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起许多重要作用的酶。它属于已知会发生自磷酸化的 Src 激酶家族。事实证明，这会导致在它们的激活过程中出现各种各样的动态行为。我们证明，在存在自磷酸化的情况下，一种现象，双稳态，已经出现在具有单个磷酸化位点的蛋白质的数学模型中。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文献中涉及 Lck 和描述特定生物过程的模型的关系，