Grid cells represent an ideal candidate to investigate the allocentric determinants of the brain’s cognitive map. Most studies of grid cells emphasized the roles of geometric boundaries within the navigational range of the animal. Behaviors such as novel route-taking between local environments indicate the presence of additional inputs from remote cues beyond the navigational borders. To investigate these influences, we recorded grid cells as rats explored an open-field platform in a room with salient, remote cues. The platform was rotated or translated relative to the room frame of reference. Although the local, geometric frame of reference often exerted the strongest control over the grids, the remote cues demonstrated a consistent, sometimes dominant, countervailing influence. Thus, grid cells are controlled by both local geometric boundaries and remote spatial cues, consistent with prior studies of hippocampal place cells and providing a rich representational repertoire to support complex navigational (and perhaps mnemonic) processes.DOI:http://dx.doi.org/10.7554/eLife.21354.001 Different types of neural correlates of space are found in the hippocampal formation, including place cells, grid cells, boundary cells, and head direction cells . These cBehavioral studies  and elecGrid cells are presumed to provide a universal metric for the animal’s movements in space and for the cognitive map . StudiesTo gauge the degree of control exerted on grid patterns by the distal landmarks vs. the geometry of the proximal boundaries, we dissociated the reference frames embodied by these two sets of cues. Visually prominent cues were affixed to the walls of the experimental room  platform rotation (ROT20), virtually all grids from all rats rotated by a similar amount . HoweverPlatform control of the grids could reflect either an influence of the local landmarks within the platform itself  or the geometric structure of the platform boundaries. To disambiguate these alternatives, we rotated the platform 70° CW. If the grids were controlled by the platform itself, we would expect a 70° CW rotation with respect to the room, which would be measured as a 10° CW rotation due to the 60° symmetry of the grid. On the other hand, if the grids preserved the STD alignment relative to the platform's geometric structure, but rotated relative to the physical platform itself, we could observe a 20° CCW rotation with respect to the room, which is geometrically congruent to a 70° CW rotation . A thir. One of (69) = 8, p<7.5x10−13; 34 ± 11% vs. 7 ± 5% proportion of grid period; In all of the responses described so far, the grids were primarily anchored to the platform’s geometric boundaries, but the room cues broke the geometric symmetry of the square platform and also exerted a countervailing influence that tended to produce an under-rotation of the grid. By contrast, the other mode in (119) = 507, p<4.6x10−16; 18 ± 11% vs. 7 ± 4% proportion of grid period; (119) = 68, p<1.5x10−20).In the translation manipulation , the platform was shifted by half its length along the room's longer axis . The fir118 = 10.85, p<1.8x10−19; significant at p<0.05 in 5/7 rats [4/7 in thinned datasets]). This systematic under-translation, alongside the under-rotations observed in ROT20 and ROT70 . We grouped these differences by rat, reference frame used to compute the difference , and paired type of the manipulations involved in the difference . Of the 36 such groups from four rats that met criteria for circular statistical testing (n > 7), 31 groups (each comprising 3–13 distinct recording days) from all four rats were found to be significantly different from 0° , indicating that relative rotations across identified manipulations were generally systematic with respect to all three reference frames. High angular concentration was measured in these groups , further indicating that grid reorientations across the same manipulations were precisely reproduced over multiple days.Taken together, these analyses indicated that grid angular drift from all three reference frames tended to be manipulation-specific and precisely controlled over time.Beyond the typical under-rotations and under-translations described above, idiosyncratic  neural correlates of the conflict between reference frames were observed.2 test for proportions with Yates correction for continuity: χ2(1)=5.3, p<0.021). The selective loss of regular grid structure was apparent from the first day ROT70 was experienced by the rat and continued up to the last day in which grid cell recordings were available for ROT70, 17 days later , the equilateral-triangular grid pattern was often selectively disrupted in ROT70, even though the cell continued to fire in discrete, multiple fields . We consys later . The losys later  than thoys later . Thus, iIn another rat , STD sessions repeated at the end of the day (STD2) consistently displayed a different alignment of the grid compared to the first STD sessions of the same day . A few oExamples of divergence between grid and boundary representations were also observed in a second rat  when the grid strongly dissociated from the platform reference frame . These correlations were found to be high in both STD (median correlation >0.68 in each rat) and manipulated sessions (median correlation >0.69 in each rat), suggesting that there was no major intra-session grid drift or change of anchoring within a session .In order to determine if the population of grid cells maintained a coherent response to the manipulations performed in this experiment, we quantified the spatial coupling of simultaneously recorded grid cells, both within and across grid scales. We considered all the possible pairings of grids that had quantitatively distinct spatial firing patterns  in a given session. We measured their coupling by (1) the difference of the two grid rotations elicited by the manipulation performed in that session, and (2) a joint correlation measuring how well the STD rate maps match the corresponding non-STD rate maps after they are rotated and translated rigidly together by their average rotation and translation .Of the 476 pairs from six rats, 81% displayed a rotation difference <5° and 88% had joint correlation >0.7 , indicatThe present experiments demonstrate that the world lying beyond current navigation boundaries contributes to determining the allocentric reference frame of two-dimensional grid maps. While platform geometry usually exerted a dominant—but rarely absolute—influence on the grids, in some cases the grid map appeared embedded in the metric structure of the room and dissociated from the platform . Neural This ability has fundamental implications. Grid cell properties can be reconciled or contrasted with those of place cells, which have long been known to respond to both extra- and intra-maze inputs e.g, , but latMoreover, a grid cell system subject to distal control is ideally suited to fit Tolman’s original inspiration for the cognitive map as a ‘comprehensive-map’ , p. 193.The response of grid cells to the conflicting reference frames was diverse in frame preference, extent of under/over rotation/translation, and, in one rat, grid regularity. These differences were generally manipulation-specific and consistent over many recording days. Thus, they do not reflect repeated errors of a grid stabilization process that reacts haphazardly to the conflicting cues each time they are experienced. Rather, these repeatable phenomena possibly reflect an underlying discriminating process of the type that is hypothesized to produce different place cell maps and context-dependent memories through global remapping of place cell’s firing locations . PreviouIn principle, the correction of path-integration errors required for stabilizing the grid could rely primarily on local boundaries  even wheGrids of similar spacing remain rigidly coupled during manipulations that elicit their global realignment or rescaling, including during hippocampal remapping . By forcGrid coordination was found to be very high even for grids of markedly distinct scale . This fiFurther experimental and theoretical work is also needed to clarify the relationship between our observations and those by Eight male Long-Evans rats  were housed individually on a 12:12 hr light-dark cycle (dark cycle started at a consistent time point varying among rats between 10am–12pm). One rat was excluded from the analyses because its recordings did not yield any grid cells. Before the training protocol started, the rats were given one week for acclimation to the facility and human handling. The rats were 5 ½ –6 ½ months old and 470–590 g at the time of surgery. Surgeries largely followed previous protocols and strategies for MEC recordings  to chronPost-mortem histological analysis of recording locations followed standard procedures e.g., . BrieflyThe apparatus was located in a room (355 × 280 cm) with a constellation of visually prominent cues . A dim sBoth types of platforms were mounted on rails that allowed the rotations and translation of the platform with respect to the room. The experimental manipulations consisted of either rotations of the platform around its geometric center in the clockwise direction  or the translation of the platform by half its size along one of its axes (‘SHIFT’), starting from a standard (‘STD’) configuration of the platform. In the STD configuration the platform edges and room walls were parallel. The translation direction in SHIFT was parallel to the longer side of the room and kept constant throughout the experiments. Reproducibility of the manipulations across days and rats was aided by a laser pointer system that allowed precise placement of the platforms in repeated locations.Training and experiments were started at or after the beginning of the circadian dark period. The animals were trained to forage in the platform in the STD configuration during a pre-surgery and post-surgery phase, before experiments were started. At the beginning of each training session the rat was carried on a pedestal into one corner/quadrant of the platform, where it was released. During training this release location never changed. The experimenter paced and paused haphazardly around the room while throwing food pellets  at a semi-regular rate and toward semi-random locations to encourage continuous locomotion and uniform sampling of the area and discourage stereotyped trajectories. On training and recording days the animals were kept at >80%  of their free-feeding weight as necessary to motivate foraging behavior. The pre-surgery phase lasted 8–13 days and terminated when the animal foraged for >50 min with minimal interruption and relatively uniform spatial sampling. (This pre-training procedure led us to prioritize ‘good runners’ as surgery candidates.) After completion of the pre-training phase the animal was put back on a free-feeding diet for 4–16 days before surgery was performed and then again for 5–24 days during post-surgery recovery.Experiments commenced when the rat’s behavior was similar to its pre-surgery levels (after 6–10 days of post-surgery training) and well-isolated cells from putative MEC recording sites were encountered. The experiment day always began with an STD session, but the rat was released from a random corner/quadrant. In the following sessions, the platform was manipulated in full light conditions while the rat rested on its pedestal a few meters away, in sight of the whole experimental scene. No attempt at a disorienting the animal was ever performed. Lights were then dimmed again and the rat carried and released into a random corner/quadrant of the platform to start the new session. During electrophysiological recordings, the recording implant was connected to cables reaching a commutator mounted above the ceiling about the center of the ring source of light. The weight of these cables was counterbalanced by a pulley system. Each session (STD or manipulated) lasted 20–50 min to ensure ample and repeated sampling of the whole platform; 2–7 such sessions were performed each experiment day until scarce or no recording opportunities were estimated