At first glance, the question of how the brain represents three-dimensional space appears to be a straightforward problem. This review by Jeffery and colleagues highlights instead the thorny nature of the question. The main problem is that most mammals are surface-dwelling animals, and it becomes tricky to devise proper experiments to determine whether these organisms encode space as an isotropic, volumetric representation when they move along surfaces that extend in three dimensions. The “bicoded map” proposal of Jeffery et al. suggests that three-dimensional space is represented not as a true volumetric map, but as a patchwork of diversely oriented, local, quasi-planar maps. Neurophysiological data informing this issue are themselves fragmentary and limited to a few studies that employed complementary strategies (e.g., with respect to the orientation of the animal's body) while addressing different functional correlates of space (e.g., head-direction cells vs. grid cells). Much experimental work is therefore needed to empirically evaluate the debated theoretical scenarios.
The implicit assumption in many experiments is that spatial locations are represented in a global reference frame (e.g., the laboratory room), and that the local apparatus is merely a substrate for the animal to move (actively or passively) in and out of different locations in the global reference frame. However, it is increasingly clear from both behavioral and neurophysiological studies that hippocampal spatial representations are tied more strongly to the local apparatus frame of reference than the global frame of reference when the two frames are translated relative to each other (Knierim & Hamilton Reference Knierim and Hamilton2011). Hence, all experiments on three-dimensional representations of space that employ surface-dwelling animals must address the problem of interacting reference frames when the 3D volume of the global reference frame is sampled serially via surface-bound navigational epochs. For example, in an experiment not discussed in the target article, place fields were bound to the behavioral track, rather than the x, y, or z coordinates of the room, when the track was moved to different locations in both horizontal and vertical axes of the room (Knierim & Rao Reference Knierim and Rao2003). These results suggest that the spatial representation was tied to the local reference frame of the track, rather than to the room coordinates, precluding any strong interpretation regarding whether the cells represented two-dimensional or three-dimensional space in the global reference frame.
One key experiment considered by the authors involved rats running up and down a helical path (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011). Firing fields from grid cells and place cells repeated themselves in corresponding positions of all or nearly all laps. Although Jeffery et al. interpret this result as evidence of a diminished representation of space in the z-axis, this result could be also interpreted as the laps sharing an identical representation under the control of the frame of reference established by the recurring, stereotypical lap. This interpretation is strongly supported by a study using planar circular and square spiral paths (Nitz Reference Nitz2011): Place fields recurred in corresponding positions of each spiral loop, similar to the repeated firing on the different levels of the helical track. The sizes of the fields grew in lockstep with the concentric loops, except for those fields that recurred at the corners of square spirals. These findings suggest a form of pattern detection operating on the geometrical features of the lap.
The second experiment with neural recordings considered by Jeffery et al. concerned rats climbing on a vertical pegboard (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011). Grid cells fired in patterns of vertical stripes, suggesting that the vertical wall was “slicing into” a columnar extension of a classic two-dimensional grid pattern existing on the contiguous floor (which was not sampled in this experiment). This is perhaps the strongest piece of evidence supporting the authors' theoretical proposal, but how would one test this model rigorously? One simple idea is to record the grids on the floor, and then have the rat do the pegboard task as the pegboard is moved to different locations/orientations relative to the floor. As the pegboard slices into different columns, the pattern of stripes should be predictable based on the floor-based grid vertices being intersected by the pegboard. However, once again, the interplay of reference frames may prevent a simple answer. Place cells (Knierim & Rao Reference Knierim and Rao2003; O'Keefe & Burgess Reference O'Keefe and Burgess1996; Siegel et al. Reference Siegel, Neunuebel and Knierim2007) and grid cells (Derdikman et al. Reference Derdikman, Whitlock, Tsao, Fyhn, Hafting, Moser and Moser2009; Savelli & Knierim Reference Savelli and Knierim2012; Savelli et al. Reference Savelli, Yoganarasimha and Knierim2008) are strongly influenced by local boundary manipulations, and boundary-responsive neurons are found in multiple hippocampus-related regions (Boccara et al. Reference Boccara, Sargolini, Thoresen, Solstad, Witter, Moser and Moser2010; Lever et al. Reference Lever, Burton, Jeewajee, O'Keefe and Burgess2009; Savelli et al. Reference Savelli, Yoganarasimha and Knierim2008; Solstad et al. Reference Solstad, Boccara, Kropff, Moser and Moser2008). If the floor-based grid becomes bound to the pegboard in the first recording, this grid may reset identically at the boundary formed by the base of the pegboard, regardless of where the pegboard is moved. The vertical fields predicted to project over the pegboard from this grid would then remain unchanged, too. This is just one example of a general concern applicable to similar experimental designs in which a surface reference frame is moved relative to another.
The authors make the provocative argument that even animals that truly navigate in three-dimensional volumes – birds, bats, insects, fish – are likely to use a bicoded strategy, rather than a volumetric representation that is isotropic and metric in all three axes. The question can be addressed in these animals without the need of a surface substrate that may be in conflict with a global reference frame. A recent study (Yartsev & Ulanovsky Reference Yartsev and Ulanovsky2013) did not find elongation along a single common axis in three-dimensional place fields recorded from the hippocampus of freely flying bats, seemingly in contrast with the bicoded map hypothesis.. Future experiments in the same species can test if this result applies to grid cells as well. Regardless of the outcome, it will not be clear whether surface-dwelling creatures will show the same results. Understanding the proper reference frame of the “cognitive map” is one of the crucial problems that must be resolved in order to interpret the data from animals running on surfaces in three-dimensional space, and the reference frames may differ across terrestrial, arboreal, and flying animals.
