Galaktooligosakkarit Sentezinin Matematiksel Modellenmesi: Aspergillus oryzae kaynaklı β-Galaktosidaz Kinetiğine İlişkin Bilgiler
Öz
Bu çalışmanın amacı, elde edilen deneysel verileri literatürde tanımlanmış laktoz hidrolizi ve galaktooligosakkaritlerin sentezi için belirlenmiş transgalaktosilasyon mekanizmalarına dayalı matematiksel bir modele uyumlu hale getirmektir. Galaktooligosakkaritler, laktozun β-galaktosidaz katalizli transgalaktosilasyon reaksiyonları aracılığıyla sentezlenen özel bifidojenik faktörler olarak bilinirler. Galaktooligosakkarit sentez mekanizmasının, aynı nükleofillere ve substratlara sahip hidroliz ve transferaz reaksiyonlarının eş zamanlı olarak gerçekleşmesi nedeniyle matematiksel modellemesi zorluklar içermektedir. Bu nedenle araştırmacılar, meydana gelen ara reaksiyonları veya glukoz ve galaktozun inhibe edici etkilerini göz ardı ederek mekanizmayı basitleştirmeye çalıştılar. Bu çalışma, reaksiyon mekanizmasının karmaşıklığını göz önünde bulundurarak doğruluk ile uygulanabilirlik arasında denge sağlamak amacıyla çeşitli kinetik modellerin uygunluğunu değerlendirmektedir. Sürekli karıştırmalı tank reaktörü kullanılarak elde edilen deneysel veriler, glukoz ve galaktoz inhibitörlerini içeren modifikasyonlarla kinetik modellere (Model A ve B) adapte edilmiştir. COPASI yazılımı, model denklemleri test etmek amacıyla kullanılmıştır. Toplam 8 adet model, 6 tekrarlı deneysel veri setinde (sıcaklık:45°C, laktoz konsantrasyonu:18.25 Briks ve enzim konsantrasyonu:10 ünite g laktoz çözeltisi-1) uygunluğu test edilmiştir. Çözümleme sırasıyla “random research” ve “particle swarm” algoritmaları kullanılarak gerçekleştirilmiştir. Model değerlendirmeleri, glukoz ve galaktoz inhibitörlerini içeren Model B'nin deneysel ve simüle veriler arasında en yakın uyumu sağladığını göstermiştir. Çalışma, glukoz ve galaktozun galaktooligosakkarit sentezi verimliliği üzerindeki inhibitör etkilerinin önemini ortaya koymuştur. Glukoz ve galaktoz inhibitörlerini içeren Model B, galaktooligosakkarit veriminin öngörülmesi ve laktoz dönüşümü, üretkenlik, ürün bileşimi gibi parametreler üzerindeki önemli etkisi nedeniyle A. oryzae kaynaklı β-galaktosidaz kinetiğinin daha iyi anlaşılmasına katkı sağlayacak önemli bir araçtır. Çalışma sonucunda elde edilen bulgular, galaktooligosakkarit üretim verimliliğini artırmak için optimizasyon stratejilerine rehberlik edecek ve enzimatik galaktooligosakkarit sentezi konusunda literatüre katkı sağlayacaktır.
Anahtar Kelimeler
Kinetik Transgalaktosilasyon Hidroliz Galaktooligosakkaritler A. oryzae
Etik Beyan
Bu çalışma için etik kuruldan izin alınmasına gerek yoktur.
Destekleyen Kurum
This research received partial support from the Scientific Research Projects Fund of Istanbul Technical University (ITUBAP, Project ID: MDK-2017-40556).
Proje Numarası
ITUBAP, Project ID: MDK-2017-40556
Teşekkür
The β-galactosidase from Aspergillus oryzae was generously provided by Enzyme Development Corporation (EDC), New York, USA.
Kaynakça
- Bakken, A. P., Hill Jr, C. G. and Amundson, C. H. (1992). Hydrolysis of lactose in skim milk by immobilized β‐galactosidase (Bacillus circulans). Biotechnology and Bioengineering, 39(4): 408-417.
- Bates, D. M. and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. Wiley, New York, U.S.A.
