Nonlinear models of the first synapse in the light-adapted fly retina

Abstract

1. Randomly modulated light stimuli were used to characterize the nonlinear dynamic properties of the synapse between photoreceptors and large monopolar neurons (LMC) in the fly retina. Membrane potential fluctuations produced by constant variance contrast stimuli were recorded at eight different levels of background light intensity. 2. Representation of the photoreceptor-LMC input-output data in the form of traditional characteristic curves indicated that synaptic gain was reduced by light adaptation. However, this representation did not include the time-dependent properties of the synaptic function, which are known to be nonlinear. Therefore nonlinear systems analysis was used to characterize the synapse. 3. The responses of photoreceptors and LMCs to random light fluctuations were characterized by second-order Volterra series, with kernel estimation by the parallel cascade method. Photoreceptor responses were approximately linear, but LMC responses were clearly nonlinear. 4. Synaptic input-output relationships were measured by passing the light stimuli to LMCs through the measured photoreceptor characteristics to obtain an estimate of the synaptic input. The resulting nonlinear synaptic functions were well characterized by second-order Volterra series. They could not be modeled by a linear-nonlinear-linear cascade but were better approximated by a nonlinear-linear-nonlinear cascade. 5. These results support two possible structural models of the synapse, the first having two parallel paths for signal flow between the photoreceptor and LMC, and the second having two distinct nonlinear operations, occurring before and after chemical transmission. 6. The two models were cach used to calculate the synaptic gain to a brief change in photoreceptor membrane potential. Both models predicted that synaptic gain is reduced by light adaptation.

On the Computations Analyzing Natural Optic Flow: Quantitative Model Analysis of the Blowfly Motion Vision Pathway

“…For these values, the function qualitatively fits the linear component of the blowfly LMC response (Juusola et al, 1995) at approximately the brightness conditions of our electrophysiological analysis (Kern et al, 2005).…”

“…(1) In the basic model, the entire peripheral preprocessing is jointly modeled as a single first-order linear low-pass filter with a fixed time constant of p ϭ 8 ms, approximating the corner frequency measured for the response of blowfly photoreceptors to white-noise luminance fluctuations (Juusola et al, 1995;van Hateren and Snippe, 2001). The output of this low-pass filter is inverted to account for the sign inversion of the synapse between the photoreceptor and LMC (Laughlin, 1994).…”

Electrophysiological Method for Recording Intracellular Voltage Responses of <em>Drosophila</em> Photoreceptors and Interneurons to Light Stimuli <em>In Vivo</em>

“…Such precision would be impossible with today's optical imaging techniques, which are noisier and slower. Moreover, the method can be used to characterize small cells' electrical membrane properties both in current-and voltage-clamp configurations 5,29,33,36,[40][41][42]49 , providing valuable data for biophysical and empirical modeling approaches 7,8,11,33,[49][50][51][52][53][54] that link experiments to theory.…”

Inferring input nonlinearities in neural encoding models

“…In practice this method is most suitable when an appropriate reduction in the parameter space can be identified (e.g. Young & Calhoun, 2005); otherwise, the number of parameters tends to be too large for such models to be practical (see also Juusola et al, 1995 for a comparison between Volterra series and cascade models).…”

“…The bilinear model, and implicitly the full-rank model, have appeared before in the context of Hammerstein cascades or NL cascade models (e.g. Narendra & Gallman, 1966;Hunter & Korenberg, 1986;Juusola et al, 1995;Bai, 1998;Westwick & Kearney, 2001). Here, we give these models a probabilistic basis, allowing for the construction of principled regularization techniques (section 2.5); estimation of error bars (section 2.6); we draw connections between the full-rank model and the bilinear model (section 2.3); and we extend the formulation of the bilinear model to the framework of predicting point-process spike trains (section 2.9), leading to the Generalized Bilinear Model or the "NLNP model".…”