiology, Salmonella enteritidis, Escherichia coli, Animals, Temperature, Disinfection, Hydrogen Peroxide, Electrolysis, Eggs, Chickens, Time Factors, Oxford university, Food Sciences, Detergents, and Hydrogen-Ion Concentration
Novel plastic composite supports (PCS), composed of equal parts polypropylene and agricultural products, were evaluated as supports for biofilm production in the bioreactor. Various reduced nitrogen content media (2.5 – 10 g/L yeast... more
Novel plastic composite supports (PCS), composed of equal parts polypropylene and agricultural products, were evaluated as supports for biofilm production in the bioreactor. Various reduced nitrogen content media (2.5 – 10 g/L yeast extract and 2.5 – 10 g/L peptone) were tested with equal parts of PCS rings and discs during 48-hr repeated-batch fermentations for nisin production and compared to a suspended-cell culture during pH controlled (pH 6.8) and pH uncontrolled fermentations. Also, fed-batch fermentation with glucose addition was attempted to prevent glucose depletion during fermentation. Results demonstrated that there was no significant increase in nisin production or productivity rates using PCS with any reduced content media over the suspended-cell control during either pH condition. Attempts to increase glucose concentration in the fed-batch fermentations slightly improved nisin production. The metabolism of nisin production and possible nisin absorption by L. lactis cel...
The lignocellulosic biomass is comprised of three major components: cellulose, hemicellulose, and lignin. Among these three, cellulose and hemicellulose were already used for the generation of simple sugars and subsequent value-added... more
The lignocellulosic biomass is comprised of three major components: cellulose, hemicellulose, and lignin. Among these three, cellulose and hemicellulose were already used for the generation of simple sugars and subsequent value-added products. However, lignin is the least applied material in this regard because of its complex and highly variable nature. Regardless, lignin is the most abundant material, and it can be used to produce value-added products such as lignin-modifying enzymes (LMEs), polyhydroxyalkanoates (PHAs), microbial lipids, vanillin, muconic acid, and many others. This review explores the potential of lignin as the microbial substrate to produce such products. A special focus was given to the different types of lignin and how each one can be used in different microbial and biochemical pathways to produce intermediate products, which can then be used as the value-added products or base to make other products. This review paper will summarize the effectiveness of ligni...
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The usage of lignocellulosic biomass in energy production for biofuels and other value-added products can extensively decrease the carbon footprint of current and future energy sectors. However, the infrastructure in the processing of... more
The usage of lignocellulosic biomass in energy production for biofuels and other value-added products can extensively decrease the carbon footprint of current and future energy sectors. However, the infrastructure in the processing of lignocellulosic biomass is not well-established as compared to the fossil fuel industry. One of the bottlenecks is the production of the lignocellulolytic enzymes. These enzymes are produced by different fungal and bacterial species for degradation of the lignocellulosic biomass into its reactive fibers, which can then be converted to biofuel. The selection of an ideal feedstock for the lignocellulolytic enzyme production is one of the most studied aspects of lignocellulolytic enzyme production. Similarly, the fermentation enhancement strategies for different fermentation variables and modes are also the focuses of researchers. The implementation of fermentation enhancement strategies such as optimization of culture parameters (pH, temperature, agitati...
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Menaquinone-7 (MK-7) is the key form of vitamin K used as a dietary supplement and its production revolves around Bacillus subtilis natto. Current fermentation strategies, which suggest static fermentations without aeration and agitation,... more
Menaquinone-7 (MK-7) is the key form of vitamin K used as a dietary supplement and its production revolves around Bacillus subtilis natto. Current fermentation strategies, which suggest static fermentations without aeration and agitation, can be problematic for large scale MK-7 production due to biofilm formation. The use of biofilm reactors, therefore, is proposed in the present study, which could utilize both agitation and aeration without interrupting MK-7 secretion. In this study, biofilm reactors were constructed using the selected plastic composite support (PCS) and B. subtilis natto strain for MK-7 production. Using response surface methodology (RSM), optimum growth parameters including temperature, pH, and agitation were determined in a glycerol-based medium. Results were presented in a statistical model (R 2 = 0.90), leading to optimum growth conditions of temperature (35 °C), agitation (200 rpm) and pH (6.58). Model-predicted MK-7 concentration was validated and MK-7 conce...