- Boon, M., Janssen, A. and Van der Padt, A. (1999). Modelling and parameter estimation of the enzymatic synthesis of oligosaccharides by β‐galactosidase from Bacillus circulans. Biotechnology and Bioengineering, 64(5): 558-567.
- Boon, M., Janssen, A. and Van‘t Riet, K. (2000). Effect of temperature and enzyme origin on the enzymatic synthesis of oligosaccharides. Enzyme and Microbial Technology, 26(2-4): 271-281.
- Chen, C. W., Ou-Yang, C. C. and Yeh, C. W. (2003). Synthesis of galactooligosaccharides and transgalactosylation modeling in reverse micelles. Enzyme and Microbial Technology, 33(4): 497-507.
- Cheng, C. C., Yu, M. C., Cheng, T. C., Sheu, D. C., Duan, K. J. and Tai, W. L. (2006). Production of high-content galacto-oligosaccharide by enzyme catalysis and fermentation with Kluyveromyces marxianus. Biotechnology letters, 28(11): 793-797.
- Cinar, K., Gunes, G. and Gulec, H. A. (2020). Enzymatic synthesis of prebiotic carbohydrates from lactose: Kinetics and optimization of transgalactosylation activity of β‐galactosidase from Aspergillus oryzae. Journal of Food Process Engineering. 43(8): e13435.
- Costa, R. S., and Vinga, S. (2016). Control analysis of the impact of allosteric regulation mechanism in an Escherichia coli kinetic model: Application to serine production. Biochemical Engineering Journal, 110: 59-70.
- Freitas, F. F., Marquez, L. D., Ribeiro, G. P., Brandão, G. C., Cardoso, V. L. and Ribeiro, E. J. (2011). A comparison of the kinetic properties of free and immobilized Aspergillus oryzae β-galactosidase. Biochemical Engineering Journal, 58: 33-38.
- González-Delgado, I., López-Muñoz, M. J., Morales, G. and Segura, Y. (2016). Optimisation of the synthesis of high galacto-oligosaccharides (GOS) from lactose with β-galactosidase from Kluyveromyces lactis. International Dairy Journal, 61: 211-219.
- Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P. and Kummer, U. (2006). COPASI-a complex pathway simulator. Bioinformatics, 22(24): 3067-3074.
- Hsu, C., Lee, S. and Chou, C. (2007). Enzymatic production of galactooligosaccharides by β-galactosidase from Bifidobacterium longum BCRC 15708. Journal of Agricultural and Food Chemistry, 55(6): 2225-2230.
- Huber, R., Kurz, G. and Wallenfels, K. (1976). A quantitation of the factors which affect the hydrolase and transgalactosylase activities of β-galactosidase (E. coli) on lactose. Biochemistry, 15(9): 1994-2001.
- Huerta, L. M., Vera, C., Guerrero, C., Wilson, L. and Illanes, A. (2011). Synthesis of galacto-oligosaccharides at very high lactose concentrations with immobilized β-galactosidases from Aspergillus oryzae. Process biochemistry, 46(1): 245-252.
- Iqbal, M.W., Riaz, T., Mahmood, S., Liaqat, H., Mushtaq, A., Khan, S., Amin, S. and Qi, X. (2023). Recent advances in the production, analysis, and application of galacto-oligosaccharides. Food Reviews International, 39(8): 5814-5843.
- Iwasaki, K., Nakajima, M. and Nakao, S. (1996). Galacto-oligosaccharide production from lactose by an enzymic batch reaction using β-galactosidase. Process biochemistry, 31(1): 69-76.
- Jenab, E., Omidghane, M., Mussone, P., Armada, D. H., Cartmell, J. and Montemagno, C. (2018). Enzymatic conversion of lactose into galacto-oligosaccharides: The effect of process parameters, kinetics, foam architecture, and product characterization. Journal of Food Engineering, 222: 63-72.
- Kim, C. S., Ji, E. S. and Oh, D. K. (2004). A new kinetic model of recombinant β-galactosidase from Kluyveromyces lactis for both hydrolysis and transgalactosylation reactions. Biochemical and Biophysical Research Communications, 316(3): 738-743.
- Manucci, F. (2009). Enzymatic synthesis of galactooligosaccharides from whey permeate (M.S. Thesis). Dublin Institute of Technology, Dublin, Ireland.
