Entorhinal cortex receptive fields are modulated by spatial attention, even without movement
Spatial representations , in the form of place cells and grid cells , have been identified in rodents ( Hafting et al . , 2005; O'Keefe and Dostrovsky , 1971 ) , bats ( Yartsev et al . , 2011; Yartsev and Ulanovsky , 2013 ) , macaque monkeys ( Killian et al . , 2012 ) and humans ( Jacobs et al . , 2013; Ekstrom et al . , 2003 ) . The hippocampal formation , however , also contributes to the processing of memories ( Squire and Wixted , 2011 ) , and conceptual similarities between spatial navigation and the processes involved in remembering and planning suggest that grid cells might support cognitive functions besides spatial navigation ( Buzsáki et al . , 2013 ) . This idea resonates well with the recent demonstration that grid cells are active during the exploration of images with eye-movements , that is by overt attention ( Killian et al . , 2012 ) . These findings revealed that grid cells do not only track an animal's location in space , but can also represent the gaze position of the animal . Shifts of gaze location usually correspond to shifts in attention ( Hoffman , 1998; Rolfs et al . , 2011 ) , and the neural substrate for overt and covert attention is largely overlapping ( Corbetta et al . , 1998 ) . Accordingly , grid cells in the entorhinal cortex are potentially capable of representing not only gaze location but the locus of attention in general . Here , we investigated whether firing fields of entorhinal cells are activated by movements of covert attention , in the absence of any physical movement . Attention functions as an important control for mental processes ( Petersen and Posner , 2012 ) ; accordingly , the hypothesis that grid cells participate in a range of cognitive functions predicts that grid cells may be activated by movements of attention . Here , we tested this prediction by recording from single units in the entorhinal cortex in monkeys trained to perform a task of covert attention .
To examine spatial representations of cells in the entorhinal cortex during the movement of covert attention , we recorded the neuronal activity of 141 neurons in the entorhinal cortex of two rhesus macaque monkeys performing a covert attention tracking task . The monkeys were trained to maintain central fixation while attending to a small ( 1° ) dot that moved around the computer monitor ( see Figure 1 ) . The task of the monkey was to respond by quickly releasing a response bar when the dot changed color . The color change occurred after a random time interval ( 700 – 2000 ms ) following trial onset . Over the course of a recording session , the dot traced out several Hamiltonian cycles , thereby ensuring that in the limit of infinitely many cycles each screen location was visited equally often . Monkeys performed the task at >70% accuracy , with the majority of errors due to saccades to outside of the fixation window . Depending on their motivation , monkeys completed between two and eight cycles per session . In order to examine spatial representations among entorhinal neurons , we evaluated the standard gridness measure ( Solstad et al . , 2008; Langston et al . , 2010; Brandon et al . , 2011 ) along with a novel analysis of the depth of firing rate modulation within the firing fields . Grid cells possess a regular firing field with increased firing rates at the nodes of equilateral triangles that evenly tile space . Importantly , tiling space with equilateral triangles leads to 2D autocorrelation functions with six peaks arranged in a hexagonal structure around the center peak . Whether or not a cell's firing field shows this regular pattern is usually evaluated by quantifying the 60° rotational symmetry of the 2D autocorrelation ( Solstad et al . , 2008; Langston et al . , 2010; Brandon et al . , 2011 ) . An important property of the gridness score is that the autocorrelation normalizes away the absolute firing rate modulation over space . That is , a cell that shows only a weak change in firing rate as a function of space might have the same gridness as a cell that shows a strong change in firing rate . The gridness score is therefore susceptible to noise , and homogeneous firing fields might produce high gridness scores by chance . Furthermore , for downstream read out of the grid signal the size of firing rate modulation , for example the signal to noise ratio is relevant . To better differentiate between noisy and grid-like firing fields , we computed for each cell an index of firing field modulation from its estimated rate map and a gridness score from its 2D autocorrelation function ( see Materials and methods ) . To assess the statistical significance of spatial representations in our recorded neurons , we computed the same indices on simulated cells with grid , place , or homogeneous firing fields . Cells were simulated by creating spike-trains with an inhomogeneous Poisson ( IP ) process ( Figure 2 ) . The rate function of the IP process was determined by the dot’s trajectory through a firing field and a noise parameter that varied the influence of noise for each simulated cell ( see Materials