Network Analysis of Rat Spatial Cognition: Behaviorally-Established Symmetry in a Physically Asymmetrical Environment

<div><h3>Background</h3><p>We set out to solve two inherent problems in the study of animal spatial cognition (i) What is a “place”?; and (ii) whether behaviors that are not revealed as differing by one methodology could be revealed as different when analyzed using a different approach.</p> <h3>Methodology</h3><p>We applied network analysis to scrutinize spatial behavior of rats tested in either a symmetrical or asymmetrical layout of 4, 8, or 12 objects placed along the perimeter of a round arena. We considered locations as the units of the network (nodes), and passes between locations as the links within the network.</p> <h3>Principal Findings</h3><p>While there were only minor activity differences between rats tested in the symmetrical or asymmetrical object layouts, network analysis revealed substantial differences. Viewing ‘location’ as a cluster of stopping coordinates, the key locations (large clusters of stopping coordinates) were at the objects in both layouts with 4 objects. However, in the asymmetrical layout with 4 objects, additional key locations were spaced by the rats between the objects, forming symmetry among the key locations. It was as if the rats had behaviorally imposed symmetry on the physically asymmetrical environment. Based on a previous finding that wayfinding is easier in symmetrical environments, we suggest that when the physical attributes of the environment were not symmetrical, the rats established a symmetric layout of key locations, thereby acquiring a more legible environment despite its complex physical structure.</p> <h3>Conclusions and Significance</h3><p>The present study adds a behavioral definition for “location”, a term that so far has been mostly discussed according to its physical attributes or neurobiological correlates (e.g. - place and grid neurons). Moreover, network analysis enabled the assessment of the importance of a location, even when that location did not display any distinctive physical properties.</p> </div

Object layout and paths of locomotion for an exemplary rat in each group.

<p>The location of 4, 8, and 12 objects in a symmetrical (left) and an asymmetrical (right) layout is depicted in the top row (a). The paths of locomotion for a single exemplary rat in depicted below for each layout (b).</p

Building a network of places.

<p>The rationale for establishing the criterion of 12 cm diameter and the transformation of stopping coordinates into a network is illustrated for one rat. a. <i>Stopping coordinates: -</i> these are as the x-y coordinates of a single rat, as extracted from the tracking system (Ethovision). The large black circle represents the arena perimeter, each red dot represents a stopping coordinate at which the rat stopped for one second or longer, and the black squares represent the location of the objects. b. <i>Nodes under the application of a 12-cm circle around the additional stopping coordinate:-</i> As shown, with this diameter the nodes (circles) coincide with the objects and behavior. c. <i>Nodes under the application of a 9-cm circle around the additional stopping coordinate:-</i> As shown, with this diameter stopping coordinates around the same object split into several nodes, resulting in a mismatch between behavior and nodes. d. <i>Nodes under the application of a 14-cm circle around the additional stopping coordinate:-</i> As shown, with this diameter the bottom node encompasses the stopping coordinates of two objects (see the red dots of these objects in a.). e. <i>Topologic graph:-</i> The presentation of the network after the transformation of stopping coordinates into nodes (red circles). Arrows between nodes represent the links (passes) between nodes. Note that the location of a red circle does not represent the physical location of that node. Likewise, the circles that represent the nodes in b-d do not represent the real size of the node but the number of stopping coordinates included in that node.</p

The distinction between key-nodes and other nodes.

<p>The nodes for each rat in the 4-object layout were ranked from high to low according to the number of stopping coordinates. The rank is depicted on the x-axis, whereas the mean (±SEM) number of stopping coordinates in each rank is depicted on the y-axis. Scale for both axes is logarithmic. The nodes above the dashed horizontal line are those that were considered as key nodes. As shown, there were four key nodes in the symmetrical layout compared with five key nodes in the asymmetrical object layout.</p

Physical location of the network nodes.

<p>For both the symmetrical (left) and asymmetrical arenas (right), the object layout is depicted in the left-hand column. The network nodes were placed in their respective physical location in the arena, and are shown for 3 rats in each object layout and object number. For each rat, the open circles represent the nodes in their physical location in the arena, and the diameter of the circle represents the number of stopping coordinates within each node (and not the physical area of the node). Key nodes are depicted in open red circles, whereas key nodes that are not located on objects are depicted in red circles filled with green. The rest of the nodes are depicted in light blue. As shown, in the asymmetrical layout with 4 objects, rats established a fifth node that is not located on an object.</p

Building a node from stopping coordinates.

<p>The algorithm for transforming stopping coordinates into a network node (a) and a visualized process of building a single node (b).</p

Dissociation between postrhinal cortex and downstream parahippocampal regions in the representation of egocentric boundaries

Navigation requires the integration of many sensory inputs to form a multi-modal cognitive map of the environment, which is believed to be implemented in the hippocampal region by spatially tuned cells [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]. These cells encode various aspects of the environment in a world-based (allocentric) reference frame. Although the cognitive map is represented in allocentric coordinates, the environment is sensed through diverse sensory organs, mostly situated in the animal’s head, and therefore represented in sensory and parietal cortices in head-centered egocentric coordinates. Yet it is not clear how and where the brain transforms these head-centered egocentric representations to map-like allocentric representations computed in the hippocampal region. Theoretical modeling has predicted a role for both egocentric and head direction (HD) information in performing an egocentric-allocentric transformation [ 11 , 12 , 13 , 14 , 15 ]. Here, we recorded new data and also used data from a previous study [ 16 ]. Adapting a generalized linear model (GLM) classification [ 17 ]; we show that the postrhinal cortex (POR) contains a population of pure egocentric boundary cells (EBCs), in contrast with the conjunctive EBCs × HD cells, which we found downstream mostly in the parasubiculum (PaS) and in the medial entorhinal cortex (MEC). Our finding corroborates the idea of a brain network performing an egocentric to allocentric transformation by HD cells. This is a fundamental building block in the formation of the brain’s internal cognitive map

The SLUGGS Survey: stellar kinematics, kinemetry and trends at large radii in 25 early-type galaxies

Due to longer dynamical time-scales, the outskirts of early-type galaxies retain the footprint of their formation and assembly. Under the popular two-phase galaxy formation scenario, an initial in situ phase of star formation is followed by minor merging and accretion of ex situ stars leading to the expectation of observable transitions in the kinematics and stellar populations on large scales. However, observing the faint galactic outskirts is challenging, often leaving the transition unexplored. The large-scale, spatially resolved stellar kinematic data from the SAGES Legacy Unifying Galaxies and GlobularS (SLUGGS) survey are ideal for detecting kinematic transitions. We present kinematic maps out to 2.6 effective radii on average, kinemetry profiles, measurement of kinematic twists and misalignments, and the average outer intrinsic shape of 25 SLUGGS galaxies. We find good overall agreement in the kinematic maps and kinemetry radial profiles with literature. We are able to confirm significant radial modulations in rotational versus pressure support of galaxies with radius so that the central and outer rotational properties may be quite different. We also test the suggestion that galaxies may be more triaxial in their outskirts and find that while fast rotating galaxies were already shown to be axisymmetric in their inner regions, we are unable to rule out triaxiality in their outskirts. We compare our derived outer kinematic information to model predictions from a two-phase galaxy formation scenario. We find that the theoretical range of local outer angular momentum agrees well with our observations, but that radial modulations are much smaller than predicted