Encoding the fine-structured mechanism of action potential dynamics with qualitative motifs

Abstract

This work presents a neuroinformatic method for deriving mechanistic descriptions of fine-structured neural activity. This is a new development in the computer-assisted analysis of dynamics in conductance-based models, which is illustrated using single compartment models of an action potential. A sequence of abstract, qualitative motifs is inferred from this analysis, forming a template that is independent of the specific equations from which they were abstracted. The template encodes the assumptions behind the model reduction steps used to derive the motifs, and so specifies quantitative information about their domains of validity. The template representation of a mechanism is converted to a hybrid dynamical system, which is simulated as a sequence of low-dimensional reduced models (in this example, phase plane models) with appropriate switching conditions taken from the motifs. We demonstrate the validity of the template on a detailed single neuron model of spiking taken from the literature, and show that the corresponding hybrid system simulation closely mimics the spiking dynamics of the full model.

Hybrid Models and Biological Model Reduction with PyDSTool

“…(E.g., see [43] for an example of exploring this issue in biomechanical modeling.) In addition, algorithms have recently been developed that assist with the inference of mechanistic relationships in ordinary differential equation (ODE) models, and also with the systematic and semi-automated construction of the resulting reduced descriptions in terms of hybrid systems [44]–[46].…”

Inferring and quantifying the role of an intrinsic current in a mechanism for a half-center bursting oscillation

“…The resulting set of states and transitions is summarized in Table 1, which will be referred to as the "template" of the bursting rhythm's mechanism (after [19]). As we focus on I h only, the template does not exhaustively list all properties of the system in each state.…”

“…A functionally driven reduction of all currents involved in this feedback could be expected to allow meaningful quantification of the degree to which release plays a role in comparison to escape. It may also facilitate phase plane and bifurcation analysis of the hybrid dynamics for these feedback loops, for instance along the lines of [1,11,19,24,26].…”

“…The formalized description of the escape-release mechanism took the form of a "template" that categorizes gross functional states of the system and indicates characteristic transitions between them [19]. A template is more explicit about its assumptions than a natural language description, and provides a clearer means to distinguish causal connections from correlations in the changing activity between the model's components.…”

Geometric analysis of soft thresholds in action potential initiation and the consequences for understanding phase response curves and model tuning

“…Recent mathematical and computational work on the space-clamped Hodgkin-Huxley (H-H) model of neural excitability identifies major dynamic features of the changing nullclines in 2D phase plane projections during action potential (AP) initiation [1,2]. Such analysis provides novel mechanistic and geometric understanding (in terms of interplay between variables and currents) of the “soft threshold” dynamics.…”