Lifetime of a structure evolving by cluster aggregation and particle loss, and application to postsynaptic scaffold domains

Abstract

The dynamics of several mesoscopic biological structures depend on the interplay of growth through the incorporation of components of different sizes laterally diffusing along the cell membrane, and loss by component turnover. In particular, a model of such an out-of-equilibrium dynamics has recently been proposed for postsynaptic scaffold domains which are key structures of neuronal synapses. It is of interest to estimate the lifetime of these mesoscopic structures, especially in the context of synapses where this time is related to memory retention. The lifetime of a structure can be very long as compared to the turnover time of its components and it can be difficult to estimate it by direct numerical simulations. Here, in the context of the model proposed for postsynaptic scaffold domains, we approximate the aggregation-turnover dynamics by a shot-noise process. This enables us to analytically compute the quasi-stationary distribution describing the sizes of the surviving structures as well as their characteristic lifetime. We show that our analytical estimate agrees with numerical simulations of a full spatial model, in a regime of parameters where a direct assessment is computationally feasible. We then use our approach to estimate the lifetime of mesoscopic structures in parameter regimes where computer simulations would be prohibitively long. For gephyrin, the scaffolding protein specific to inhibitory synapses, we estimate a lifetime longer than several months for a scaffold domain when the single gephyrin protein turnover time is about half an hour, as experimentally measured. While our focus is on postsynaptic domains, our formalism and techniques should be applicable to other biological structures that are also formed by a balance of condensation and turnover.

From growing bubbles and dendrites to biological forms

“…However, this growth is proposed to be counterbalanced by the turnover of gephyrin molecule into the cytoplasm. This leads to the formation and maintenance of a long-lived structure of finite size [58]. Analogous turnover mechanisms have been proposed in the context of lipid rafts [49] and the arrest of coarsening by chemical reactions has also been studied theoretically [59].…”

Reciprocal stabilization of glycine receptors and gephyrin scaffold proteins at inhibitory synapses

“…Haselwandter and colleagues treated the GlyR and gephyrin populations as a reactiondiffusion system and proposed that postsynaptic domains are formed by a Turing-like instability (17,21). More recently, we hypothesised that gephyrin domains are in a nonequilibrium stationary state where the desorption of synaptic gephyrin proteins into the cytoplasm is balanced by the capture of diffusing GlyR-gephyrin complexes (19,20). In this project, we set out to put these different ideas to the test by directly measuring the exchange dynamics of GlyRs and gephyrin at synapses using population measurements based on photoconversion and time-lapse imaging in cultured spinal cord neurons.…”

“…(16,17)). Several models have been put forward to explain the formation of stable gephyrin domains arising from receptor-scaffold interactions (17)(18)(19)(20).…”

Local accumulation times in a diffusion-trapping model of synaptic receptor dynamics

“…However, it is known that scaffolding proteins and other synaptic components are also transported into and out of a synapse, albeit at slower rates [24]. Several experimental and modeling studies have analyzed the joint localization of gephyrin scaffolding proteins and GlyRs at synapses [25,26,27,28,29], showing how stable receptor-scaffold domains could arise dynamically.…”