Mathematical modelling of synaptic tagging and capture mechanisms to investigate morphological changes during synaptic plasticity : A thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy at Lincoln University

Abstract

The synaptic tagging and capture (STC) hypothesis not only explains the integration and association of synaptic activities, but also the formation of learning and memory. The synaptic pathways involve in the synaptic tagging and capture phenomenon are called STC pathways. It is challenging to associate the physical attributes of STC pathways with structural changes along with synaptic strength. Mathematical modelling and computational analysis provide a way to explain the complexity of STC mechanisms along with their structural impact on a single dendritic spine. In this study, we develop mathematical models based on significant reported networks involved in synaptic tagging. We use this model to explore events associated with synaptic tagging candidates and evaluate them against the assumption based on STC hypothesis. Our model explains the integrated activities of kinases (CaMKII, PKA, MAPK/ERK) in response to the initial stimulation and setting of tags, the effect of this on overall synaptic tag strength, and the induction of L-LTP with protein synthesis. We use this model to investigate the behaviour of different published synaptic tagging candidates and examine it against the criteria laid out in the synaptic tagging hypothesis. Our model reveals that CaMKII activation (Tag1) is critical for the setting of the initial tag; however, coordinated activity with other kinases and the biochemical pathway is necessary for the tag to be stable. Similarly, PKA modulates NMDAR-mediated Ca2+ signalling. PKA and CaMKII likely act in concert in the process of tagging. We extend our model to investigate structural aspects of synaptic plasticity; we add the effects of actin remodelling and AMPARs anchoring on spine dynamics. The Spine model verifies that AMPARs are anchored in the PSD via scaffolding proteins and cytoskeletal elements to ensure reliable synaptic transmission. We introduce critical variables in the Extended-spine model to analyse the contribution of significant events leading to dendritic spine structural change. Our model associates the physical and structural aspects of synaptic plasticity link with spine dynamics. We find that a simple activation-inhibition loop can be used as paradoxical signalling to investigate the dynamics of kinases like CaMKII, the RhoGTPases-Rho and Cdc42, and actin remodelling. Hence, the interface between actin barbed end generation and signalling is a source of natural robustness, regardless of model sensitivity to kinetic parameters.