to remain . In some cases the STD session was repeated again during the day between manipulation sessions or at the end of the day.The animal position and head orientation were tracked via an array of multi-colored light-emitting diodes (LEDs) rigidly connected to the head implant, similar to previous experiments . The LEDTetrodes were made by twisting 12.5 or 17 µm nichrome wire . The tips were electroplated with gold, until the wire impedance was lowered to ~200 kOhms. The electrophysiological signal passed first through a unity-gain preamplifier headstage . For spikes, the signal was differentially amplified against a tetrode in a quiet area  and amplified between 2000 and 10,000 times and filtered in the 600–6000 Hz bandwidth. Waveforms crossing a >35 µV threshold on one of the four tetrode channels were sampled for 1 ms at 32 kHz on all four tetrode channels. These putative spikes were manually assigned to one or more putative cells (units) with the use of a custom spike-sorting program . Waveform characteristics (amplitude peak and area under waveform in most cases) on the four tetrode channels were plotted and cluster boundaries were manually drawn. For local field potential (LFP) recordings, the signal was differentially amplified 4000 times against the signal from a screw implanted in the skull, filtered in the 1–475 Hz bandwidth, and continuously sampled at 1 kHz.Tetrodes were advanced by 40 µm up to a few hundred µm every day while the rat sat on the resting pedestal, until the tetrode tips were judged to be in MEC based on the detection of the theta rhythm in the LFP, unit activity, and anatomical considerations. One or two tetrodes in the array were moved faster in search of the phase reversal of the LFP theta wave known to occur near the layer II/I boundary of MEC , and werRate maps were calculated in the camera reference frame from the tracked animal and spike positions. Epochs of immobility or very slow locomotion were excluded from these calculations. To estimate the rat’s speed, its trajectory was first smoothed by convolving both raw x,y position time series with a clipped Gaussian mask with variance = 300 ms. The mask values were renormalized at each step. Rat’s speed in cm/s was calculated for each of the 30 Hz frame intervals based on the rat displacement between the two consecutive frames. Epochs longer than 500 ms, in which the speed remained below 3 cm/s, were expunged from the original, unsmoothed trajectory and from the spike train. The rat positions left in the unsmoothed trajectory were then binned in 3 × 3 cm bins to produce an occupancy map of the rat’s dwell time in each bin. The firing rate map was obtained by dividing the count of spikes occurring in each bin by the total occupancy in the same bin. Bins with less than 50 ms dwell time were marked as unoccupied  and excluded in visualization and analysis. The rate map was then smoothed by a clipped 2D Gaussian mask with 5 × 5 bins and variance = 2. The values of the mask were dynamically renormalized to account for unoccupied bins falling within the mask at each convolution step. If less than five occupied bins fell within the mask at any step, the output bin in the smoothed map was marked as unoccupied . ‘Bootstrapped’ rate maps were obtained by repeating the entire procedure after the spike train was resampled with replacement to obtain a new spike train of equal size 100 times, yielding 100 bootstrapped rate maps for each original rate map.Procedures for the evaluation of the grid structure (‘gridness’ test) and its geometric features were adapted from previous studies  and applorientation of the grid is defined as the average direction of these canonical semi-axes. The scale of the grid is defined as the average distance of the three correlation fields (their centers of mass) defining the canonical axes from the center of the autocorrelogram, converted to cm according to the size of the rate map bins. Elliptical distortion is measured by an elliptical index (ranging from 0 to 1) defined as 1 - B/A, where B and A are respectively the length of the shorter and longer axis of the ellipse fit to the centers of mass of the six correlation fields most closely surrounding the central field.The autocorrelogram is the special case of a crosscorrelogram calculated on two copies of the same rate map. The main geometric features of a grid were extracted from the autocorrelogram. Discrete regions of at least 20 contiguous bins of the autocorrelogram with correlation uniformly >0.1 were first identified as correlation fields. Three canonical grid axes running through the centers of mass of the correlation fields were chosen similarly to : AX0 is Gridness scores were calculated similarly to prior papers . If the ad hoc and a rate map was classified as one produced by a grid cell if all criteria were met:In most previous studies e.g., , a thresThe gridness score was ≥0.1.All six correlation fields defining the annulus could be identified as described above.The angles subtended by the grid semi-axes were >30° and <90°.The elliptical index of the autocorrelogram was <0.5.The distance of the correlation fields from the ellipse was never greater than 20% of their distance from the center of the autocorrelogram.The scale of the grid was <125 cm , making their autocorrelogram-based geometric characterization ambiguous).The gridness score was ≥0.1 for at least 95 out of the 100 bootstrapped rate maps when the procedure was repeated starting from these maps.‘thinning’ of the dataset below to mitigate related statistical concerns.) Because day to day decisions on the number of sessions to run and on electrode adjustment were influenced by knowledge of the presence of grid cells in the recordings, the proportions of cells that were found to be grid cells are prone to these sampling biases and are not intended to represent well-controlled, biological estimates of grid cell prevalence.In the last step, we did not use the typical method of shuffling the spike train relative to the position time series to test for statistical significance of grid cells e.g., , but insTo evaluate the geometric response of a grid cell to a given manipulation, we considered the rate maps of the grid cell in the STD and manipulation sessions if both rate maps satisfied the grid cell classification criteria. Rate maps were always calculated with respect to the camera reference frame, using one camera for all rotation manipulations , and a second camera identically centered with respect to the translated platform in the translation manipulation . The rotation performed by the grid was calculated as the difference of grid direction in the STD and manipulated conditions. If more than one STD session was run on the same day, the last STD run before the manipulated session under consideration was used as a reference for this session. Because of its 60° symmetry, rotations of an ideal hexagonal grid can be unambiguously defined within a circular range between −30° and 30°, where −30° and +30° are equivalent.To calculate the grid rotation with respect to the platform reference frame, the rotation of the platform was subtracted from the measured grid rotation in the room (producing positive angles for over-rotations and negative angles for under-rotations of the grid with respect to the platform). The grid rotations thus computed, as well as the platform rotation when indicated on plots, are reported within the  grid angular range. For example, a 70° CW rotation of the platform is equivalent to a 10° CW rotation in grid angular space, in the sense that a grid that perfectly tracks the platform in ROT70 displays a change of direction of 10° between the STD and ROT70. Analogously, the platform rotation by 45° CW in ROT45 is equivalent to 15° CCW in grid angular space.Similarly, we computed the grid rotation with respect to the reference frame given by the platform geometry (geometric reference frame). This geometric reference frame was specified by the 90° symmetric configuration of the square platform that implied the smallest rotation with respect to the room. The only manipulations in which the geometric reference frame dissociated from the platform reference frame  were ROT70 and ROT45, for which the geometric reference frame rotated respectively 20° CCW and 15° CW in grid angular space. The rotation of the grid with respect to the geometric reference frame was calculated as for the platform reference frame: the rotation of this reference frame was subtracted from the grid rotation measured in the room and reported in the  grid angular range.After the rotation of the grid was determined, we measured the grid phase shift that was required to complete the alignment of the grid in the STD and the manipulation sessions. These calculations were also dependent on the reference frame. To calculate the grid phase shift in the room reference frame in all types of manipulations (other than SHIFT), we rotated the STD rate map by the grid rotation measured in the room reference frame, so as to have the grids in the two conditions directionally aligned. We then computed the crosscorrelogram of the two rate maps. The grid phase shift was given by the vector representing the displacement of the center of mass of the most central correlation field in the crosscorrelogram from the center of the crosscorrelogram. The phase shift relative to the platform reference frame was analogously computed on a new crosscorrelogram obtained after the STD rate map was rotated by the same angle of rotation applied to the platform  ± the grid rotation in the platform reference frame (see above). An analogous procedure was also used to calculate the phase shift relative to the geometric reference frame, if this frame differed from the platform frame of reference. For example, a grid rotating 5° CW in the room reference frame in ROT70 performs a rotation of 5° CCW relative to the platform reference frame  and a rotation of 25° CW relative to the geometric reference frame (because the expected rotation angle by a grid perfectly tracking the frame = 20° CCW). Accordingly, the phase shift for the platform frame is extracted from the crosscorrelogram of the STD and ROT70 rate maps after the STD rate map was rotated by 70° CW +5° CCW = 65° CW, whereas the phase shift for the geometric frame is extracted from the crosscorrelogram obtained after rotating STD rate map by 20° CCW +25° CW = 5° CW.In SHIFT experiments, the geometric and platform reference frames coincide and are directionally aligned with the room reference frame. Grid rotation is therefore the same for all the reference frames. Grid phase shifts, however, will be different if calculated relative to the room or the platform/geometric frame. We first apply the same step as above: the STD rate map is rotated to equalize its grid direction with the SHIFT grid, and the phase shift is measured in the crosscorrelogram of the two maps. Because both rate maps are calculated in the platform reference frame , this is the grid phase shift relative to both the platform and geometric reference frames. To compute the phase shift relative to the room, we need to compare the observed platform-based phase shift with the one expected if the same grid were to remain perfectly anchored to the room and the platform were to reveal a different region of its pattern . The platform-based phase shift expected in this scenario occurs along the platform translation axis and equals the remainder of the division between the magnitude of the platform translation (68.5 cm) and the period of the grid projected along the translation axis. This phase shift can be expressed as a fraction of the grid period  in radians:after α is normalized between –π and π. The observed platform-based phase shift can be analogously expressed asγ = β - α represents the phase shift seen in the room frame, also expressed in radians. After normalizing γ between –π and π, the room-based phase shift is calculated in cm asWe analyzed the geometric coordination of grid cells in any manipulation by two measures of grid coupling in pairs of simultaneously recorded grid cells. We wanted to compare