PRC heterogeneity and firing rate differences independently limit stochastic synchronization of model neurons. *A–D*: mean within-cell (*A* and *B*; *n* = 27 comparisons) and between-cell (*C* and *D*; *n* = 91 comparisons, |ΔFR_{ij}| ≤ 5 Hz) spike time cross power spectra (*A* and *C*) and correlation-induced spike time coherence (*B* and *D*) as a function of firing rate in noisy phase oscillator models with frequencies, PRCs, and CV_{ISI} distributions replicating in vitro findings (thin traces, ±SE). For these spectral analyses, spike trains are convolved with an 8-ms square-wave pulse before cross power spectra are calculated. *Inset*: mean spike time correlogram with time rescaled to the period of each model neuron pair. For comparisons between model neurons with low firing rate differences (*C*), *T* is the mean period of the 2 model neurons. *E*: the correlation-induced spike time coherence integrated from 15–75 Hz is greater in homogeneous populations (within-cell comparisons; solid black line) than in heterogeneous populations (between-cell comparisons, |ΔFR_{ij}| ≤ 5 Hz; black dashed line), as observed in vitro (). Reducing all between-cell PRC (=PRC; light gray line) or firing rate (=FR; dark gray line) differences to zero significantly increased coherence, confirming that both PRC heterogeneity and small firing rate differences (0–5 Hz) impact stochastic synchronization (*P* = 1.8 × 10^{−15}, 2-way ANOVA, within-cell > =PRC, =FR > between-cell, |ΔFR_{ij}| ≤ 5 Hz, Tukey's test). *F1*: high firing rate differences between noisy phase oscillators {|ΔFR_{ij}|: (0,5] Hz, *n* = 91; |ΔFR_{ij}|: (5,10] Hz, *n* = 74; |ΔFR_{ij}|: (10,15] Hz, *n* = 59; |ΔFR_{ij}|: (15,20] Hz, *n* = 61} also significantly limit correlation-induced spike time coherence (*P* = 2.1 × 10^{−42}, |ΔFR_{ij}|: (0,5] Hz > |ΔFR_{ij}|: (5,10] Hz, |ΔFR_{ij}|: (10,15] Hz, |ΔFR_{ij}|: (15,20] Hz; |ΔFR_{ij}|: (0,5] Hz > |ΔFR_{ij}|: (5,10] Hz < |ΔFR_{ij}|: (10,15] Hz, |ΔFR_{ij}|: (15,20] Hz, Tukey's test}. *F2*: mean absolute PRC differences (thin lines, ±SE) across the 4 levels of firing rate differences considered in *F1. G*: reducing all between-cell PRC differences to zero (=PRC; light gray line) does not significantly increase spike time coherence between cells with high firing rate differences (15–20 Hz). In contrast, reducing all between-cell firing rate differences to zero (=FR; dark gray line) significantly raises coherence to levels near those observed in homogeneous populations {*P* = 3.2 × 10^{−75}, 2-way ANOVA, within-cell > =PRC, =FR, between-cell, |ΔFR_{ij}|: (15,20] Hz; within-cell > =FR > =PRC, |ΔFR_{ij}|: (15,20] Hz, Tukey's test}.

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