Phase information is conserved in sparse, synchronous population-rate-codes via phase-to-rate recoding

Neural computation is often traced in terms of either rate- or phase-codes. However, most circuit operations will simultaneously affect information across both coding schemes. It remains unclear how phase and rate coded information is transmitted, in the face of continuous modification at consecutive processing stages. Here, we study this question in the entorhinal cortex (EC)- dentate gyrus (DG)- CA3 system using three distinct computational models. We demonstrate that DG feedback inhibition leverages EC phase information to improve rate-coding, a computation we term phase-to-rate recoding. Our results suggest that it i) supports the conservation of phase information within sparse rate-codes and ii) enhances the efficiency of plasticity in downstream CA3 via increased synchrony. Given the ubiquity of both phase-coding and feedback circuits, our results raise the question whether phase-to-rate recoding is a recurring computational motif, which supports the generation of sparse, synchronous population-rate-codes in areas beyond the DG.

Supplementary Figure 5. Robustness of phase-to-rate recoding to GC membrane noise.Noise was simulated with a current injection at the soma of each granule cell.The noise current was drawn from a normal distribution of mean 0 and different standard deviations (sd) in b, c & d (all panels show the same cell on the left).a GC membrane voltage without noise.b Membrane noise (sd = 50pA) was chosen such that voltage traces matched in house in vivo recordings (also see 9 ).On the right, results of spatial information analysis with GC rate-controlled data.c,d same as (b) but with ~5 and 10x realistic noise levels (sd=0.25 and 0.5nA, note that due to the low-pass filtering property of the membrane, voltage deflections are smaller than would be expected for constant current injections of the same amplitude).The significant phase-to-rate translation is robust to sd = 0.25 nA and lower membrane noise.At sd = 0.5 nA membrane noise the feedback inhibitory effect on shuffling is no longer significant.Two-way repeated measures ANOVA with Dunnett's post-test (middle) or paired t-test (right).n=10 grid seeds for all groups.* indicates p<0.05, *** p<0.001.Source data are provided in Source Data.xlsx.Full statistics are shown in supplementary tables 15-17.Supplementary Figure 6.Robustness of phase-to-rate recoding given counter-cyclical LEC input.LEC inputs were modeled as non-homogeneous Poisson spiking with countercyclical modulation and no spatial information.a LEC input properties: To model a coincident 'similar' contextual input from LEC, we assumed the exact same subpopulation of LEC cells were active, but contained no further rate or phase information (spike-trains were instantiated with different Poisson seeds).b Density distribution of action potentials for the MEC grid cell input used throughout the main part of the study (left) and the counter cyclical LEC input (right).All histograms of the figure contain data from a single grid seed with 20 Poisson seeds of a single trajectory.c On the left is the spike count of granule cell spikes with the LEC input being off compared to 20 LEC cells, each contacting 100 randomly chosen granule cells.LEC synapses are located at the distal dendrite of the granule cells (425 µm from the soma).The LEC input makes more granule cells fire earlier and also causes more late firing.On the right are the results of the spatial information analysis.d & e show the same as c but with more LEC synapses.e shows that phaseto-rate recoding occurs even when the LEC synapses cause a strong shift in granule cell distribution.).Truncated AP's in the voltage trace were added for illustrative purposes.Note the pronounced facilitation at the granule cell (GC) to CA3 Pyramidal (Pyr.)synapse.c Illustration of a combined excitatory/inhibitory input to a pyramidal cell, when accounting for approximate cell stoichiometry and mean firing rates (which lead to many IPSCs for any EPSC).Note that in this case a 20 Hz input does not suffice to fire the pyramidal cell, but a 50 Hz input does.d Mean firing rates of the extended model for 40 pA IPSC amplitude and 20 ms STDP timescale (white circles in e,g,h).e Dependence of mean CA3 pyramidal firing rate for different inhibitory strengths and STDP timescales.The empirically plausible range of activity for CA3 is 0.3 to 5Hz 13,14 , i.e. the blue area in the plot.Note that, where this firing rate is exceeded (green and yellow area), the networks exhibits runaway excitation with implausibly high firing rates (≥200Hz).f Mean weight increases for 40 pA IPSC amplitude and 20 ms STDP timescale.g Dependence of mean weight increases for different inhibition strengths and STDP timescales, as well as the ratio between full and no feedback network (right).h Mean weight increase when weights are first normalized to mean rates (panel e).Note that values >2 (~0 to 20pA inhibition) fall into the range of runaway excitation and are arguably not meaningful.Source data are provided in Source Data.xlsx.Full statistics are shown in supplementary tables 30,31.

Suppl. Fig. 8b
Grid How big is the difference?How big is the difference?Mean of differences (B -A) -0,01630838 Mean of differences (B -A) -0,004324750 SD of differences 0,006460059 SD of differences 0,0008824175 SEM of differences 0,001615015 SEM of differences 0,0002206044 95% confidence interval -0,01975070 to -0,01286605 95% confidence interval -0,004794957 to -0,003854543 R squared (partial eta squared) n=10 grid seeds for all groups.*** indicates p<0.001.Source data are provided in Source Data.xlsx.Full statistics are shown in supplementary tables 18-20.Supplementary Figure 13.Extended CA3 model.a Schematic of the CA3 model plus the added complexities of the extended model.b Examples of the modelled monosynaptic currents and voltages based on a brief 20Hz stimulus of three pulses (matched to Toth et al., 2000

Supplementary Table 21. Statistics for Supplementary Fig. 7c -200 LEC synapses per cell, identical input Suppl. Fig. 7d no
LEC for comparison (note: fewer iterations were simulated than in the main fig.2i)

Supplementary Table 22. Statistics for Supplementary Fig. 7d -no LEC synapses (same as Fig.2i) for comparison Suppl. Fig. 8b rate
Positional rate information analysis, 12cm smoothing

Supplementary Table 28. Statistics for Supplementary Fig. 11a -positional rate information analysis for only early theta (0-pi) Suppl. Fig. 11b
Positional phase info analysis for only the first half of theta