Fig 1.
Place cell in the hippocampus and grid cell in the medial entorhinal cortex of the rodent brain.
(A) Anatomical location of the hippocampus and the medial entorhinal cortex (MEC) in the rodent brain. (B) Anatomical neural circuit of the hippocampus and the MEC. Grid cell (blue) in layer III of the MEC provides direct synaptic input to place cell (red) in the hippocampus. (C) Examples of spiking patterns of a grid cell (top, blue) and a place cell (bottom, red) while a rodent navigates (trajectory of a rodent: gray line) around a 1 m × 1 m square environment (black square). A grid cell generates spikes (blue dots) at multiple locations, forming haxagonal grid patterns (black hexagon) called “grid fields” (top) while a place cell generates spikes (red dots) selectively at one or more specific locations (bottom) called a place field.
Fig 2.
In vivo-like oscillatory interference (OI) grid cell model.
(A) Trajectory of a rodent navigating within a 1 m × 1 m square environment obtained from in vivo recording (black line) and spikes (red dots) simulated with conventional oscillatory interference (OI) grid cell model is superimposed to the trajectory. (B) Firing rate of grid cell in the square environment, called the “firing rate map” (red: peak firing rate (323.53 Hz); blue: no spike (0 Hz)). (C) Gaussian distribution (σ = 0.069, center of grid field to border = 3σ) used to model in vivo-like grid field spike pattern (red dots). (D) Spikes (red dots) from in vivo-like OI grid cell model plotted over trajectory (black line). (E) Firing rate map of in vivo-like OI grid cell model (red: peak firing rate (21.51 Hz); blue: no spike (0 Hz)).
Fig 3.
Grid fields of in vivo-like OI model, in vivo grid cell data, and OI model.
(A) Spike (red dots) over trajectory (black line) and (B) firing rate map simulated with in vivo-like OI model. (C) The spatial autocorrelogram of firing rate map plotted as color plot (correlation coefficient of 1.0: yellow, correlation coefficient of 0.0: blue). (D-F) Same figures as (A-C), but with in vivo grid cell data. (G-I) Same figures as (A-C), but with grid cell spikes simulated with conventional OI grid cell model.
Fig 4.
Comparison of in vivo-like OI model, in vivo grid cell data, and OI model.
(A) Maximum firing rate, (B) grid field area, (C) grid spacing between grid fields and (D) grid score of in vivo-like OI model (empty), in vivo grid cell data (gray), and the OI grid cell model (black). (*: p < 0.05, ** < 0.01, *** < 0.001, n.s > 0.05).
Fig 5.
Modulation of grid field orientation of in vivo-like OI model by VCO (ϕVCO) preferred direction.
(A-D) The spatial autocorrelogram of the in vivo-like OI model when ϕVCO values are (A) 0°, (B) 15°, (C) 30°, and (D) 45° with β fixed at 2 Hz/(m/s).
Fig 6.
β controls the size and spacing of grid patterns of the in vivo-like OI model.
(A-F) The spatial autocorrelogram of the in vivo-like OI model when β values are (A) 1.0, (B) 1.5, (C) 2.0, (D) 2.5, (E) 3.0, and (F) 3.5 Hz/(m/s) with ϕVCO fixed at 30°. (G) Grid field size (open circle) plotted as a function of β, fitted with an exponential curve (black line, r2 = 0.96). (H) Grid field spacing (open circles) plotted as a function of β, fitted with an exponential curve (black line, r2 = 0.96).
Fig 7.
Summation of 250 spatiotemporally random grid cell inputs to single distal dendritic synapse of place cell could generate grid-to-place field transformation.
(A) Pool of 10,000 grid cells generated with in vivo-like OI grid cell model through varying orientation (ϕVCO) and spacing (β). (B) 250 grid cells, each with different spatiotemporal grid field patterns, were randomly selected from the pool and were used to generate excitatory inputs to Hodgkin-Huxley hippocampal place cell model through a synapse located 315.95 μm from the soma. (C) Distribution of (ϕVCO, β) of 250 randomly selected grid cells (color bar: number of grid cells). (D) Spikes of Hodgkin-Huxley place cell model (red dots) plotted over trajectory (black line). (E) Firing rate map of the Hodgkin-Huxley place cell model. (F) The proportion of viable place fields generated by 100 different sets of grid field patterns, each set containing 250 spatiotemporal random grid fields patterns.
Fig 8.
Summation of 250 spatiotemporally random grid cell inputs to spatially distributed synapses in distial dendrites of place cell model could generate grid-to-place field transformation.
(A) 250 grid cells, each with different spatiotemporal grid field patterns, were randomly selected from the pool and were used to generate excitatory inputs to Hodgkin-Huxley hippocampal place cell model through 250 excitatory synapses spatially distrubted at 300–400 μm from the soma. (B) Spikes of Hodgkin-Huxley place cell model (red dots) plotted over trajectory (black line). (C) Firing rate map of the Hodgkin-Huxley place cell model.
