Quantifying the environment's temperature effect on gene expression: Lyapunov exponent and multifractal dimension approach

Our understanding of the protein synthesis mechanism has influenced our ability to provide microorganisms with the conditions for adapting to future environmental change. In this study, theoretical modeling by considering the environment temperature and the delay in response of mRNA level to variation of protein and mRNA degradation rate has been proposed. The influence of environment temperature and time delay in gene regulation results in oscillatory behavior at the mRNA level. An elevation in the mRNA degradation rate proficiently governs the protein synthesis pathway, while an increment in the protein degradation rate yields a limiting effect on the transcriptional phase. Transcription steps can be controlled, by controlling the length of time delay. The calculation of Lyapunov exponents across a broad spectrum of values reveals the inherent chaos within the dynamics of protein synthesis.