and methods ) . Simulated cells with a homogeneous firing field therefore control for any potential grid-like structure in the dot's trajectory . The resulting joint distributions of gridness scores and firing field modulation indices represent the likelihood of observing particular patterns of results . To differentiate grid cells , we computed the log likelihood ratio for comparing grid cells with place cells and homogeneous cells ( Figure 3 and Materials and methods ) . The resulting log likelihood ratio expresses how much more likely it is that a specific gridness score and firing field modulation index combination is produced by a grid cell compared to homogeneous or place cells . To control our false-discovery rate , we determined the appropriate threshold for classification performance on simulated non-grid cells . Out of 141 recorded neurons , we identified 20 cells ( 14% ) with a log likelihood ratio of >4 . 25 deciban ( corresponding to a false discovery rate <5% ) in favor of cells with spatially structured firing fields according to the two criteria of modulation index and gridness score . Cells classified as grid cells had a lower mean firing rate ( 0 . 47 Hz ) compared to those classified as other cells ( 1 . 22 Hz ) , and higher average gridness ( 1 . 29 vs . 0 . 51 ) and firing field modulation index values ( 0 . 1 vs . 0 . 04 ) . We also tested more conservative thresholds of 10 and 20 deciban ( false discovery rates of 1 . 26% and 0 . 07% , respectively ) , which require more evidence to classify a cell as a grid cell . Regardless of the threshold used , we were able to identify a population of neurons that were labeled as grid cells on an individual basis with high significance ( X2 ( 1 , N = 141 , FDR = 0 . 05 ) = 25 . 0 , p < 0 . 0001 , 20 , 9 and 3 cells w . r . t . to false discovery rates for different thresholds ) . We also identified candidate cells that qualitatively resembled grid cells but which could also be explained by assuming a noisy place like firing field ( lower right points in Figure 3 ) . We , furthermore , sought to validate our novel statistical approach with two different control analyses . First we recorded neuronal activity of 307 neurons from the hippocampus in monkeys performing the same task . There are currently no reports of grid cells in the hippocampus and these neurons can therefore serve as a baseline to determine our empirical false discovery rate . Classifying these cells with the same measures and the 5% FDR threshold yielded an empirical false-discovery rate of 8 . 5% . The FDR is slightly higher than the FDR derived from simulations because the hippocampal recordings likely contain a different ratio of spatially structured ( e . g . place cells ) to spatial noise cells . Yet , in the entorhinal cortex ( see above ) , we find significantly more grid-cells than expected from a FDR of 8 . 5% ( X2 ( 1 , N = 141 , FDR = 0 . 085 ) = 5 . 9 , p = 0 . 016; p < 0 . 05 for classifying with the 10 and 20 deciban thresholds as well ) . Second , we used a bootstrapping analysis to create a joint distribution of indices when the association between firing rate and the dot’s position is destroyed . To this end , we estimated the firing rate of each neuron along the dot’s trajectory and shuffled trajectory segments of 50 ms length ( 700 permutations ) . We again computed both indices and found an empirical false discovery rate of 5 . 5% . These control analyses suggest that our main analysis provides an adequate control for the false discovery rate . We calculated two further controls to eliminate the possibility that our results could be due to the specific set of trajectories used in each session . First , combining spikes generated by different firing fields destroys the spatial structure of the individual firing fields . Any residual grid-like spatial structure of a pooled unit is therefore due to the specific stimulus conditions . We therefore pooled all neurons in each recording session and calculated gridness scores and firing field modulation indices . None of these pooled units was classified as having a grid-like firing field ( average and max gridness score 0 . 36/0 . 96 , average and max firing field modulation 0 . 02/0 . 11 ) . Second , we investigated the spatial periodicity of trajectories in isolation . For each recording session , we pooled all trajectories and computed gridness scores and firing field modulation indices by assuming an equal firing rate at all locations . None of these units was classified as a grid cell ( average and max gridness score 0 . 1/1 . 17 , average and max firing field modulation 0 . 018/0 . 033 ) . These controls demonstrate that our results are not due to an inherent grid-like structure in the trajectories . As a last control , we examined whether our results might be confounded by the monkeys overtly tracking the dot with small eye-movements inside the fixation window within a trial . To investigate this , we compared the distance of the eye to the fixation cross with the dot’s distance to the fixation cross . If eye-movements tracked the dot’s position , these signals should be strongly correlated in each trial . However , we found no substantial correlations between eye-position and dot position . Average correlations within a session were small ( mean = −0 . 