hippocampal networks can display sequences of neuronal activation at the temporal resolution of behavior , or compressed within the period of network oscillations ( buzski , 2010 ) .
the occurrence and organization of these sequences are thought to underlie numerous fundamental operations of the hippocampus , from the sensing of sensory cues and building a cognitive map of the environment , to mnemonic and planning functions ( dragoi and tonegawa , 2011 ; skaggs and mcnaughton , 1996 ; wilson and mcnaughton , 1994 ) . at the behavioral timescale ,
these sequences were first shown to occur in the presence of external landmarks that provide successive cues organizing neuronal activity through exteroception .
for example , hippocampal place cells are sequentially activated at consecutive positions in space when a rodent explores an environment naturally delivering serially ordered external landmarks ( dragoi and buzski , 2006 ) , even when only tactile and visual cues are provided ( royer et  al . , 2012 ) .
however , the sequential activation of hippocampal neurons at the behavioral timescale can also be disengaged from external landmarks and instead occur in the absence of changing sensory or feedback cues .
this involves self - organized internal mechanisms but happens within a behaviorally relevant context  for example , during the delay period of a memory task ( itskov et  al . , 2011 ;
, 2013 ; pastalkova et  al . , 2008 ; wang et  al . , 2014 ) .
to some extent , the reward that guides an animal s behavior within a defined task also provides an external drive on hippocampal dynamics .
hence , so far it remains unknown whether hippocampal activity can also be organized at population level in the absence of any driving external goal .
it is also unknown whether the span of hippocampal sequences is intrinsically predetermined in time or space in the absence of any temporal and spatial boundary . indeed ,
both externally and internally triggered sequences observed until now at the timescale of behavior always cover a finite spatial and temporal extent that is constrained by external factors such as the temporal organization of the task ( pastalkova et  al . , 2008 ) or the size of the environment explored in space ( ravassard et  al . , 2013 ) .
this is an important issue , since it defines the intrinsic determinants and behavioral reach of hippocampal population coding . here
, large - scale two - photon calcium imaging was used to capture population dynamics while resolving single - cell behavior in the ca1 region of awake mice .
a simple experimental paradigm was implemented to record spontaneous dynamics while minimizing the influence of external spatiotemporal landmarks or limits , which allows separating the contributions of time , distance , and external motivation to neuronal firing . in these conditions , we show that hippocampal dynamics self - organize into sequences of neuronal activation recurring one after another within discrete run epochs and each spanning accross a fixed traveled distance .
these recurring sequences translate into a behavioral correlate , since spontaneous run epochs display some stereotypy : they distribute as multiple integers of the distance unit represented in the sequences .
we propose that such sequences could be a default internal dynamic template for spatiotemporal processing in the hippocampus .
to observe hippocampal dynamics , we examined the spatiotemporal distribution of neuronal activity in the ca1 pyramidal layer using two - photon calcium imaging of awake head - restrained mice allowed to self - regulate their motion in the dark on a  nonmotorized treadmill ( royer et  al . , 2012 )
in contrast to previous studies , we chose not to deprive mice of water or food so that their behavior was not guided toward receiving any reward . in this way , during each daily imaging session , mice spontaneously traveled on the track through the alternation of run epochs ( interquartile range 410 s ; see figure  s1 available online ) and rest epochs ( from 10 to 74 s ; figure  1a ) . within run
epochs , mice moved at various speeds ( average 10.4  cm / s , range : 520  cm / s ) and displayed short periods of immobility ( < 2 s ; figures 1d and s1 ; see experimental procedures ) . to map neuronal activity across consecutive days
, we used a viral vector ( aav2/1.syn - gcamp5 g ) that makes gabaergic and glutamatergic ca1 neurons express the calcium indicator gcamp5 ( akerboom et  al . , 2012 ) .
in order to image from a large population of neurons ( 1,000 cells , figure  1 ) , we used a low - magnification objective that allows for imaging a 400   400  m field of view centered on the stratum pyramidale ( figure  1b ) after surgical implantation of a chronic glass window on the hippocampus ( dombeck et  al . ,
this surgical procedure was previously shown to allow for the reliable recording of place cell activity ( dombeck et  al . , 2010 ) , and we show it has no impact on exploratory activity ( figure  s2 ) . after three to five habituation sessions ,
mice running on an empty self - paced treadmill in the dark were imaged ( figure  1a ) , an experimental configuration that allows studying ca1 dynamics under the sole influence of self - motion cues .
