I'm reading the article "A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology" by Y. Dabaghian, F. Mémoli, L. Frank, G. Carlsson

I try to understand the following graph:

enter image description here

In part a) of the graph, we are seeing a bunch of colored points. These points are in the hippocampus of the rat as opposed to the idea that these points are in the plane on which the rat is moving, and so each point is a place cell of the hippocampus that has fired at some moment in some place of the plane on which the rat is moving. Normally there is a huge number of points in this picture but we chose to put only those who fired, those who did not fire are deleted from the picture of part a). Also, each point (which means each place cell) has one color, and two place cells having the same color designate that the two place cells are considered identical and will be treated as a single place cell in the part b) of the figure.

In part b), we record the time at which each point has fired, with each point being represented by a bar on the time axis and all the bars are identical (same height, and same thickness).

In part c) the picture is in the plane on which the rat is moving as opposed to the idea that the picture of part c) is in the hippocampus of the rat. In part c) we are trying to derive the place fields from part b). Deriving the place fields means here that we are deriving the path that the rat has taken. In particular, place fields are in the plane on which the rat is moving and not in the hippocampus, and each place field in the plane is determined by seeing which place cells in the hippocampus has fired at that area of the plane.

Is my understanding correct? I'm not a specialist but I need to understand each detail of this graph because my work depends on it. My confusion comes from the fact that there are two regions here: the hippocampus of the rat and the plane on which the rat is moving and I need to be sure in which region the picture is.


You have a couple small misunderstandings that I think are making it hard to understand the figure. There is no map of the hippocampus pictured here!

1) Note: this is a schematic figure. These aren't real data, although there are real data that show this pattern. This is meant to be an easy to understand diagram that explains how place cells work.

2) Panel (a) is EXTERNAL SPACE. Essentially it's a "top down" view of a floor that the rat is running around on.

3) Panel (b) shows spike trains for three different cells: theses cells have been arbitrarily color-coded. The hash shows the times that cells 1, 2, or 3 fired spikes. There are just three cells shown in this figure: there aren't any combinations of cells considered one color or multiple cells in one color, just three cells and three colors.

4) Panel (a) is showing how researchers have connected spiking data, like in (b), to the animal's location. The procedure is this:

  • Start with a blank map of space.
  • Record from Cell 1. Every time cell 1 fires, mark a blue dot in panel (a) indicating where the animal was when Cell 1 fired.
  • Record from Cell 2. Every time cell 2 fires, mark a green dot in panel (a).
  • Record from Cell 3. Every time cell 3 fires, mark a red dot in panel (a).
  • (the previous steps could be done for many more than 3 cells simultaneously or in sequence; in this example they are just using 3 cells)

5) Panel (c) is in world space, just like in panel (a), and it shows a hypothesized way that the animal could be using the activity of cells 1, 2, and 3 to determine where it is in space. A researcher recording from cells 1, 2, and 3 could also use those recordings to make a guess of where the animal is. If only cell 3 fires within some window of time (an appropriate window is indicated by the outlined ovals in (b) ), and cells 1 and 2 do not, then the best guess is that the animal is in the upper left area that's shaded only red. If all three cells fire, then the best guess is that the animal is in the very center overlapped region of space.

The dashed line shows a hypothetical path the animal might take through it's environment. If the animal took this path, we'd expect to see place cells firing just like they did in panel (b): first only the blue cell, then blue+green, then all three, then red+green, and finally red only.

6) Very importantly: the animal has way way more cells encoding place than just these three. It would be really confusing to plot them all out in discriminable colors like these, but it is this more complex map with thousands of dimensions that gives the animal a good internal representation of its current location.

Hope this helps!

  • $\begingroup$ Thank you very much, the only thing that remains ambiguous is panel a). Indeed, cofiring corresponds to two or the three place cells to fire at the same place in the floor, and when this happens we will see three points with three different colors one over the other as if they make the same point but we don't see any occurrence of this in panel a), could it be that they did that on purpose for simplicity of the picture since a point with three different colors would not be representable in the picture or did they supposed that there is no cofiring in this picture to make drawing simpler? $\endgroup$ – palio Dec 8 '17 at 21:59
  • $\begingroup$ also why in panel b) the authors replaced the dots by bars, does this have a meaning or just a mere visualization choice ? $\endgroup$ – palio Dec 8 '17 at 22:00
  • 1
    $\begingroup$ Spikes are point processes in time, whereas space is continuous. a) is a representation of spikes in space; b) is a representation of spikes in time. There's no time dimension in (a), except for how time is represented non-continuously as changes in space. If you notice in (b), even at periods of cofiring, the spikes may not be perfectly synchronous. If the animal moves, the points are in different space. Again, these are also schematic data plotted to give you an idea of what's going on; in real data, you could have thousands more points and might make the figure hard to read. $\endgroup$ – Bryan Krause Dec 8 '17 at 23:19

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