005 ) and within the expected range of correlations when we shuffled trials in time and thereby assigning eye-movement positions to dot trajectories from different parts within a session ( mean 0 . 001 , 5 and 95% percentile: −0 . 02 , 0 . 02 ) . We conclude that the monkeys did not track the dot with small eye movements . Systematic biases in receptive field size and position caused by hemisphere or eccentricity specific processing should show up as systematic biases in firing rate across the visual field . We therefore computed two asymmetry indices . The first quantifies the difference in firing rate between the right and left side of the visual field . While cells classified as grid cells ( 5% FDR ) in both animals showed , on average , increased firing rates on the contralateral side of the visual field relative to the recorded hemisphere , these differences were not consistent across cells ( mean contralateral-ipsilateral = 0 . 06 , t = −1 . 99 , p = 0 . 06 , one sample t-test ) . Second , we computed an index that compares average firing rate within the central five degrees of visual field around the fixation cross with the rest of the visual field . We again found no difference in firing rate ( mean center-periphery = 0 . 08 , t = 1 . 7 , p = 0 . 10 ) . These numbers , however , have to be taken with a grain of salt . In each monkey , we recorded from only one hemisphere , making an intra-monkey comparison of left/right visual field responses difficult . Furthermore , the experiment was not designed to optimize investigation of systematic changes with eccentricity . For such an experiment , monkeys trained to covertly track targets at high eccentricity and as well as having more recording time for each neuron with attention directed to eccentric locations would be desirable . These two constraints interact and make respective experiments highly challenging . An important caveat is that our experimental conditions are most sensitive for firing fields with a size that allows multiple repetitions of the grid on the screen . Larger firing fields might appear like place or homogeneous cells , and firing fields with spacing smaller than the spacing of our trajectories will appear as spatially structured noise . We can therefore make no definitive statements about the percentage of grid cells in the entorhinal cortex , and our results likely represent a conservative estimate . Future studies could address this issue by a ) using a larger screen to allow for larger field sizes and b ) using fixation locations that are not centered to compensate for the loss of visual acuity at large eccentricities . For example , repeating the current experiment with a larger screen and additional fixation locations at the current screen corners would increase the covered area four-fold .
In summary , our results provide strong evidence that the activation of cells in entorhinal cortex with spatially structured firing fields does not require physical movement through an environment . Previous results demonstrated that , in stationary monkeys , grid cells can be activated by eye movements as monkeys visually explore complex scenes ( Killian et al . , 2012 ) . Here , our findings suggest that even eye movements are not required to activate cells with grid-like firing fields and that firing fields in the entorhinal cortex cells can represent the location of attention . That spatial representations in the hippocampal formation can represent locations other than the animal’s current position has been shown in rodents through the identification of theta phase precession ( O'Keefe and Recce , 1993 ) and the demonstration that ensembles of hippocampal place cells fire in sequence within a theta cycle , representing places in front of and behind the animal ( Muller and Kubie , 1989; Skaggs and McNaughton , 1996; Jensen and Lisman , 1996 ) . More recent studies have shown that sequential firing of hippocampal place cells can represent anticipation of upcoming locations ( Diba and Buzsáki , 2007 ) , future possible paths when the rat is at a choice point ( Johnson and Redish , 2007; Singer et al . , 2013 ) , and even behavioral trajectories toward a remembered goal in a 2D environment ( Pfeiffer and Foster , 2013 ) . While it is difficult in rodents to assess the location of attention distinct from the location of the animal , these data are consistent with the idea that hippocampal sequences may reflect the animal’s attention being directed along a specific spatial trajectory . Paying attention to the just-completed trajectory could serve to enhance encoding of that experience . Correspondingly , directing attention to future possible paths could serve as a retrieval mechanism to enable optimal choice behavior . These findings also resonate well with reports of grid-like six-fold symmetric BOLD activity while participants imagine navigating in a familiar environment ( Horner et al . , 2016 ) , imagine directions between locations in a large-scale virtual city ( Bellmund et al . , 2016 ) , and navigate a purely abstract concept space ( Constantinescu et al . , 2016 ) . The data presented here demonstrate that entorhinal cells with grid-like firing fields can similarly encode information apart from the animal’s current location . In agreement with Killian et al . ( 2012 ) , we found a percentage of grid cells ( 14% ) that is lower than reports from recording in rats ( e . g . 