Neuronal Dynamics: Mathematical Modeling of Neural Activity

This module introduces the fundamental concepts of neuronal modeling by exploring basic mathematical representations of neurons. Students will learn how to construct and analyze simple neuron models that capture essential features of neuronal behavior, providing the foundation for understanding more complex neurodynamics.

This module covers the classic Hodgkin-Huxley model, which describes the ionic mechanisms underlying action potentials in neurons. Students will explore biophysical modeling approaches that incorporate the detailed cellular mechanisms responsible for neuronal excitability and spike generation.

This module introduces two-dimensional neuron models and the mathematical technique of phase plane analysis. Students will learn how to visualize and analyze the dynamics of neuronal systems using phase portraits, nullclines, and stability analysis to understand different firing patterns and behaviors.

This module continues the exploration of two-dimensional neuronal models while introducing dendritic modeling. Students will learn about the computational properties of dendrites, how they process and integrate synaptic inputs, and their role in neuronal computation and information processing.

This module examines the variability in neuronal spike patterns and how neurons encode information through their firing patterns. Students will explore different theories of neural coding, including rate coding and temporal coding, and learn how to analyze spike train statistics and information content.

This module focuses on the role of noise in neuronal systems and how it affects neural coding. Students will learn about stochastic neuron models, the sources of noise in the nervous system, and how neurons can use noise constructively for information processing and coding.

This module covers methods for estimating neuronal model parameters from experimental data and techniques for both encoding and decoding neural information. Students will learn statistical approaches for fitting models to data and methods for extracting information from neural activity patterns.