PRINCIPLES OF CALCIUM WAVE PROPAGATION IN NEURONS: COMPUTATIONAL STUDY AND DERIVATION OF EMPIRICAL LAWS

Abstract

Calcium (Ca2+) is a universal second messenger that regulates the most important activities of the cell. Growing evidence shows Ca2+ is of importance in the pathogenesis of various brain diseases, such as Alzheimer’s Disease(AD). Modern science suggests that synaptic Ca2+ overload plays an important role in synaptic loss, which consequently increases the incidence of AD. This merits building and solving a calcium signaling model to predict calcium concentration in neurons. Accurately solving the spatial-temporal calcium signaling model via numerical method is fundamentally challenging because of (1) the detailed resolution of geometry, and (2) nonlinearity due to the complex membrane exchange mechanisms. Despite the modern computing power, the computational cost will be overwhelming when a neural network of actual size is considered.iv v The first part of the dissertation focuses on solving a partial differential equation system on cell level geometries by reducing three-dimensional problem to two-dimensional or one-dimensional problem. Firstly, we find the dominating physiologic and geometric parameters to activate stably propagating waves, and investigate how the wave velocity, duration, and amplitude depend on the dominating parameters. We implement the simulations on perfectly rotational symmetric dendrites for which the problem can be reduced to two dimensions. We show that the reduction is valid by a direct comparison of numeric solutions using 2D and 3D geometries. Then we study the threshold of parameters for stable waves. Secondly, we find empirical laws which express the wave velocity and wave amplitude as functions of dominating parameters. The second part of this dissertation is focusing on waves on branching dendrites. First of all, we apply a single stimulation to one of the child branches to determine if the calcium signal can propagate through the junction area and trigger a signal in the other branches. Various parameters of a branch point are considered, including branching angle, radius ratio of child dendrite to parent dendrite and ER radius. Numerical experiments are carried out and the corresponding physiological interpretations are given. The empirical laws enable predicting activating signal stability and strength at the branch point and consequently predicting wave properties in the other dendrites.