32% in Sargolini et al . , 2006 ) . We see several possible explanations for this discrepancy . First , our task design is limited to detecting a subset of grid cells who’s firing fields match the size of the screen and the spacing of the dot’s trajectory , thereby potentially underestimating the true percentage of grid cells in macaque entorhinal cortex . Second , our task design does not attach significance to the spatial position of the dot . It is possible to solve the task without knowing where the color change occurs . Thus , it seems plausible that our observations reflect the entorhinal cortex in an attenuated state and that we would observe stronger grid cell activity if the precise dot position was relevant . Future work could address these points by enlarging the screen , including more fixation locations around which the moving dot needs to be observed , and by making the spatial position relevant . The latter might be achieved by introducing an invisible spatial reward field , such that the monkey does not need to detect a color change but only respond when the dot passes through high reward areas on the screen . A good strategy would thereby require integration of the spatial position of received reward to infer the layout of the reward field . Future experiments examining links between grid cell responses and behavior are critical for advancing our understanding of the function of the entorhinal cortex .
Each recording session consisted of the presentation of several cycles of the moving dot . Cycles were smoothed Hamiltonian cycles through a 23 × 23 grid with 1°spacing and therefore showed no center bias . Each cycle consisted of an average of 114 trials and took the monkeys an average of 13 min to complete . The speed of the dot changed as a function of the trajectory’s curvature , slowing down during corners and speeding up during straight parts . The average speed of a typical trajectory was 1 . 95°/s , with a maximum of 3 . 75°/s . Each trial ended with the correct detection of the color change , a missed detection , or when the monkey looked outside of the 4 . 5° × 4 . 5° central fixation window . In subsequent trials , the dot reappeared at its ending location from the previous trial . After the completion of a cycle , the next cycle was chosen randomly from a set of 100 precomputed trajectories . Excluding fixation errors monkeys performed the task at 85% accuracy across all sessions ( min = 70% , max = 94% , std = 8% ) and 87% accuracy across cycles ( std = 13% ) . We only analyzed data from trials with correct detection of the color change and constant fixation within the fixation window . The monkeys were head-fixed and seated in a chair such that the monitor's center corresponded to their neutral eye position . Spikes were recorded ( 40 kHz ) from the entorhinal cortex with a laminar electrode array mounted on a tungsten microelectrode ( 12-site , 150-μmm spacing; FHC ) . Rate maps were computed with a standard Gaussian smoothing procedure ( Killian et al . , 2012; Brandon et al . , 2011 ) . Gridness scores were calculated using standard equations ( 5 , 14–16 ) , but we additionally validated that our implementation was highly accurate in distinguishing grid from non-grid cells in simulated data ( see ‘Gridness score implementation’ , ‘Unit simulation’ , ‘Log likelihood ratios and classification of units’ and methods Figures 2 , 4 , 5 ) . We computed a firing field modulation index to separate spatially structured firing fields from homogeneous noise-dominated fields . The firing field modulation index captures how much of the spatial variation in firing rate can be explained by the mean firing rate over space:ffm ( g ) = ( ∑igi2−∑iμ ( g ) 2 ) /∑igi2where g is the two-dimensional rate map which is linearly indexed by i and μ ( g ) is the mean firing rate . Significance was established by computing the log10 likelihood ratio between the likelihood that a specific cell’s gridscore and firing field modulation index was produced by a noisy grid-cell or a cell with a noisy homogeneous or noisy place field like firing field ( see ‘Log likelihood ratios and classification of units’ ) . All experiments were carried out in accordance with protocols approved by the Emory University and University of Washington Institutional Animal Care and Use Committees . We recorded neuronal activity in the entorhinal cortex in one male and one female monkey ( maccaca mulatta ) trained to perform a covert attention tracking task . Before each session , the monkey’s chair was positioned such that the eye-screen distance was 60 cm . Monkeys were head-fixed during recordings such that this distance never changed . Reward was delivered through a tube positioned in front of the monkey’s mouth and reward delivery was always accompanied by an auditory beep . The task required the monkeys to attend to a dot as it moved across the screen . The monkey's task was to maintain central fixation within a 4 . 