Dr Allen Cheung - Neurocomputational Theory of Spatial Navigation

Research directions

The goal of my research is to understand how brain cells and brain circuits acquire and process information required for successful spatial navigation. Spatial navigation is one of the most important, widespread and oldest brain functions in the animal kingdom. It may well be the case that many brain functions are intimately related to spatial navigation. In the broadest sense, spatial navigation involves non-random movements which increase the likelihood of finding a goal location. What are the neural computations involved? How do brain cells and circuits carry out such computations? 

A multipronged approach is used in this research. The first approach is to develop, from first principles, an in-depth and quantitative theoretical understanding of the principles of spatial navigation in different environments, particularly focusing on the limits of what can and cannot be achieved. The second approach is to use behavioural and in vivo recording data to build systems-level and neural network models of spatial navigation, guided by established theoretical principles. Finally, in collaboration with experimentalists, theoretical predictions will be tested in future experiments.

At a systems level, the ability to handle spatial uncertainty is arguably the single most important determinant of the success or failure of any navigation task. However, the neural mechanisms which animals use to manage uncertainty remain unclear. Nervous systems are inherently noisy, leading to limitations on the types of sensory information and even the types of neural representations of space which can be used for spatial navigation. Through natural selection, neural noise can therefore shape both brain circuits and computational algorithms used for spatial navigation.

Basic mathematical theory can be used to prove the surprising result that in the absence of compass information, open field navigation is impossible beyond a few steps (Cheung et al. 2007, Cheung et al. 2008a). Many sophisticated sensory systems have evolved in the animal kingdom capable of extracting compass information such as the E-vector (e.g. insects), geomagnetic field (e.g. birds) and visual landmarks (e.g. mammals). At a cellular level, the mammalian head direction system, and POL neurons of the insect central complex may provide the type of directional representation compatible with open field navigation strategies such as path integration.

During spatial navigation, in order to maintain an accurate representation of current position, the brain needs to utilize internal (idiothetic) and external (allothetic) information in the right way. It can be shown theoretically that there is only one class of spatial representation which can update current position from moment to moment, and tolerate neural noise (Vickerstaff & Cheung 2010, Cheung & Vickerstaff 2010). All members of this class of representation have to be world-centred (allocentric) and do not have angular components in the encoding of positions. This class of representations excludes many existing models of insect path integration. Yet interestingly, most existing mammalian models of grid cells and place cells fulfil these criteria – raising the possibility that such neuronal properties may have emerged through evolution due to the need to tolerate noise.

Much of the in vivo recording data related to spatial navigation come from rodents in confined experimental arenas. There is growing evidence, mainly from behavioural studies in arthropods, that only a few visual snapshots provide sufficient spatial information to carry out a range of navigation tasks. In confined arenas, it can be shown that the arena geometry is inextricably linked to the visual image. Therefore, seemingly complex behavioural patterns may emerge through a simple strategy of matching memorized and current views of an experimental arena, challenging the need for less parsimonious, often abstract models of mammalian spatial navigation (Sturzl et al. 2008, Cheung et al. 2008b).

Finally, there remains the open question of whether multiple channels of sensory information need to be unified into some sort of multimodal representation, perhaps forming a kind of “cognitive map”, during spatial navigation. In rodents, errors accumulate in the head direction system in total darkness, whereas relatively stable place fields have been observed. It can be shown quantitatively that the two (independent) observations are incompatible if it is assumed that idiothetic information is processed separately from boundary information, even assuming a perfect representation of the boundary geometry (unpublished research). In contrast, place fields with spatial information content (comparable to what has been observed) can occur in simulation if boundary information is combined in a Bayes-optimal way with idiothetic movement information. It is hypothesised that a multimodal representation exists in rats involving boundary vector or border cells, and place cells.

  Selected Publications

• Cheung, A., Zhang, S.W., Stricker, C. and Srinivasan, M.V. (2007) “Animal navigation: The difficulty of moving in a straight line,” Biological Cybernetics. 97: 47-61.
• Cheung, A., Zhang, S.W., Stricker, C. and Srinivasan, M.V. (2008a) “Animal navigation: General characteristics of directed walks,” Biological Cybernetics. 99: 197-217
• Stürzl, W., Cheung, A., Cheng, K. and Zeil, J. (2008). “The information content of panoramic images I: The rotational errors and the similarity of views in rectangular experimental arenas,” Journal of Experimental Psychology: Animal Behaviour Processes. 34(1): 1-14.
• Cheung, A., Stürzl, W., Zeil, J. and Cheng, K. (2008b). “The information content of panoramic images II: View-based navigation in nonrectangular experimental arenas,” Journal of Experimental Psychology: Animal Behaviour Processes. 34(1): 15-30.
• Vickerstaff, R. and Cheung, A. (2010) “Which coordinate system for modelling path integration,” Journal of Theoretical Biology. 263: 242-261.
• Cheung, A. and Vickerstaff, R. (2010) “Finding the way with a noisy brain,” PLoS Computational Biology. 6(11): e1000992.
• Luu, T., Cheung, A., Ball, D. and Srinivasan, M.V. (2011) “Honeybee flight: A novel ‘streamlining’ response,” Journal of Experimental Biology. 214(13): 2215-2225. [Reviewed by Dyer A, Rosa M: 2011. F1000.com/11541956.]

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