Cortical Activity is a Mess: The Trouble with Averaging

Neuroscientists recording activity of single neurons in cortex have known for a long time that neural activity in cortex can be extremely variable. Even when the timing of a stimulus presentation or behavioral measurements are tightly controlled, a cortical neuron is likely to fire action potentials at slightly different times and rates on any given trial.

Take a look at this example raster, where each tick represents an action potential, each line is a separate trial, and the green vertical bar is the time when a stimulus was presented (or a behavior was measured):

 spikes

Looking closely at the timing of cortical action potentials, it is striking how noisy the activity appears, despite being aligned to the same event. The distribution of spikes is usually well described as a Poisson process, where the timing of any one spike is independent from the times of other spikes (this is only an estimation, since realistically the timing of spikes is constrained by a neuron’s refractory period - a neuron can’t produce action potentials closer than 1ms apart).

A natural reaction to that variability is to average it out. This has produced sensical results in many cases, and has supported models for various cognitive phenomena. One prominent example that has taken advantage of averaged cortical neuron activity is the Ramping model of decision making. The model attempts to explain how one could make a decision about a sensory stimulus when that stimulus is imperfect, or noisy.

The classic example, used in many neurophysiology experiments, is a video of moving dots, where each dot moves in a random direction at any given time point, but overall is biased to the left or right. An experimental subject looking a display of randomly moving dots has to decide whether they are on the whole moving left or right, and the difficulty of that decision depends on the coherence of motion (at 100% coherence, all dots are moving in one direction; at 0%, there is no net movement). The Ramping model requires some cognitive process to observe the noisy dots and count the evidence for leftward vs. rightward motion over time, until the counts hit some internal threshold, at which time the decision is made.

 

[youtube https://www.youtube.com/watch?v=Cx5Ax68Slvk]

As with many experiments of neural recordings, the phrase “ask and ye shall receive” proved true here (not to underplay how difficult it probably was to gather the data): neurons in the macaque Lateral Intraparietal Area, just downstream of motion-sensitive neurons in area MT, responded to the moving dots with ramping firing rates whose slopes were correlated with the coherence of the dots’ motion1,2, just as the model predicted. 

Those ramping firing rates came from averages of single neurons’ responses over many noisy trials. In a paper published in Science in July 2015, Jonathan Pillow and lab mates asked if the ramping might actually be just an average of many instantaneous jumps in firing rates3. If a neuron’s firing rate jumps instantly but at slightly different time points on each trial, the average firing rate would look like a ramp. To answer this question, Pillow’s team modeled the neurons’ spiking as Poisson processes whose rates of firing were distributed either according to a ramping model or a stepping one.

ramps

Because the stepping wasn’t a measured variable (but rather a latent one imposed on the data by the researchers), in order to get the right parameters for their models, the team simulated neural activity using Markov Chain Monte Carlo (MCMC). 

Not surprisingly, when each trial’s activity was aligned to the inferred step time rather than stimulus onset, the average firing rate turned from a ramp to a step. The stepping model seems to capture the neural activity qualitatively, but is it actually better than the ramping model? This is a crucial question that plagues many models of neural activity. Because the models in this paper were based on Bayesian statistics, with real data serving as a guide for the parameters, the authors were able to directly compare the two models using information criteria that compare how well the models fit the data and how many parameters were needed for each (the more parameters are needed for a model to fit the data, the more likely it is to be overfit; at the extreme end of this spectrum, a model could have as many parameters as there are data points, in which case the model would be useless), and showed that the Stepping model was more parsimonious with the data than the Ramping model.

Sources:

1. Newsome, W. T., Britten, K. H., & Movshon, J. A. (1989). Neuronal correlates of a perceptual decision. Nature.

2. Roitman, J. D., & Shadlen, M. N. (2002). Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience, 22(21), 9475–9489.

3. Latimer, K. W., Yates, J. L., Meister, M. L. R., Huk, A. C., & Pillow, J. W. (2015). Single-trial spike trains in parietal cortex reveal discrete steps during decision-making. Science, 349(6244), 184–187. http://doi.org/10.1126/science.aaa4056