coordination of grids both within similar scale groups and between different scale groups. However, a complication with the second measure (described below) arises when considering that grids of the same spatial scale can have high spatial correlations if their phases and orientations overlap, but grids at different spatial scales by definition cannot produce high correlations. Thus, for these analyses, we only analyzed grid pairs with quantitatively distinct spatial firing patterns (Pearson correlation of STD rate maps < 0.5) to minimize the potential influence of this asymmetry in possible correlations.The first measure was the absolute difference between the rotations of the first grid and second grid with respect to their STD condition. Small values of this measure indicate that the two grids rotated by about the same angle, while larger values are indicative of a directional dissociation of the two grids caused by the manipulation. The second measure took into account the whole spatial distribution of firing expressed by the rate maps of the two grids. Its goal was to verify if a single, rigid transformation of both STD rate maps can produce firing patterns that are spatially correlated with those observed in the manipulated session, for both cells at once (a ‘joint correlation’):STD and RM2STD be the rate maps of grid cells 1 and 2 in STD, and RM1M and RM2M their rate maps in the manipulated condition, with RM1STD, RM2STD, RM1M, and RM2M calculated in a common reference frame:Let RM1STD and RM2STD relative to STD (using the methods described above) and calculate the average rotation ρ of the two rate mapsCalculate the rotation magnitudes and directions of RM1STD and RM2STD relative to STD (using the methods described above) and calculate the average phase shift vector γ of the two rate mapsCalculate the phase shift vectors for RM1STD, RM2STD, RM1M, and RM2MIndividually mean-center and normalize RM1STD, RM2STD) into a 3D vector VSTD by aligning the two rate maps along the Z axisStack  as in 4.Produce an analogous 3D vector VSTD by ρ around the Z axis and shift it by γ in the X,Y planeRotate VSTD and VM into 1D vectors so that corresponding entries in VSTD and VM preserve the correspondence of rate maps and spatial bins.Linearize vectors VSTD and VMThe joint correlation is the cosine of the angle subtended by the linearized VControl distributions for both measures of coupling (rotation difference and joint correlations) were obtained after the alignment of each grid pair was randomly perturbed 10 times. Each of the STD rate maps was independently rotated by an angle drawn from a uniform distribution between −30° and 30°. Each of the rate maps in the manipulated conditions was shifted in a direction drawn from a uniform distribution between −180° and 180° and by a distance drawn uniformly between 0 and the scale of the grid.In studies like this, measurements of functional properties of single units—presumed to represent different cells—are typically considered as the independent and identically distributed samples on which statistical testing is based. Accordingly, the experimenter should try to minimize the chances that the same cell was included more than once in the dataset submitted to a given test. We note that this approach might not be suitable for grid cells. It is not clear whether sampling from different, simultaneously recorded grid cells provide observations to be considered more statistically independent than sampling from the same grid cell in repeated experiments. In fact, grid cells of similar scale have been shown to act in a geometrically coordinated fashion  possiblyA comprehensive solution to this statistical problem is beyond the scope of the present study and we opted to keep with the conventional approach used in previous grid cell studies. Our primary analyses were carried out using each grid cell recorded as an independent data point. To reinforce the conclusions from the primary analyses, we report data from individual rats where appropriate. We also repeated each statistical test in a ‘thinned’ dataset, obtained by enforcing the constraint that no two units recorded in different days from the same tetrode can be both present in the dataset if their estimated anatomical distance along the tetrode trajectory was less than 150 µm. The constraint was generally enforced on samples intended as the combination of the unit itself  and the manipulation type: a unit that is discarded for one manipulation may be retained for another, depending on whether the suspected duplicate from another day had been subjected to the same manipulation. The only exception in which we thinned by unit identity alone, with no consideration of the manipulation type, was the comparison of proportions of cells passing the gridness test in different manipulations for rat 387 . The thinning procedure was completely automated with no manual intervention. In all but a few cases (specified in the text), all results and conclusions from the data were consistent between the full and the thinned data sets .Because of the grid 60° symmetry, grid directions and rotations were defined in a circular range from −30° to +30° and wrapping around at these extremes (i.e. −30° =+30°). Accordingly, to perform statistical tests and comparisons on angles denoting grid directions and rotations, we employed circular statistical methods after the  range and sample angles were linearly mapped onto the full circle spanning the  range. Test statistics are reported in this transformed angular space, whereas descriptive statistics are reported in the original  range, unless otherwise noted. Rao’s test for circular uniformity  was used In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been favorably evaluated by Timothy Behrens (Senior Editor) and three reviewers, one of whom is a member of our Board of Reviewing Editors. The following individuals involved in review of your submission have agreed to reveal their identity: César Rennó-Costa (Reviewer #2); Alessandro Treves (Reviewer #3).Thank you for submitting your article "Framing of grid cells within and beyond navigation boundaries" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:The reviewers all felt that this paper was a significant advance in understanding the behavior of grid cells in the context of conflicting local and distal cues. They agreed that the study provides useful information for theory and experiment. The reviewers all felt that the methods were sound and experiments carefully executed.Essential revisions:A specific shared comment by the reviewers was that the text and figures should be clarified. They also felt that the Discussion should be focused and shortened.Reviewer #1:This paper looks at grid cell response changes in a context where a local platform moves or rotates in a large room with prominent landmarks. The authors show clearly that distal cues do indeed contribute to grid maps. The study systematically goes about showing this. They compare local vs. distal cues for rotation at different angles, and translation. They find that even for moderate platform movements, there is a small but consistent drag from distal cues. There is a consistent set of cases where ambiguous rotations are remapped according to the distal cues.Overall, this is an interesting advance of the literature on place cell remapping and distal vs. local cues, to grid cells.I would like the authors to further examine a point arising from their experiments on rat and manipulation-specific stability. Is the difference between rats just the sampling of cells, say from subsets of grid cells with potentially different cue responses? From Figure 8 and related text about the coordination between cells in an animal it looks like it is between rats, but I would like the authors to discuss.It would be interesting if there were a behavioral correlate of differences between rats. For example, the authors discuss rat 387, which seemed to experience a strong influence of the room frame of reference. The authors clearly have full tracking data. Is there anything in the behavior that might correspond to this physiological measurement?Reviewer #2:The article provides evidence that rats can use both local cues (accessible through tact) and distal cues (reachable through sight) to anchor the allocentric reference frame of the internal map to the environment (grid cells). The main findings are: (1) one cue type is dominant; grid cells pattern will change coherently to one type or the other whenever the cues are independently modified; (2) modifications are not limited to rotations and are also observed for translations indicating that the underlying mechanism is not just a head-direction system reset; (3) the changes are animal- and modification-specific and remain constant across many days; (4) grid cells from different scales change coherently; and (5) conflictual cues might lead to grid degradation in specific cells of specific animals.I do not find the reported results surprising. Similar results have been reported for place cells whereas grid cells realign following changes in the place cells firing patterns. However, the authors present countervailing evidence to the emerging view that local borders are the sole determinants of the grid cells firing pattern. Therefore, despite the lack of a "surprising factor", the work is timely and relevant. The paper provides many "missing pieces of the puzzle" of how grid cells actually work and I can see myself in the near future, as a theoretical scientist, using this manuscript as reference. Importantly, the methodology seems to be rigorous, aligned to the community standards and is scientifically sound. Thus, I would recommend its acceptance for publication granted that my concerns (described below) and minor clarity issues in the manuscript are solved.The authors base their analysis on unusually long exploratory sessions  reflecting the authors' attention to the statistics. However, it concerns me whether drift in the grid cell activity during such a long period contaminates the statistics. Mainly, the grid cell pattern could possibly switch between different anchors in time. If so, it would interfere in the gridness values and grid orientation. To better understand this issue, the authors could examine the stability of the grid cells comparing the first and second halves of the exploration or come with a metric about how long does it take for the grid map to stabilize. They can compare these analyses in STD and conflictual conditions.Some interesting work have shown that grid cells are not uniform across the environment and that large environments can get compartmented. The size of the platform in this study is rather large (137x137cm if compared to 80x80cm in other studies). I'm concerned if whether the reported dominance is uniform across the whole platform. One possible side effect of the compartmentation is that grid cells might not be regarded as grid cells (low grid score). The authors could segment the apparatus and analyze different parts separately. They can look whether the anchor in one side of the arena is the same as in another side (same for center vs. borders).Reviewer #3:This is an important contribution, reporting the effects on grid cell firing patterns of incongruent proximal and distal cues. The experimental work addresses issues I was (and likely many others were) wondering about, and in my view it should be published without delay. The analysis stays mostly close to the data, which I appreciate.My only mild criticism has to do with the hypothesis testing formatting of some of the analyses, which is not necessarily the authors' choice as it may have been largely an attempt to meet presumed reviewer requests, and with the lengthy discussion, which by morphing it into almost a review paper blunts the impact of the experimental findings.Hypothesis testing is only really appropriate if there is the expectation that one cause-effect relationship or at least one correlation should dominate all others, an expectation that can then be tested statistically. It is inappropriate in most neural coding contexts, where