Research Paper: Mathematical modeling of gene expression: chaos approach

Document Type : Research Paper

Authors

1 PhD Student, Department of Physics, Urmia University of Technology, Urmia, Iran

2 Professor, Department of Physics, Urmia University of Technology, Urmia, Iran

Abstract

Gene is a factor encoding genetic information and the basic unit of inheritance. Gene expression is a phenomenon consisting of two complex stages of transcription and translation. In this study, the yeast cell of Saccharomyces cerevisiae evolution is investigated due to the importance of the gene expression phenomenon. To clarify the accuracy of the obtained results, we have used experimental data on the Saccharomyces cerevisiae yeast cell from the gene bank. We are using chaos theory to study gene expression due to the nonlinear dynamics of the phenomenon. The obtained results predict that, by increasing the rate of degradation in the messenger arena to 0.03, we have reached the threshold value for the gene expression phenomenon. Also, we have recognized that increased transcription is associated with an increased mRNA degradation rate. The optimal values of transcription delay rate (18.2 min) and protein degradation rate (0.03) were obtained. There was a good agreement between the experimental and theoretical results.

Keywords

Main Subjects


[1] Muller HJ., Variation due to change in the individual gene, The American Naturalist, 56, 32-50, 1922.
[2] San Segundo-Val, I. and Sanz-Lozano, C. S., Introduction to the gene expression analysis., Molecular genetics of asthma, 29-43, 2016.
[3] Shim, G., Kim, D., Park, G.T., Jin, H., Suh, S.K. and Oh, Y.K., Therapeutic gene editing: delivery and regulatory perspectives, Acta Pharmacologica Sinica, 38, 738-753, 2017.
[4] Copling, S., Srinivasan, M., and Sharma, P., Understanding Model Independent Genetic Mutations through Trends in Increase in Entropy, Open Journal of Biophysics, 12, 165-171, 2022.
[5] Arnold, B. J., Huang, I., and Hanage, W. P., Horizontal gene transfer and adaptive evolution in bacteria, Nature Reviews Microbiology, 20, 206-218, 2022.
[6] Hooshmand, S. E., Jahanpeimay Sabet, M., Hasanzadeh, A., Kamrani Mousavi, S. M., Haeri Moghaddam, N., Hooshmand, S. A and Karimi, M, Histidine‐enhanced gene delivery systems: The state of the art, The Journal of Gene Medicine, 24, e3415, 2022.
[7] Passmore, L. A., and Coller, J., Roles of mRNA poly (A) tails in regulation of eukaryotic gene expression, Nature Reviews Molecular Cell Biology, 23, 93-106, 2022.
[8] Gonzales, D. T., Yandrapalli, N., Robinson, T., Zechner, C., and Tang, T. D., Cell-free gene expression dynamics in synthetic cell populations, ACS synthetic biology, 11, 205-215, 2022.
[9] Fefilova, A. S., Fonin, A. V., Vishnyakov, I. E., Kuznetsova, I. M., and Turoverov, K. K., Stress-Induced Membraneless Organelles in Eukaryotes and Prokaryotes: Bird’s-Eye View, International Journal of Molecular Sciences, 23,5010, 2022.
[10] Li, L., Du, N., Chen, J., Zhang, K., Tong, W., Zheng, H., and Gao, F., Establishment and Application of a Quantitative PCR Method for E248R Gene of African Swine Fever Virus, Veterinary Sciences, 9, 417, 2022.
[11] Kim, J., Yoon, Y., Park, H. J., and Kim, Y. H., Comparative Study of Classification Algorithms for Various DNA Microarray Data, Genes, 13, 494, 2022.
[12] Chen, T., He, H. L., and Church, G. M., Modeling gene expression with differential equations, In Biocomputing’99, 29-40, 1999.
[13] Sharma, A., and Adlakha, N., Delay Differential Equation Model of Gene Expression, Advances in Systems Science and Applications, 20, 73-90, 2020.
[14] Peccoud, J., Ycart, B., Markovian modeling of gene-product synthesis. Theoretical population biology, 48, 222-234, 1985.
[15] Ramirez-Garcia, A., Rementeria, A., Aguirre-Urizar, J. M., Moragues, M. D., Antoran, A., Pellon, A., and Hernando, F. L., Candida albicans and cancer: Can this yeast induce cancer development or progression, Critical reviews in microbiology, 42, 181-193, 2016.
