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 quasistationary 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.
Highlights
Synapses play a central role in learning and memory
II A, we introduce and analyze a simplified model for the fluctuating domain dynamics in which we retain the rate rm [Fig. 1(f)] of clusters of different sizes aggregating with the immobile fluctuating domain, reducing the impinging dynamics to a shot-noise process [10]
When cluster aggregation dominates over particle loss for small domain sizes, domains typically fluctuate around a large mean size n 1, for a long time as compared to 1/kd, before eventually losing all their particles and disappearing
Summary
Synapses play a central role in learning and memory. The determination of their components, of their structure and of their dynamics has been the focus of numerous investigations. III A that the proposed simplified model provides a good approximation to the quasistationary size distribution and lifetime of domains measured in numerical simulations of diffusing clusters This requires choosing kinetic parameters for which the cluster survival is long compared to the single-molecule turnover time but short enough to be observed and quantified in numerical simulations. Some of them have been viewed as condensed structures in thermodynamic equilibrium [12,13] Others, such as lipid rafts [14,15] and E-cadherin clusters [16], have been proposed to be formed and maintained as nonequilibrium steady states by condensation and recycling of components, somewhat analogously to the model for postsynaptic scaffold domains proposed in Ref. The methods used in the present paper should be generalizable to these other cases
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
