An Example: Modeling Rat Hippocampus

The hippocampus is one of the main brain areas thought to be responsible for memory, and much of the research on it is done by studying rats finding their way around mazes. Rats are made to swim in cloudy water mazes with hidden platforms, run through plastic tubing with scented compartments, and wear microelectrode arrays to record neural activity. We have data about the circumstances under which rodents can learn and remember the location of these hidden platforms and scented tubes, and we also know a lot about what some of the neurons in the hippocampus and surrounding regions do while the rodents are performing these tasks.

Since the 1970s we’ve known about place cells in hippocampus, which fire when the rat is in a particular area or field in an environment. Different populations of cells code different locations, and together they form a cognitive map. In different environments the fields of particular cells and populations are unrelated; new fields spontaneously pop up. These cognitive maps have some other peculiar properties too. They rotate when the visual cues rotate, suggesting that they are tied to visual input, but they also persist in the dark, suggesting that they are independent of visual input. So although these cells respond to

visual cues, they keep tracking the rat’s location as the rat moves, even if the rat can’t see where it is in the environment. Using a mixture of cues, these cells keep track of where in the environment the rat is located.

Rats are capable of path integration too: they can find a direct route back to a goal location (such as their nest, a food source, or a pleasant smell) from wherever they are in an environment. They can do this no matter what route they took to get there, and even if they can’t see the goal location. So this ability is neither dependent on remembering their route, nor on visually orienting themselves in the environment based on landmarks. It seems that the route taken is somehow combined with their end location to generate a sense of the geometry of the space.

Until recently it wasn’t known where in the brain this path integration might be per- formed, nor how it worked. Redish and Touretzky(1997) proposed a connectionist model of how information from place cells could be combined with information about head direction and self-motion to achieve path integration, and laid out criteria that must apply to the brain area responsible for this component of the system. Essentially these were that it must be connected to the head direction, vestibular, and motor systems, as well as the place cells, and that its activity should be correlated with the animal’s position. This first model was partly a mathematical demonstration, showing how a problem could possibly be solved, and partly a rough anatomical hypothesis to be tested. They proposed a how-possibly mecha- nism that could solve the problem, and a functional description of an unknown component in that mechanism.

Anatomists and physiologists took over from there, and subsequently, Fyhn et al.(2004) found grid cells in entorhinal cortex that had the required properties of Redish and Touret- zky’s model, confirming the anatomical hypothesis. The functional description provided by the connectionist model led to the discovery of a region with the right characteristics. The discovered grid cells turned out to also have the peculiar property of having firing fields that form hexagonal grids at various scales and orientations. It was assumed that these hexagonal firing fields must either be involved somehow in supporting the function these cells perform in path integration, or be a side-effect of the mechanism supporting grid cells’ role in path integration, but it was not clear how exactly hexagonal firing fields and path integration

might relate. Over the course of the next couple of years the electrophysiological properties of these cells were more fully characterized, providing further clues about their exact role in achieving path integration.

The partial description of the grid cell sub-mechanism provided by these electrophysio- logical studies led in turn to further modeling work. Fuhs and Touretzky(2006) proposed a more detailed computational model of path integration, incorporating the physiological data about grid cells that had been gathered. The new model showed that “hexagonally spaced activity bumps can arise spontaneously on a sheet of neurons in a spin glass-type neural network model,” and provided “a mechanism by which such cells could satisfy the compu- tational requirements for path integration” (Fuhs and Touretzky 2006). Spin glass models are a type of connectionist network where each unit is connected to its closest neighbors in a multi-dimensional grid. The spin glass model described a how-plausibly mechanism for how the hexagonal grids might arise, based on what was known about the local network structure in entorhinal cortex, and the assumption that dendrites are closely packed.9

O’Keefe and Burgess (2005) proposed an alternative schematic model of how grid cells and place cells connect to give rise to path integration. Their model is “not inconsistent with” Redish and Touretzky’s model, they say, and like the spin glass model, supposes that grid cells must be connected to their nearest neighbors. What they emphasize is the importance of another known fact about the hippocampus: place cells have cyclic firing patterns which correlate with movement (called the phase precession effect). An animal’s location in a field correlates with the timing of place cell spikes relative to the EEG theta wave, while firing rate correlates with running speed, according to O’Keefe and Burgess (2005). In Burgess et al. (2007) they expanded on this model, and implemented it computationally. Essentially their model explains the hexagonal grid pattern as the effect of interference between multiple dendritic subunits tuned to different directions. Their model unifies the hexagonal grid pattern phenomenon and the phase precession effect as elements of the same system. They also note that the effectsFuhs and Touretzky(2006) describe might be added to their model

9_{Incidentally, spin glass models are another nice example of a generic mechanism. The model’s formalism}

was first developed for describing the behavior of disordered magnets, but it has been widely applied in connectionist modeling of psychological and brain processes, as well as in financial modeling. Spin glass models are a particular kind of Ising model, which is even more general. Additionally, they got the name spin glass models, by analogy to the positional disorder of glass.