spontaneous behavior remained highly variable and did not display any significant repetition pattern from one day to the next ( figures s1c  s1f ) .
this lack of behavioral stereotypy enabled disentangling the relative contributions of time and distance to the firing of neurons .
unexpectedly ( kentros et  al . , 2004 ; pastalkova et  al . ,
g ) , we found that ca1 dynamics displayed recurring sequences of neuronal firing exclusively during run epochs in 28 imaging sessions ( five mice ; figure  1c ; movie s1 ) . statistical analysis using data reshuffling established that sequences were not occurring by chance ( p  < 0.001 , see experimental procedures ) .
these sequences repeatedly engaged a sparse and scattered neuronal population that represented about 5% of all imaged neurons and 36% of the total fraction of active cells during run ( figure  1b ) .
cells engaged in these sequences were spatially intermingled with other run active cells that displayed variable activity patterns ( figures 1b and 1c ) , including sustained firing ( 25% of active cells , figure  1c ) , or uncorrelated and sparse activation onsets ( 39% of active cells , figure  s3 ) .
recent studies have addressed the relative influence of external sensory cues or behavioral context on the patterning of hippocampal dynamics , and it is now well established that , at the single - cell level , these can be controlled by absolute or relative location and time depending on the available and relevant stimulus for the task at hand ( aghajan et  al . , 2014 ; chen et  al . , 2013 ; itskov et  al . , 2011 ;
kraus et  al . , 2013 ; ravassard et  al . , 2013 ) .
we thus asked whether the sequences of neuronal activation observed here were driven by absolute location or time .
we can exclude a modulation of neuronal firing by the absolute position on the treadmill ( as could occur if an undetected cue was left on the track ) since ( 1 ) sequence recurrence never matched the length of the treadmill ( 180  cm , figure  2d ) and ( 2 ) as expected from a 0.05 statistical cutoff , less than 5% of the cells recruited in sequences displayed significantly location - modulated activation ( 1,048 cells out of 28 sessions , p  < 0.05 , kolmogorov - smirnoff uniformity test on firing onset distribution along the treadmill , figure  2e ) .
similarly , sequences could not be integrating absolute elapsed time because ( 1 ) sequences could repeat one after another either within the same run epoch ( defined as periods where speed exceeds 2  cm / s , figure  3a ) or separated by rest periods of variable duration ( figures 1a and s1 ) ; and ( 2 ) sequences could be transiently perturbed during short immobility gaps ( figure  s1 ) and then resumed when running restarted , since the slope during the pause was significantly different from that before and after it ( figure  1d ) .
analysis was therefore next restricted only to run epochs in order to determine whether neuronal sequences were constrained by the integration of time or distance during mouse travel . to test whether sequences integrated travel duration or distance , we analyzed , for each imaging session , the correlation between the slopes of the sequences ( in the temporal or spatial domain ) and the median mouse speed of the corresponding run epochs .
if the progress of neuronal activation was set by the run distance , then the temporal slope of the sequences ( expressed as cell / s ) should correlate with speed while the spatial slope ( in cm / cell ) should be constant and thus independent from speed ( figures 2a and 2b ) .
for each imaging session , we calculated the spearman correlation coefficient between the temporal or spatial slope and the speed ( figure  2b ) ; this analysis is a robust way to assess distance or time representation in noisy data ( see data simulation in figures s3b 
, sequences could be modulated by time and distance ( 28 imaging sessions , n  = 5 mice , figures 2b and s1 ) . however , in many cases they were principally modulated by distance alone ( 14 out of 28 sessions , spearman p  < 0.05 ; table s1 ) . in the intermediate cases , both time and distance representations seemed to intermingle ( 11 out of 28 ) , whereas time alone was organizing neuronal activation in a minority of the sessions ( 3  out of 28 ) .
this demonstrates that , as previously described at single - cell level , hippocampal dynamics capture both spatial and temporal information at the population level ( kraus et  al . , 2013 ) .
however , when integrating information at the population level over each imaging session , we observe that on average distance is more likely to be represented in our experimental conditions ( figures 2b and s1 ) . as distance - modulated sequences
were frequent , analysis was next restricted to the imaging sessions in which these were observed ( n  = 14 sessions , 5 mice , 493 sequences , experimental procedures , and figure  s1 g ) .