- Mueller, I., Kiedorf, G., Runne, E., Seidel-Morgenstern, A. and Hamel, C. (2018). Synthesis, kinetic analysis and modelling of galacto-oligosaccharides formation. Chemical Engineering Research and Design, 130: 154-166.
- Neri, D. F., Balcão, V. M., Costa, R. S., Rocha, I. C., Ferreira, E. M., Torres, D. P., Rodrigues, L. R., Carvalho Jr, L. B. and Teixeira, J. A. (2009). Galacto-oligosaccharides production during lactose hydrolysis by free Aspergillus oryzae β-galactosidase and immobilized on magnetic polysiloxane-polyvinyl alcohol. Food Chemistry, 115(1): 92-99.
- Osman, A. (2016). Synthesis of Prebiotic Galacto-Oligosaccharides: Science and Technology. In: Probiotics, Prebiotics, and Synbiotics, Eds: Watson, R.R., Preedy, V.R. Academic Press, U.S.A.
- Özdinç, N. and Velioğlu, H.M. (2022). The Production of Crude Invertase From The By-products of Baker’s Yeast (Saccharomyces cerevisiae) Factory. Journal of Tekirdag Agricultural Faculty, 19(2): 456-464.
- Palai, T. and Bhattacharya, P. K. (2013). Kinetics of lactose conversion to galacto-oligosaccharides by β-galactosidase immobilized on PVDF membrane. Journal of Bioscience and Bioengineering, 115(6): 668-673.
- Palai, T., Kumar, A. and Bhattacharya, P. K. (2016). Enzyme immobilization/bioconjugation in producing galactio-oligosaccharidies from lactose: developments of kinetic models and bio-reactors. Materials Today: Proceedings, 3(10): 3568-3586.
- Palai, T., Mitra, S. and Bhattacharya, P. K. (2012). Kinetics and design relation for enzymatic conversion of lactose into galacto-oligosaccharides using commercial grade β-galactosidase. Journal of bioscience and bioengineering, 114(4): 418-423.
- Palai, T., Singh, A. K. and Bhattacharya, P. K. (2014). Enzyme, β-galactosidase immobilized on membrane surface for galacto-oligosaccharides formation from lactose: kinetic study with feed flow under recirculation loop. Biochemical Engineering Journal, 88: 68-76.
- Rodriguez-Fernandez, M., Cardelle-Cobas, A., Villamiel, M. and Banga, J. R. (2011). Detailed kinetic model describing new oligosaccharides synthesis using different β-galactosidases. Journal of biotechnology, 153(3-4): 116-124.
- Sanz-Valero, J. I. (2009). Production of galacto-oligosaccharides from lactose by immobilized b-galactosidase and posterior chromatographic separation (Ph. D. Thesis). The Ohio State University, Ohio, U.S.A.
- Shin, H. J. and Ji-Won, Y. (1998). Enzymatic production of galactooligosaccharide by Bullera singularis beta-galactosidase. Journal of microbiology and biotechnology, 8(5): 484-489.
- Tanaka, Y., Kagamiishi, A., Kiuchi, A. and Horiuchi, T. (1975). Purification and properties of β-galactosidase from Aspergillus oryzae. The Journal of Biochemistry, 77(1): 241-247.
- Uran, H., Sanlidere Aloglu, H. and Cetin, B. (2020). Determining of Some Quality Properties of Sucuks Produced by Lactulose Addition. Journal of Tekirdag Agricultural Faculty, 18(1): 58-70.
- Urrutia, P., Rodriguez-Colinas, B. R., Fernandez-Arrojo, L. A., Ballesteros, A. O., Wilson, L., Illanes, A. and Plou, F. J. (2013). Detailed analysis of galactooligosaccharides synthesis with β-galactosidase from Aspergillus oryzae. Journal of Agricultural and Food Chemistry, 61(5): 1081-1087.
- Vera, C., Guerrero, C. and Illanes, A. (2011). Determination of the transgalactosylation activity of Aspergillus oryzae β-galactosidase: effect of pH, temperature, and galactose and glucose concentrations. Carbohydrate Research, 346(6): 745-752.
- Warmerdam, A., Boom, R. M. and Janssen, A. E. (2013). β-galactosidase stability at high substrate concentrations. Springerplus, 2(1): 402.