5 × 4 . 5° window and to release a bar when the moving dot changed color . Gaze location was monitored with an infrared eye-tracking system ( ISCAN , Inc . ) , whose camera was placed underneath the screen . Each trial began with the onset of a central fixation cross . After the monkey fixated the cross for 300 ms , a moving dot appeared . The dot moved for a random duration between 700 and 2000 ms before it changed color ( from light gray to white on a dark grey background ) . After the color change , a bar release that occurred within 700 ms was counted as a successful detection . Early and late bar releases as well as fixational breaks were counted as errors . Upon bar release or 700 ms after the color change the moving dot disappeared . The monkey was rewarded with a food-based slurry on successful trials . In the next trial , which started 1 s after reward delivery , the dot continued on the same trajectory , i . e . starting from where it had disappeared in the previous trial . Monkeys worked for as long as they were well-motivated and completed between two and eight cycles per session . Monkeys were taught the covert attention task with the following sequence of simpler tasks . First , monkeys were trained in a fixation task in which they were rewarded for keeping fixation for some duration on the central fixation cross . As soon as behavior in the fixation task was stable , the dot was introduced behind the fixation cross and monkeys were now rewarded for releasing a bar when the dot changed color . As part of their general training and habituation monkeys had previously been taught a similar color change task , allowing them to transition to this task . In the beginning , the dot changed color after short durations ( 300–500 ms ) , which were prolonged until the final duration was achieved . Next , the experimenter manually moved the dot in small steps away from the fixation cross . This was practiced until monkeys would reliably fixate the fixation cross and detect color changes of the . The dot followed trajectories that visited different parts of the screen only once during the course of an entire cycle . Such trajectories are called Hamiltonian cycles and ensure that the distribution of dot locations is not biased to specific locations . To create such trajectories , we covered the screen with a matrix of 23 × 23 nodes ( 1° spacing ) that evenly covered an area of −11:11° of visual angle on the screen . We conceptualized this matrix as a graph where neighboring grid nodes are connected such that the dot can move along the vertices of this graph . Creating a Hamiltonian cycle now amounts to finding a sequence that visits all nodes in this graph exactly once . This problem is identical to the traveling salesman problem . Accordingly , each trajectory was created by using the Concorde ( http://www . math . uwaterloo . ca/tsp/concorde/ ) traveling salesman problem solver to find a path that visits each node of the 23 × 23 graph exactly once . We changed the random seed for each sequence to generate unique sequences . Next , we linearly connected all graph nodes to create path through the graph . The x and y coordinates of this trajectory were smoothed with a Gaussian kernel with σ = 60° to yield a smooth trajectory . The smoothing also ensured that the dot continuously changed its speed ( mean for a typical trajectory 1 . 95°/s , 3 . 75°/s maximum ) . At the beginning of a recording session and after completion of each cycle , the next trajectory was chosen randomly from a precomputed set of 100 trajectories . Stimuli were displayed on a 19’ CRT monitor with a refresh rate of 120 Hz . Spikes ( 40 Khz ) were recorded from the EC with a laminar electrode array mounted on a tungsten micro electrode ( AXIAL array: 12-site , 30 μm diameter , 150 μm spacing , FHC , Inc . ) with recording hardware from Plexon Inc . Subsequent analysis was carried out with custom MATLAB ( The MathWorks , Natick , MA ) and python code ( https://github . com/nwilming/ovtcvt [Wilming , 2018]; copy archived at https://github . com/elifesciences-publications/ovtcvt ) . Recordings from monkey MP ( male ) were carried out in the right hemisphere and recordings from monkey PW ( female ) were in the left hemisphere . Recording sites were planned with the help of MRI scans of each monkey and an atlas . Recording sites were located in the posterior part of the entorhinal cortex and close to the rhinal sulcus . Each recording started by slowly lowering a stainless steel guide tube containing the laminar array through a craniotomy . The array was then slowly advanced to its final position while the monkey conducted unrelated tasks . Recordings were started a few minutes ( ~10 ) after the array reached its final position to allow the tissue around the electrode to settle . Spikes were sorted using offline methods ( OfflineSorter , Plexon Inc . ) . We discarded units that did not show stable firing behavior through an entire cycle . In total , we analyzed 69 units from