• 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.
• 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.

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?

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??)

• Neural responses typically depend on many stimulus properties, start with one.
• Simple approach
  • Count the number of spikes fired during the presentation of a stimulus.
  • Repeat stimulus presentation many times to better estimate the mean count
  • Vary the stimulus attribute of interest, s
  • Plot result and (optionally) fit parameterized function to data

• Monkey motor cortex example from earlier task!
  • Monkey trained to reach in different directions, s
  • Count number of spikes during arm movement
  • Repeat movement many times to better estimate  the mean count

• Tuning curves describe the MEAN FIRING RATE, given a stimulus
• They DO NOT describe how the firing rate varies from trial to trial

• Single-trial responses are probabilistic, not deterministic
• Noise models describe the probability distribution, representing the firing rate on any given trial, about the mean f(s).
• Standard deviation for the noise distribution can be
  • Independent of the mean f(s) - additive noise
  • Dependent of the mean e.g., Poisson noise
• We will soon discuss a stochastic spike generator model (Poisson) that will allow us to examine noise in finer detail

• A complete description of the stochastic relationship b/w a stimulus and a response would require us to know the probabilities corresponding to every sequence of spikes that can be evoked by the stimulus!
  • However, the number of possible spike sequences is typically so large that determining or even roughly estimating all of their probabilities of occurrences is impossible
  • Instead we must rely on some statistical model that allows us to estimate the probability of an arbitrary spike sequence!
    • AND SO WE BEGIN MODELING!

• Point Process - stochastic process that generates a sequence of events, APs
• Renewal Process - point process where the probability of an event depends only on the immediately preceding event (intervals b/w successive events are independent)
• Poisson Process - point process where no dependence at all on preceding events (events are statistically independent)

 

The Poisson process is an extremely useful and widely used, approximation of stochastic neuronal firing.