- Yin, H., Bultema, J. B., Dijkhuizen, L. and van Leeuwen, S. S. (2017). Reaction kinetics and galactooligosaccharide product profiles of the β-galactosidases from Bacillus circulans, Kluyveromyces lactis and Aspergillus oryzae. Food chemistry, 225: 230-238.
Mathematical Modelling of Galactooligosaccharides Synthesis: Insights into Aspergillus oryzae Derived β-Galactosidase Kinetics
Öz
The objective of this study was to adapt experimental data with a mathematical model based on transgalactosylation mechanisms identified in the literature for the synthesis of galactooligosaccharides and lactose hydrolysis. Galactooligosaccharides, synthesized from lactose through β-galactosidase-catalyzed transgalactosylation reactions, are acknowledged as specific bifidogenic factors among prebiotic carbohydrates. Modelling galactooligosaccharide synthesis is challenging due to simultaneous hydrolysis and transferase reactions with identical nucleophiles and substrates. Therefore, researchers tried to simplify the mechanism by ignoring intermediate reactions or inhibitory effects of glucose and galactose. This study explored various kinetic models, considering the complexity of the reaction mechanism and balancing accuracy with feasibility. Experimental data from galactooligosaccharide synthesis using a continuous stirred tank reactor was adapted to kinetic models (Models A and B) with modifications, incorporating glucose and galactose inhibitions. The COPASI software was used for testing fitness of reaction models. Eight models were evaluated for their suitability, utilizing six replicated experimental datasets under specific reaction conditions, including a temperature of 45°C, lactose concentration of 18.25°Brix, and enzyme concentration of 10-unit g lactose solution-1. The analysis was conducted using the "random research" and "particle swarm" algorithms. Model evaluations revealed that Model B, augmented with glucose and galactose inhibitions, provided the closest alignment between experimental and simulated data. The study underscored the significance of glucose and galactose impacts on galactooligosaccharide synthesis efficiency. The Model B, with addition of glucose and galactose inhibitions, emerged as a valuable tool for predicting galactooligosaccharide yield, contributing to a deeper understanding of A.oryzae-derived β-galactosidase kinetics due to its significant influence on parameters such as productivity, conversion of lactose, and composition of product. The findings will guide optimization strategies for enhanced galactooligosaccharide production efficiency, advancing knowledge in enzymatic galactooligosaccharide synthesis.
Anahtar Kelimeler
Kinetics Transgalactosylation Hydrolysis Galactooligosaccharides A. oryzae
Etik Beyan
There is no need to obtain permission from the ethics committee for this study.
Destekleyen Kurum
This research received partial support from the Scientific Research Projects Fund of Istanbul Technical University (ITUBAP, Project ID: MDK-2017-40556).
Proje Numarası
ITUBAP, Project ID: MDK-2017-40556
Teşekkür
The β-galactosidase from Aspergillus oryzae was generously provided by Enzyme Development Corporation (EDC), New York, USA.
Kaynakça
- Bakken, A. P., Hill Jr, C. G. and Amundson, C. H. (1992). Hydrolysis of lactose in skim milk by immobilized β‐galactosidase (Bacillus circulans). Biotechnology and Bioengineering, 39(4): 408-417.
- Bates, D. M. and Watts, D. G. (1988). Nonlinear Regression Analysis and Its Applications. Wiley, New York, U.S.A.
- Boon, M., Janssen, A. and Van der Padt, A. (1999). Modelling and parameter estimation of the enzymatic synthesis of oligosaccharides by β‐galactosidase from Bacillus circulans. Biotechnology and Bioengineering, 64(5): 558-567.
- Boon, M., Janssen, A. and Van‘t Riet, K. (2000). Effect of temperature and enzyme origin on the enzymatic synthesis of oligosaccharides. Enzyme and Microbial Technology, 26(2-4): 271-281.
- Chen, C. W., Ou-Yang, C. C. and Yeh, C. W. (2003). Synthesis of galactooligosaccharides and transgalactosylation modeling in reverse micelles. Enzyme and Microbial Technology, 33(4): 497-507.
- Cheng, C. C., Yu, M. C., Cheng, T. C., Sheu, D. C., Duan, K. J. and Tai, W. L. (2006). Production of high-content galacto-oligosaccharide by enzyme catalysis and fermentation with Kluyveromyces marxianus. Biotechnology letters, 28(11): 793-797.
