ULTRASTRUCTURAL NEURONAL MODELING OF CALCIUM DYNAMICS UNDER TRANSCRANIAL MAGNETIC STIMULATION

Abstract

A paramount question in the study of Calcium (Ca2+) signaling is how this ion regulates a wide spectrum of cellular processes, which include: fertilization, proliferation, learning, memory, and cell death. All of these processes are the result of synaptic strengthening and weakening. Part of the answer lies in the spatial-temporal interactions of Ca2+ at the extracellular and intracellular levels of a neuron. Within these levels of a neuron there is a complex concert of Ca2+ ion exchange and transport mechanisms that are activated (or inactivated) by external stimuli and it remains to be studied the role of these interactions at the ultrastructural scale. One mode of external stimulation is by Transcranial Magnetic Stimulation (TMS) and repetitive TMS (rTMS). TMS is a noninvasive brain stimulation method to modulate humanbrain activity by generating a strong magnetic field near the cranium. The magnetic field induces an electric field which depolarizes neurons; therefore, TMS is used in clinical applications to treat neuropsychiatric and neurological disorders. However, it is not well known the effect of TMS on intracellular Ca2+ interactions; therefore, I endeavor to determine the types of calcium interactions that occur when a neuron experiences TMS. I also determine how intracellular calcium mechanisms are affected by TMS stimuli. In particular, the cellular regulators of calcium are given by: the internal Ca2+ store (“calcium bank”) of a neuron called the endoplasmic reticulum (ER) with spine apparatus (SA), the voltage dependent calcium channels (VDCCs), and calcium influx at synaptic spines. Ultimately, the ER is responsible for synaptic plasticity and from here I determined under what conditions does TMS cause intracellular calcium to induce synaptic plasticity. For the first part of this dissertation I describe the neurobiology, model equations, and methods that are employed in understanding the role of intracellular calcium. Simulating calcium dynamics at the ultrastructural level is computationally expensive when including the effects of TMS in concert with intracellular calcium transport mechanism. Therefore, I also identify the numerical methodologies that provide the best results in terms of numerical accuracy to the physiology of the intracellullar dynamics and the parameters such as error and time step size that yield sufficient results. I will also describe the framework used in this study (i.e., UG4) and the pipeline for performing my studies, this includes: the process from microscopy to computational domains, generating and preserving mesh features, the choice of numerical methods, and the process of parallelizing the simulations. In the second part, I dive into the electro-dynamic mechanisms that cause voltage propagation through a neuron. This is of particular importance, because many ion membrane transport mechanisms depend on plasma membrane voltage. The simulations coded and executed in MatLab are used to drive calcium dynamics which is discussed in the third part of the dissertation. I will also take the opportunity to explain a case study involving virtual reality with the Hodgkin-Huxley electrical model for voltage propagation. Additionally, I incorporate synaptic communication which is driven by TMS protocols or simulated by voltage clamps, and both provide a mechanism by which intracellular calcium transients occurs. For the third chapter I discuss the calcium dynamic mechanisms that are inside of neurons and I discuss the methodology I take to setup a simulation and perform simulations. This includes the steps taken to process microscopy images to generate computational domains, implementing the model equations, and utilizing appropriate numerical schemes. I also discuss several preliminary examples as proof of concept to my simulation pipeline and I give results involving the regulation of calcium with respect to intracellular mechanisms. The fourth part of this dissertation describes the steps for running TMS simulations using voltage data from electrical simulations to drive calcium signaling events. In particular, I discuss the tool NeMo-TMS which uses voltage and calcium simulations together to draw conclusions with respect to intracellular calcium propagation. I describe the multi-scale paradigm that is used, model equations, and computational domains that are used and provide several examples of results from this modeling pipeline. Of particular importance, I provide discussion on the coupling of data from electrical simulations and biochemical simulations, i.e. I use TMS induced voltage data to drive voltage dependent calcium release and I examine the effects of TMS induced back propagating action potentials.