Figure 1. Relationship between input and output correlation. A, Stimulation paradigm in which neurons 1 and 2 receive fluctuating input I1, I2, with mean μ1, μ2, and variance σ12, σ22. Fluctuating input was modeled as an Ornstein–Uhlenbeck process with τ = 5 ms. Some fraction of that input is shared, or correlated, as defined by the input correlation c. Output firing rate ν1, ν2, and the output correlation coefficient ρ (=spike train covariance C normalized by variance) were measured. B, Plotting output correlation ρ against input correlation c shows how much correlation is transferred by the pair of neurons. The slope of that curve, denoted correlation susceptibility S, is ≤1 but has been shown to depend on input parameters μ and σ (de la Rocha et al., 2007). C, Input correlation c can only be unambiguously decoded from ρ (without knowledge of other input parameters) if S does not vary with other input parameters. The dashed curves on the bottom plots show horizontal cross-sections through 3-D plots (top) at different μ. An invariant ρ–c relationship (left) is conducive to good correlation-based coding, whereas a variable relationship (right) is not unless a more complicated decoding scheme is invoked. D, If ν is tuned to μ, then fluctuations around μ will produce fluctuations in ν whose magnitude depends on ∂ν/∂μ. If neurons 1 and 2 receive input with correlated fluctuations, ν1 and ν2 will be comodulated. Amplitude of ν comodulation naturally depends on ∂ν/∂μ, rendering ρ and ν cotuned to μ. In that scenario, rate comodulation will not provide information about μ beyond that already provided by rates ν1 and ν2, but this does not rule out spike-time synchronization providing information about σ if input fluctuations are considered signal rather than noise.