Spatio-temporal correlations can drastically change the response of a MAPK pathway

Abstract

Multisite covalent modification of proteins is omnipresent in eukaryotic cells. A well-known example is the mitogen-activated protein kinase (MAPK) cascade where, in each layer of the cascade, a protein is phosphorylated at two sites. It has long been known that the response of a MAPK pathway strongly depends on whether the enzymes that modify the protein act processively or distributively. A distributive mechanism, in which the enzyme molecules have to release the substrate molecules in between the modification of the two sites, can generate an ultrasensitive response and lead to hysteresis and bistability. We study by Green's Function Reaction Dynamics (GFRD), a stochastic scheme that makes it possible to simulate biochemical networks at the particle level in time and space, a dual phosphorylation cycle in which the enzymes act according to a distributive mechanism. We find that the response of this network can differ dramatically from that predicted by a mean-field analysis based on the chemical rate equations. In particular, rapid rebindings of the enzyme molecules to the substrate molecules after modification of the first site can markedly speed up the response and lead to loss of ultrasensitivity and bistability. In essence, rapid enzyme-substrate rebindings can turn a distributive mechanism into a processive mechanism. We argue that slow ADP release by the enzymes can protect the system against these rapid rebindings, thus enabling ultrasensitivity and bistability.MAP kinase | Multisite phosphorylation | Reaction diffusion | Simulation M APK cascades are ubiquitous in eukaryotic cells. They are involved in cell differentiation, cell proliferation, and apoptosis (1). MAPK pathways exhibit very rich dynamics. It has been predicted mathematically and shown experimentally that they can generate an ultrasensitive response (2-4) and exhibit bistability via positive feedback (5). It has also been predicted that they can generate oscillations (6,7,8), amplify weak but attenuate strong signals (9), and give rise to bistability due to enzyme sequestration (10, 11). MAPK pathways are, indeed, important for cell signalling, and for this reason they have been studied extensively, both theoretically (2, 3, 6-19) and experimentally (2,4,5,7,16,(20)(21)(22). However, with the exceptions of refs. 7, 9, 11, 15, and 19, the pathway is commonly modeled by using chemical rate equations (2, 3, 6, 8, 10, 12-14, 16, 17). This is a mean-field description, in which it is assumed that the system is well-stirred and that fluctuations can be neglected. Here, we perform particle-based simulations of one layer of the MAPK cascade using our recently developed GFRD algorithm (23, 24). Our simulations reveal that spatio-temporal correlations between the enzyme and substrate molecules that are ignored in the commonly employed mean-field analyses can have a dramatic effect on the nature of the response. They can not only speed up the response, but also lead to loss of ultrasensitivity and bistability.The response time, the sharpness of the ...

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