T细胞和巨噬细胞中基础和活化转录的新型HIV-1模型的数学分析和潜在治疗意义
Mathematical analysis and potential therapeutic implications of a novel HIV-1 model of basal and activated transcription in T-cells and macrophages
摘要：
HIV-1影响着全世界数千万人。目前的治疗通常涉及抗逆转录病毒药物的鸡尾酒，这在减少病毒和延长寿命方面是有效的。然而，目前还没有FDA批准的HIV-1转录抑制剂。此外，只有少数尝试模拟HIV-1的转录过程。在这项工作中，我们扩展了DeMarino et al.（2020）中引入的一种新的HIV-1转录三态模型，该模型已根据实验数据开发和验证。在将该模型拟合到体外数据之后，已经观察到HIV-1在T细胞和巨噬细胞中的转录过程的显著差异。特别是，T细胞中HIV-1启动子的激活似乎随着Tat蛋白接近临界阈值而迅速发生。相比之下，同样的过程在巨噬细胞中发生得更顺利。在这项工作中，我们进行了系统的数学分析的模型，以补充实验数据拟合和敏感性分析较早进行。我们推导出该模型的显式解，得到原模型的精确转录过程衰减率，然后研究非线性对系统行为的影响，包括正平衡的存在性和局部及全局稳定性.我们能够显示的稳定性的积极的稳定状态在有限的情况下，在一般情况下的全球稳定性仍然是一个悬而未决的问题。通过对转录抑制药物治疗的效果进行建模，我们为它有效降低病毒载量提供了一个重要的条件。此外，我们的数值模拟和分析指出，转录抑制剂的效果可以通过与标准治疗同步来增强，例如联合抗逆转录病毒治疗，以减少总剂量和毒性。
英文摘要：
HIV-1 affects tens of millions of people worldwide. Current treatments often involve a cocktail of antiretroviral drugs, which are effective in reducing the virus and extending life spans. However, there is currently no FDA-approved HIV-1 transcription inhibitor. Furthermore, there have only been a few attempts to model the transcription process in HIV-1. In this work, we extend a novel three-state model of HIV-1 transcription introduced in DeMarino et al. (2020) that has been developed and validated against experimental data. After fitting this model to in vitro data, significant differences in the transcription process of HIV-1 in T-cells and macrophages have been observed. In particular, the activation of the HIV-1 promoter in T-cells appears to take place rapidly as the Tat protein approaches a critical threshold. In contrast, the same process occurs smoother in macrophages. In this work, we carry out systematic mathematical analyses of the model to complement experimental data fitting and sensitivity analysis performed earlier. We derive explicit solutions of the model to obtain exact transcription process decay rates for the original model and then study the effect of nonlinearity on the system behavior, including the existence and the local and global stability of the positive equilibrium. We were able to show the stability of the positive steady state in limiting cases, with the global stability in the general case remaining an open question. By modeling the effect of transcription-inhibiting drug therapy, we provide a nontrivial condition for it to be effective in reducing viral load. Moreover, our numerical simulations and analysis point out that the effect of the transcription-inhibitor can be enhanced by synchronizing with standard treatments, such as combination antiretroviral therapy, to allow the reduction of total dosages and toxicity.
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