Facilitated By

San Antonio Medical Foundation

A unified framework to study history dependence in the nervous system

The University of Texas at San Antonio

The University of Texas at San Antonio is an emerging Tier One research institution with nearly 29,000 students.

Principal Investigator(s)
Santamaria, Fidel
Funded by
Natl Inst of Health
Research Start Date

The brain uses previous activity in order to adapt to an ever changing environment. This history

dependence adaptation takes place at all scales of organization of the nervous system. The objective of this theory

project is to develop a shared formalism that can be applied to multiple history dependent phenomena, from the

biochemical reactions that underlie synaptic plasticity, to the emergent patterns in complex neural networks. At

the core of this formalism is the recognition that most models of neuronal activity are based on the classical

reaction-diffusion equation. In Aim 1 we will prove that a generalization of this equation, the fractional order

reaction diffusion equation, provides all the natural mathematical tools to incorporate history dependence into

neuronal function analysis. The fractional order exponent of the fractional derivative is a parameter that captures

the emergent interactions of multiple elements that cause the history dependent process. We will develop the

equations for specific cases of activation of membrane conductances, the membrane voltage, and firing rate

activity. In Aim 2 we will apply this formalism to three examples. The first one will be to study how history

dependence in the biochemical reactions that underlie synaptic long term depression in cerebellar Purkinje cells

depend on the complexity of the structure of the dendritic tree. We will test whether history dependence caused by

a process known as anomalous diffusion could enhance the sensitivity of the biochemical reaction. The second

example will use a simplified model of history dependence spiking that is characterized by a history dependent

exponent. We will derive families of membrane conductances that match this exponent and will build

Hodgkin-Huxley models to test whether they produce history dependent spiking activity. Finally, we will study

the effects of using history dependent synaptic or neuronal elements in networks dynamics. We will test the

hypothesis that criticality, a condition in which information transmission is optimized can be robustly

implemented with history dependent neurons. Overall, this project will form an understanding.

Collaborative Project
Basic Research