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Menaquinone-7 (MK-7), a subtype of vitamin K, has received a significant attention due to its effect on improving bone and cardiovascular health. Current fermentation strategies, which involve static fermentation without aeration or... more
Menaquinone-7 (MK-7), a subtype of vitamin K, has received a significant attention due to its effect on improving bone and cardiovascular health. Current fermentation strategies, which involve static fermentation without aeration or agitation, are associated with low productivity and scale-up issues and hardly justify the commercial production needs of this vitamin. Previous studies indicate that static fermentation is associated with pellicle and biofilm formations, which are critical for MK-7 secretion while posing significant operational issues. Therefore, the present study is undertaken to evaluate the possibility of using a biofilm reactor as a new strategy for MK-7 fermentation. Bacillus species, namely, Bacillus subtilis natto, Bacillus licheniformis, and Bacillus amyloliquifaciens as well as plastic composite, supports (PCS) were investigated in terms of MK-7 production and biofilm formation. Results show the possibility of using a biofilm reactor for MK-7 biosynthesis. Baci...
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Menaquinone-7, a highly valuable member of the vitamin K series, has significant effects on preventing osteoporosis and cardiovascular disease besides its positive effects on blood coagulation. In this review, chemical and biological... more
Menaquinone-7, a highly valuable member of the vitamin K series, has significant effects on preventing osteoporosis and cardiovascular disease besides its positive effects on blood coagulation. In this review, chemical and biological aspects of menaquinone-7 are briefly summarized followed by a critical review on upstream and downstream processing developments for its production and recovery, including solid versus liquid fermentations, static versus agitated fermentations and online versus post-production recovery. Latest research outcomes for improving industrial scale production of menaquinone-7 are summarized and recommendations are given for areas of future research.
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Bacterial cellulose (BC) can be grown into any desired shape such as pellicles, pellets, and spherelike balls, depending on the cultivation method, additives, and cell population. In this study, Acetobacter xylinum (ATCC 700178) was grown... more
Bacterial cellulose (BC) can be grown into any desired shape such as pellicles, pellets, and spherelike balls, depending on the cultivation method, additives, and cell population. In this study, Acetobacter xylinum (ATCC 700178) was grown in the production medium with different concentrations of carboxylmethylcellulose (CMC) and were evaluated for BC production by using a PCS biofilm reactor. The results demonstrated that BC production was enhanced to its maximum (∼13 g/L) when 1.5% of CMC was applied, which was 1.7-fold higher than the result obtained from control culture. The major type of the produced BC was also switched from BC pellicle to small pellets. The ratio of BC pellets in suspension increased from 0 to 93%. Fourier transform infrared (FTIR) spectroscopy demonstrated that CMC was incorporated into BC during fermentation and resulted in the decreased crystallinity and crystal size. The X-ray diffraction (XRD) patterns indicated that CMC-BC exhibited both lower crystallinity (80%) and crystal size (4.2 nm) when compared with control samples (86% and 5.3 nm). The harvested BC was subjected to paper formation and its mechanical strength was determined. Dynamic mechanical analysis (DMA) results demonstrated that BC paper sheets exhibited higher tensile strength and Young&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s modulus when compared with regular paper.
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To evaluate the efficacy of diffusion magnetic resonance imaging and compare with cerebrospinal fluid (CSF) flow imaging in patients with hydrocephalus before and after treatment. Twenty patients with hydrocephalus (group 1, pediatric,... more
To evaluate the efficacy of diffusion magnetic resonance imaging and compare with cerebrospinal fluid (CSF) flow imaging in patients with hydrocephalus before and after treatment. Twenty patients with hydrocephalus (group 1, pediatric, with primary aqueductal stenosis, n = 10; group 2, adult, with normal-pressure hydrocephalus, n = 10) and 20 age-matched healthy subjects that served as controls were examined. Cerebrospinal fluid flow velocity interval was calculated as the mean absolute values of the peak craniocaudal velocity and caudocranial velocity on CSF flow measurements. On diffusion magnetic resonance imaging, apparent diffusion coefficient (ADC) values from 8 regions were evaluated. The decrease in ADC values after treatment was significant in both groups (P &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; 0.001 for both). Preoperative mean CSF flow velocity interval value was significantly lower in group 1 and significantly higher than postoperative and control group values in group 2 (P &amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt; 0.001 for all). The ADC values increase in hydrocephalus and decrease significantly after treatment. Preoperative ADC value may serve as baseline, and the change in ADC may be an indicator of response to treatment and CSF flow measurements.
