Figure 1

Schematized protocols for PRC measurement in neurons. (a) Protocol for fPRC measurement: isolated nonoscillatory neuron $i$ is silent at rest, but emits a burst in response to an initial input. An online protocol detects this burst and thereafter delivers a stimulus at fixed delay Δ after the initiation of each subsequent burst for $N$ cycles. Response times $t_{rk}$ are measured after each input. (b) The fPRC consists of averages ${\overline{t}}_r$ tabulated across Δ. (c) Definition of terms: stimulus delay Δ and response time $t_r$ during 1:1 phase-locking are shown for bursting neurons $i$ and $j$. The shaded and hatched regions correspond to the burst duration. (d) Graphical method for prediction: fPRCs for each component neuron are plotted on the appropriate axes such that any point of intersection gives a solution mode of 1:1 phase-locking. Stability is calculated as described in the text. (e) Protocol for spPRC measurement provided for comparison: phase shift to an ongoing oscillatory rhythm with period $P_0$ is measured in isolated neuron $x$ by delivering a single-pulse stimulus at delay Δ and measuring the resulting interval $P_1$. (f) The spPRC consists of the relative change in period $P_1$-P${}_0$ tabulated across delay Δ. Both terms are scaled to phase ϕ on [0,1) by normalizing by $P_0$.Reuse & Permissions

Figure 2

Schematic of the pyloric network.Reuse & Permissions

Figure 3

Comparison of (a) model and (b) biological results showing that fPRCs measured in (i) isolated component neurons make (ii) predictions that match (iii) simulated or experimental observations of network activity. Summarized observations from column (iii) are indicated by asterisks (*) plotted in column (ii). Parameter $g_s$ was varied to produce families of three fPRCs for each neuron in (b)(ii). All intersections in (b)(ii) were calculated to be stable. To avoid clutter in (b)(ii), confidence bounds of +/−1 standard error are shown as the shaded area for only one fPRC from each component neuron and for the observed activity. Observations at multiple points in experimental time were necessary in (b) to determine the degree of stationarity of the biological system.Reuse & Permissions

Figure 4

Summary of results. Predicted (Pred) network (a) phase and (b) period are compared to observed (Obs) behavior for four experimental preparations.Reuse & Permissions