Gautam Pankaj, Kashyap Dinesh, Biswas Debabrata, Sinha Sudipta Kumar
Department of Chemistry, Indian Institute of Technology Ropar, Rupnagar, Punjab, India.
Department of Physics, Bankura University, Bankura, West Bengal, India.
R Soc Open Sci. 2025 Jun 4;12(6):241487. doi: 10.1098/rsos.241487. eCollection 2025 Jun.
Nuclear factor-κB (NF-κB) participates in various cellular processes to encompass cell fate through differential gene expression, but the underlying molecular mechanism behind this phenomenon is still elusive. Two factors in this process can control the gene expression for determining the cell's fate: (i) synthesized proteins may have a considerable lifetime and (ii) gene activation may be slow or delayed. To address the first factor, we argue that the NF- B system experiences cellular variability, often considered the origin of environmental noise for protein production, which influences cellular decisions at the molecular level as they have a considerable lifetime. We employ unified coloured noise approximation to obtain analytical expressions for the protein mean number obtained from our theoretical model and stochastic simulation. We find that these fluctuations influence mean protein numbers and induce bimodality. However, for the second factor, we rely on experimental findings, where the time delay in gene activation plays an essential role in protein production. Our bifurcation analysis demonstrates that the system exhibits saddle-node bifurcations for the instantaneous case, but it experiences the Hopf bifurcation and oscillates between two states in the presence of the time delay. In a nutshell, as NF-κB dynamics influence downstream expression, this study may provide insight into how to adjust parameters to control gene expressions.
核因子-κB（NF-κB）通过差异基因表达参与各种细胞过程以决定细胞命运，但其背后的分子机制仍不清楚。此过程中有两个因素可控制决定细胞命运的基因表达：（i）合成的蛋白质可能具有相当长的寿命，以及（ii）基因激活可能缓慢或延迟。为了解决第一个因素，我们认为NF-κB系统存在细胞变异性，这通常被认为是蛋白质产生的环境噪声的来源，由于蛋白质具有相当长的寿命，它在分子水平上影响细胞决策。我们采用统一色噪声近似来获得从我们的理论模型和随机模拟中得到的蛋白质平均数的解析表达式。我们发现这些波动会影响平均蛋白质数量并诱导双峰性。然而，对于第二个因素，我们依赖实验结果，其中基因激活的时间延迟在蛋白质产生中起重要作用。我们的分岔分析表明，对于瞬时情况，系统表现出鞍结分岔，但在存在时间延迟的情况下，它会经历霍普夫分岔并在两个状态之间振荡。简而言之，由于NF-κB动力学影响下游表达，本研究可能为如何调整参数以控制基因表达提供见解。
