From Grid Cells to Place Cells: A Gauss Distribution Activation Function Model_Journal of Biomedical Engineering

Authors：

YUNaigong ^1,2 ,  FANGLue ^1,2 , LUOZiwei ^1,2 , YUANYunhe ^1,2 , JIANGXiaojun ^1,2 , CAIJianxian ^1,2

1. College of Electronic and Control Engineering, Beijing University of Technology, Beijing 100124, China;
2. Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing University of Technology, Beijing 100124, China;

Corresponding author：

FANGLue, Email: 1621069902@qq.com

Keywords：

grid cells; place cells; entorhinal cortex; hippocampus; gauss distribution activation function

DOI：

10.7507/1001-5515.20160184

Video：

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Abstract Full text Figures/Tables Video References Cited by

It has been found that in biological studies, the simple linear superposition mathematical model cannot be used to express the feature mapping relationship from multiple activated grid cells' grid fields to a single place cell's place field output in the hippocampus of the cerebral cortex of rodents. To solve this problem, people introduced the Gauss distribution activation function into the area. We in this paper use the localization properties of the function to deal with the linear superposition output of grid cells' input and the connection weights between grid cells and place cells, which filters out the low activation rate place fields. We then obtained a single place cell field which is consistent with biological studies. Compared to the existing competitive learning algorithm place cell model, independent component analysis method place cell model, Bayesian positon reconstruction method place cell model, our experimental results showed that the model on the neurophysiological basis can not only express the feature mapping relationship between multiple activated grid cells grid fields and a single place cell's place field output in the hippocampus of the cerebral cortex of rodents, but also make the algorithm simpler, the required grid cells input less and the accuracy rate of the output of a single place field higher.

Citation： YUNaigong, FANGLue, LUOZiwei, YUANYunhe, JIANGXiaojun, CAIJianxian. From Grid Cells to Place Cells: A Gauss Distribution Activation Function Model. Journal of Biomedical Engineering, 2016, 33(6): 1158-1167. doi: 10.7507/1001-5515.20160184 Copy

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2.	KNIERIM J J. Neural representations of location outside the hippocampus[J]. Learn Mem, 2006, 13(4): 405-415.
3.	SOLSTAD T, MOSER E I, EINEVOLL G T. From grid cells to place cells: a mathematical model[J]. Hippocampus, 2006, 16(12): 1026-1031.
4.	HAFTING T, FYHN M, MOLDEN S, et al. Microstructure of a spatial map in the entorhinal cortex[J]. Nature, 2005, 436(752): 801-806.
5.	MOSER E I, KROPFF E, MOSER M B. Place cells, grid cells, and the brain's spatial representation system[J]. Annu Rev Neurosci, 2008, 31: 69-89.
6.	O'KEEFE J, DOSTROVSKY J. The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat[J]. Brain Res, 1971, 34(1): 171-175.
7.	JEFFERY K J, BURGESS N. A metric for the cognitive map: found at last?[J]. Trends Cogn Sci, 2006, 10(1): 1-3.
8.	ROLLS E T, STRINGER S M, ELLIOT T. Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning[J]. Network, 2006, 17(4): 447-465.
9.	YU N G, WANG L, LI T, et al. Competitive neural network model from grid cells to place cells[J]. Control & Decision, 2015, 30(8): 1372-1378.
10.	FRANZIUS M, VOLLGRAF R, WISKOTT L. From grids to places[J]. J Comput Neurosci, 2007, 22(3): 297-299.
11.	DE ALMEIDA L, IDIART M, LISMAN J E. The input-output transformation of the hippocampal granule cells: from grid cells to place fields[J]. J Neurosci, 2009, 29(23): 7504-7512.
12.	CHENG S, FRANK L M. The structure of networks that produce the transformation from grid cells to place cells[J]. Neuroscience, 2011, 197(197): 293-306.
13.	GUANELLA A, VERSCHURE P F. Prediction of the position of an animal based on populations of grid and place cells: a comparative simulation study[J]. J Integr Neurosci, 2007, 6(3): 433-446.
14.	AZIZI A H, SCHIEFERSTEIN N, CHENG Sen. The transformation from grid cells to place cells is robust to noise in the grid pattern[J]. Hippocampus, 2014, 24(8): 912-919.
15.	KNIERIM J J. From the GPS to HM: place cells, grid cells, and memory[J]. Hippocampus, 2015, 25(6): 719-725.
16.	MHATRE H, GORCHETCHNIKOV A, GROSSBERG S. Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex[J]. Hippocampus, 2012, 22(2): 320-334.
17.	CASTRO L, AGUIAR P. A feedforward model for the formation of a grid field where spatial information is provided solely from place cells[J]. Biol Cybern, 2014, 108(2): 133-143.
18.	TOCKER G, BARAK O, DERDIKMAN D. Grid cells correlation structure suggests organized feedforward projections into superficial layers of the medial entorhinal cortex[J]. Hippocampus, 2015, 25(12): 1599-1613.
19.	SLOVITER R S, BRISMAN J L. Lateral inhibition and granule cell synchrony in the rat hippocampal dentate gyrus[J]. J Neurosci, 1995, 15(1 Pt 2): 811-820.
20.	DORDEK Y, MEIR R, DERDIKMAN D. Extracting grid characteristics from spatially distributed place-cell inputs using non-negative PCA[J]. arxiv, 2015: 03711.
21.	SANDERS H, RENNÓ-COSTA C, IDIART M, et al. Grid cells and place cells: an integrated view of their navigational and memory function[J]. Trends Neurosci, 2015, 38(12): 763-775.