such distance - modulated sequences ( ds ) repetitively engaged the same neurons within an imaging session ( figures 1c and 2c , on average 70% ) .
a period of travel could therefore sometimes not be represented within neuronal dynamics ( a  nonencoded travel distance , 
this indicated that dss do not provide a metric integrating the total distance covered by the mouse but instead display a finite size that is intrinsically set .
this  nonencoded travel distance  did not involve the coordinated firing of another group of cells , as only one recurring pattern of neuronal activation was detected per session .
also , as expected , the onsets of the calcium transients of the neurons engaged in the ds ( ds neurons ) were not locked to the treadmill lap in contrast to those of the neurons displaying location - dependent firing after a few days of spontaneous run in the presence of serial tactile cues ( i.e. , place cells , n  = 3 mice , figure  2d ) . neither were these onsets periodic , given the occurrence of  nonencoded traveled distances  between sequences . nor were the dss triggered by a undetectable cue on the track ( figure  2e ) .
therefore , in conditions dominated by idiothetic cues , some fixed distance metric can be represented in the hippocampus in the form of recurring sequences of neuronal activation .
we next asked whether the finite size of the ds was due to experimental limitations , or instead could represent an intrinsic metric for distance . to this aim , we first analyzed the topographical arrangement of ds neurons .
the spatial distribution of ds neurons within the pyramidal layer did not display any remarkable pattern since these were not more clustered than expected by chance , even when taking into account their time of recruitment within the sequence ( figure  s4 ) .
this indicates that our imaging field of view sampled from a random representative subset of ds neurons and that the distance span covered by each sequence was unlikely to be truncated .
thus , the distance encoded at population level in the ds could be set by the mouse behavior or conversely , spontaneous runs could be internally predetermined by the spatial extent of the ds . in order to address the former hypothesis ,
we have plotted the distribution of the mouse speed centered on the time of ds start or stop .
we first used the first ds of each run epoch as a reference ( figure  3b ) . in this case ,
ds onsets were time - locked to the start of the run ( figure  3b1 ) whereas ds offsets occurred before its end ( figure  3b2 ) .
ds could also repeat in the middle of a run epoch one after another ( figure  3a ) , and this repetition is expected to be triggered by an external drive , such as a short pause in mouse run or a cue on the track . to test the first possibility
, the onsets and offsets of these ds were specifically used as a reference for the mouse speed distribution plots ( figures 3b3 and 3b4 ) . surprisingly , no significant pause or deceleration were observed . however , speed significantly increased by about 20% ( figure  3b3 ) .
this is a potentially interesting finding that may relate to the mechanisms of sequence initiation given that the firing frequency of ca1 pyramidal neurons increases with speed ( hirase et  al . , 1999 ;
in addition , ds repetition was not linked to a cue on the track ( uniformity kolmogorov - smirnov test figure  3c , p > 0.1 ) .
hence , both the onset and offset of a ds could be uncorrelated to the start and end of the run , in contrast to previous reports where the span of neuronal activation sequences was constrained by the underlying task ( kraus et  al . , 2013 ;
, 2008 ; ravassard et  al . , 2013 ; royer et  al . ,
this shows the intrinsic finite extent of sequences of neural activation in ca1 that encode traveled distance without being locked to behavior .
we thus refer to such discrete span of the ds as the  distance unit  ( du ) encoded at population level within the imaging session .
quantification of the du for each imaging session revealed that these spanned across a wide range ( 12112  cm , figure  4a ) , even for the same mouse across imaging days , indicating that this value is not preset .
we took advantage of this variability to test if , as for place cells where the size of place fields scales with that of the explored environment ( diba and buzski , 2008 ; muller and kubie , 1987 ; okeefe and burgess , 1996 ) , the  average distance field width  ( experimental procedures ) linearly scaled with the du .
such a relationship could be observed ( figure  4e , pearson , r  = 0,94 , p  <
0.001 ) , indicating a shared property between distance and place fields . since the du could considerably vary across days , we compared the set of neurons involved within the ds from one imaging session to the next .
almost one - third of the cells involved within a ds one day were still recruited the next ( 28%   8% , three sessions paired , two mice , figures 4b and 4c ) .