- Cinar, K., Gunes, G. and Gulec, H. A. (2020). Enzymatic synthesis of prebiotic carbohydrates from lactose: Kinetics and optimization of transgalactosylation activity of β‐galactosidase from Aspergillus oryzae. Journal of Food Process Engineering. 43(8): e13435.
- Costa, R. S., and Vinga, S. (2016). Control analysis of the impact of allosteric regulation mechanism in an Escherichia coli kinetic model: Application to serine production. Biochemical Engineering Journal, 110: 59-70.
- Freitas, F. F., Marquez, L. D., Ribeiro, G. P., Brandão, G. C., Cardoso, V. L. and Ribeiro, E. J. (2011). A comparison of the kinetic properties of free and immobilized Aspergillus oryzae β-galactosidase. Biochemical Engineering Journal, 58: 33-38.
- González-Delgado, I., López-Muñoz, M. J., Morales, G. and Segura, Y. (2016). Optimisation of the synthesis of high galacto-oligosaccharides (GOS) from lactose with β-galactosidase from Kluyveromyces lactis. International Dairy Journal, 61: 211-219.
- Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P. and Kummer, U. (2006). COPASI-a complex pathway simulator. Bioinformatics, 22(24): 3067-3074.
- Hsu, C., Lee, S. and Chou, C. (2007). Enzymatic production of galactooligosaccharides by β-galactosidase from Bifidobacterium longum BCRC 15708. Journal of Agricultural and Food Chemistry, 55(6): 2225-2230.
- Huber, R., Kurz, G. and Wallenfels, K. (1976). A quantitation of the factors which affect the hydrolase and transgalactosylase activities of β-galactosidase (E. coli) on lactose. Biochemistry, 15(9): 1994-2001.
- Huerta, L. M., Vera, C., Guerrero, C., Wilson, L. and Illanes, A. (2011). Synthesis of galacto-oligosaccharides at very high lactose concentrations with immobilized β-galactosidases from Aspergillus oryzae. Process biochemistry, 46(1): 245-252.
- Iqbal, M.W., Riaz, T., Mahmood, S., Liaqat, H., Mushtaq, A., Khan, S., Amin, S. and Qi, X. (2023). Recent advances in the production, analysis, and application of galacto-oligosaccharides. Food Reviews International, 39(8): 5814-5843.
- Iwasaki, K., Nakajima, M. and Nakao, S. (1996). Galacto-oligosaccharide production from lactose by an enzymic batch reaction using β-galactosidase. Process biochemistry, 31(1): 69-76.
- Jenab, E., Omidghane, M., Mussone, P., Armada, D. H., Cartmell, J. and Montemagno, C. (2018). Enzymatic conversion of lactose into galacto-oligosaccharides: The effect of process parameters, kinetics, foam architecture, and product characterization. Journal of Food Engineering, 222: 63-72.
- Kim, C. S., Ji, E. S. and Oh, D. K. (2004). A new kinetic model of recombinant β-galactosidase from Kluyveromyces lactis for both hydrolysis and transgalactosylation reactions. Biochemical and Biophysical Research Communications, 316(3): 738-743.
- Manucci, F. (2009). Enzymatic synthesis of galactooligosaccharides from whey permeate (M.S. Thesis). Dublin Institute of Technology, Dublin, Ireland.
- Mueller, I., Kiedorf, G., Runne, E., Seidel-Morgenstern, A. and Hamel, C. (2018). Synthesis, kinetic analysis and modelling of galacto-oligosaccharides formation. Chemical Engineering Research and Design, 130: 154-166.
- Neri, D. F., Balcão, V. M., Costa, R. S., Rocha, I. C., Ferreira, E. M., Torres, D. P., Rodrigues, L. R., Carvalho Jr, L. B. and Teixeira, J. A. (2009). Galacto-oligosaccharides production during lactose hydrolysis by free Aspergillus oryzae β-galactosidase and immobilized on magnetic polysiloxane-polyvinyl alcohol. Food Chemistry, 115(1): 92-99.
- Osman, A. (2016). Synthesis of Prebiotic Galacto-Oligosaccharides: Science and Technology. In: Probiotics, Prebiotics, and Synbiotics, Eds: Watson, R.R., Preedy, V.R. Academic Press, U.S.A.