[16] Huertas, M. J., and Michán, C., Paving the way for the production of secretory proteins by yeast cell factories, Microbial Biotechnology, 12, 1095, 2019.
[17] Shankar, V., Mahboob, S., Al-Ghanim, K. A., Ahmed, Z., Al-Mulhm, N., and Govindarajan, M., A review on microbial degradation of drinks and infectious diseases: A perspective of human well-being and capabilities, Journal of King Saud University-Science, 33, 101293, 2021.
[18] Cervelli, T. and Galli, A., Yeast as a tool to understand the significance of human disease-associated gene variants, Genes, 12, 1303, 2021.
[19] Carmona-Gutierrez, D., Bauer, M. A., Zimmermann, A., Aguilera, A., Austriaco, N., Ayscough, K., and Madeo, F., Guidelines and recommendations on yeast cell death nomenclature, Microbial Cell, 5, 4, 2018.
[20] Kato, S., Han, S. Y., Liu, W., Otsuka, K., Shibata, H., Kanamaru, R.,and  Ishioka, C., Understanding the function–structure and function–mutation relationships of p53 tumor suppressor protein by high-resolution missense mutation analysis, Proceedings of the National Academy of Sciences, 100, 8424-8429, 2003.
[21] Monk, N. A., Oscillatory expression of Hes1, p53, and NF-B driven by transcriptional time delays, Current Biology, 13, 1409-1413, 2003.
[22] Ko, M. S., A stochastic model for gene induction, Journal of theoretical biology, 153, 181-194, 1991.
[23] Akutsu, T., Miyano, S., and Kuhara, S., Identification of genetic networks from a small number of gene expression patterns under the Boolean network model, In Biocomputing'99,17-28, 1999.
[24] Murphy, K., and Mian, S., Modelling gene expression data using dynamic Bayesian networks, Technical report, Computer Science Division, University of California, Berkeley, CA, 104, 1999.
[25] Kim, P. M., and Tidor, B., Limitations of quantitative gene regulation models: a case study, Genome Research, 13, 2391-2395, 2003.
[26] Wu, F. X., Zhang, W. J., and Kusalik, A. J., Modeling gene expression from microarray expression data with state-space equations, In Biocomputing, 581-592, 2004.
[27] Miller, E., pham, J., Hunt j., and Laplace L., A continuous model of gene expression, California State Polytechnic University, Pomona, 2005.
[28] DeRisi JL., Iyer VR., and Brown PO., Exploring the metabolic and genetic control of gene expression on a genomic scale, Science, 278, 680-6, 1997.
[29] Behnia, S., Fathizadeh, S., and Akhshani, A., DNA spintronics: Charge and spin dynamics in DNA wires, The Journal of Physical Chemistry C, 120, 2973-2983, 2016.
[30] Androulakis, I. P., Yang, E., and Almon, R. R., Analysis of time-series gene expression data: methods, challenges, and opportunities. Annu, Rev. Biomed. Eng, 9, 205-228, 2007.
[31] Gutierrez, J. M., Rodrıguez, M. A., and Abramson, G., Multifractal analysis of DNA sequences using a novel chaos-game representation, Physica A: Statistical Mechanics and its Applications, 300, 271-284, 2001.
[32] Dori-Bachash, M., Shema, E., and Tirosh, I., Coupled evolution of transcription and mRNA degradation, PLoS biology, 9, 2011.
[33] Verdugo, A., and Rand, R., Hopf bifurcation in a DDE model of gene expression, Communications in Nonlinear Science and Numerical Simulation, 13, 235-242, 2008.
[34] Narayanan, K., and Makino, S., Interplay between viruses and host mRNA degradation. Biochimica Et Biophysica Acta (BBA)-Gene Regulatory Mechanisms, 1829, 732-741, 2013.
[35] Ingolia, N. T., Ribosome footprint profiling of translation throughout the genome, Cell, 165, 22-33, 2016.
[36] Wu, Q., Medina, S. G., Kushawah, G., DeVore, M. L., Castellano, L. A., Hand, J. M., ... and Bazzini, A. A., Translation affects mRNA stability in a codon-dependent manner in human cells, elife, 8, 2019.
[37] Linder, B., Fischer, U., and Gehring, N. H., mRNA metabolism and neuronal disease. FEBS letters, 589, 1598-1606, 2015.
[38] Wu, X. P., and Eshete, M., Bifurcation analysis for a model of gene expression with delays, Communications in Nonlinear Science and Numerical Simulation, 16, 1073-1088, 2011.