@article {Sch{\o}yen2022.08.18.504379,
	title = {Coherently Remapping Toroidal Cells But Not Grid Cells are Responsible for Path Integration in Virtual Agents},
	journal = {BioRxiv},
	year = {2022},
	publisher = {Cold Spring Harbor Laboratory},
	abstract = {Animals employ a neural system to map physical environmental position to neural activity and encode allocentric location. Grid cells, proposedly a vital component of this system, form a population code of space by firing in characteristic tessellated triangles of locations. This population code remaps across environments and behavioural states, independently of specific sensory inputs, pointing to a substrate of standard computation across environments, which many speculate to be path integration. However, testing whether these cells are crucial for path integration is outside the scope of current experiments and calls for complementary methods, possibly given by computational models. Recently, normative artificial neural network models have shown that path integration and grid-cell-like activity can be found in recurrent neural networks (RNNs) trained to navigate in a simulated two-dimensional environment. Remarkably, the emergent spatial profile of these grid-like cells is similar to biological cell responses in that they set up a toroidal structure. Here, we extend the RNN normative model to multiple environments and show that cells that form the toroidal structure are crucial for path integration. However, cells selected through the grid cell score, a common defining property of grid cells, are much less important and comparable to randomly selected cells. Moreover, we show that the model can navigate multiple environments and that toroidal cells remap across environments in a biologically plausible way. Results demonstrate a causal relation between toroidal cells and path integration in virtual agents and propose a mechanism of remapping in grid cells based on remapping in place cells. The work is anticipated to impact both experimental and computational neuroscience and machine learning due to the methods employed and the evaluation of results. For example, we propose explicit experiments that can evaluate both the model{\textquoteright}s validity and the role of grid cells in navigation. Moreover, the model may elucidate how high-dimensional data is mapped to low-dimensional structures, possibly providing a substrate for interpolation.Competing Interest StatementThe authors have declared no competing interest.},
	doi = {10.1101/2022.08.18.504379},
	url = {https://www.biorxiv.org/content/early/2022/09/16/2022.08.18.504379},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Fyhn, Marianne and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43003,
	title = {Emergent Place Cells and Remapping in a Recurrent Neural Network Model},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Markus Borud {Pettersen} and Sch{\o}yen, Vemund and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43001,
	title = {Model-based meta reinforcement learning for alchemy},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Homa Priya {Targopula} and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43007,
	title = {Navigating Multiple Environments with Emergent Grid Cell Remapping},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43006,
	title = {Place and grid cell navigation in multiple environments},
	year = {2022},
	address = {Federation of European Neuroscience Societies},
	author = {Sch{\o}yen, Vemund and Markus Borud {Pettersen} and Holzhausen, Konstantin and Malthe-S{\o}renssen, Anders and Lepper{\o}d, Mikkel}
}
@misc {43008,
	title = {Robustness of neural networks trained with biologically inspired local learning rules},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Holzhausen, Konstantin and Lepper{\o}d, Mikkel and Malthe-S{\o}renssen, Anders}
}
@misc {43004,
	title = {On the Structural Sensitivity of the Successor Representation},
	year = {2022},
	address = {From Neuroscience to Artificially Intelligent Systems},
	author = {Rogge, Frederik and Malthe-S{\o}renssen, Anders and Fyhn, Marianne and Lepper{\o}d, Mikkel}
}
@article {26194,
	title = {A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons},
	journal = {PLOS Computational Biology},
	volume = {14},
	number = {1-26},
	year = {2018},
	month = {10/2018},
	publisher = {Public Library of Science},
	abstract = {Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.},
	doi = {10.1371/journal.pcbi.1006510},
	url = {http://dx.plos.org/10.1371/journal.pcbi.1006510},
	author = {Solbr{\r a}, Andreas and Bergersen, Aslak and van den Brink, Jonas and Malthe-S{\o}renssen, Anders and Gaute T. {Einevoll} and Halnes, Geir},
	editor = {Barreto, Ernest}
}
@article {23901,
	title = {Integrasjon av beregninger i fysikkundervisningen},
	journal = {Uniped},
	volume = {4},
	year = {2015},
	pages = {303 - 310},
	publisher = {Universitetsforlaget},
	url = {https://www.idunn.no/uniped/2015/04/integrasjon_av_beregninger_ifysikkundervisningen},
	author = {Malthe-S{\o}renssen, Anders and Hjorth-Jensen, M. and Hans Petter {Langtangen} and M{\o}rken, Knut}
}
@misc {Simula.SC.65,
	title = {Optimal Coupling in a Multiscale Model},
	howpublished = {Poster at the Kongsberg Seminar on geology, Kongsberg, Norway},
	year = {2007},
	author = {Enger, H{\r a}kon and Feder, J. and Malthe-S{\o}renssen, Anders and Hans Petter {Langtangen}}
}
