What is the neural code?

1. What is the neural code? Puchalla et al., 2003

2. What is the neural code? • Encoding: how does a stimulus cause the pattern of responses? • what are the responses and what are their characteristics? • neural models: what takes us from stimulus to response; • descriptive and mechanistic models, and the relation between them. • Decoding: what do these responses tell us about the stimulus? • Implies some kind of decoding algorithm • How to evaluate how good our algorithm is?

3. What is the neural code? Single cells: spike rate spike times spike intervals

4. What is the neural code? Single cells: spike rate: what does the firing rate correspond to? spike times: what in the stimulus triggers a spike? spike intervals: can patterns of spikes convey extra information?

5. What is the neural code? Populations of cells: population coding correlations between responses synergy and redundancy

6. Receptive fields and tuning curves Tuning curve: r = f(s) Gaussian tuning curve of a cortical (V1) neuron

7. Receptive fields and tuning curves Tuning curve: r = f(s) Hand reaching direction Cosine tuning curve of a motor cortical neuron

8. Receptive fields and tuning curves Retinal disparity for a “near” object Sigmoid/logistic tuning curve of a “stereo” V1 neuron

9. Reverse correlation Fast modulation of firing by dynamic stimuli Feature extraction Use reverse correlation to decide what each of these spiking events stands for, and so to either: -- predict the time-varying firing rate -- reconstruct the stimulus from the spikes

10. Reverse correlation Gaussian, white noise stimulus: unbiased stimulus which samples all directions equally S(t) r(t) Compute the average stimulus leading up to a spike.

11. Reverse correlation

12. Stimulus = Fluctuating Potential (generates electric field) Spike Train of a Neuron in the ELL of a fish Spike-Triggered Average

13. The spike triggered average of the Hodgkin Huxley neuron

14. What is the language of single cells? • What are the elementary symbols of the code? • Most typically, we think about the response as a firing rate, r(t), or a modulated • spiking probability, P(r = spike|s(t)). • We measure spike times. • Implicit: a Poisson model, where spikes are generated randomly with • local rate r(t). • However, most spike trains are not Poisson (refractoriness, internal dynamics). Fine temporal structure might be meaningful. • Consider spike patterns or “words”, e.g. • symbols including multiple spikes and the interval between • retinal ganglion cells: “when” and “how much”

15. Multiple spike symbols from the fly motion sensitive neuron Spike Triggered Average 2-Spike Triggered Average (10 ms separation) 2-Spike Triggered Average (5 ms)

16. spike-triggering stimulus feature decision function Decompose the neural computation into a linear stage and a nonlinear stage. stimulus X(t) f1 spike output Y(t) x1 P(spike|x1 ) x1 To what feature in the stimulus is the system sensitive? Gerstner, spike response model; Aguera y Arcas et al. 2001, 2003; Keat et al., 2001 Modeling spike generation Given a stimulus, when will the system spike? Simple example: the integrate-and-fire neuron

17. spike-triggering stimulus feature decision function stimulus X(t) f1 spike output Y(t) x1 P(spike|x1 ) x1 Modeling spike generation The decision function is P(spike|x1). Derive from data using Bayes’ theorem: P(spike|x1) = P(spike) P(x1 | spike) / P(x1) P(x1) is the prior : the distribution of all projections onto f1 P(x1 | spike) is the spike-conditional ensemble : the distribution of all projections onto f1 given there has been a spike P(spike) is proportional to the mean firing rate