To couple the initial linear-nonlinear system to the kinetics block, the output of the nonlinearity, u(t), scales one or two rate constants. Although this means that the transition rate is proportional to the nonlinearity output, a higher-order dependence—such as the dependence of vesicle release on a higher power of the calcium concentration—can be captured in the nonlinearity itself.

We fit LNK models using a constrained optimization algorithm (see Experimental Procedures). The filter and nonlinearity were reduced to a set of 20 parameters, and the kinetics block contributed 5 parameters. The activation rate ka was scaled by the input, and most other rate constants were fixed. In addition, to capture the contrast dependence of the rate of slow adaptation, the input scaled the rate Selleck Tyrosine Kinase Inhibitor Library of slow recovery ksr. The motivation for scaling of the slow rate constant by the input is discussed further below. We compared the LNK model output to the cell’s membrane potential response across the entire recording (300 s). The model accurately captured the response at all times,

including contrast transitions at both decreases and increases in contrast (Figure 2C, Figure S1). The correlation coefficient between the model and the response was 88 ± 4% (90 ± 2% for bipolar cells [n = 5], 89 ± 4% for selleck chemicals amacrine cells [n = 9], and 86 ± 4% for ganglion cells [n = 7]), mean ± SEM. We then compared these values to the intrinsic variability of each cell by repeating a stimulus sequence two to three times. The accuracy of the model was nearly that of the variability

between repeats of the Rolziracetam stimulus, which was 90 ± 5% (92 ±2% for bipolar cells, 92 ± 4% for amacrine cells, and 89 ± 6% for ganglion cells) (Figures 2D and 2E). Thus, the LNK model accurately captured the membrane potential response to changing contrast for inner retinal neurons. We then assessed how well the LNK model captured adaptive properties by fitting LN models to both the data and to the LNK model. Examining the temporal filters of these LN models, the LNK model captured the fast change in temporal processing between low and high contrast (Figure 3A). In addition, the LNK model captured fast changes in sensitivity between low and high contrast as well as fast and slow changes in baseline membrane potential (Figure 3B). Across a population of cells, the LNK model closely matched the temporal filtering and average overall sensitivity of the cell’s response across the full range of contrasts (Figures 3C and 3D). After a contrast step, the LNK model matched the fast change in average membrane potential of a cell across a range of contrast transitions (Figure 3E). Finally, the LNK model matched slow changes in baseline as the model matched the near steady-state average membrane potential value of a cell at the end of 20 s of constant contrast (Figure 3F).