Fig 1.
Overview of analysis approach.
A Information-theoretic measures of predictability and information transfer: active information storage (AIS) quantifies the predictability of a processes’ current state xt from its immediate past x−, transfer entropy (TE) quantifies the information transfer from a source process X to a target process Y by quantifying the predictability of the target’s current state, yt from the sources’ past, x−, in the context of the target’s immediate past, y−. B Local storage-transfer correlations (LSTC) relating local AIS (lAIS) as a measures of predictability and local TE (lTE) as a measure of information transfer: if a neuron codes for predictable input a positive correlation is expected, if the neuron codes for unpredictable input, a negative correlation is expected (adapted from [5]). C Realizations of predictive coding in the cortex (adapted from [11]): bottom-up sensory input (dotted arrows) is compared to predictions propagated in top-down direction from a hierarchically higher cortical level (solid arrows) that represent the current prior about the input (white bars). Error coding assumes that bottom-up information represents predictions errors while reliability coding assumes that bottom-up information represents enhanced input. See main text for details. D Physiology of the retinogeniculate synapse and recording sites [12, 13]: Recordings were collected from in- and outputs to the synapse between retinal ganglion cells (RGC) and layer A principal cells (PC) in the lateral geniculate nucleus (LGN). We estimated local active information storage (lAIS, blue arrow) within the synapse input, and local transfer entropy (lTE, red arrow) between in- and output of the synapse. Schematic representations of known connections of PC and RGC are shown in grey (round markers indicate synapses): excitatory cells in layer 6 of primary visual cortex (V1) form feedback connections with LGN PC and also project to LGN inhibitory interneurons (int) and perigeniculate nucleus (PGN). Interneurons provide inhibitory input to LGN PC: intrageniculate interneurones (int) mediate feed-forward inhibition from RGC cells, while PGN cells provide recurrent inhibition [12, 14]; PGN interneurons further form reciprocal, inhibitory connections amongst each other (dashed line).
Fig 2.
Correlation between contribution and local storage-transfer correlations (LSTC) for all spike pairs.
LSTC was stronger for cell pairs with higher contribution (percentage of LGN spikes triggered by an RGC spike), i.e., synapses that were more strongly connected.
Fig 3.
State-dependent and -independent information transfer from RGC to LGN cell.
State-dependent and -independent information transfer from RGC to LGN cell, measured by the synergistic information, Isyn(Yt; XS, YS) (dark gray), and unique information, Iunq(Yt; XS) (light gray). In 11 out of 16 pairs, more than half of the transferred information was independent of the LGN cell’s past state.
Fig 4.
Local storage-transfer correlations (LSTC) for exemplary cell pairs.
Histograms of LSTC for representative cell pairs with highest (pairs 10 and 11) and lowest (pairs 12 and 15) contribution, respectively. The first column shows histograms for all spikes, the second column for relayed spikes, and the third column for non-relayed spikes. An RGC spike was considered relayed to the LGN if it was followed by an LGN spike with the delay reconstructed during lTE estimation. Rows show individual cell pairs. Relayed spikes showed positive lTE and generally positive lAIS, while non-relayed spikes led to zero or negative lTE and lower lAIS.
Fig 5.
Information dynamics of relayed versus non-relayed RGC spikes.
An RGC spike was considered relayed to the LGN if it was followed by an LGN spike with the delay reconstructed during lTE estimation. Relayed spikes were accompanied by higher lAIS than non-relayed spikes. Also, relayed spikes led to high lTE in comparison to non-relayed spikes. A–C Spike-triggered average (STA) for lAIS values (A all RGC spikes, B relayed spikes, and C non-relayed spikes); D Mean lAIS for relayed and non-relayed RGC spikes, for each cell pair. lAIS was higher for relayed (dark blue) than for non-relayed (light blue) RGC spikes (p < 0.001*** for a permutation test with 1000 permutations). E–G STA for lTE values (E all RGC spikes, F relayed spikes, and G non-relayed spikes); H Mean lTE values for relayed and non-relayed RGC spikes, for each cell pair. lTE was higher for relayed (dark red) then for non-relayed (light red) RGC spikes (p < 0.001*** for a permutation test with 1000 permutations). I–K STA of RGC spike trains (I all RGC spikes, J relayed spikes, and K non-relayed spikes). Relayed RGS spikes were more often preceded by a spike than non-relayed spikes. L–N STA of LGN spike trains, aligned with corresponding RGC spike train with respect to the reconstructed delay (L all RGC spikes, M relayed spikes, and N non-relayed spikes). As expected, relayed RGC spikes were always followed by an LGN spike, while this was not generally the case for all spikes.
Fig 6.
Information dynamics of inter-spike intervals (ISI).
Predictability of the RGC spike train, measured by lAIS, was highest for spikes with the most frequent preceding ISI. Information transfer across the synapse, measured by lTE, was also highest for RGC spikes with the most frequent preceding ISI. While predictability was high for relayed and non-relayed RGC spikes, information transfer was only high for relayed spikes. A Distribution of ISI pooled over all cell pairs (maximum at 2 ms). B Distribution of ISI for relayed RGC spikes, pooled over all cell pairs (maximum at 2 ms). C Mean lAIS at RGC spike as a function of the preceding ISI (maximum at ISI = 3 ms, dashed vertical line, shaded area indicates ±1SD); D Mean lTE at RGC spike by preceding ISI (maximum at ISI = 2 ms, grey vertical line, shaded area indicates ±1SD); E Mean lAIS at relayed (dotted line) and non-relayed (dashed line) RGC spikes as functions of the preceding ISI (maxima at ISI = 3 ms for relayed spikes, dotted vertical line, and at ISI = 3 ms for non-relayed spikes, dashed vertical line, shaded area indicates ±1SD); F Mean lTE at relayed (dotted line) and non-relayed (dashed line) RGC spikes as functions of the preceding ISI (maxima at ISI = 2 ms for relayed spikes, dotted vertical line, and at ISI = 38 ms for non-relayed spikes, dashed vertical line, shaded area indicates ±1SD).
Fig 7.
Spike-triggered averages (STAs) for spike tuples.
STAs for spike tuples with a silence time of 20 ms and inter-spike interval (ISI) up to 20 ms (aligned on first spike in a tuple). Left column shows lAIS values averaged over cell pairs for ISI of 1 ms to 10 ms, right column shows averaged lTE values (shaded areas indicate ±1SD). The lTE values are shifted by the individual delay between RGC and LGN cell for each pair such that a spike at index t = 0 indicates a transferred spike with a delay corresponding to the reconstructed information transfer delay. The predictability of the second RGC spike in a tuple, measured by the lAIS, was high for ISI from 3 ms to 7 ms, while first spikes in a tuple were unpredictable as indicated by no or negative lAIS. Information transfer measured by lTE was high for all RGC spikes with highest values for the second spike in a tuple.