“to maintain the relative locations of the grids and enhance their stability and precision” (Burgess et al. 2007). Because the Burgess and O’Keefe model accounts for more data, and incorporates it into a more complete picture of the anatomy and physiology of the hippocampus and surrounding regions, it is considered more plausible than the Fuhs and Touretzky(2006) model.

My point is not to argue for or against either of these models; characterizing the hip- pocampal system in rats is an ongoing project. What I take from this example is that within a single research project, computational models played several roles. First a model was pro- posed requiring a fairly general kind of physiological mechanism. The characterization of this mechanism provided guidance to anatomists and physiologists, helping them to locate a previously unknown component of the system based on its required functional properties. Once an anatomical region with the right functional properties was found and further in- vestigated by physiologists, its newly discovered properties required explanation. A more detailed model was built explaining both how the newly discovered properties might arise from plausible physiological conditions, and how the component might perform its function within the whole system. An alternative model was then built that could explain the same phenomenon in a different way, and at the same time unify the explanation with that of another, related phenomenon.

In short, computational models were used to aid in the discovery of a brain region of interest, to provide possible mechanisms to explain a curious effect, to show how several components might function together in a complex system, and to challenge an hypothesis by providing an alternative, more unified solution. For the purpose of discovery, very little bio- logical detail was required. In showing that an effect could arise given plausible constraints, a more mathematical demonstration was provided. To argue for a more unified alternative theory, relatively more biological detail was needed.

In this example, models intended for different purposes leaned towards different char- acterizations of the role of connectionist models from among the options described earlier, demonstrating that part of the ambiguity may stem from there being a variety of reasons for building connectionist models. None of the models in this example fit just one characteriza- tion perfectly though. Redish and Touretzky (1997) was mostly theory of mind, combined

with proof of concept and implementation. Fuhs and Touretzky (2006) was predominantly proof of concept, combined with neural simulation. Burgess et al. (2007) was fairly evenly split between neural simulation and alternative theory (but not of mind), with a bit of proof of concept mixed in. This hybrid nature of typical connectionist models is a topic I’ll pick up in the next chapter.

4.5.1.1 Discovering Mechanisms As may have been apparent, this episode of research on rat hippocampus happens to fit the mechanistic framework described in Chapter 3 ex- tremely well. The path integration system began as a functional description, combined with a few of the known entities responsible for it, but mostly gaps. Redish and Touretzky(1997) proposed a mechanism sketch; they described the sorts of features they expected to find in the unknown path integrator entity, described what each of the known entities must do, and specified how they all should work together to provide productive continuity. Some of the details of the other entities were already known, but the path integrator entity remained a gray box: its function was specified, but the entity performing the function was unknown. The entity was then identified by physiologists, and some details about its activities were filled in, turning it from a gray box into a more fully elaborated entity. Fuhs and Touret- zky (2006) then proposed a lower-level sketch of how that sub-mechanism might work, plus added more details to the overall sketch describing how it fit into the mechanism as a whole. In doing so, they instantiated the spin-glass schema which originated in physics, but had previously been instantiated in other neural networks. O’Keefe and Burgess(2005) provided an alternative mechanism sketch, which connected laterally to a previously proposed mech- anism for another phenomenon. Burgess et al. (2007) added more details to that sketch, bringing it closer to being a fully-specified mechanism. Given all the constraints available, Burgess et al.’s model seems to be the more plausible alternative.

This interpretation of connectionist modeling as being concerned with discovering, ex- ploring, and adjudicating between mechanisms is also consistent with what the modelers involved say they’re up to. Fuhs and Touretzky (2006) describe their work as proposing and describing mechanisms. Redish and Touretzky (1997) say that their model “is constrained by both behavioral and neurophysiological data,” consistent with a multi-level hierarchy of

mechanisms with constraints coming from both above and below. Burgess et al. say that their model provides a mechanism for path integration and an alternative to previous mod- els (Burgess et al. 2007, 810). The advantages they cite are that their model integrates more diverse findings and makes testable physiological predictions. The method used in these models also matches quite well with the typical examples of computational modeling in cognitive neuroscience that I reviewed at the beginning of the chapter.

Thinking of connectionist modeling as a set of tools for discovering and exploring mech- anisms may be a more apt characterization of the role they play in the cognitive and neural sciences than the various suggestions made by supporters of connectionism in response to the attack by Fodor and Pylyshyn (1988), and by critics of connectionism. I will further explore this role for connectionist models, and models more generally in the next chapter.