Neural Comput - Continuation-based numerical detection of after-depolarization and spike-adding thresholds.

Tópicos

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Resumo

The changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by the analysis and numerical investigation of a class of mechanistic mathematical models. We focus on a hippocampal pyramidal neuron model and study the occurrence of bursting related to the after-depolarization (ADP) that follows a brief current injection. This type of burst is a transient phenomenon that is not amenable to the classical bifurcation analysis done, for example, for periodic bursting oscillators. In this letter, we show how to formulate such transient behavior as a two-point boundary value problem (2PBVP), which can be solved using well-known continuation methods. The 2PBVP is formulated such that the transient response is represented by a finite orbit segment for which onsets of ADP and additional spikes in a burst can be detected as bifurcations during a one-parameter continuation. This in turn provides us with a direct method to approximate the boundaries of regions in a two-parameter plane where certain model behavior of interest occurs. More precisely, we use two-parameter continuation of the detected onset points to identify the boundaries between regions with and without ADP and bursts with different numbers of spikes. Our 2PBVP formulation is a novel approach to parameter sensitivity analysis that can be applied to a wide range of problems.

Resumo Limpo

chang neuron fire pattern signatur brain function interest understand chang evolv function neuron biophys properti address import problem analysi numer investig class mechanist mathemat model focus hippocamp pyramid neuron model studi occurr burst relat afterdepolar adp follow brief current inject type burst transient phenomenon amen classic bifurc analysi done exampl period burst oscil letter show formul transient behavior twopoint boundari valu problem pbvp can solv use wellknown continu method pbvp formul transient respons repres finit orbit segment onset adp addit spike burst can detect bifurc oneparamet continu turn provid us direct method approxim boundari region twoparamet plane certain model behavior interest occur precis use twoparamet continu detect onset point identifi boundari region without adp burst differ number spike pbvp formul novel approach paramet sensit analysi can appli wide rang problem

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