Modelling calmodulin dependent calcium signalling involved with synaptic plasticity : A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Lincoln University

Abstract

Neurotransmission of synapses is plastic in that they get modulated to increase or decrease conductivity (this is known as synaptic plasticity). Synaptic plasticity consists of two opposing forces: long term potentiation (LTP) which strengthens synapses; and long term depression (LTD) which weakens synapses. LTP and LTD are associated with memory formation and loss respectively. Synaptic plasticity is controlled at a molecular by Ca²⁺-mediated protein signalling. Here, Ca²⁺ binds the protein, calmodulin (CaM) which modulates synaptic plasticity in both directions. This is because Ca²⁺- bound CaM activates both LTD- and LTP- inducing proteins. Understanding how CaM responds to Ca²⁺ signalling, and how this translates into synaptic plasticity is therefore important to understand synaptic plasticity induction. In this thesis, CaM activation by Ca²⁺ and calmodulin binding to downstream proteins was mathematically modelled using differential equations. CaM was first modelled in isolation to determine its kinetic binding properties with Ca²⁺. By performing local and global sensitivity analyses of Ca²⁺ binding/unbinding parameters, distinct binding properties between the two Ca²⁺ binding lobes were found. The difference between the binding lobes was exacerbated as intracellular Ca²⁺ stimulation rose. A full model of the two opposing pathways of synaptic plasticity was then employed. Simulations were monitored, and global sensitivity analyses were performed to determine how Ca²⁺/CaM signalling occured at various Ca²⁺ signals. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM getting redistributed from low affinity to high affinity binding targets. Specifically, CaM was redistributed away from LTD- inducing proteins to bind the high affinity LTP-inducing protein, calmodulin dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM binding protein targets. This model thereby showed a novel form of CaM signalling by which the two opposing pathways can crosstalk indirectly. The model also investigated how cAMP is regulated by CaM. It was found that CaMKII can repress cAMP production by repressing CaM-regulated proteins which catalyse cAMP production. The model also found that at low Ca²⁺ stimulation levels typical of LTD- induction, CaM-signalling was unstable and is therefore unlikely to alone be sufficient to induce synaptic depression. Overall, this thesis showed how limiting levels of CaM may be a fundamental aspect of Ca²⁺ regulated signalling which allows crosstalk among proteins without requiring to interact directly. Understanding synaptic plasticity can help understand neurodegenerative disease and although the current study is focused on synaptic plasticity, understanding CaM regulation has implications in numerous other cell types.