The molecular composition of presynaptic and postsynaptic neuronal terminals is dynamic, and yet long-term stabilizations in postsynaptic responses are necessary for synaptic development and long-term plasticity. The need to reconcile these concepts is further complicated by learning- and memory-related plastic changes in the molecular make-up of synapses. Advances in single-particle tracking mean that we can now quantify the number and diffusive properties of specific synaptic molecules, while statistical thermodynamics provides a framework to analyse these molecular fluctuations. These quantitative descriptions of the processes underlying the turnover, long-term stability and plasticity of postsynaptic receptors help us to understand the balance between local molecular turnover and synaptic structural identity and integrity. These diffusive properties are altered in several neurodegenerative disorders, such as Alzheimer's and Parkinson's disease, which are associated with the presence of abnormally structured or misfolded protein assemblies. Cell-to-cell transfer of misfolded proteins has been proposed for the intra-cerebral propagation of these diseases. When released, misfolded proteins diffuse in the 3D extracellular space before binding to the plasma membrane of neighboring cells, where they diffuse on a 2D plane. This reduction in diffusion dimension and the cell surface molecular crowding promote deleterious interactions with native membrane proteins, inducing bias in the diffusion properties promoting clustering and further aggregation of misfolded protein assemblies at the cell surface. These processes open up new avenues for therapeutics development targeting the initial interactions of deleterious proteins with the plasma membrane or the subsequent pathological signaling.