tl;dr: populations encoding 2- and 3-D quantities need shape and size heterogeneity to increase encoded information. We show how one can measure these heterogeneities using Bayesian inference, which offers a principled way of handling noisy, incomplete neural data. [n=16/n]

More broadly, this framework produces a bunch of testable predictions beyond place fields. And, we propose a principled method for testing these predictions in other populations. [15/n]

With our theory, we can also quantify just how much more information about spatial position these populations encode than if they all shared the same size/shape. [14/n]

With our new method in hand, we turned back to rodent place fields. As the theory predicts, place fields appear to exhibit high degrees of size and shape heterogeneity! (ticks in d,e are sessions) [13/n]

We show that doing this overcomes the issues we identified with tuning measurement based on the STA. With it, we can identify shape and size heterogeneity in simulated populations far more accurately. Our method is also less biased by the occupancy pattern of the animal. [12/n]

We propose a new Bayesian approach. We use it to explicitly quantify how uncertain we are about a field’s tuning based on how limited data is. Then we use this uncertainty to weight our estimates of field properties when measuring the degrees of shape and size heterogeneity. [11/n]

In the context of place cells, this refers to the rat not traversing the environment perfectly uniformly. These biases can skew the measurements of shape and size heterogeneity. So, we figured that a different way of measuring receptive fields was necessary to test our theory.[10/n]

But, we ran into some roadblocks. Many existing methods for measuring tuning curves rely on the STA. We show in our work that the STA is sensitive to biases arising from limited or incomplete sampling of the environment. [9/n]

While size heterogeneity in place fields has been documented, shape heterogeneity has been relatively understudied. So, we followed the predictions of our framework and tried to measure the degree of place field size and shape heterogeneity. [8/n]

So, we introduced shape heterogeneity. When receptive fields vary in size and shape, populations can better encode 2- and 3-D quantities. But this property reverses for higher-dimensional stimuli. Size heterogeneity remains useful, while shape heterogeneity becomes harmful. [7/n]

We dive into why this is in the manuscript, but I’ll spare the details here. This finding is fairly curious, because we know that place fields in rodents (encoding 2D spatial location) and bats (encoding 3D spatial location) have variably sized RFs… [6/n]

Let’s start with size heterogeneity, where we find dimensionality-dependence: Heterogeneously sized RFs increase info of one dimensional stimuli (head direction, eg). And >3-D stimuli. Strikingly, size heterogeneity isn’t helpful for encoding 2- or 3-D variables. [5/n]

…until now! We derived the amount of information encoded about a stimulus in spiking activity as a function of the degree of the population’s RF heterogeneity. To make the theory general, we derived this relationship for arbitrary stimulus dimensionalities. [4/n]

Why would the brain prefer such variability? Is there a general coding benefit associated with heterogeneously sized receptive fields? This question has been asked in specific populations and under specific conditions, but a theory that unifies these accounts is lacking… [3/n]

Populations across the brain have differently sized and shaped receptive fields. A striking example of this is hippocampal CA1 place cells, whose receptive fields can be mere centimeters across or as large as a few meters in size (fig from Rich et al., 2014) . [2/n]