How grid cells could code memories of episodes, and more, in the brain.

In my prior post, I wrote about Professor Michael Hasselmo’s book on grid cells in the brain, which create a type of GPS grid as we walk through a space.   But the main point of the book is that grid cells plus ‘place cells’ can be part of a circuit for storing episodic memory.
Professor Hasselmo gives a scenario of one of his work days where he parks his car in one of many spots in the college garage, and then walks down Cummington street, passes one of his students, and then continues to his office where he speaks with his wife, and so forth.   The memory of this set of episodes involves a trajectory through space.   It also involves a point of view – for instance, which direction on Cummington street was he walking and what was he looking at.   The point of view can be thought of as a directional component of a vector.   Memory also involves time – such as how fast he was walking down the street.   When he is sitting in a chair in his office and talks on the phone his position in space doesn’t change, but time does.
You and I normally remember in sequence, but we can relive one segment and then jump back in time to remember an earlier segment.
In his model, Grid cells are the inputs to ‘place cells’, where place cells indicate your position in a space (grid cells fire at every point in an imaginary grid stretched across the space, but a place cell might fire if, for example, you were in the center of a room (or the corner of a farmer’s field).  You also have ‘head direction’ cells, which code for where your gaze is pointing.   If we combine head direction with speed information, we have velocity (speed plus direction, though one problem with this theory is that you could be walking sideways while your gaze is straight up).  We will assume that ‘head direction’ cells don’t just code direction, they also code speed, and therefore are really ‘velocity’ cells.   Hasselmo sometimes uses a more general term “action” to describe what ‘head direction’ cells do, as if they are responsible for your movement.
In his model you could have grid cell activations leading to place cell activations which in turn lead to velocity cell activation and then the velocity updates the grid cells, altering their frequency and relative phase, and that then leads in a loop back to place cells.   It takes a while for the information to propagate in each step. So you can have a simulation of you going through space, at the speed in which you originally traversed it.
Lets examine in more depth:
The ‘velocity’ cells are driven by your senses that tell you how fast and what direction you are going.
The velocity in turn, causes frequency differences between two cells that normally fire at the same frequency  and this also implies that those cells will probably be out of phase when the creature stops moving.
Grid cells differ in their response to velocity.   Some have a frequency that changes only gradually with velocity, others have a more dramatic dependence on velocity.   Grid cells can also start at different initial phases.   The result is that each grid cell corresponds to a different grid – maybe the spacing between the gridlines is different, or the difference is in the orientation in which the grid overlays space, or both.
When you learn a trajectory, your movements and behavior drive head direction cells, which then drive grid cells which in turn drive place cells which have synapses on the original head direction cells.  Learning the trajectory involves strengthening some of the links between the place cells and the head direction cells.
In contrast, when you remember a trajectory, the main driver of the head cells is not sensory inputs and not behavior, rather, it is the place cells.   The cue for retrieval could be your current location as coded by place cells, or it could be environmental stimuli that were previously associated with a particular pattern of place cells.   For instance, a sight of the  Art Museum in New York’s Central Park could send signals to a particular place-cell vector. The velocity cells have to fire in recollection just as long as they did in the real event, because their firing at the correct rate for the correct amount the time creates the phase differences in the grid cells that existed in the original real-life scenario.
You are able to distinguish actually having an experience from remembering it, and Prof Hasselmo speculates that the different drivers of the head direction cells in two cases give you a way of knowing the difference.
Professor Hasselmo cautions that this mechanism is not the only possible one, for instance, you could have time-interval cells that fire at steady intervals and independently fire cells for place and for action.
If you model this mechanism with a neural net, you would have one weight matrix from place cells to head direction cells (WHP) and another matrix between the grid cells and the place cells (WPG).


There are objections to chaining models based on experimental data showing that participants can  retrieve the end of a sequence after missing one or more items, or they can retrieve the wrong order of items in a sequence.   Hasselmo gives alternatives, where for instance a cue activates time cells, or as the creature moves it activates ‘arc length’ cells.   The latter measure one dimensional distance, and are useful, oddly enough, because they are missing the direction information.   Imagine you are riding a bicycle with a device that measures your distance from the start of your ride.   You also have a list of directions.   One direction says, “at 5 miles, turn left on Magpie road.”   The route then makes a loop and comes back to the same point, at which point your set of directions says  “at 10 miles, don’t repeat your loop on Magpie road, but go up to Crawfish Hill Road.   Since you have been keeping track of your distance, you know what to do.   If you just had 2 dimensional information, such as where you currently are on a map, and no memory of other than that, you would not know which road to take.   You need to know how far you’ve gone so far.   That is what the firing of arc-length cells would tell you.  ‘Place’ cells alone could not tell you which ‘head direction’ cell should fire next, in the case of a loop like this.
Another alternative might be ‘time cells’   (“after 1 hour of biking, take Magpie road, after two hours take Crawfish Hill Road”.)

In the prior examples, the phase differences that make grid cells fire are driven by arc cells or ‘time cells’, and not head-direction (velocity) cells.   (A velocity cell minus direction information is essentially an arc cell)

In the example of remembering at what parking spot you parked your car in the garage next to your workplace, you don’t want yesterday’s parking spot to interfere with today’s.    As  you walk into the garage, a trajectory would fire, and perhaps at ambiguous points the arc-cells or the time-cells would lead you in the correct direction.   The cue that resets the arc cells has to be some difference between today and yesterday.
To remember what you saw at different parts of your day – walking away from your car, and then along the street, and then into your building, and who you talked to, there would be a learned association between specific ‘place cell vectors’ and the sensory patterns that you experienced.   One advantage of this two-way association is that remembering a particular sensory cue can activate the place cells that were firing when you first were at that spot and the memory sequence could start in mid-trajectory.
If  you see the same room only at rare intervals, it has been found that grid cells and place cells show the same (stable) firing each time.   In the model, this requires sensory cues to set the phase of firing of grid cells to the same starting point.
The associations for this type of memory requires associations between the code for space and time with the coding of actions, items, or events. The code for space and time comes in the form of place cells, arc length cells, and time cells.   These are associated with actions in the form of speed cells and head direction cells.  The model also uses bidirectional associations between the code for space and time with cells coding features of individual events.   So a trajectory can cue the retrieval of an event (remembering what happened when you opened the door to the tiger cage in the zoo) or conversely, seeing a picture of a tiger can remind you of your quick trajectory out of the tiger cage and out of the Zoo.   In addition, an association of one item can lead to a trajectory of other items and events.


We could start speculating here.   Any “train of thought” is a sequence where one item leads to another.   Could grid cells and place cells be involved?   Hasselmo also has a chapter on goal directed behavior where place cells propagate signals along a path back from a goal, which meet grid cells signals propagating forward.   This sounds like problem solving – not just remembering a path.
When we look at any part of a room, we are focussed on only a small part of the room – at any moment, we assume the rest of the room is as we recently saw it.   Perhaps our experience of a room is a trajectory around the room associated at various positions with objects such as book shelves, chests of drawers, and lamps.  In fact, researchers at Numenta, a company that attempts to understand the cortex, hypothesize that every object in that room is itself represented by some type of grid cell trajectory and that these grid cells are in every column of the cortex.   They also believe that objects are ‘recursive’ – so for instance when you look at a cup with a handle, the handle itself has its own grid cell trajectory.
How We Remember – Michael Hasselmo (2012 – MIT)

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