monkey MP ( seven sessions ) and 72 units from monkey PW ( eight sessions ) . See Table 1 . Neural recordings from the hippocampus were conducted in a similar manner . Four independently moveable tungsten microelectrodes ( 1 to 3 MΩ , FHC Inc . ) were lowered down into the hippocampus with the use of coordinates derived from MRI scans . Recordings took place in the left anterior portion of the hippocampus in one monkey ( PW ) and in the right posterior portion of the hippocampus in another monkey ( TO ) . Neurons were recorded from CA1-CA4 subfields , dentate gyrus , and subiculum . For the hippocampal recordings , we recorded from the covert attention task for two to six cycles per session following a ~ 1 hr recording during which monkeys freely viewed images . Rate maps and autocorrelation functions were computed analogously to Killian et al . ( 2012 ) . We computed 2D histograms of spike and dot positions with bins of size 0 . 5° × 0 . 5° . To estimate a firing rate map , we smoothed both histograms with a Gaussian kernel ( σ = 1 . 25° ) and divided the spike counts by the amount of time the dot spent in the respective locations . 2D autocorrelations were computed by shifting the firing rate map relative to itself and computing the coefficient of correlation for the overlapping maps . Our statistical analysis proceeded in several steps . Our goal was to classify the reconstructed firing fields of recorded units as grid-like or not grid-like . In a first step , we identified two measures of firing behavior that were suitable for this classification . In a second step , we estimated the joint distribution of these measures when the generating cell is either a noisy grid cell , a cell with a noisy homogeneous firing field or a noisy place field like cell . This allowed us to compute a log likelihood ratio that indicates whether or not a firing field is caused by a grid cell or by the other types of simulated cells . We then used the log likelihood ratio for classification of cells as grid cells or other cells . Both of these steps made extensive use of spike trains of simulated neurons . We therefore first describe our model for simulating spike trains and then describe the classification process . We simulated units by assuming that firing behavior is the result of an inhomogeneous Poisson process ( IP ) . This process allows to model different firing rates for different positions of the moving dot . The rate function of the IP is determined by a firing field , through which the dot passes , and a noise component . Sampling from the IP defined by this rate function yields artificial spike trains caused by the underlying noisy grid field . We simulated spike trains from noisy grid-like , noisy homogeneous or noisy place field-like firing fields . Grid-like firing fields were created by placingλ ( x , y ) =∑pϵP𝒩 ( ( x , y ) , [ ( px+o ) cos⁡θ−pysin⁡θ , ( px+o ) sin⁡θ+pycos⁡θ ) ] , σ ) P={3iDS , jD}∪{3 ( iDS+SD2 ) , jD+D2}∀i∈Z 2D Gaussian distributions at the nodes of a grid that tiles space with equilateral triangles: where λ ( x , y ) is the firing rate of the grid field at location ( x , y ) , D is the distance between peaks , S is a scaling parameter , θ rotates the grid field , o shifts the grid field and σ specifies the size of each grid node . The grid component of the rate function represents the firing rate in the firing field along several randomly drawn dot trajectories . The dot trajectories transform the 2D firing field into a 1D time- and space-varying firing rate . Simulated units were evaluated with the same pool of trajectories used for the recorded units . The noise component of the rate function is drawn from an exponential distribution ( rate = 1 ) for each location in the trajectory . The amount of noise and grid signal in the timeλ ( t ) =R[βsignalλGrid ( t ) + ( 1−βsignal ) λNoise ( t ) ]and space varying firing rate is governed by the parameter β signal : λGrid , λNoise are the grid- and noise-dependent components of the firing rate and are scaled to have an expected firing rate of 1 . βsignal , with 0 < βsignal <1 , specifies how much the grid signal contributes to the firing rate . R is the desired mean firing rate ( here uniformly sampled from the empirical firing rates ) . λ ( t ) is therefore the firing rate of the IP . Spike trains were then generated by producing a sample from the IP defined by the time- and space-varying firing rate λ ( t ) . The rate function has a temporal resolution of 120 Hz . Methods Figure 2 shows a graphical overview of unit simulations . We simulated 5000 grid cell units for each of nine different βsignal values ( i2 for evenly spaced i between 0 . 18 and 1 ) . All other parameters were drawn from random distributions:D∼u ( 7 , 16 ) σ∼u ( 1 , 2 ) θ∼u ( 0 , 90 ) S∼min ( 1 . 5 , max ( 0 . 5 , N ( 1 , 18 ) ) ) C∼u ( 2 , 6 ) o∼u ( −2 . 5 , 2 . 