As we navigate around, we often have a sense of where we are in space. Actually, knowing the self-location relative to the environment is a fundamental ability for the purpose of survival. How does the brain support such ability? Tolman (1948) proposed that the brain should be able to maintain a “cognitive map” of the physical space [174]. The discovery of place cells in rodent hippocampus around 1970s has triggered a lot of following up research on the neural basis of spatial map in the brain [132, 133]. The most salient property of place cells is that its firing activity is sparse in space. Individual place cell typically fires when only animal is within a particular spot in space [132], although some place cells fire in multiple spots in space. As we know more about the place cells, it becomes clear that the firing activities of the place cells are also correlated with many other factors besides the animal’s spatial location, including odor, recent experience, time and others [138, 2, 136]. The interpretations of these multi-perplexing responses are still subjected to debates.
clear whether the spatial information is originated within hippocampus or inherent from other brain areas. The discovery of grid cells in dorsal-medial Entorhinal Cor- tex offers some new insight to this question[86, 75]. Now it appears that place cell may, at least partially, inherent the spatial information from grid cells. Place cells, grid cells, together with heading direction cells[172] and boarder cells[159] may con- sist the neural underpinning of our sense of space during navigation. Studying the properties and functions of these cell may provide us a unique chance to uncover how the space is represented in the mammalian brain, and how spatial maps in the brain support navigation behaviors, which are critical for the survival of mammals.
Grid cells
In 2004, Fyhn et al., discovered that in dorsal band of Entorhinal Cortex (EC) of the rat’s brain, neurons typically show tuning preference for space, similar as the place cells [75]. However, unlike place cells, these cells typically fire in the multiple spatial locations. In 2005, a following up paper by Hafting et al., demonstrated that, surprisingly, the spatial firing fields of the cells in dmEC lies on a triangular grid [86]. These cells are thus termed as “grid cells”. Because the highly regular firing pattern of the grid cells, it is immediately suggested that the grid cells may encode a metric of the space [86, 129]. Grid cells are also found in pre-and parasubiculum [19], two brain regions next to EC. Although the response pattern of grid cells can be partially manipulated by cues in the environment [86], overall the major factor
which determines the response of the grid cells response appear to be the animal’s location in space.
Why are grid cells not discovered in the studies before Hafting et al. (2005) [86]? One major reason seems to be that previous experiments have used smaller testing rooms, which were not enough to reveal the lattice structure of the grid. In a small environment, typically only one or even zero firing field of individual grid cells could be observed. However, in larger recording rooms, the pattern of the grid become visually apparent. The grid is particularly evident when the two dimensional au- tocorrelation map of the grid firing map is calculated which effectively reduce the noise in the original firing rate map by averaging [86]. Originally found in rats, the grid cells are later discovered in mice[74], and in bats [187]. There are some indirect evidence from fMRI signal suggesting that grid cells may also exist in humans [54]. Recently, my colleagues and I have reported the first direct observation of grid-like response in human brain by analyzing data from single neuron recording of human epilepsy patients, while they were performing a virtual navigation task [94].
The response pattern of individual grid cell can be characterized by three pa- rameters, the spacing, the orientation, and the spatial phase. Locally, the grid cells in rodents share similar spacing and orientation [86, 164]. The spatial phase seems to be shifted randomly such that nearby cells do not have nearby phases[86]. Therefore, there seems to be no topographical relationship in the spatial phase. Interestingly, the grids in EC have different scales manifested in the spacing of
the grids. Furthermore, the scales increase systematically along the dorsal-ventral axis [86, 26]. At the dorsal most, the spacing of the grid is about 50cm, while at the 75% of the dorsal-ventral axis, the spacing of the grid can be several meters to 10 meters, according to the recording when rats running on a 18 meters linear track[26].
One particular important property of grid cells is that they are organized in discrete structure [164]. By a fine sampling of grid cells along about half of the dorsal-ventral axis of EC, Stensola et al. (2012) demonstrates that grid cells could be clustered based on the scale, orientation and ellipticity [164]. The cells within one cluster share the same scale, orientation and ellipticity. The individual cluster is termed as a module. These authors found up to 5 modules within individual animal. However, because the recording was only done up to 50% of the dorsal ventral axis of EC, more modules should be expected in whole EC. A simple linear extrapolation suggests that the number of the grid cell modules in rodent EC should be ∼ 10. Strikingly, the data also suggest that the grid scales follow a geometric progression. In this particular data set, the scaling factor was found to be ∼1.42, while in a previous study, the scaling factor was reported be∼1.7 with a relatively smaller sample size [11].
The grid cells have attracted many computational investigations since it is dis- covered. Most research have focus on the mechanisms and algorithms of how the grid-like response could be generated. Existing models have exploiting mechanisms
of pattern formation[176] in attractor network [72, 28, 20] and oscillatory interfer- ence [30, 89], as well as spike rate adaptation [106].
While these computational models of grid cells aim to address thehow question, the question of why the grid cells firing pattern should be as observed remain mys- terious. In Chapter 4, I ask the fundamental issue in terms of why it is desirable to use the grid code to form a representation of the space. I show that the idea of
efficient processing of spatial information quantitatively accounts for the functional
architecture of the grid cells observed in the rodent’s brain.