Dynamics of Neural Systems: From Intracellular Transport in Neurons to Network Activity

Abstract

Neurodegenerative diseases such as Alzheimer’s disease (AD) are all results of neurons losing their normal functionality. However, the exact mechanics of neurodegeneration remains obscure. Most of the knowledge about this class of diseases is obtained by studying late stage patients. Therefore, the mechanism proceeding the late stages of such diseases are less understood. Better understanding of respective mechanisms can help developing in early diagnostic tools and techniques to enable more effective treatment methods. Analyzing the dynamics of neural systems can be the key to discover the underlying mechanisms, which lead to neurodegenerative diseases. The dynamics of neural systems can be studied in different scales. At subcellular level, dynamics of axonal transport plays an important role in AD. In particular, anterograde axonal transport conducted by kinesin-1, known conventionally as kinesin, is essential for maintaining functional synapses. The stochastic motion of kinesin in the presence of magnetic nanoparticles is studied. A novel reduced-order-model (ROM) is constructed to simulate the collective dynamics of magnetic nanoparticles that are delivered into cells. The ROM coupled with the kinesin model allows the quantification of the decrease in processivity of kinesin and in its average velocity under external loads caused by chains of magnetic nanoparticles. Changes in the properties of transport induced by perturbations have the potential to decipher normal transport from impaired transport in the state of disease. In single-cell level analysis, Ca2+ transients in ASH neuron of C. elegans model organism is studied in the context of biological conditions such as aging and oxidative stress. A novel mathematical model is established that can describe the unique Ca2+ transients of ASH neuron in C. elegans including its “on” and “off” response. The model provides insight into the mechanism that governs the observed Ca2+ dynamics in ASH neuron. Hence, the proposed mathematical model can be utilized as a tool that offers explanation for changes induced by aging or oxidative stress in the neuron based on the observed Ca2+ dynamics. Network level analysis of neurons does not require methods of extremely high spatial and temporal resolution compared to the analysis in subcellular and cellular level. Yet, malfunction in smaller scales can manifest themselves in dynamics of larger scales. In particular, impairment of synaptic connections and their dynamics can jeopardize the normal functionality of the brain in pathological conditions such as AD. The impact of synaptic deficiencies is investigated on robustness of persistence activity (essential for working memory, which is adversely affected by AD) in excitatory networks with different topologies. Networks with rich-clubs are shown to have higher robustness when their synapses are impaired. Hence, monitoring changes in the properties of the neural network can be utilized as a tool to detect defects in synaptic connections. Moreover, such defects are shown to be more devastating if they occur in synapses of highly active neurons. Impairments of synapses in highly active neurons can be directly linked to subcellular processes such as depletion of synaptic resources. Using stochastic firing rate models, the parameters that govern synaptic dynamics are shown to influence the capability of the model to possess memory. The decrease in the release probability of synaptic vesicles, which can be caused by loss of axonal transport, is shown to have a detrimental effect on memory represented by the firing rate of population models.