cause-effect relations are merely convenient short-hands for directed interactions, and interactions tend to be multifarious. It is particularly inappropriate in studies like this one, where competing interactions are quantitatively set against each other. In my view the authors should recast their analyses in the language of quantifying the strength of each interaction they look at, rather than extracting p-values. For example, in the three-way competition thought to occur in the ROT70 condition, would a low p for the "intermediate" hypothesis of room control be distinguishable for a specific combination of the two extremal hypotheses of platform and geometric control, with little room control?Further, the emphasis on hypothesis testing at the single cell level, over the first 6 figures, largely obscures the splendid population result reported, perhaps not so perspicuously, in Figures 7, 8, which in my view should be highlighted. Panel 7C seems like an extremely strong result, which goes unnoticed in a crowded figure. Panel 7D might be equally important, but I cannot make out the pink and blue dots, and I am not sure what it says. Overall, Figure 7 points out how perfect gridness is a misconceived notion, to be handled with care, not used as a basis for all analyses. Figure.8 casts similar doubts on the notion of segregated grid modules.In the Discussion, much space is devoted to a minute review of classical literature on cue control, whereas I would focus on grids, and in relation to grids on the 3 outstanding questions which these beautiful experiments pose:i) What makes a multi-peak cell appear, in an idealized setting, as a quasi-perfect triangular grid? I lean of course towards the proposal outlined in our adaptation model , whereas the authors discuss only the rather implausible attractor and oscillatory interference models, which are inconsistent, in their pristine form, with a host of earlier data;ii) Can multiple grid maps coexist in the same module, in contrast to the Fyhn et al. 2007 result? This I think is the core suggestion one gets from Figure 7, and if validated it would open up an entirely new perspective on grid coding ;iii) Are the modules segregated ab initio, e.g. in terms of connectivity, or do they self-organize and maintain a complex web of mutual interaction ? Essential revisions:A specific shared comment by the reviewers was that the text and figures should be clarified. They also felt that the Discussion should be focused and shortened.Reviewer #1:[…] I would like the authors to further examine a point arising from their experiments on rat and manipulation-specific stability. Is the difference between rats just the sampling of cells, say from subsets of grid cells with potentially different cue responses? From Figure 8 and related text about the coordination between cells in an animal it looks like it is between rats, but I would like the authors to discuss.As the reviewer points out, the differences appear to be mostly rat-based and unlikely to emerge from the sampling of functionally distinct subsets of grid cells in different rats. This is an important point that we failed to emphasize appropriately. To address it we have added a table to the paper , which i“The difference of response expressed by the bimodal distribution of rotations in ROT70  is unlikely to result from the sampling of functionally differentiated neuronal networks .”This table is relevant to the manipulation in which the differences between rats were most prominent, namely ROT70 and its bimodal rotation response distribution. The table describes the composition of each mode in terms of brain areas, rats, number of units (and number of tetrodes from which the units were recorded). A diverse set of anatomical regions is represented in both modes, whereas rat identity is almost perfectly segregated by mode, with the exception of 1 unit from rat 292 belonging to the left mode and 6 to the right mode. These 7 units were recorded in the same area (putatively parasubiculum) and by the same tetrode.Moreover, as observed by the reviewer, Figure 8 on grid coordination also indirectly suggests that the response is unlikely to depend on sampling biases. To reinforce this indication, we have added information in the Results section on the number of pairs in the different clusters of Figure 8 that comprised grid cells recorded on different tetrodes and specifically from different areas:“In most pairs the two grid cells were anatomically adjacent as they were recorded from the same tetrode, but in many other cases they were recorded on different tetrodes . In some of the latter cases the recording sites were ascertained to be in different layers of MEC or in MEC and parasubiculum .”We suspect that individual experience and/or apparatus type might be the factors influencing the response type, but statistical validation of this impression would require a far greater number of rats – hence we originally refrained from discussing these factors. We have briefly acknowledged these considerations at the end of the second paragraph of the Discussion section:“In our experiments differences in the relative dominance of distal and local cues appeared to depend on individual differences between rats and/or the type of apparatus, rather than on the anatomical regions where the grid cells were recorded . These considerations seem to rule out pronounced differences in the coverage patterns across or within sessions. The loss of grid regularity but not of the multi-peaked nature of the rate maps seems to rule out the possibility that the representation of place fields in the rate maps was somehow compromised by behavioral aberrations.In consideration of the reviewer’s question, we have more carefully examined rats’ velocities. The speed distribution in rat 387 is minimally higher in ROT70 than in the other types of manipulated sessions pooled together (median speed 12.7 vs. 12.4 cm/s), but similarly minimal differences were found in other rats too, or when other types of manipulations were singled out. In most cases, the sign of these differences did not depend on the size of the sliding time window used to compute the velocities (66ms and 1s) and the differences were found to be statistically significant . We refrain from interpreting these particular results, as the effect sizes are very small. As mentioned in the response to the previous comment, our impression is that the type of apparatus and individual differences played a role in the emergence of different responses in different rats, but the statistical validation of this impression requires a larger number of rats. By the same token, we think that a systematic and well controlled investigation of the link between individual behaviors and the relative influence of distal vs. proximal cues on grid cells may be prohibitively long with current recording strategies/techniques.Reviewer #2:[…] The authors base their analysis on unusually long exploratory sessions  reflecting the authors' attention to the statistics. However, it concerns me whether drift in the grid cell activity during such a long period contaminates the statistics. Mainly, the grid cell pattern could possibly switch between different anchors in time. If so, it would interfere in the gridness values and grid orientation. To better understand this issue, the authors could examine the stability of the grid cells comparing the first and second halves of the exploration or come with a metric about how long does it take for the grid map to stabilize. They can compare these analyses in STD and conflictual conditions.As the reviewer points out, the unusually longer sessions were motivated by sampling/statistical objectives. The experimenter typically waited until the rat roughly covered the whole arena >2 times, so that estimates of local firing rates could be based on repeated visits of the same spot. The concern raised by the reviewer is important. To address it we calculated the Pearson correlation of the two rate maps derived respectively from the first and second half of each session that lasted longer than 30 minutes in all rats but rat 387, which had already been separately analyzed in this way. These correlations were found to be very high in both STD and manipulated sessions, suggesting the absence of major intra-session grid drift or change of anchoring. The correlations in STD and the manipulated sessions were not found to be significantly different. We added this information at the end of the subsection “Neural correlates of the local vs. remote cue conflict”:“To mitigate concerns that these idiosyncratic responses, as well as the previously described minor and major dissociations from the platform reference frame, resulted from spatially unstable grids, we extended the analysis employed above for rat 387 to the recording sessions obtained from the other rats. […] These correlations were found to be very high in both STD (median correlation > 0.68 in each rat) and manipulated sessions (median correlation > 0.69 in each rat), suggesting that there was no major intra-session grid drift or change of anchoring within a session .”Some interesting work have shown that grid cells are not uniform across the environment and that large environments can get compartmented. The size of the platform in this study is rather large (137x137cm if compared to 80x80cm in other studies). I'm concerned if whether the reported dominance is uniform across the whole platform. One possible side effect of the compartmentation is that grid cells might not be regarded as grid cells (low grid score). The authors could segment the apparatus and analyze different parts separately. They can look whether the anchor in one side of the arena is the same as in another side (same for center vs. borders).These are very important points. Local distortions certainly occur, not limited to the selective loss of gridness in ROT70 concerning rat 387. This was clear to us from close inspection of the rate maps. We are very interested in knowing how these local distortions relate to the recent work the reviewer hinted at . We had noticed that some of these distortions (including 387) might result from an anisotropic balance of relative dominance of the two reference frames, possibly center vs. periphery, as the reviewer also wondered. Compartment-based analyses of the kind employed in the cited studies and recommended by the reviewer can in principle quantify these effects. But for compartmentalized analyses to work, enough vertices of the grid would need to fall within each compartment to make a reliable local autocorrelogram. Unfortunately, we anticipate that this would not be the case for most of our data. Prior to our original submission, we made progress on devising alternative analyses, but we realized that such effort would evolve into a study of its own that is best dealt with separately.To gauge the extent to which the issue raised by the reviewer affects our dataset, we identified all the manipulated sessions that failed to pass our gridness test even if they did so in the previous and next session . This criterion minimizes the chance that the loss of gridness was caused by mounting noise in the recordings, so we reasoned that these were the most likely candidates in which a loss of gridness caused by a compartmented response could be observed. Visual inspection of their rate and spike/trajectory maps suggested that in the majority of these cases the failure to pass the gridness test could be likely attributed to (1) poorer spatial sampling (i.e. not uniformly repeated multiple times) that did not pass the bootstrap part of our gridness test or (2) a large grid dissociating from the platform and losing a vertex (or a large part of it), making its grid structure no longer detectable. In no case did the number of visible vertices seem to allow the type of analysis discussed above. Because we are not able to adequately address the reviewer’s concern with our current data, we believe it would be best to not discuss the issue in the paper. However, if the reviewer insists that this is an important point that we must address, we