Autophosphorylation and the dynamics of the activation of Lck

TL;DR

This paper investigates the dynamical behaviors of Lck kinase activation, demonstrating bistability and oscillations through mathematical modeling, with implications for immune cell signaling and cancer immunotherapy.

Contribution

It introduces a mathematical model showing bistability and oscillations in Lck activation, highlighting complex dynamical behaviors not previously characterized.

Findings

Bistability occurs in models with a single phosphorylation site.

Lck models exhibit oscillatory behavior.

Results relate to T cell activation and immune checkpoint therapy.

Abstract

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.