Do direction selective retinal ganglion cells encode information uniformly?

A major goal of sensory neuroscience is to understand the system's response to individual stimuli. Although mutual information (MI) continues to be a useful tool when applying Information theory to neural systems, it does not suffice when trying to understand how informative individual stimuli are. In general such knowledge may be crucial for understanding the functional organization of sensory systems. To investigate this, we focus on ON-OFF Direction Selective Retinal Ganglion Cells (dsRGC). These cells respond robustly to motion in their preferred direction, and sparsely to motion in the opposite direction. Each of the 4 different subtypes of dsRGC responds preferentially to motion along 1 of the 4 cardinal directions (Oyster and Barlow, Science, 1967). Given the discreteness and exclusivity of the preferred directions, we pose the question: can and does this system homogeneously encode all possible directions? Here we apply the Stimulus Specific Information (SSI, Butts, Network, 2003):
$SSI(\theta) = \sum_{r \in R}p(r|\theta) \{ H[\Theta] - H[\Theta | r] \}$
where $\Theta$ and $R$ are the stimulus and response ensembles respectively, and $H$ denotes the entropy. The SSI is a decomposition of the MI over the stimulus ensemble $\Theta$ so that $\sum_{\theta \in \Theta} p(\theta) SSI(\theta) = MI[\Theta; R]$ We use this measure to quantify the sensitivity of quadruplets of dsRGCs, containing one cell per cardinal direction, recorded from rabbit retinas (Franke et al. Neuron 2016). We show that quadruplets' sensitivity is surprisingly homogeneous across directions $\theta \in \Theta$. Additionally, quadruplets with tuning parameters inferred from retinal recordings show a more homogeneous sensitivity than populations with “non-natural” tuning parameters, namely with smaller/ larger tuning curve widths. Furthermore, given that by construction the average of the SSI equals MI, we show that the stimulus response of these cells is not consistent with the efficient coding hypothesis insofar as they do not necessarily maximize MI, given fixed resources. Instead, we provide evidence that a more complex trade-off occurs where the population achieves a relatively high, but globally suboptimal, value of MI while striving to maximize the minimum of the SSI. This indicates that instead of maximizing the average quantity of encoded information, the system prioritizes avoiding a situation where certain stimuli are very poorly encoded (i.e. blindspots).