5 ) where C is the number of dot trajectories used for the simulation . Parameters are given in degrees of visual angle and ranges were chosen to allow broad coverage of potential grid-like firing fields . We discarded all firing fields that had less than three peaks in the area covered by the trajectory; these are a priori not recognizable as grid-like . This resulted in 27 , 450 units whose firing rate was determined by a grid-like firing field . We also simulated units based on spatially structured firing fields that were non grid-like . We used place-like firing fields that had only one peak by setting the spacing parameter of the grid-like firing fields to larger than twice the screen size . The standard deviation was randomly drawn from the interval [3 , 4] to allow large parts of the trajectory to be influenced by the place field . The scaling was set to 1 . We used 15 βsignal values ( i2 evenly spaced i between 0 and 1 ) and simulated 2500 units with each βsignal value . This resulted in 37 , 500 simulated units whose firing fields ranged from completely uniform ( βsignal = 0 ) to spatially structured fields ( βsignal > 0 ) . To summarize , we simulated a large range of plausible grid fields that can be resolved by our trajectories . In addition , we simulated cells with noisy homogeneous firing fields and cells with a noisy place-like firing field . Computation of the gridness score is analogous to ( Langston et al . , 2010; Brandon et al . , 2011 ) . In this computation , an ellipse is fit around six peaks in the 2D autocorrelation function and the rotational correlation is computed at 30 , 60 , 90 , 120 and 150 degrees . The gridness is then defined as:Gridness=min ( rc ( 60 ) , rc ( 120 ) ) −max ( rc ( 30 ) , rc ( 90 ) , rc ( 150 ) ) where rc ( x ) refers to the rotational correlation at angle x . Brandon et al . ( 2011 ) noted that this measure is sensitive to how the ellipse is fit in the 2D autocorrelation . Choosing the closest six peaks , for example , might include a peak that is due to noise in the firing field and omits a 'correct' peak that is further away . We used a two-step procedure to fit an ellipse . In a first step , potential ellipses that likely contain six peaks and six valleys were identified . This was achieved by predicting for a large space of possible grid fields where the most central peaks and valleys would be in the 2D autocorrelation for this grid field . Grid fields were parameterized by grid spacing , aspect ratio , size of the peaks , rotation of the grid field and shift of the peaks along the ellipse . Ther ( x , y ) =∑αϵPN ( ( x , y ) , μ ( α+L ) , σ ) +12∑αϵPN ( ( x , y ) , μ ( α+L+30 ) , σ ) P={0 , 60 , 120 , 180 , 240 , 300}μ ( α ) = ( t ( α ) xcosθ−t ( α ) ysinθ , t ( α ) xsinθ+t ( α ) ycosθ ) t ( α ) = ( −SDsinα , Dcosα ) prediction r ( x , y ) was computed according to the following equations: where D is the grid spacing , θ is the rotation of the grid field , σ describes the size of the grid peaks , S relates to the aspect ratio of the grid field and L describes the shift of the peaks along the ellipse . We constrained the set of candidate ellipses to those that passed through at least one non-central peak in the 2D autocorrelation . Methods Figure 4 shows several example predictions . The second step consisted of selecting ellipses that capture structure in the 2D autocorrelation . To this end , we computed the RMSE ( root-mean-square error ) between all ellipse predictions and the 2D autocorrelation functions . We then used a minimum shift algorithm to select ellipses that captured six peaks and valleys in the autocorrelation function better than ellipses in the local neighborhood of possible ellipses ( the window of the minimum shift algorithm is N/5 ) . The final gridness score was then the maximum of the gridness scores computed for these ellipses . To evaluate the power of the gridscore implementation to separate grid cells from non-grid cells , we computed gridness scores for all simulated units with grid-like firing fields . We then compared how well the gridscore separated units with firing rates determined by noise ( βsignal = 0 ) from those whose firing rate was at least partly determined by the grid firing field ( βsignal >0 ) . To this end , we computed ROC curves and used the area under the curve as a measure of discriminatory power . Methods Figure 5 shows these ROC curves and the AUC as a function of βsignal . To classify cells as grid-like we transform gridness scores and firing field modulation ( ffm ) index combinations into a single likelihood value . This mapping is derived via simulating many different random firing fields , place like firing fields or grid-like firing fields and computing gridness scores and ffm index values . This allows us to differentiate cells based on an estimate of the likelihood that a given gridness score and ffm index is generated by a grid-like firing field or other firing fields . To differentiate grid cells from non-grid cells , we computed the log likelihood ratio that compares the evidence that a gridscore and firing field modulation ( ffm ) combination is generated by a grid cell to the evidence that it is generated by a cell with a homogeneous or place field-like firing field:log10 ( Pgrid ( gridscore , ffm ) /Pnongrid ( gridscore , ffm ) ) The probabilities Pgrid and Pnongrid were computed from the simulation results with grid-like , place field-like and homogeneous firing fields . Since the gridness score and ffm index are continuous values , we locally pool simulated gridness scores and ffm indices to compute the likelihood . This pooling is carried out by a Kernel density estimate and the bandwidth ( size of pooling ) is determined via 10-fold cross validation . We thus estimated each probability distribution with a kernel density estimator and used these estimates to derive the likelihood estimates . Since the gridness score and firing field modulation measures are bounded , we applied a logit transformation to avoid boundary artifacts . We only considered units with βsignal > 0 . 