Phase Shift in Grid Cells

I would like to fully understand the phase shift in the grid cell in MEC. From my understanding, since there is a hexagonal (i.e. equilateral triangle) lattice, and hence there are 3 $\phi$'s, I have the following questions in regards to that:

1). If there are 3 $\phi$'s, how does the phase shift happen in (I guess) 3 phases, i.e. why are there 3 shifts? I am just very confused at a fundamental level: why does the phase shift happen, is it because of the phase resettling in neurons?

2). As Wikipedia defines it: "Phase shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities", so my question is, what is the "quantity" in the example with grid cells or what is "the phase difference between two or more quantities" here?

In other words, why there is the 1st shift, the 2nd and the 3rd? Why do the second and the third happen? Is it because the pattern of grid cells is an equilateral triangle and the 1st type of signal produces the 1st grid field (the blob) and the 2nd type of signal produces the 2nd blob, here I edited this picture to illustrate my thought:

and we can see, if we model it with cosine, since

• Can you include a reference you are basing some of your confusion on? My initial read through your question suggests that you might be mixing together a couple concepts but I'm not certain (and it's been awhile since I thought in depth about grid cells, but I don't know of a resident grid cell expert here on biology.se). – Bryan Krause May 12 '17 at 21:48
• Or to be a little less vague...when people are talking about phases in grid cells I am most familiar with phases with respect to theta, an oscillation in time, not spatial phase. So there is no reason for those phases to be in particular unit steps, like pi/3. Maybe this is where you are getting your "3 ϕ"s idea from so that's what I am wondering about a reference for. – Bryan Krause May 12 '17 at 21:50
• I think this is about soft matter physics + hexacon + phase shift. Can you please describe your wished area. – Léo Léopold Hertz 준영 May 13 '17 at 12:09
• There are two phases I can think of: The time phase in relation to the theta rhythm, as mentioned by Bryan Krause and the spatial phase. If you change the spatial phase, it means you are shifting the whole grid in relation to the environment it encodes without rotating the grid. Apart from these two, I don't know what the third phase could be. – a tiger May 15 '17 at 16:03
• This might help: scholarpedia.org/article/Grid_cell (written by the Mosers themselves) "The grid of each cell can be described by three parameters: o) spacing (the distance between fields), o) orientation (the tilt of the grid relative to a reference axis), and o) spatial phase (displacement in the x and y directions relative to an external reference point)." – a tiger May 15 '17 at 16:04