1. CANTO C B, WOUTERLOOD F G, WITTER M P. What does the anatomical organization of the entorhinal cortex tell us?[J]. Neural Plast, 2008: 381243.
2. KNIERIM J J. Neural representations of location outside the hippocampus[J]. Learn Mem, 2006, 13(4): 405-415.
3. SOLSTAD T, MOSER E I, EINEVOLL G T. From grid cells to place cells: a mathematical model[J]. Hippocampus, 2006, 16(12): 1026-1031.
4. HAFTING T, FYHN M, MOLDEN S, et al. Microstructure of a spatial map in the entorhinal cortex[J]. Nature, 2005, 436(752): 801-806.
5. MOSER E I, KROPFF E, MOSER M B. Place cells, grid cells, and the brain's spatial representation system[J]. Annu Rev Neurosci, 2008, 31: 69-89.
6. O'KEEFE J, DOSTROVSKY J. The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat[J]. Brain Res, 1971, 34(1): 171-175.
7. JEFFERY K J, BURGESS N. A metric for the cognitive map: found at last?[J]. Trends Cogn Sci, 2006, 10(1): 1-3.
8. ROLLS E T, STRINGER S M, ELLIOT T. Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning[J]. Network, 2006, 17(4): 447-465.
9. YU N G, WANG L, LI T, et al. Competitive neural network model from grid cells to place cells[J]. Control & Decision, 2015, 30(8): 1372-1378.
10. FRANZIUS M, VOLLGRAF R, WISKOTT L. From grids to places[J]. J Comput Neurosci, 2007, 22(3): 297-299.
11. DE ALMEIDA L, IDIART M, LISMAN J E. The input-output transformation of the hippocampal granule cells: from grid cells to place fields[J]. J Neurosci, 2009, 29(23): 7504-7512.
12. CHENG S, FRANK L M. The structure of networks that produce the transformation from grid cells to place cells[J]. Neuroscience, 2011, 197(197): 293-306.
13. GUANELLA A, VERSCHURE P F. Prediction of the position of an animal based on populations of grid and place cells: a comparative simulation study[J]. J Integr Neurosci, 2007, 6(3): 433-446.
14. AZIZI A H, SCHIEFERSTEIN N, CHENG Sen. The transformation from grid cells to place cells is robust to noise in the grid pattern[J]. Hippocampus, 2014, 24(8): 912-919.
15. KNIERIM J J. From the GPS to HM: place cells, grid cells, and memory[J]. Hippocampus, 2015, 25(6): 719-725.
16. MHATRE H, GORCHETCHNIKOV A, GROSSBERG S. Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex[J]. Hippocampus, 2012, 22(2): 320-334.
17. CASTRO L, AGUIAR P. A feedforward model for the formation of a grid field where spatial information is provided solely from place cells[J]. Biol Cybern, 2014, 108(2): 133-143.
18. TOCKER G, BARAK O, DERDIKMAN D. Grid cells correlation structure suggests organized feedforward projections into superficial layers of the medial entorhinal cortex[J]. Hippocampus, 2015, 25(12): 1599-1613.
19. SLOVITER R S, BRISMAN J L. Lateral inhibition and granule cell synchrony in the rat hippocampal dentate gyrus[J]. J Neurosci, 1995, 15(1 Pt 2): 811-820.
20. DORDEK Y, MEIR R, DERDIKMAN D. Extracting grid characteristics from spatially distributed place-cell inputs using non-negative PCA[J]. arxiv, 2015: 03711.
21. SANDERS H, RENNÓ-COSTA C, IDIART M, et al. Grid cells and place cells: an integrated view of their navigational and memory function[J]. Trends Neurosci, 2015, 38(12): 763-775.

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