15 as simulations of grid cells for the grid density estimate . Smaller βsignal values produced firing fields qualitatively close to those obtained with βsignal = 0 and thereby inflated the likelihood of observing small gridness scores and firing field modulation values from the grid cell simulation . Removing these units for the density estimation therefore makes our estimates more conservative . The log likelihood ratio expresses how much evidence we have that a particular gridness score and firing field modulation combination is produced by a grid cell relative to the evidence for place cells or cells with a homogeneous firing field . To evaluate the power of the log likelihood approach to separate grid cells from non-grid cells , we compared how well the log likelihood value separated units with firing rates determined by noise ( βsignal = 0 ) from those whose firing rate was at least partly determined by the grid firing field ( βsignal>0 ) . In analogy to our evaluation of different gridness scores , we used the area under ROC the curve as a measure of discriminatory power . Methods Figure 5B shows AUC as a function of βsignal in comparison to only using the gridness score . The log likelihood approach performed better than only using the gridness score for all noise levels . Figure 6 shows 2D autocorrelation functions and ratemaps for all EC cells .
Grid cells in the entorhinal cortex allow for the precise decoding of position in space . Along with potentially playing an important role in navigation , grid cells have recently been hypothesized to make a general contribution to mental operations . A prerequisite for this hypothesis is that grid cell activity does not critically depend on physical movement . Here , we show that movement of covert attention , without any physical movement , also elicits spatial receptive fields with a triangular tiling of space . In monkeys trained to maintain central fixation while covertly attending to a stimulus moving in the periphery we identified a significant population ( 20/141 , 14% neurons at a FDR <5% ) of entorhinal cells with spatially structured receptive fields . This contrasts with recordings obtained in the hippocampus , where grid-like representations were not observed . Our results provide evidence that neurons in macaque entorhinal cortex do not rely on physical movement .
When driving home from work , we can easily tell where we are along our route . A network of regions deep within the brain acts a little like an inbuilt GPS and tracks our position relative to other objects in the environment . Cells in one of these brain regions , called the entorhinal cortex , construct a map of our surroundings . The map resembles a grid of tessellating triangles , and the cells that produce it are called grid cells . Whenever we move onto a corner of one of the triangles , the corresponding grid cells start to fire . This firing enables the brain to track our movements . But grid cells may do more than support navigation through the physical world . They may also help us navigate through our memories . Evidence suggests that we organize our knowledge and experiences into mental maps . These maps connect related concepts just as physical maps connect nearby locations . In principle , the brain systems that support physical navigation may also enable us to access the information within our mental maps . But for this to be true , cells such as grid cells must respond to movement in mental space as well as in physical space . Wilming et al . have now tested this possibility by training macaque monkeys to detect a color change in a dot moving across a screen . The monkeys had to keep their eyes fixed on the center of the screen throughout the task . This meant they could not move their eyes to track the dot . Instead they had to mentally move the focus of their attention . Wilming et al . monitored the activity of cells in the entorhinal cortex as the monkeys mentally followed the dot . As predicted , some of the cells fired in a triangular grid-like pattern similar to that seen when animals move through their environment . Grid cells can thus fire in the absence of physical movement . These findings bring us closer to understanding how brain circuits that code for spatial locations also support other mental processes . Evidence from many sources suggests that structures within the brain’s medial temporal lobe , including the entorhinal cortex , contribute to memory . The next challenge is to identify how these brain regions encode spatial and other types of information and use them to form memories .