Principal dynamic mode analysis of action potential firing in a spider mechanoreceptor

Abstract

The encoding of mechanical stimuli into action potentials in two types of spider mechanoreceptor neurons is modeled by use of the principal dynamic modes (PDM) methodology. The PDM model is equivalent to the general Wiener-Bose model and consists of a minimum set of linear dynamic filters (PDMs), followed by a multivariate static nonlinearity and a threshold function. The PDMs are obtained by performing eigen-decomposition of a matrix constructed using the first-order and second-order Volterra kernels of the system, which are estimated by means of the Laguerre expansion technique, utilizing measurements of pseudorandom mechanical stimulation (input signal) and the resulting action potentials (output signal). The static nonlinearity, which can be viewed as a measure of the probability of action potential firing as a function of the PDM output values, is computed as the locus of points of the latter that correspond to output action potentials. The performance of the model is assessed by computing receiver operating characteristic (ROC) curves, akin to the ones used in decision theory and quantified by computing the area under the ROC curve. Three PDMs are revealed by the analysis. The first PDM exhibits a high-pass characteristic, illustrating the importance of the velocity of slit displacement in the generation of action potentials at the mechanoreceptor output, while the second and third PDMs exhibit band-pass and low-pass characteristics, respectively. The corresponding three-input nonlinearity exhibits asymmetric behavior with respect to its arguments, suggesting directional dependence of the mechanoreceptor response on the mechanical stimulation and the PDM outputs, in agreement to our findings from a previous study (Ann Biomed Eng 27:391-402, 1999). Differences between the Type A and B neurons are observed in the zeroth-order Volterra kernels (related to the average firing), as well as in the magnitudes of the second and third PDMs that perform band-pass and low-pass processing of the input signal, respectively.