Ph.D Thesis

Ph.D StudentHillel Ori
SubjectExcitability Phase Diagram: Theoretical Construction and
Experimental Demonstration
DepartmentDepartment of Medicine
Supervisors PROF. Shimon Marom
PROF. Erez Braun
Full Thesis textFull thesis text - English Version


The objective of the research was to develop a framework for investigating the robustness of neural activity despite large variance in the parameters defining it, theoretically and experimentally.

The theoretical aim was to obtain a low-dimension representation of excitability (the process of action potential generation), and to make a "road map" relating the excitability status of a cell - whether excitable, oscillatory or quiet - to its underlying biophysical parameters. First, I simulated the Hodgkin-Huxley equations governing neuronal excitability (Hodgkin 1952) using thousands of random biophysical parameter sets from the physiological range and classified the results into the three excitability statuses. I showed that many sets of parameters result in an unresponsive behavior and that the solutions are very sensitive to parametric variations. This contrasts with the behavior of biological neurons, which maintain relatively invariant patterns of activity in the face of perturbations and are seemingly more robust compared to the classic Hodgkin-Huxley type models used to describe them.

Next, I combined the Hodgkin-Huxley parameters into two lumped entities, denoted “S” and “K”. S (stands for “Structure”) represents the cell capacitance and the densities of ion-channels. K (stands for “Kinetics”) represents the ion-channels’ opening and closing rates. I positioned on the K-S plane the outcomes of the simulations according to their parameters and found that the three excitability statuses are nicely clustered in clouds. The K-S representation is, therefore, a phase diagram; changes in the underlying parameters imply movements of the system on the phase diagram.

The experimental aim was to validate this K-S phase diagram. This entails probing the system many times in different locations on the K-S plane, which is presumably impossible in an intact system. Therefore, a bio-synthetic approach was embraced, where I combined biological and artificial “building blocks” to establish a minimal excitable system which offers enhanced control over K and S. The biological portion consisted of a Xenopus oocyte expressing heterologous ion channel population of preference, e.g. a potassium conductance. An artificial conductance of interest (e.g. sodium) was added to the oocyte using an established method called “Dynamic Clamp”, which is a special type of Current Clamp. These two conductances interact through the common membrane voltage of the oocyte - a minimal bio-synthetic excitable system is established.

This novel biological-artificial hybrid facilitated validation of the phase diagram, enabling positioning of the system in a desired location on the phase diagram (utilizing the “knobs” provided by the artificial component). Thus densely probing the K-S map, I then reconstructed the 'quiet'-'responsive' phase transition.

The phase diagram obtained, along with the ability to navigate a system upon this map, opened the way to further investigate whether biologically expressed conductances can contribute to excitability robustness. I demonstrated history-dependent dynamics (hysteresis) in several 'directional walks' on the K-S plane, indicating that slow-gating dynamics of the ion channel population participate in shaping system trajectory on the phase diagram.