Department for Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK.
Institut für Mathematik, Johannes Gutenberg-Universität, Staudingerweg 9, 55099, Mainz, Germany.
Bull Math Biol. 2021 May 1;83(6):64. doi: 10.1007/s11538-021-00900-9.
Lck (lymphocyte-specific protein tyrosine kinase) is an enzyme which plays a number of important roles in the function of immune cells. It belongs to the Src family of kinases which are known to undergo autophosphorylation. It turns out that this leads to a remarkable variety of dynamical behaviour which can occur during their activation. We prove that in the presence of autophosphorylation one phenomenon, bistability, already occurs in a mathematical model for a protein with a single phosphorylation site. We further show that a certain model of Lck exhibits oscillations. Finally, we discuss the relations of these results to models in the literature which involve Lck and describe specific biological processes, such as the early stages of T cell activation and the stimulation of T cell responses resulting from the suppression of PD-1 signalling which is important in immune checkpoint therapy for cancer.
Lck（淋巴细胞特异性蛋白酪氨酸激酶）是一种在免疫细胞功能中发挥多种重要作用的酶。它属于 Src 激酶家族，已知该家族激酶会发生自身磷酸化。事实证明，这会导致在其激活过程中发生各种显著的动力学行为。我们证明，在存在自身磷酸化的情况下，一个具有单个磷酸化位点的蛋白质的数学模型中已经存在双稳性现象。我们进一步表明，Lck 的某个模型表现出振荡。最后，我们讨论了这些结果与涉及 Lck 并描述特定生物学过程的文献模型之间的关系，例如 T 细胞激活的早期阶段以及由于 PD-1 信号抑制而导致的 T 细胞反应的刺激，这在癌症的免疫检查点治疗中很重要。