in addition , although no serial external cues were provided to support and recall the sequence organization , the relative order of the neurons within the sequences was also maintained ( figures 4c and s4b ) .
last , we asked whether the template metric provided by the du shaped spontaneous mouse runs .
to this aim , analysis was focused on the distribution of the distance traveled within single run epochs ( that comprised a detected ds ) , expressed in du ( rather than cm ) . the median value of this normalized distance , calculated per imaging session , segregated into two groups ( group 1 , 12 du , 235 run epochs , 10 sessions ; group 2 , 2.53.2 du , 90 run epochs , 4 sessions ; figure  s4c ; table s1 ) .
when pooling together group 1 , we noticed that the distribution was significantly bimodal with peaks at 1.1 and 2.1 du ( figures 4d and s4 ; p  < 0.001 , see experimental procedures ) , whereas it was log - normal without normalization .
regarding group 2 distribution bimodality , the occurrence of imaging sessions displaying a majority of run epochs with more than 2ds was too infrequent to draw any significant conclusion .
thus , spontaneous run epochs tended to distribute as integer multiples of the distance intrinsically integrated in the respective ds .
this further supports the idea that dss are a representation of distance encoded in the hippocampal network .
this study shows that sparse and stereotyped chains of neuronal activation , integrating spatiotemporal components of behavior , spontaneously recur one after another , without any external drive , in the hippocampus under the influence of self - motion .
we show that the  distance unit  associated to these intrinsically finite sequences provides a population metric for distance encoded in ca1 dynamics .
this du is not entirely engraved , as it could vary on a daily basis .
however , the partial replay of sequences from one day to the next strongly suggests the existence of internally prewired networks ( dragoi and tonegawa , 2014 ) .
animals were more likely to travel spontaneously once or twice the  distance unit ,  suggesting that linear path integration may use dead reckoning cycles and that this internal representation is limited . in natural environments , this function is complemented by landmark recognition ( mcnaughton et  al . , 1991 ) .
in contrast , in the absence of external cues , integer multiples of the du operate as attractor states for spontaneous behavior .
this finding was made possible by a combination of factors that were not gathered before ( chen et  al .
, 2013 ; kraus et  al . , 2013 ; pastalkova et  al . , 2008 ; poucet et  al . , 2014 ; ravassard et  al . ,
2013 ) and that include ( 1 ) the absence of sensory or cognitive external drive , ( 2 ) the absence of reward , ( 3 ) the absence of temporal or spatial borders ( solstad et  al . , 2008 ) , ( 4 ) the sampling of activity from a large number of neurons , ( 5 ) a large range of running speeds to allow disentangling elapsed time from distance even for short travels , and ( 6 ) the use of a one dimensional environment .
last , we can not exclude that keeping head direction signals constant also contributed in revealing such stereotyped dynamics ( cowen and nitz , 2014 ; sargolini et  al . , 2006 ) .
it is also possible that the filtering of neuronal spiking , an experimental limitation of the use of calcium indicators , is here providing a first integration step of hippocampal dynamics .
besides spatial cognition and memory , sequences of neuronal activation have been previously reported in different brain regions and species where they have been associated with a variety of brain computations , including song generation ( long et  al . , 2010 ) , odor encoding ( wehr and laurent , 1996 ) , choice decision ( harvey et  al . , 2012 ;
, 2008 ) , associative learning ( modi et  al . , 2014 ) , or brain - state transitions ( luczak et  al . , 2007 ) . here
they can repeat one after another within a continuous behavioral episode , sometimes following a spatiotemporal gap lacking any significant neuronal activity pattern .
interestingly , spontaneous repetition of neuronal activation has been reported at the single - cell level for example for cells displaying multiple place fields when large environments are explored ( rich et  al . , 2014 ) , and at the population level when identical repeating environments are successively explored ( mizuseki et  al . , 2012 ) .
the same way that cells with multiple place fields somehow provide a natural segmentation of large environments , it is possible that the repetition of finite sequences reflects a similar phenomenon where an infinite environment is divided into discrete cognitive chunks ( gupta et  al . , 2012 ) .
this activity repetition may reflect a self - generated behavioral strategy ( cabral et  al . , 2014 ) or the limit of the internal representation of the world , the latter being more likely for
hence , for a given imaging session , we observed that mice could run once or twice the du , with no strategical preference for either one of these options .