At first glance, the question of how the brain represents three-dimensional space appears to be a straightforward problem. This review by Jeffery and colleagues highlights instead the thorny nature of the question. The main problem is that most mammals are surface-dwelling animals, and it becomes tricky to devise proper experiments to determine whether these organisms encode space as an isotropic, volumetric representation when they move along surfaces that extend in three dimensions. The “bicoded map” proposal of Jeffery et al. suggests that three-dimensional space is represented not as a true volumetric map, but as a patchwork of diversely oriented, local, quasi-planar maps. Neurophysiological data informing this issue are themselves fragmentary and limited to a few studies that employed complementary strategies (e.g., with respect to the orientation of the animal's body) while addressing different functional correlates of space (e.g., head-direction cells vs. grid cells). Much experimental work is therefore needed to empirically evaluate the debated theoretical scenarios.
The implicit assumption in many experiments is that spatial locations are represented in a global reference frame (e.g., the laboratory room), and that the local apparatus is merely a substrate for the animal to move (actively or passively) in and out of different locations in the global reference frame. However, it is increasingly clear from both behavioral and neurophysiological studies that hippocampal spatial representations are tied more strongly to the local apparatus frame of reference than the global frame of reference when the two frames are translated relative to each other (Knierim & Hamilton Reference Knierim and Hamilton2011). Hence, all experiments on three-dimensional representations of space that employ surface-dwelling animals must address the problem of interacting reference frames when the 3D volume of the global reference frame is sampled serially via surface-bound navigational epochs. For example, in an experiment not discussed in the target article, place fields were bound to the behavioral track, rather than the x, y, or z coordinates of the room, when the track was moved to different locations in both horizontal and vertical axes of the room (Knierim & Rao Reference Knierim and Rao2003). These results suggest that the spatial representation was tied to the local reference frame of the track, rather than to the room coordinates, precluding any strong interpretation regarding whether the cells represented two-dimensional or three-dimensional space in the global reference frame.
One key experiment considered by the authors involved rats running up and down a helical path (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011). Firing fields from grid cells and place cells repeated themselves in corresponding positions of all or nearly all laps. Although Jeffery et al. interpret this result as evidence of a diminished representation of space in the z-axis, this result could be also interpreted as the laps sharing an identical representation under the control of the frame of reference established by the recurring, stereotypical lap. This interpretation is strongly supported by a study using planar circular and square spiral paths (Nitz Reference Nitz2011): Place fields recurred in corresponding positions of each spiral loop, similar to the repeated firing on the different levels of the helical track. The sizes of the fields grew in lockstep with the concentric loops, except for those fields that recurred at the corners of square spirals. These findings suggest a form of pattern detection operating on the geometrical features of the lap.
The second experiment with neural recordings considered by Jeffery et al. concerned rats climbing on a vertical pegboard (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011). Grid cells fired in patterns of vertical stripes, suggesting that the vertical wall was “slicing into” a columnar extension of a classic two-dimensional grid pattern existing on the contiguous floor (which was not sampled in this experiment). This is perhaps the strongest piece of evidence supporting the authors' theoretical proposal, but how would one test this model rigorously? One simple idea is to record the grids on the floor, and then have the rat do the pegboard task as the pegboard is moved to different locations/orientations relative to the floor. As the pegboard slices into different columns, the pattern of stripes should be predictable based on the floor-based grid vertices being intersected by the pegboard. However, once again, the interplay of reference frames may prevent a simple answer. Place cells (Knierim & Rao Reference Knierim and Rao2003; O'Keefe & Burgess Reference O'Keefe and Burgess1996; Siegel et al. Reference Siegel, Neunuebel and Knierim2007) and grid cells (Derdikman et al. Reference Derdikman, Whitlock, Tsao, Fyhn, Hafting, Moser and Moser2009; Savelli & Knierim Reference Savelli and Knierim2012; Savelli et al. Reference Savelli, Yoganarasimha and Knierim2008) are strongly influenced by local boundary manipulations, and boundary-responsive neurons are found in multiple hippocampus-related regions (Boccara et al. Reference Boccara, Sargolini, Thoresen, Solstad, Witter, Moser and Moser2010; Lever et al. Reference Lever, Burton, Jeewajee, O'Keefe and Burgess2009; Savelli et al. Reference Savelli, Yoganarasimha and Knierim2008; Solstad et al. Reference Solstad, Boccara, Kropff, Moser and Moser2008). If the floor-based grid becomes bound to the pegboard in the first recording, this grid may reset identically at the boundary formed by the base of the pegboard, regardless of where the pegboard is moved. The vertical fields predicted to project over the pegboard from this grid would then remain unchanged, too. This is just one example of a general concern applicable to similar experimental designs in which a surface reference frame is moved relative to another.
The authors make the provocative argument that even animals that truly navigate in three-dimensional volumes – birds, bats, insects, fish – are likely to use a bicoded strategy, rather than a volumetric representation that is isotropic and metric in all three axes. The question can be addressed in these animals without the need of a surface substrate that may be in conflict with a global reference frame. A recent study (Yartsev & Ulanovsky Reference Yartsev and Ulanovsky2013) did not find elongation along a single common axis in three-dimensional place fields recorded from the hippocampus of freely flying bats, seemingly in contrast with the bicoded map hypothesis.. Future experiments in the same species can test if this result applies to grid cells as well. Regardless of the outcome, it will not be clear whether surface-dwelling creatures will show the same results. Understanding the proper reference frame of the “cognitive map” is one of the crucial problems that must be resolved in order to interpret the data from animals running on surfaces in three-dimensional space, and the reference frames may differ across terrestrial, arboreal, and flying animals.