will add a discussion after consultation with the editors.Reviewer #3:[…] My only mild criticism has to do with the hypothesis testing formatting of some of the analyses, which is not necessarily the authors' choice as it may have been largely an attempt to meet presumed reviewer requests, and with the lengthy discussion, which by morphing it into almost a review paper blunts the impact of the experimental findings.Hypothesis testing is only really appropriate if there is the expectation that one cause-effect relationship or at least one correlation should dominate all others, an expectation that can then be tested statistically. It is inappropriate in most neural coding contexts, where cause-effect relations are merely convenient short-hands for directed interactions, and interactions tend to be multifarious.We are generally sympathetic to these comments. One of us (F.S.) personally harbors strong reservations on frequentist statistics and “classical” hypothesis testing in general and favors a Bayesian perspective on data analysis and inference. It is particularly inappropriate in studies like this one, where competing interactions are quantitatively set against each other. In my view the authors should recast their analyses in the language of quantifying the strength of each interaction they look at, rather than extracting p-values. For example, in the three-way competition thought to occur in the ROT70 condition, would a low p for the "intermediate" hypothesis of room control be distinguishable for a specific combination of the two extremal hypotheses of platform and geometric control, with little room control?In most cases those tests were not employed to establish which reference frame dominated the representation, but were used to validate the grid geometrical dissociation from each given reference frame (including what looked to be the dominant one). The only exception is the comparison of phase shift magnitude in the last paragraph of the subsection “Grid anchoring to both local and remote cues in rotation experiments”. Our extensive use of scatterplots to display the entire distribution of grid rotation and phase shift in almost any circumstance  reflects our impression that the strength of interactions is amenable to direct visual assessment. Dominance of a given reference frame (or lack thereof) should be immediately evident by visual inspection of the whole dataset.eLife has stringent requirements in terms of data and statistics presentation, in line with the standards that the general biomedical audience has come to expect. Another reviewer praised our attention to statistics. Because of journal requirements and current standards in the field, we have chosen to keep the statistics as they are.In spite of our general agreement with the reviewer on these epistemological issues, we do not share the reviewer’s opinion that discarding the statistics would be beneficial to the dissemination of our findings. Further, the emphasis on hypothesis testing at the single cell level, over the first 6 figures, largely obscures the splendid population result reported, perhaps not so perspicuously, in Figure 7, 8, which in my view should be highlighted. Panel 7C seems like an extremely strong result, which goes unnoticed in a crowded figure. Panel 7D might be equally important, but I cannot make out the pink and blue dots, and I am not sure what it says. Overall, Figure 7 points out how perfect gridness is a misconceived notion, to be handled with care, not used as a basis for all analyses. Figure 8 casts similar doubts on the notion of segregated grid modules.Thank you. We have split Figure 7 . Panels E and F were moved to a different figure . Panels A-D are now in Figure 6 by themselves and were enlarged to address the issue of their clarity. We also replotted Figure 7D  without transparency (α = 0). We originally used a high level for transparency to render overlapping dots but we find that the new version has more color contrast without having lost information.In the Discussion, much space is devoted to a minute review of classical literature on cue control, whereas I would focus on grids, and in relation to grids on the 3 outstanding questions which these beautiful experiments pose:i) What makes a multi-peak cell appear, in an idealized setting, as a quasi-perfect triangular grid? I lean of course towards the proposal outlined in our adaptation model , whereas the authors discuss only the rather implausible attractor and oscillatory interference models, which are inconsistent, in their pristine form, with a host of earlier data;ii) Can multiple grid maps coexist in the same module, in contrast to the Fyhn et al. 2007 result? This I think is the core suggestion one gets from Figure 7, and if validated it would open up an entirely new perspective on grid coding ;iii) Are the modules segregated ab initio, e.g. in terms of connectivity, or do they self-organize and maintain a complex web of mutual interaction ?We have now removed much of the detailed review on cue control (extensive pruning throughout the Discussion section). We also share the reviewer’s captivation with these three theoretical points. Some of the data we presented intriguingly speak to these points, along the lines suggested by the reviewer. However, with regard to (i) and (ii), the data were quantified in only one rat or another. Hence, we hesitate to speculate at length about their theoretical implications in this paper, but we address these points as follows:With regard to (i) we more explicitly addressed the differences between grid distortions in rat 387 and previously documented cases of grid distortions in the Discussion:“This highly selective grid disruption was triggered by the conflict between proximal and distal cues in the absence of any structural alteration of the platform. Thus, the grid disruption cannot be attributed to tensions induced by the platform frame alone  but probably to the grid system’s attempt to reconcile proximal and distal inputs.”We also completed the discussion of the implications of multi-scale coordination by explicitly addressing the model of grid formation developed in Kropff and Treves 2008 and further extended in Si, Kropff and Treves 2012, alongside a slightly less detailed discussion of the attractor and oscillatory models of grid formation:“In a third type of model, Hebbian learning of a grid-forming synaptic pattern is enabled by the spatiotemporal interaction of fast adaptive neural dynamics and spatial inputs that vary on a much slower behavioral timescale . […] Future work with this model could investigate how these geometric properties extend to similarly inter-connected populations of grid cells spanning multiple scales.”With regard to (ii) we commented on the examples in Figure 7 (different grid maps in STD vs STD2) in the context of place cell global remapping and memory:“A seeming counter-example to the involvement of grid framing in proper context recall was instead noticed in one rat in which different grid maps were produced in identical cue configurations at the beginning and end of the experimental day . But even in this case a short-term memory process appeared at play, since we anecdotally found the later grid map to reflect the recent history of experimental interventions , which could be regarded as a form of contextual discrimination.”With regard to (iii) we briefly pointed out the implications of the findings in Figure 8 for the nature and development of intra-module functional relationships:“Thus the mechanism responsible for the cross-scale grid coupling observed in our data may not always be active, and it is therefore unlikely to rely solely on genetically or developmentally hardwired networks.”


A method is proposed for efficient laser modification of fused silica and sapphire by means of a burst of femtosecond pulses having time separation in the range 10–3000 ps. Modification enhancement with the pulse separation increase in the burst was observed on the tens picoseconds scale. It is proposed that accumulated transient tensile strain in the excitation region plays a crucial role in modification by a sub-nanosecond burst. Control of heat deposition with sub-microsecond bursts of femtosecond pulses permits the of writing of waveguides with a circular cross-section4.Femtosecond laser direct writing and micromachining attract considerable interest for a variety of applications ranging from integrated optics and microfluidics to printable flat optics and multi-dimensional optical data storage. A regular train of femtosecond pulses generated by a femtosecond oscillator or regenerative amplifier is commonly used in laser material processing. Micromachining with temporally shaped pulses or femtosecond pulse trains exploits material dependent electronic relaxation processes. It has been applied, for example, to creating sub-wavelength features via control of ionization processes on a sub-picosecond time scale5. The strain develops nearly 100 times quicker than the accumulation of heat; that is, on a sub-nanosecond scale. Probably this is the reason why stress and strain have not yet been used in the control of laser processing of materials.In addition to heating, the creation of a pressure wave and rarefaction in the modified zone are other important factors determining laser induced structural changes3. The interval between pulses in a burst is defined by the femtosecond laser repetition rate and cannot be less than some tens of nanoseconds. A more sophisticated setup allowing control of the energy of each pulse in the burst makes use of a passive resonator with Pockels cell4. With such a setup the pulse separation interval obviously cannot be reduced to less than around 10 ns, because reduction of the cavity length is limited by the space occupied by the Pockels cell inside the cavity. To our knowledge there are no laser writing setups allowing the generation of bursts with pulse separation intervals in the range 10–10000 ps. Accordingly, the interaction of focused femtosecond pulses with materials in the regime of such bursts has not yet been investigated.In the heat accumulation regime the simplest burst generation technique is based on pulse picking from a continuous train of pulses6. An enhanced change in refractive index was obtained in a waveguide written by a train of double pulses separated by intervals in the range 400–800 ps7. This last observation has been attributed to additional absorption by colour centres, assumed to be a product of STE relaxation. This in turn could suggest that a burst of pulses, separated by a few tens or hundreds of picoseconds, would produce material modification greater than modification produced by a single pulse with the same energy.An enhancement of the strength of nanograting induced birefringence was observed upon writing with a train of double pulses, when the interval between pulses was less then 50 ps, presumably due to increased absorption of self-trapped excitons (STE)In this paper we will propose and demonstrate a method for efficient micromachining of silica glass and sapphire by means of sub-nanosecond bursts of femtosecond pulses with decaying amplitudes in each burst. We show that a burst with pulse separation interval in the range 10–3000 ps activates an additional mechanism of femtosecond modification based on simultaneous actions of the laser pulse and rarefaction or tensile strain, produced by the cumulative action of previous laser pulses in the burst. Contrary to common belief, we observed an increase in refractive index change with increase of time separation between pulses in the burst on a time scale of 0–100 ps, which we connect with the setting time of tensile strain in the modifying region.Transform-limited pulses with a duration of 180 fs were generated by an ytterbium solid-state laser system at 1030 nm. A high precision translation stage (Aerotech ALB1000) was set up to move the sample – either a fused silica plate or a z-cut sapphire plate – between laser shots and perpendicularly to the beam. An Olympus objective lens (NA = 0.65) was used to focus the laser beam, with correction of spherical aberrations, into the sample. We investigated the modifications and non-linear absorption of pulses arising in a single shot regime. That is, either a single pulse or burst of pulses was focused on a pristine region of a sample. For the silica experiment, the laser beam was focused so that the beam-waist was located at a depth of 150 μm. For the sapphire experiment, the laser beam was focused at a depth of 90 μm.t in the range 70 ps–8 ns. On the interior side the mirrors had a partially reflecting chirp-free dielectric coating with reflection coefficient of 76.5%, and on the exterior side an AR coating designed for wavelength of 1030 nm. (2) To generate bursts with shorter inter-pulse separation, we used a monolithic Fabry-Perot cavity consisting of a single plane-parallel fused silica plate, with sides parallel to within 2 arc seconds, reflection coefficient of 76.0%, and thicknesses varying from 1 to 7 mm. Depending on the plate thickness, this second type of cavity produces bursts with inter-pulse separation Δt in the range 10–70 ps.In order to produce pulse bursts with various different inter-pulse separations, we used two different kinds of Fabry-Perot cavities . The transmittance data were collected and stored on a computer.In order to investigate the dependence of energy deposition in fused silica on the pulse separation interval we measured the dependence of the non-linear transmittance of a glass plate on the incoming energy of the original pulse or the burst of pulses Refractive index change and birefringence in the laser modified point regions were investigated with a bright field microscope Olympus BX61 operating in transmitting mode, equipped with a 14-bit CCD camera, motorized object table and quantitative birefringence imaging system (CRi Abrio Imaging System).