therefore , ds may represent the full capacity of the available working memory for a given experience .
when animals are trained for a particular task , sequential neuronal activation covers the entire length of the task at hand ( in time or space ) ( dragoi and buzski , 2006 ; itskov et  al . , 2011 ;
2014 ) . as a consequence of the intrinsic finite size , sequences scale to match the experienced episode , which implies that the coding resolution is inversely proportional to the size of the task
hence , we observed that  average distance field width  linearly scaled with the du .
absolute distance from a fixed starting point has recently been reported to be represented in hippocampal firing at single - cell level ( kraus et  al . , 2013 ) and to contribute to place coding in the absence of visual cues ( chen et  al . , 2013 ) or in virtual environments ( ravassard et  al . , 2013 ) .
the critical implication of self - body cues in the distance representation within place fields has recently been demonstrated in virtual environments ( chen et  al . , 2013 ) .
from that , it was thus expected , in our particular conditions where self - motion cues are prominent , that sequential neuronal firing integrates traveled distance .
however , the single - cell activity recorded here can not provide a measure of run distance since run epochs comprise periods of non - encoded distance .
in addition , in the case of the ds described here , as reported before for single - cell hippocampal activity ( kraus et  al . , 2013 ) , it is very likely that time is also contributing to single - cell firing .
probably best supporting that point is the fact that the organization of sequences was not affected by short rest periods , indicating that some cells are bridging the temporal gap between two diconstinuous runs within a single sequence .
alternatively , information may be transiently stored and hidden for example in the decaying synaptic weights over time accross short temporal gaps ( less than one second long ) ( buonomano and maass , 2009 ) .
distance was known to be represented within hippocampal dynamics at a shorter timescale , in the form of the sequential firing of place cells sharing overlapping place fields within a theta cycle ( dragoi and buzski , 2006 ) .
interestingly , theta phase precession is preserved after stimulation - induced perturbation of hippocampal activity ( zugaro et  al . , 2005 ) , the same way sequences described here resumed after a short immobility period . in addition , theta sequences were recently shown to be critically related to internally generated hippocampal sequences formed during an episodic memory task ( wang et  al . , 2014 ) .
it will thus be important to examine the link between these two temporal scales of distance representation , which may ultimately require determining the translation of distance sequences in a two - dimensional environment .
sequences were also shown to occur at an even more compressed timescale , during sharp wave activity and quiet wakefulness .
these sequences reflect previous sensory experience ( buzski et  al . , 1992 ; karlsson and frank , 2009 ) . in the same way
, distance sequences may recapitulate a recent experience thus supporting the view of the hippocampus as a  relational processing system  ( eichenbaum and cohen , 2014 ) , linking sequential body movements to an existing distance template supported by internally preconfigured networks . in this way
, these may contribute to the generation of place fields in the absence of proximal sensory cues as likely occurs in the dark ( poucet et  al . , 2014 ) , or when large environments are explored ( wang et  al .
, 2014 ) . these may also contribute to temporal integration when time becomes a more prominent component ( macdonald et  al .
future studies are needed to address the cellular mechanisms of sequence generation , in particular their link to entorhinal inputs from grid cells , the standard metric for space in the brain ( moser and moser , 2008 ) , or to medial septum inputs that pace the internal hippocampal clock at theta frequency .
the preconfigured character of hippocampal dynamics , dominated by a small minority of active cells in many states and contexts ( mizuseki and buzski , 2013 ) , may provide a cellular substrate by which hippocampal dynamics spontaneously collapse into these default sequences , based on the preferential activation of a highly excitable subset of neurons triggering a chain of pre - existing functional links .
interestingly , sequences of neuronal activation lacking spatial specificity ( cheng and ji , 2013 ) have been recently observed in an alzheimer disease model , suggesting that these may represent the minimum default operational mode of the hippocampus when sensory perception is reduced .
all protocols were performed under the guidelines of the french national ethic committee for sciences and health report on  ethical principles for animal experimentation  in agreement with the european community directive 86/609/eec under agreement # 01413 .
male adult wild type swiss mice ( n = 8 , 2540 g body weight ) were used for experiments .
