Stochastic Differential Equation Model for Cerebellar Granule Cell Excitability

Neurons in the brain express intrinsic dynamic behavior which is known to be stochastic in nature. A crucial question in building models of neuronal excitability is how to be able to mimic the dynamic behavior of the biological counterpart accurately and how to perform simulations in the fastest possible way. The well-established Hodgkin-Huxley formalism has formed to a large extent the basis for building biophysically and anatomically detailed models of neurons. However, the deterministic Hodgkin-Huxley formalism does not take into account the stochastic behavior of voltage-dependent ion channels. Ion channel stochasticity is shown to be important in adjusting the transmembrane voltage dynamics at or close to the threshold of action potential firing, at the very least in small neurons. In order to achieve a better understanding of the dynamic behavior of a neuron, a new modeling and simulation approach based on stochastic differential equations and Brownian motion is developed. The basis of the work is a deterministic one-compartmental multi-conductance model of the cerebellar granule cell. This model includes six different types of voltage-dependent conductances described by Hodgkin-Huxley formalism and simple calcium dynamics. A new model for the granule cell is developed by incorporating stochasticity inherently present in the ion channel function into the gating variables of conductances. With the new stochastic model, the irregular electrophysiological activity of an in vitro granule cell is reproduced accurately, with the same parameter values for which the membrane potential of the original deterministic model exhibits regular behavior. The irregular electrophysiological activity includes experimentally observed random subthreshold oscillations, occasional spontaneous spikes, and clusters of action potentials. As a conclusion, the new stochastic differential equation model of the cerebellar granule cell excitability is found to expand the range of dynamics in comparison to the original deterministic model. Inclusion of stochastic elements in the operation of voltage-dependent conductances should thus be emphasized more in modeling the dynamic behavior of small neurons. Furthermore, the presented approach is valuable in providing faster computation times compared to the Markov chain type of modeling approaches and more sophisticated theoretical analysis tools compared to previously presented stochastic modeling approaches

Activity-dependent bulk endocytosis: control by molecules and signalling cascades

Synaptic vesicle (SV) recycling in the presynapse is essential for the maintenance of neurotransmission. During mild stimulation clathrin-mediated endocytosis (CME) dominates, however during intense stimulation activity-dependent bulk endocytosis (ADBE) is the dominant form of membrane retrieval. The aim of this thesis was to determine how the signalling molecule GSK3 controlled ADBE, with the hypothesis that this enzyme was required at multiple stages of this endocytosis mode. I also hoped to identify a specific cargo for ADBE. I found that during intense action potential stimulation, a localised calcium increase is necessary for the activation of Akt, which inhibited GSK3. This activation was mediated via a phosphatidylinositol 3-kinase (PI3K)-dependent mechanism. Furthermore, I found that phosphatidylinositol 4-kinaseIIα (PI4KIIα), a molecule whose abundance is regulated by GSK3, had a key role in ADBE. Specifically, I found that the absence of PI4KIIα accelerated CME but inhibited ADBE and that PI4KIIα controls CME and ADBE via distinct mechanisms. The PI4KIIα study revealed potential cross-talk between CME and ADBE. To determine whether modulation of either endocytosis mode impacts on the other, the retrieval of genetically-encoded reporters of SV cargo was monitored during intense stimulation during inhibition of either CME or ADBE. The recovery of almost all SV cargo was unaffected by ADBE inhibition but was arrested by abolishing CME. In contrast, VAMP4-pHluorin retrieval was perturbed by inhibiting ADBE and not by blocking CME. Knockdown of VAMP4 also arrested ADBE, indicating that in addition to being the first identified ADBE cargo, it is also essential for this endocytosis mode to proceed