φ was obtained by mathematical processing of bright field images with quantitative phase microscopy software (QPM)8. The images were taken and a corresponding QPM treatment was carried out for two viewing directions, one along the direction of propagation of the writing laser beam (top view), and the other perpendicular to it (side view). Three bright field images were captured to calculate one mapping of the optical path. One image was taken with the translation stage in the focus position and the other two images were taken with the translation stage moved, with accuracy of 0.1 μm, to positions defocused by ±1μm. The bright field images were taken with an interference filter transmitting at 503 nm with bandwidth of 10 nm. The objective lens had NA = 0.45 for the top view and NA = 0.75 for the side view, and the condenser diaphragm was set at NA = 0.2. The spatial filter was set to 2.0 during the QPM analysis.In the first step, mapping of the optical path 9:φ is optical phase for unmodified region of glass. The inverse Abel transform yields the radial dependence of change in the refractive index, following measurement of optical path distribution:The 3D distribution of the refractive index in modifications made in silica glass was calculated by use of the inverse Abel transform. It was assumed that modified points have axial symmetry relative to the direction of the laser beam. By imposing such a symmetry assumption, the optical path mapping observed in the direction perpendicular to the laser beam (side view) can be presented by the Abel transform10:R is the radius of the treated region, which is of cylindrical form. The change in refractive index is negligible at the boundary of this region. M is the number of terms in the sum that are necessary for a good approximation and was taken to be equalled to 15. Integration of formulas  are presented in Fig. It was found that, contrary to what happens with a single pulse, a burst produces a birefringent microstructure in fused silica. Two birefringent spots form a dumbbell-like structure with the slow axis coinciding with the line connecting the spots, while the region between the spots remains birefringence free Fig. . Orientaφ − φ0 for the side view in the centre of a modification. Typical profiles of OPD for two orthogonal orientations of the dumbbell-like structure relative viewing directions and two different inter-pulse intervals are shown in Fig. Δn in silica glass is shown in Fig. All modifications in silica glass produced by bursts with pulse separation interval in the range 10–3000 ps have pronounced negative optical phase difference (OPD) 11. A burst with the same energy inscribes modifications having pronounced negative refractive index change along major part of the modification length. Maxima of positive changes in the refractive index are shifted to the modification boundary.A single pulse produces modification of the refractive index with a recognisable profile elongated in the direction of the laser beam, which is strongly varying along this direction with change of sign located almost in the centre of the modification3D distributions of refractive index change in silica glass were built for series of modifications produced by bursts with various pulse separation intervals. The peak negative refractive index change was defined for each distribution, and results are summarised in Fig. For sapphire, the method of inverse Abel transform could not be applied for the available sample, because it had not a polished facet for the side view, and the only data collected was that of OPD. However, the response of sapphire can be analysed on the assumption that the correlation between OPD and refractive index change is the same for sapphire as for silica. Mapping OPD by viewing along the direction of the laser beam (top view) was obtained using QPM for the same modifications in silica glass, for which refractive index change were obtained using inverse Abel transform. As functions of the inter-pulse separation interval, the dependence of OPD for silica Fig.  was founDependence of the birefringence retardance upon the pulse separation interval in the burst resembles the dependence of refractive index change in silica glass. It has pronounced maxima at 95 ps and 1 ns for burst energy close to the inscription threshold energy, and becomes zero for higher pulse separation intervals, for which there is no modification Fig. . The ret12, while the dependences of burst transmittance for the inter-pulse separation intervals 200–2000 ps are differed by steeper drops at energy close to the modification threshold  could be expanded in two terms:T1 is transmittance of the first pulse in the burst, Tbt(Δt) is transmittance of the last part of the burst, that is, from the second pulse to infinity, Ein is energy of the burst, E1 is energy of the first pulse, Ebt is energy of the burst tail, that is, of the last part of the burst. The dependence of the burst tail transmittance Tbt(Δt) on the inter-pulse interval was obtained from (5) taken into account that E1 = Ein/2.4 and Ein = E1 + Ebt. The result for the fixed burst energy of 145 nJ is plotted in the insert of Fig. Δt not exceeding 40 ps. The transmittance of the burst tail decreases in the range 40–200 ps, reaches a flat region on the scale 200–1000 ps, and then rises for inter-pulse intervals of more than 1 ns.The dependence of single pulse transmittance on the pulse energy has a recognizable shapeold Fig. . It is i13. In silica glass, over a time-scale of the order of 150 fs, free electrons and holes become locked to self-trapped excitons (STE)15, and so, for long pulses (>0.2 ps) STE efficiently absorbs laser pulses. In sapphire free electrons persist for nearly 100 ps, and it is expected that they provide strong linear absorption in this time interval15. Thus the observed modification increase on a time scale of 0–100 ps is inconsistent with known dynamics of electron excitations.Femtosecond laser writing creates a permanent refractive index change in transparent dielectrics. This is initiated by multiphoton ionization, which is followed by linear absorption by the electron plasma and avalanche ionization5, and it was shown that it produces rarefaction in the modified region which develops on a sub-nanosecond time scale. We interpret the dramatic increase in the change of refractive index, resulting from the controlled increase in the pulse separation interval from 0–100 ps, as an indication that in our experiments the role of rarefaction in the modification is significantly enhanced. We suppose that, if a laser pulse interacts with an already modified region at the same moment that rarefaction starts to develop due to the preceding pulse, it leads to the enhanced generation of stable defects, and thence to an increase in the change of the refractive index. We propose that in the first approximation this extra change can be described by the formula:ε(Δt) is the first principal strain describing the largest deformation, Δt is the pulse separation interval in the burst, Δn0 is the change in refractive index produced by an ordinary single pulse with energy equal to the burst energy, η is the parameter of refractive index change enhancement due to rarefaction, and is material dependent. The integral is taken over the region of modification.The role of the shock wave in the formation of voids was investigated in16:u is the deformation vector, c is the speed of expansive waves, defined by the formula:E is Young’s modulus, ν is the Poisson ratio, and ρ is the media density. In formula . A decrease in the refractive index change and OPD for a pulse separation interval larger than 3 ns is naturally explained by relaxation of electronic excitations and corresponding tensile stress, but this time domain is beyond the scope of our current model.20. The saturation is connected with the intensity clamping effect caused by non-linear absorption in the electron-hole plasma21, restricting the density of the deposited energy. Therefore densities of structural defects, that cause refractive index change, do not increase with the increase of pulse energy. Instead, the volume of generating plasma is increased. The scenario is different for modification made by a burst. The results of non-linear transmittance measurements reveal that a necessary and sufficient condition for a burst modification is that the ionization threshold is attained with the first pulse, while energies of all subsequent pulses are insufficient for ionization. Indeed, the threshold energy for a burst is higher by a factor of 2.4 than for a single pulse; the same ratio as that between the burst energy and the energy of the first pulse in the burst . Thus a high density of stable defects and a large change in refractive index is achieved.22 can explain poor repeatability of OPD in silica glass in comparison with sapphire that is reflected in large difference of error bars in Fig. The assumption that the transient electronic excitations is responsible for absorption the burst tail and variation of glass density on nano-meter scale7, where this absorption was tentatively ascribed to unstable colour centres. Summarizing, we ascribe increased refractive index change due to burst writing by the combined effects of tensile stress and transient colour centres absorption.Absorption efficiency in silica glass increases as the interval between pulses increases, as shown in Fig. The anisotropic nature of the tensile stress arising in the plasma region can explain the birefringence and enlargement of the region of modification along the direction of polarization of the femtosecond beam Fig. . The ani23, the new method has an almost 10 times faster writing speed, because a single laser shot produces a thermally stable birefringence structure. Finally, the sub-nanosecond burst offers an increase of throughput in ultrafast laser micromachining performance.A new method for obtaining birefringent structure in silica glass due to high thermo stability opens perspectives for the development of long-term optical memory. Compared with optical memory based on volume nanogratings requiring more than 10 pulses separated by intervals longer than 1 μsWe have proposed and demonstrated a method for efficient material modification with sub-nanosecond and nanosecond bursts of femtosecond pulses with decaying amplitudes in the burst. The burst activates an additional mechanism of femtosecond modification based on the simultaneous actions of rarefaction and electronic excitation. The innovative burst produces an enhanced refractive index change and a thermally stable birefringent structure even with a single laser shot, due to localization of energy deposition through a reduction in peak pulse intensity. Transient colour centres mainly control absorption of the second and all subsequent pulses in the burst, but the crucial role in modification enhancement belongs to the transient tensile strain accumulated by the repeated action of laser pulses. The largest enhancement of refractive index change in silica glass was obtained for pulse separation intervals in the range of 50 ps–3 ns.Video S1


