Consistency of Extracellular and Intracellular Classification of Simple and Complex Cells

Using a rectification model and an experimentally measured distribution of the extracellular modulation ratio (F1/F0), we investigate the consistency between extracellular and intracellular modulation metrics for classifying cells in primary visual cortex (V1). We first demonstrate that the shape of the distribution of the intracellular metric χ is sensitive to the specific form of the bimodality observed in F1/F0. When the proper mapping between F1/F0 and χ is applied to the experimentally measured F1/F0 data, χ is weakly bimodal. We then use a two-class mixture model to estimate physiological response parameters given the F1/F0 distribution. We show, once again, that a weak bimodality is present in χ. Finally, using the estimated parameters for the two cell clases, we show that simple and complex cell class assignment in F1/F0 is more-or-less preserved in a heavy-tailed f1/f0 distribution, with complex cells being in the core of the f1/f0 distribution and simple cells in the tail (misclassification error in f1/f0 = 19%). Class assignment in f1/f0 is likewise consistent (misclassification error in F1/F0 = 15%). Our results provide computational support for the conclusion that extracellular and intracellular metrics are relatively consistent measures for classifying cells in V1 as either simple or complex. ∗Department of Biomedical Engineering, Columbia University,New York, NY 10027; (al2082, mgp2101, djw21, ps629)@columbia.edu. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research (N00014-01-0625) and NGA grant HM1582-05-C-0008 Consistency of Extracellular and Intracellular Classification of Simple and Complex Cells An Luo, Marios Philiastides, Jim Wielaard and Paul Sajda Department of Biomedical Engineering, Columbia University,New York, NY 10027 (al2082, mgp2101, djw21, ps629)@columbia.edu. Introduction It has been observed that the ratio between the amplitude of the first harmonic of the response to the mean firing rate (F1/F0) when a cell is responding to drifting sinusoidal gratings is bimodally distributed over the V1 population. Furthermore, this bimodality is perceived as evidence for the existence of two discrete classes of cells [1]. Mechler and Ringach [2] however, have proposed that the bimodality of F1/F0 does not necessarily imply the existence of two cell classes. Using a rectification model, they show that a bimodal distribution in F1/F0 can be observed even when the distribution of a parameter χ, closely linked to the intracellular modulation ratio f1/f0, is unimodal. Since f1/f0 , and therefore χ, is more directly linked to the synaptic drive of the neurons, it can be argued that it is likely to be a better metric than F1/F0 for inferring the presence of underlying cell classes. In this paper we investigate the issue of simple and complex cell classification with respect to the consistency of the extracellular and intracellular modulation ratios. Similar to [2], we model neuron responses using a rectification model. Somewhat differently, however, we use the experimentally observed data for F1/F0 reported in [2] to fit model parameters and estimate χ and f1/f0. We first show that the nonlinear mapping from F1/F0 to χ results in a weak bimodal distribution for χ if one uses the experimentally observed F1/F0 distribution. We next use a rectification model, similar to that used in [2], to estimate parameters for both a one class and two class model that best fit the experimentally observed distribution of F1/F0. Finally we use the estimated parameters for the two cell class model to investigate the consistency of simple and complex classification when labeling in F1/F0 and evaluating the class distribution in f1/f0, and vice versa. The rectification model We assume that a neuron’s membrane potential in response to a sinusoidal drifting grating at preferred orientation and spatial frequency consists of a sinusoidal waveform driven at the temporal frequency of the stimulus, with amplitude A, and mean voltage potential Vm. A neuron’s instantaneous firing rate, r(t), is assumed to be proportional to the supra-threshold membrane potential and zero if the membrane potential remains below the threshold, Vt. Eqn. 1&2 summarize this rectification model. v(t) = Vm +A cos(2πft) (1) r(t) = G[v(t)− Vt] (2) In Eqn. 2, G is the gain related to the spike generator. The intracellular modulation ratio f1/f0 is defined as A/(Vm − VI), where VI is the inhibitory reverse potential. The extracellular modulation ratio F1/F0 is given by F0 = 1 2π ∫ 2π 0 r(t)dt and F1 = 1 2π ∫ 2π 0 r(t) cos(2πft)dt. In their paper [2], Mechler and Ringach define an intracellular ratio parameter χ = (Vt − Vm)/A, and prove that F1/F0 is a nonlinear monotonic function of χ, F1/F0 = f(χ) = 