• How can we measure neural activity?

• What info do neurons encode in trains of action potentials (“spike trains”)?

• How can we model “statically” encoded information?

• Estimation/”decoding”

• How can we model/decode “dynamic” information? (filtering, Kalman, HMM)

• Signal conditioning – “spike sorting” (PCA, Expectation-Maximization)

• Beyond spike trains (LFP, EEG, imaging)

• Neurons transmit information by firing sequences of spikes
• Neural encoding – the map from stimulus to neural response. (hard)
  • Can measure how neurons respond to a wide variety of stimuli. Then construct models; attempt to predict responses to other stimuli.
  • We will discuss encoding next few lectures.
• Neural decoding – the map from response to stimulus. (easy-ish)
  • Attempt to reconstruct a stimulus, or certain aspects of that stimulus, from the spike sequence it evokes
  • We will discuss decoding extensively in the rest of this course.

Why is characterizing the stimulus → response relationship hard?

Neural responses are “complex” and variable.

 

Characterizing the stimulus → response relationship is hard because

• Spike sequences reflect both intrinsic neural dynamics and temporal characteristics of stimulus.

 

Characterizing the stimulus → response relationship is hard because

• Identifying features of response that encode changes in stimulus is difficult, especially if stimulus changes on times scale of inter-spike interval.

Characterizing the stimulus → response relationship is hard because

• Neural responses vary from trial-to-trial even when the same stimulus is presented repeatedly.

• Biophysical randomness (e.g., neurotransmitter release at presynaptic terminal, opening/closing of ion channels)
• Arousal and attention
• "Other" cognitive "junk"

• Characterizing the stimulus ➞ response relationship is hard because neural responses are “complex” and variable.
• Bottom line: modeling/predicting the exact timing of every spike is too hard
• So… we can use a model for the probability that different spike sequences are evoked by a specific stimulus.

• Stimulus features are encoded by the activities of large neural populations (e.g., b/millions).
• To model population codes we must do more than just study the firing patterns of single neurons. Why?
  • Information can be represented in correlated activity!

Correlation is complicated! How can we even begin to determine causality??

How does a population of neurons (in motor cortex) encode, with spike times, where the arm will move next?

How is the actual arm movement encoded?

• Action potentials encode and convey information through their timing.
  • AP duration, amplitude and shape are highly stereotyped.
  • Neglecting the brief duration of the actual AP (~1 ms), we can characterize an AP sequence with a list of spike times, ti.

• The sequence of APs generated by a given stimulus varies from trial to trial.
• Hence statistical / probabilistic approach.
• Neural responses can be characterized by firing rates, rather than by specific spike sequences.

• Simple firing rate = # of spikes in a time window (units of spikes per second or Hz)

• What are we missing???
  • ​Aspects of neural responses that vary in time!

Ways to approximate a time-varying firing rate from a spike train

Raw spike train

 

Counts in 100 ms windows (non-overlapping)

 

Counts in 100 ms windows (sliding window)

 

Convolution with Gaussian (what's a good sigma??)

 

Convolution with one-sided exponential (why is this more realistic for real time??)

• If we want high temporal resolution, bins must be made small but counts are then primarily zero or one

 

 

 

 

 

 

 

• Firing rate estimation is sensitive to randomness ("noise") in spike generation. We would like to discard this random component

• Spike-timing dependent plasticity (we'll pick up from here next time!)