Since the discovery of neural regions in the monkey brain that respond preferentially to multisensory stimuli presented in proximal space, researchers have been studying this specialised spatial representation in humans. It has been demonstrated that approaching auditory or visual stimuli modulate tactile processing, while they are within the peripersonal space (PPS). The aim of the current study is to investigate the additional effects of tactile expectation on the PPS-related multisensory interactions. Based on the output of a computational simulation, we expected that as tactile expectation increases rapidly during the course of the motion of the visual stimulus, the outcome RT curves would mask the multisensory contribution of PPS. When the tactile expectation remains constant during the motion, the PPS-related spatially selective multisensory processes become apparent. The behavioural results on human experiments followed the pattern predicted by the simulation. That is, rapidly changing levels of tactile expectation, caused by dynamic visual stimuli, masks the outcome of the multisensory processes within peripersonal space. This indicates that both PPS-related multisensory interactions and tactile expectations play an important role in anticipating and responding to interactions with the body. Since the initial discovery of multisensory neurons in the periarcuate cortex of monkeys  is a factor that modulates tactile expectation and, subsequently, the response time to these tactile events  as the factor to control the level of tactile expectation throughout the trial (explained below). That is, we expected that cue-reliability Fig. b, d, f aBefore we conducted a study in human participants, the interaction effects of PPS modulation and tactile expectation on response times to tactile stimuli were explored using a computational model. Following this, a tactile detection task involving approaching visual stimuli . The aim of this model was to gain insight into the changes of the response-time pattern of an imaginary observer to a tactile stimulus, while considering the current location and direction of motion of the visual distractor stimulus, and cue-reliability. It should be noted that the simulation model is intended only to approximate observable human behaviour and does not account for, or match the specific details of the underlying neural dynamics. We intended only to test if the shape of the outcome response-time patterns, and not if the absolute response times may be modulated by the aforementioned tactile expectation. We assume that the outcome response times are a result of a two-stage serial process consisting of a detection and response stage. We also assume that prior expectations directly and equally influence the amount of activation in each of these stages.The data model consisted of two serial stages see Fig. . The firIn this stage, once a tactile stimulus is delivered, the time taken for the tactile stimulus to be detected is dependent on the time taken for the underlying somatosensory module (SS) and PPS multisensory module (MS) together to reach a detection threshold. The activity of the somatosensory module is sensitive to temporal expectation, which is dependent on the distance travelled by the visual stimulus  and not to its direction. The temporal expectation is further modulated by the cue-reliability level, or the overall probability of receiving a tactile stimulus. The MS module is insensitive to temporal expectation, but is influenced by the physical location of the visual stimulus and its movement direction. That is, if the visual stimulus is within the PPS zone and is moving towards the observer, the MS module contributes to the detection of the tactile stimulus.The amount of tactile expectation at a given timepoint is a factor of the overall probability of receiving a tactile stimulus (cue-reliability) for that condition and the location of the visual stimulus along its movement trajectory  Eq. .The maximum amount of tactile expectation is determined by the cue-reliability level.The minimum amount of tactile expectation calculated by dividing the maximum amount of tactile expectation by the number of timepoints during the motion of the visual stimulus, where a tactile stimulus may be delivered:The amount of activation (generated by the combined activity of the SS module and MS module) is dependent on the level of tactile expectation, which follows the following rules:tcurrent is the tactile expectation when the tactile stimulus is delivered at timepoint tcurrent, during the motion of the visual distractor. Athreshold is the activation threshold in units. Ptactile is the probability of receiving a tactile stimulus for that probability condition (cue-reliability). tcurrent is the current timepoint from the start of the motion of the visual stimulus. This is independent of the direction of the motion of the visual stimulus. ttotal is the total duration of motion of the visual stimulus. For example, in the condition where there is a 100% probability of receiving a tactile stimulus, the amount of tactile expectation varies from 14.28 to 100, where 14.28 is the initial tactile expectation.TEAs the visual stimulus moves from the starting location to the end location (irrespective of direction of motion), the tactile expectation varies from the minimum value to the maximum value of tactile expectation range for that cue-reliability level. The amount of activation in the somatosensory module is proportional to the tactile expectation level. The model assumes that 100 units of activation are required to reach the threshold. The activation grows steadily at the rate of 0.5 units per millisecond. Based on this, given a zero-valued level of  tactile expectation, the time required to detect the presence of a tactile stimulus is 200 ms.The multisensory module is sensitive to physical location of the visual stimulus and its direction of motion, responding to the tactile stimulus only when the visual stimulus is within a spatial limit with respect to the imaginary observer while approaching the observer. The combined activity of the somatosensory and multisensory modules determines the time taken for the tactile stimulus to reach a detection threshold. That is, when both the somatosensory and multisensory modules are triggered, the time taken for the system to reach the detection threshold is lower than when only the somatosensory module is triggered. When a visual stimulus is within the spatial extent of the multisensory module, the model receives a boost of 20 units of activation, thereby reducing the detection time by 40 ms. The boundary of this spatial extent is set to be at 40 cm from the imaginary observer and conditional upon the stimulus approaching the observer. Therefore, in the receding condition, the PPS-related multisensory gain is absent.After the tactile stimulus is detected by the first stage of the model, the response stage of the model also requires reaching a response threshold to generate the final response. The response preparation in this stage is set to a starting level based on the level of expectation of a tactile event (the response generation level behaves the same way as the tactile expectation level of the somatosensory module of the tactile detection stage). Once the tactile stimulus is detected, this initial level of response preparation rises until it reaches the response threshold. Therefore, a high starting level of response preparation results in faster response times. Like the detection stage, the response stage requires 100 units of activation to reach the threshold. Activation grows steadily at the rate of 0.5 units per millisecond. The amount of initial activation is dependent on the amount of response preparation, which follows the same rules as that of the somatosensory module in the tactile detection stage.The total time taken for the model to generate a response to the tactile stimulus is, therefore, the time elapsed between the start of the detection stage and the output of the response stage. In addition to the latency generated by the two stages of processing by the model (which indicates the time taken by the participant to initiate a motor response), an additional 150 ms is added to the final response time, to account for the time taken by the observer to mechanically complete the foot pedal press required to register the response. The reason for this additional step is to extract response times from the model that lie in a range comparable to that of real human participants.The total duration of motion of the visual stimulus was set to 2300 ms, and there were seven timepoints (ranging from 0 to 2300 ms in steps of 328 ms) at which it was possible to receive a tactile stimulus. The visual stimulus was simulated to move between 0 and 90 cm from the subject in either an approaching, or receding fashion. Four ratio (cue-reliability) conditions were simulated. They were 100, 75, 50, and 25%. No noise was added to this system, so only one simulation per cue-reliability condition, timepoint, and motion direction were performed.Y is the vector of estimated response times from the curve-fitting procedure. ymin is the minimum response time obtained from the model simulation for that condition. ymax is the maximum response time obtained from the model simulation for that condition. L is the vector of locations of the visual stimulus at which the tactile stimulus is delivered. a and b are the factors estimated by the curve-fitting procedure. a is the location at which the response time reaches its mean value. It is treated as the location of the PPS boundary. b is the slope of the sigmoid curve.The response times obtained from running the model simulations were fitted using a sigmoidal and a polynomial curve Fig. . The sigA sigmoid curve was estimated for each cue-reliability condition .Y is the vector of estimated response times from the curve-fitting procedure. c and m are the coefficients estimated by the curve-fitting function. c is the intercept of the curve. m is the slope of the linear curve. L is the vector of locations at which the tactile stimulus is to be delivered.The linear fit was defined by the following function:A total of eight linear curves were estimated for each ratio condition and visual stimulus movement direction Fig. . Root meN equals the total number of data points used in each curve . The RMSE value is calculated separately for each Ratio and Direction condition, and separately for both the sigmoidal and linear curves. Here, A value of the RMSE for each curve indicates how closely the fitted curve follows the given data. Therefore, to learn which curve was a better fit for each ratio and direction condition, the RMSE values obtained for the sigmoidal and linear curve were compared Table . As expeFrom this simulation, it appeared that reducing tactile expectation to 50% was sufficient to bring forward the sigmoidal pattern of RTs assumed to be driven by multisensory interactions within the PPS. It must be mentioned, however, that by changing the amount of multisensory PPS contribution in the model , the number of tactile absent trials required to bring out the sigmoidal nature of the RTs also changes. Specifically, when the contribution of the PPS is higher, the number of the tactile absent trials