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ABSTRACT Abstract Research pertaining to the evaluation of novel processing technologies has been on the rise as the number of notable foodborne outbreaks continues to garner the publics&#39; attention. Ultra-violet (UV) light has... more
ABSTRACT Abstract Research pertaining to the evaluation of novel processing technologies has been on the rise as the number of notable foodborne outbreaks continues to garner the publics&#39; attention. Ultra-violet (UV) light has been used for almost a century for the sanitization of water and surfaces. Pulsed UV-light involves the application of UV-light in quick bursts, which increases the instantaneous energy received by the product. The goal of this research was to characterize pulsed UV-light in terms of penetration depth, microbial inactivation, and temperature increase. Two different gelled materials, agar and whey protein isolate, were studied based on their opaqueness. Sample of the gel were taken as 2 mm thick sections and analyzed for the inactivation of E. coli K12, temperature increase, and amount of UV radiation received. The inactivation curves obtained indicated that the relationship between energy dose and inactivation was non-linear and the Weibull model was used to estimate these inactivations. Three approaches were undertaken to determine the model parameters. Each model had its advantages and disadvantages but in all three it was observed that broadband energy was not a suitable predictor of microbial inactivation.
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Lysozyme is a lytic enzyme, which has antimicrobial activity. It has been used for food and pharmaceutical applications. This study was undertaken to evaluate fed-batch and continuous fermentations for the human lysozyme production in... more
Lysozyme is a lytic enzyme, which has antimicrobial activity. It has been used for food and pharmaceutical applications. This study was undertaken to evaluate fed-batch and continuous fermentations for the human lysozyme production in biofilm reactor. Results showed that addition of lactose the mid-log phase to make the concentration back to the initial level generates higher lysozyme production (177 U/ml) compared with lactose addition in late-log phase (174 U/ml) (p < 0.05). Moreover, fed-batch fermentation with glucose as initial carbon source and continuous addition of lactose with 0.6 ml/min for 10 h demonstrated significantly higher lysozyme production (187 U/ml) compared to the batch fermentation (173 U/ml) (p < 0.05). In continuous fermentation, biofilm reactor provided significantly higher productivity (7.5 U/ml/h) compared to the maximum productivity in suspended cell bioreactor (4 U/ml/h), because the biofilm reactor provided higher cell density at higher dilution r...
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Lignocellulosic materials that are the most abundant plant biomass in the world have the potential to become sustainable sources of the produced value added products. Tea processing waste (TPW) is a good lignocellulosic source to produce... more
Lignocellulosic materials that are the most abundant plant biomass in the world have the potential to become sustainable sources of the produced value added products. Tea processing waste (TPW) is a good lignocellulosic source to produce the value added products from fermentable sugars (FSs). Therefore, the present study is undertaken to produce FSs by using ultrasound-assisted dilute acid (UADA) and dilute acid (DA) hydrolysis of TPW followed by enzymatic hydrolysis. UADA hydrolysis of TPW was optimized by response surface methodology (RSM) at maximum power (900 W) for 2 h. The optimum conditions were determined as 50ºC, 1:6 (w/v) solid: liquid ratio, and 1% (w/v) DA concentration, which yielded 20.34 g/L FS concentration. Furthermore, its DA hydrolysis was also optimized by using RSM for comparison and the optimized conditions were found as 120ºC, 1:8 solid: liquid ratio and 1% acid concentration, which produced 25.3 g/L FS yield. Even though the produced sugars with UADA hydrolys...
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Lactic acid has a wide industrial application area and can be produced by fungal strains. However, excessive bulk growth form of fungi during the fermentations is a major problem, which limits the fermentation performance. Microparticles... more
Lactic acid has a wide industrial application area and can be produced by fungal strains. However, excessive bulk growth form of fungi during the fermentations is a major problem, which limits the fermentation performance. Microparticles are excellent tools to prevent bulk fungal growth and provide homogenized fermentation broth to increase uniformity and the prediction performance of the models. Therefore, in this study, addition of aluminum oxide and talcum microparticles into fermentations was evaluated to enhance the production of lactic acid by Rhizopus oryzae. The results showed that the bulk fungal growth was prevented and the lactic acid concentration increased from 6.02 to 13.88 and 24.01 g/L, when 15 g/L of aluminum oxide or 10 g/L of talcum was used, respectively, in the shake-flask fermentations. Additionally, substrate concentration, pH, and agitation were optimized in the bioreactors using response surface methodology, and optimum values were determined as 126 g/L of glucose, 6.22 pH, and 387 rpm, respectively. Under these conditions, lactic acid production further increased to 75.1 ± 1.5 g/L with 10 g/L of talcum addition. Also, lactic acid production and glucose consumption in the batch fermentation were successfully modeled with modified Gompertz model and modified logistic model. RMSE and MAE values for lactic acid production were calculated as 2.279 and 1.498 for the modified Gompertz model; 3.6 and 4.056 for the modified logistic model. Additionally, modified logistic model predicted glucose consumption with -2.088 MAE and 2.868 RMSE, whereas these values were calculated as 2.035 and 3.946 for the modified Gompertz model.