all mice were housed in standard conditions ( 12 hr light / dark cycles light off at 7:30 a.m. , housed one per cage , water and food ad libitum ) .
mice were handled before recording sessions to limit head restraint associated stress and experiments were performed during the dark cycle . in order to perform large - scale calcium imaging , mice were injected with a viral solution ( titer , 10 genomes copy / ml ; penn vector core ) of aav2/1.syn.gcamp5g.wpre.sv40 .
mice were first anesthetized ( 100 mg / kg ketamine , 10 mg / kg xylazine ) , and 500 nl of viral solution was injected at a rate of 100  nl / min into the left dorsal hippocampus at following coordinates : ap , 2  and 2.5 ; ml , 1.6 and 2.1 relative to bregma ; dv , 1.3 relative to brain surface .
the constrained tissue was allowed to recover for 1 min prior and 3 min after injections to prevent injection backwash .
after 4 days of water deprivation to transiently modify hemodynamics to help for the surgery ( 1.5 ml/24 hr ; < 20% loss of initial body weight ) , mice were anesthetized with ketamine ( 100 mg / kg ) and xylazine ( 10 mg / kg ) , and a 3 mm diameter craniotomy centered over virus injection sites was performed .
the dura was gently cut and a portion of the overlying cortex was aspirated to allow optical access to the hippocampus .
similarly to the original method , the external capsule was exposed and allowed to dry until tacky , upon which a stainless steel canula ( microgroup ) attached to a glass coverslip was placed in the hole , sealed with uncured kwik sil ( wpi ) , and fixed to the skull using super - bond ( dsm dentaire ) .
mice were allowed to recover for 46 days and then handled for 2  days in order to limit head restraint - associated stress .
mice were head - fixed on a nonmotorized treadmill ( adapted from royer et al . , 2012 ) allowing them self - paced locomotion , and all experiments
after three to five habituation sessions , mice were watchful but calm and alternated between periods of moving and resting activity during recordings .
the treadmill was made from a 180 cm black velvet seamless belt for the experiments done in the absence of external cue ( n = 5 mice ) . in the experiments aiming at imaging place cell firing ( n = 3 mice ) ,
the belt was enriched in tactile cues as follows : we delineated four zones of 45 cm displaying the following items : ( 1 ) 2 cm wide disks of white velcro ; ( 2 )  small white pressure buttons ; ( 3 ) gray diamond shaped textured plastic fabric ; ( 4 ) no cue .
for all experiments , extra sound , odor , touch , and light were minimized during the imaging session ( in preliminary experiments where the seam was too prominent we observed cue - related firing ; data not shown ) .
the mouse speed and instantaneous position were tracked using a graded wheel , as previously described ( royer et al . , 2012 )
imaging was performed with a single beam multiphoton pulsed laser scanning system coupled to a microscope ( trim scope ii , lavision biotech ) .
the ti : sapphire excitation laser ( chameleon ultra ii , coherent ) was operated at 920  nm .
images were acquired through a gasp pmt ( h7422 - 40 , hamamatsu ) using a 16 immersion objective ( nikon , na 0.8 ) .
using imspector software ( lavision biotech ) , the fluorescence activity from a 400 m field of view was acquired at 9.62 hz with a 1.85 s dwell time per pixel ( 2 m / pixel ) .
imaging fields were selected to sample the dorsal ca1 area and maximize the number of imaged neurons in the stratum pyramidale .
speed , position , and image triggers were synchronously acquired and digitized using a 1440a digidata ( axon instrument , 2 khz sampling ) and the axoscope 10 software ( axon instrument ) .
a typical imaging session occurred as follows : ( 1 ) the mouse was handled then fixed on the treadmill ; ( 2 ) five consecutive 3,000 frames movies were acquired ; ( 3 ) the mouse returned to its homecage .
run epochs were defined as continuous periods of time during which the average mouse speed exceeded 2 cm / s .
a custom - made algorithm based on pca / ica was used and combined to morphological identification .
movement correction was first performed for each frame using the cross - correlation with a reference image .
the offset pca method was next applied ( kaifosh et al . , 2013 ) .
principal components displaying a variance greater than noise were fed to an iterative ica algorithm ( mukamel et al . , 2009 ) .
cells were identified in the output of the ica using 2d - spatial wavelet filtering matching the expected cell size ( 715 m diameter ) .