Fig 9.
Different place fields generated by different sets of random grid cell inputs.
(A) 250 grid cells that were randomly selected from the pool of 10,000 grid cells and each having different distribution of (ϕVCO,β) (Color bar: number of grid cells). (B) 250 grid cells in (A) were used as inputs to the Hodgkin-Huxley place cell model and the resulting place cell spikes (red dots) are plotted over trajectory (black line). (C) Firing rate map of place cell model of (B). (D-F) Same as (A-C) but with place cell receiving different sets of 250 randomly selected grid cells having different distribution of (ϕVCO,β). Note that place fields in (C) and (F) are at different locations.
Fig 10.
A sufficient number of grid cell inputs is needed for grid-to-place cell transformation.
(A) 100 grid cells, each with different spatiotemporal grid field patterns, were randomly selected from the pool of 10,000 grid cells and used as excitatory inputs to the Hodgkin-Huxley hippocampal place cell model. (B) Place cell spikes (red dots) plotted over trajectory (black line). (C) Firing rate map of place cell model of (A). (D-F) Same as (A-C) but place cells receiving inputs from 500 randomly selected grid cells. (G-H) The proportion of viable place fields (G), and peak firing rate as a function of the number of the grid cells (H). (I) Place field area plotted as a function of the number of grid cells. The top gray horizontal dotted line denotes the upper boundary for determining viable place field size (60% of total arena size, 6,000 cm2) and the bottom horizontal gray dotted line denotes the lower boundary for determining viable place field size (15 adjacent bins, 240 cm2).
Fig 11.
Spikes of grid cells are transformed into excitatory ramp input in place cell model.
(A) 250 grid cells, each with different spatiotemporal grid field patterns, were selected from the pool of 10,000 grid cells and were used as excitatory inputs to the Hodgkin-Huxley hippocampal place cell model. (B) Spikes of place cell model (red dots) while the animal traversed (trajectory: black line) a fragment (blue line) within a place field (green). (C) Membrane voltage (Vm, black line) of the Hodgkin-Huxley place cell model when the animal traversed the blue trajectory in (B). The spikes from 250 grid cell models are summated and transformed into a right-skewed excitatory ramp input (R-ERI) in the place cell model. The spline-fitted curve (red line) and the relative peak position (RPeak = 0.75) of the R-ERI is shown. (D-E) Same figures as (B-C), but summation of excitatory input showing symmetric excitatory ramp input (S-ERI, RPeak = 0.43). (F-G) Same figures as (B-C), but summation of excitatory input showing left-skewed excitatory ramp input (L-ERI, RPeak = 0.30). (H) Distribution of RPeak of 653 ERIs generated by 100 different sets of grid field patterns, each containing 250 spatiotemporal random grid fields patterns. ERIs are divided into L-ERI, S-ERI, and R-ERI depending on the location of RPeak. (I) Ratio of the number of L-ERI (25.68 ± 1.82%), S-ERI (27.06 ± 2.09%) and R-ERI (47.26 ± 2.20%) in (H).
Fig 12.
Spatiotemporally random grid cell inputs are transformed into place cell with spike phase precssion.
(A) Top: Excitatory ramp input (ERI) of Hodgkin-Huxley hippocampal place cell model (black line) with spline-fitted curve (red line), which was used to determine the peak position of ERI (RPeak). Middle and bottom: inhibitory theta-frequency oscillation (ginh) and step current input (Istep) given to place cell model. (B) Top: Membrane voltage trace of the Hodgkin-Huxley place cell model (Vm) with ginh. Bottom: The expanded view of the dotted box above showing spike phase precession relative to ginh from 360° to 0°. Vertical tick represents spike times and dotted lines are 0°/360° of ginh. (C-E) Top: ERI (black) with spline-fitted curve (red curve). Middle: Membrane voltage trace of the Vm (black) and ginh (gray). Bottom: Phase of place cell spikes (black dot) relative to ginh plotted as a function of distance during single-pass of place field with linear-circular regression (blue line) when ERI was R-ERI (C, ρ = -10.38°/cm), S-ERI (D, ρ = 2.04°/cm), and L-ERI (E, ρ = 17.82°/cm). (F) Distribution of slope of linear-circular regression (ρ) in (C), (D) and (E) generated by 100 different sets of grid field patterns, each set containing 250 spatiotemporal random grid fields patterns. (G) Slope of linear-circular regression (ρ) of L-ERI (ρ = 9.33 ± 0.99°/cm), S-ERI (ρ = 3.94 ± 0.77°/cm), and R-ERI (ρ = -5.11 ± 1.31°/cm).