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Kuan Hao Chen,
Qi-Rong Lin,
Chi Keung ChanTo produce timely responses, animals must conquer delays from visual processing pathway by predicting motion. Previous studies [1] revealed that predictive information of motion is encoded in spiking activities of retinal ganglion cells (RGCs) early in the visual path. In order to study the predictive properties of a retina in a more systematic manner, stimuli in the form of a stochastic moving bar are used in experiments with retinas from bull frogs in a multi-electrode system. Trajectories of the bar are produced by Ornstein-Uhlenbeck (OU) processes with different time correlations (memories) induced by a butter-worth low-pass filter with various cut-off frequencies.
We then investigated the predictive properties of single RGC by calculating the time shifted mutual information (MI(x,r;δt)) between spiking output from RGCs and the bar trajectories. Intuitively, the peak position of MI(δt) is typically negative when considering the processing delay of the retina. Our measured peak positions of MI(δt) for some RGCs were characterized by both positive and negative peak position under low-pass OU (LPOU) stimulus. This finding indicates that some RGCs (P-RGCs) are predictive while the others are non-predictive (NP-RGCs). For LPOU with various correlation times, the MI peaks from the P-RGCs are positively correlated with the correlation times of the stimuli while those from the NP-RGCs are always around a fixed negative number (-50ms).
Furthermore, we apply principle component analysis [2] on the waveforms of stimuli preceding each of the neuron’s spike (spike triggered stimuli) to separate spikes into two clusters according to whether their projections to principle component are negative or positive. We find that predictive information can be extracted from the apparent non-predictive NP-RGCs when MI(δt) is obtained with spikes from each cluster. This last finding suggests that spikes from a single RGC might have different origins. Since the responses (r) from RGCs can carry information for both position (x) and velocity (v) of the moving bar, we have also performed partial information decomposition [3] for the mutual information between r and the combined state {x,v} which can be written as I[(x,v):r] = S + Ur + Ux + R where Ur and Ux are the unique contribution from x and v respectively while similarly R and S are the redundant and synergy contribution. We find that synergy from x and v is needed to produce anticipation. A simple spikes generation model with synergy from x and v is constructed to understand our experimental data.
References
1. Palmer SE, Marre O, Berry MJ, Bialek W. Predictive information in a sensory population. PNAS. 2015, 112(22).
2. Geffen MN, de Vries SEJ, Meister M. Retinal Ganglion Cells Can Rapidly Change Polarity from Off to On. PloS Biol. 2007, 5(3).
3. Williams PL, Beer RD. Nonnegative Decomposition of Multivariate Information. arxiv. 2010.