- Özdinç, N. and Velioğlu, H.M. (2022). The Production of Crude Invertase From The By-products of Baker’s Yeast (Saccharomyces cerevisiae) Factory. Journal of Tekirdag Agricultural Faculty, 19(2): 456-464.
- Palai, T. and Bhattacharya, P. K. (2013). Kinetics of lactose conversion to galacto-oligosaccharides by β-galactosidase immobilized on PVDF membrane. Journal of Bioscience and Bioengineering, 115(6): 668-673.
- Palai, T., Kumar, A. and Bhattacharya, P. K. (2016). Enzyme immobilization/bioconjugation in producing galactio-oligosaccharidies from lactose: developments of kinetic models and bio-reactors. Materials Today: Proceedings, 3(10): 3568-3586.
- Palai, T., Mitra, S. and Bhattacharya, P. K. (2012). Kinetics and design relation for enzymatic conversion of lactose into galacto-oligosaccharides using commercial grade β-galactosidase. Journal of bioscience and bioengineering, 114(4): 418-423.
- Palai, T., Singh, A. K. and Bhattacharya, P. K. (2014). Enzyme, β-galactosidase immobilized on membrane surface for galacto-oligosaccharides formation from lactose: kinetic study with feed flow under recirculation loop. Biochemical Engineering Journal, 88: 68-76.
- Rodriguez-Fernandez, M., Cardelle-Cobas, A., Villamiel, M. and Banga, J. R. (2011). Detailed kinetic model describing new oligosaccharides synthesis using different β-galactosidases. Journal of biotechnology, 153(3-4): 116-124.
- Sanz-Valero, J. I. (2009). Production of galacto-oligosaccharides from lactose by immobilized b-galactosidase and posterior chromatographic separation (Ph. D. Thesis). The Ohio State University, Ohio, U.S.A.
- Shin, H. J. and Ji-Won, Y. (1998). Enzymatic production of galactooligosaccharide by Bullera singularis beta-galactosidase. Journal of microbiology and biotechnology, 8(5): 484-489.
- Tanaka, Y., Kagamiishi, A., Kiuchi, A. and Horiuchi, T. (1975). Purification and properties of β-galactosidase from Aspergillus oryzae. The Journal of Biochemistry, 77(1): 241-247.
- Uran, H., Sanlidere Aloglu, H. and Cetin, B. (2020). Determining of Some Quality Properties of Sucuks Produced by Lactulose Addition. Journal of Tekirdag Agricultural Faculty, 18(1): 58-70.
- Urrutia, P., Rodriguez-Colinas, B. R., Fernandez-Arrojo, L. A., Ballesteros, A. O., Wilson, L., Illanes, A. and Plou, F. J. (2013). Detailed analysis of galactooligosaccharides synthesis with β-galactosidase from Aspergillus oryzae. Journal of Agricultural and Food Chemistry, 61(5): 1081-1087.
- Vera, C., Guerrero, C. and Illanes, A. (2011). Determination of the transgalactosylation activity of Aspergillus oryzae β-galactosidase: effect of pH, temperature, and galactose and glucose concentrations. Carbohydrate Research, 346(6): 745-752.
- Warmerdam, A., Boom, R. M. and Janssen, A. E. (2013). β-galactosidase stability at high substrate concentrations. Springerplus, 2(1): 402.
- Yin, H., Bultema, J. B., Dijkhuizen, L. and van Leeuwen, S. S. (2017). Reaction kinetics and galactooligosaccharide product profiles of the β-galactosidases from Bacillus circulans, Kluyveromyces lactis and Aspergillus oryzae. Food chemistry, 225: 230-238.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Gıda Biyoteknolojisi, Gıda Teknolojileri, Gıda Bilimleri (Diğer) |
| Bölüm | Makaleler |
| Yazarlar | |
| Proje Numarası | ITUBAP, Project ID: MDK-2017-40556 |
| Erken Görünüm Tarihi | 8 Mayıs 2025 |
| Yayımlanma Tarihi | |
| Gönderilme Tarihi | 26 Ocak 2024 |
| Kabul Tarihi | 25 Şubat 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 22 Sayı: 2 |