required to reduce the effects of the tactile expectation becomes lower.The aim of this simulation was to check the idea that increasing tactile expectation levels during the course of a trial could influence responses to multisensory stimulus in PPS. The actual ratio of tactile present trials necessary to cause the emergence of this effect in behaving humans can only be gleaned with experimental evidence. The following experiment was performed to test this.Mage = 22 years, SD = 3.3, 12 females, 13 right-handed, 2 left-handed). All had normal or corrected-to-normal vision. The experiment was performed according to the ethical guidelines laid down by the Declaration of Helsinki. The local ethical committee of the Faculty of Social and Behavioural Science, Utrecht University also approved the study. All the participants gave their informed consent prior to their participation in the study.Fifteen subjects between the ages of 18 and 30 were tested  that was attached to the distal phalanx on the back of both their left and right index fingers. The visual stimulus was a red dot with a diameter of 5 cm. The background of the screen was black in colour. The visual stimuli were displayed on large screen monitor (Philips BDT5530EM/06) lying flat on a table in front of them see Fig. . The scrThe experiment took place in a darkened room in the Experimental Psychology lab at Utrecht University. Each subject was seated in front of the screen where the visual stimuli were displayed. The head rested on a chin rest at a height of 18 cm from the screen to maintain a consistent viewing height across all participants. They were instructed to place their hands on the edge of the monitor that was closest to them, such that each of their index fingers were 12 cm along the length the screen see Fig. . Prior tEach trial began with the presentation of the visual stimulus on a black background appearing either at the far end of the screen (90 cm away from the tip of the index finger) or at the near end of the screen near the index finger (0 cm from the tip of the index finger), on the left or the right side of the screen (13.25 cm from the body midline). The visual stimulus remained there for a variable period between 400 and 800 ms after which it started moving. If the dot was presented at the far end of the screen, it moved towards the subject’s left or right finger in a straight line, and vice versa. Visual stimuli did not cross the midline of the screen during movement and only moved towards the finger at the same side as the visual stimulus.Lfar and Lnear, respectively). The purpose of these two locations was to encourage subjects to monitor the tactile modality throughout the duration of the trial. The visual locations of interest were L1–L5, and were delivered during the motion of the visual stimulus. On any target present trial, only one tactile stimulus could be delivered. Each location at which a tactile stimulus could be delivered was separated by 15 cm on the screen . The total duration of visual motion was always 2300 ms.From the start of the trial, there were seven locations in depth at which a tactile target could be delivered. In two conditions, the tactile stimulus was delivered when the stimulus was stationary at the far or the near end of the screen , there were two direction conditions , seven locations of the visual stimulus in depth at which the tactile stimuli may be delivered, two laterality conditions , and two target conditions . The conditions were presented in a random order.Based on the ratio, the total number of trials in the block varied. In each of the ratio blocks, each condition  was repeated approximately three times . The experiment yielded a total of 168 conditions .The 25% ratio condition contained 84 target present and 252 catch trials, the 50% ratio condition contained 112 target present trials and 112 catch trials, and the 75% ratio condition contained 84 target present trials, and 28 catch trials. After every 112 trials, the participants received a 2-min break. As a result, there were two breaks in 25% ratio condition (3 sub-blocks), one break in the 50% ratio condition (2 sub-blocks), and no break in the 75% ratio condition (1 sub-block). Before the start of a ratio block, a practice block of 15 trials was presented to acclimatise the subject to the ratio contingency. No explicit instructions regarding the ratio were given. The subjects were headphones with continuous white noise playing to mask the sound of the vibrating motors. The entire experiment took approximately 45 min.M = 6.3%, SD = 0.82%). The number of missed presses in the Lnear and Lfar conditions was also analysed. Subjects missed less than 15% of tactile targets on target present trials . All subjects missed less than 10% of the total amount of trials . All subjects were therefore included for further analysis.All subjects had less than 10% false alarms during catch trials  were calculated , Direction , and visual location during tactile stimulation (L1–L5).F  = 15.488; p < 0.001, np2 = 0.525]. Pairwise comparisons between the three ratio conditions revealed a significant difference between all conditions. RTs in the 50% condition  were significantly faster than in the 25% condition . RTs increased with the distance from the subject  = −3.992, p = 0.002), RT15 < RT75  = −5.624, p < 0.001), and RT30 < RT75  = −5.06, p < 0.001).The effect of location was significant , and between direction and location  = 17.37; p < 0.001, np2 = 0.553). As the goal of the study was to understand the nature of the tactile response-time patterns with respect to visual stimulus location for every ratio condition, and motion direction, we did not further analyse the interaction effects. Instead, we deferred their interpretation to the curve-fitting procedure.There was a significant interaction between ratio and direction [For this procedure, each participant’s response times obtained during the motion of the visual stimulus (L1–L5) were submitted into a curve-fitting procedure. In this process, the best fitting sigmoidal and linear curves were fit to the mean response times of each subject, for every ratio and direction condition. The equation used for the sigmoidal and linear curves is found in Eqs.  and 3),,3), respt tests on the RMSE values obtained for each pair of sigmoidal and linear curves were performed  = −2.78, p = 0.015) and ratio 25%  = −2.3, p = 0.03). The sigmoid-RMSEs were significantly lower for these two ratio conditions . There were no differences between the RMSE values for the linear and the sigmoid fit in the 75% condition for both approaching  = 0.54, p = 0.59) and receding directions  = 0.35, p = 0.73). In addition, for the 25 and 50% ratio receding curves, there were no differences between the RMSEs for the sigmoidal and linear fits  = 0.27, p = 0.79; receding ratio 50: mean difference = 5.6, t (14) = 1.21, p = 0.24).Significant differences in RMSE were found between the linear and sigmoid fits only in the approaching condition for the 50% ratio .To test if the midpoint of the sigmoid (reflecting the boundary of the PPS representation) differed between ratio conditions, we tested the boundaries for those conditions in which the sigmoidal curve was a better fit. There were no significant differences between the midpoints of both curves indicating that the boundary of PPS remained the same despite the probability of overt tactile expectation . When we wanted to limit the influence of tactile expectation, a low level of cue-reliability was used . It was expected that non-predictive and counter-predictive cues could reduce the overall level of tactile expectation and keep them at a more uniform level during the course of the trial.First, we used simulated data from a model that accounted for the interplay between PPS modulation on multisensory interactions and tactile expectation. It was observed that when the visual stimulus approached the subject, the resulting response-time pattern was linear (with a high slope) when tactile expectation was high. These results indicate that the linear effect of tactile expectation on RTs masks any multisensory effects of the PPS space. When tactile expectation was reduced, and maintained at a constant level throughout the motion of the visual stimulus (using low cue-reliability), the visuo-tactile interactions specific to the PPS remained. In other words, during low cue-reliability conditions (50 and 25% chance of a tactile target), the pattern of the response times was better explained by a sigmoidal function than a linear function. In the receding conditions, at all cue-reliability levels, the linear function was a better fit.To test the predictions of the model, an experiment was conducted with human participants, in which they had to respond to a tactile stimulus delivered to their left or right finger-tip, while a task-irrelevant dynamic visual stimulus either approached or receded from them. The tactile stimulus was delivered at one of several timepoints during the motion trajectory of the visual stimulus or not at all during catch trials. To induce different ranges of tactile expectancies across different blocks, the visual cue-reliability was varied across blocks . In accordance with the simulation, the RT pattern in the behavioural data was better explained by a sigmoidal function, but only in the approaching condition, for the 50 and 25% ratios. In the receding conditions, our behavioural data did not show any PPS-related multisensory modulations, which is in line with the observation that PPS is mainly responsive to stimuli approaching the body , it is reasonable to assume that tactile expectation is absent. Therefore, tactile expectation would not influence PPS-related multisensory interactions and motor output in such cases. In contrast, there are also many situations where one might need to engage with looming objects that will eventually encroach the PPS . In these situations, the stereotypical protective actions of PPS need to be suppressed so that the goal-specific motor output may be initiated. It is in these situations that tactile expectation is likely to affect PPS space-related sensory-motor processes.Previous studies have shown that the subjective hazard rate  of the upcoming stimulus is a factor that greatly influences the anticipation of the stimulus  is the hazard rate at location L, and Ptactile is the overall probability of receiving a tactile stimulus in the trial. The objective hazard rates in our study in the 100% condition (including the static locations), therefore, are 1/7, 1/6…. 1/1, which are non-linear in relationship. However, the behavioural response times where tactile expectation plays a role , seem to be linearly changing in our study. As our subjects’ temporal expectation is additionally informed by the location of the looming stimulus, which is less permeable to perceptual biases, a mathematical description of the subjective hazard rates, which are expected to directly influence tactile expectation, is more difficult to arrive at in our study. In the absence of this information, a linear approximation seems to fit the behavioural outcomes.Here, It must also be noted that given our design, it is difficult to disentangle the different sources of influence that tactile expectation provides. For instance, the expectation of the vibro-tactile stimulus may have directly influenced tactile processing  is non-continuous in nature. That is, even if there is a linearly changing relationship between visual stimulus location and the response time, this method will likely indicate the presence of the boundary. Therefore, we believe that it might be best to reserve this method for body parts where a more vigorous method such as the one used in this study and previous studies has previously demonstrated a multisensory boundary for PPS (Canzoneri et al. In conclusion, tactile expectation and multisensory interactions in PPS may both play an important role in anticipating and responding to objects that may approach the body. As demonstrated here, their relative contributions likely depend on the nature and the expectation of the interaction.