the obtained roi were finally smoothed using a closing algorithm thus defining the active cell population .
gcamp fluorescence traces were smoothed in time ( gaussian filtering , s=5s ) before fed to the offset pca algorithm ( kaifosh et al . , 2013 )
. the smoothing adds correlation between neighbouring time points in order to gather the activity of cells that fire successively . the principal component which displayed recurring fluorescence patterns during each run epoch ( among the five with the highest variance )
the reason for manual selection was ( 1 ) the need to select a principal component that contained information about population activity during run epochs ( i.e. , displaying transients at each run ) ; and ( 2 ) among the five extracted principal components , it also often happened that traces reflecting for example high activity of a single neuron outside from run epochs or movement artifacts , were considered as holding the most information by the pca .
the derivative of that principal component ( figure s3 , green ) was then cross - correlated with the activity of each individual cell .
the use of the derivative preferentially select cells with short calcium transient and thus remove cells that fire during the entire run epoch which are not part of a sequence .
the correlation coefficients thus obtained were used as a metric to determine the participation of each cell to recurring activity : a threshold was calculated applying otsu 's method ( otsu , 1979 ) to the distribution of this metric in the cell population ( figure s3 ) .
cells whose correlation was higher than the threshold were considered as involved in such recurring activity .
note that in several instances ( 37 out of 65 imaging sessions from five mice , see figure s1 g ) , no recurring pattern was detected . to identify another group of cells that would display another recurring pattern , we reiterate this procedure with the previously identified cells removed .
after reshuffling between active cells independently in each run epoch , i.e. , the fluorescence trace is divided in different time interval inside which cells activity is permuted ( e.g. , cell 1 gets the activity of cell 5 during the first run epoch and of cell 3 during the second one , etc . ) , no recurring activity ( at least two sequences of five cells ) was detected which validated our detection method ( 0 occurrence out of 1,000 reshufflings ) . for each recurring activity pattern
, cell activation onset was defined by the  maximum of the first derivative of the smoothed trace ( gaussian filtering , s = 2s ) .
cells were then ordered in a sequence according to their median onset delay in each run epoch .
the sequences that involved at least half of the cells were linearly fitted using a regression algorithm that ignores outliers ( matlab function robustfit ) .
the fits displaying a robust root mean square error exceeding 20% of the duration of the sequence were discarded .
the remaining sequences were used for all quantitative analysis ( n = 389 fitted sequences , 79% of all sequences ) .
this linear fit provided the slope ( in cell / s ) of each sequence . to assess
whether the dynamics of these sequences depended on run distance , we analyzed the correlation between the slope and the corresponding median speed . in the case of a statistically significant correlation ( p < 0.05 , spearman , n = 14 out of 28 sessions )
, a distance unit du that links the speed v , the slope s , and the number of cells n could be defined as follows : du is the spatial extent of the run distance from the first to the last cell of the  sequence .
the same analysis was performed in the spatial domain by converting activation onsets in time to onsets in space using the measured mouse position .
a few sessions ( 3 out of 28 ) displayed a significant correlation , which indicated that run time could also modulate sequence dynamics .
short pauses were defined as the periods when the speed was lower than 2  cm / s for more than 500 ms and less than 2 s. to analyze whether the occurrence of short pauses affected the dynamics of ds , the distribution of neuronal activation onsets centered on each pause start was computed .
the five sessions that displayed more than ten pauses ( n = 3 mice ) were kept for further analysis . in addition , only pauses which roughly occurred in the middle of a sequence ( 20%80% of sequence completion ,
n = 91 pauses ) could be analyzed , since information was needed about cell activation before and after the pause .
we next used the onset of the last cell before the pause as a reference to center all sequences on the pause .
in that way , the arrangement of the sequences around the pauses could be pooled across sessions .
the evolution of the normalized temporal slope was measured using a linear fit over a sliding window of six cells ; the 95% confidence interval was calculated using the distribution of these slopes before the pause ( n = 8 slope values , gaussian approximation ) . in order to reveal a potential link between the animal 's speed and the dynamics of the ds
, speed was normalized across sessions and pooled using a 20 s time window centered either on the onsets or the offsets of ds .
these were calculated using the median activation onsets of the first or last five cells in the sequence , respectively .
the 95% confidence interval was calculated using the speed distribution before the pause ( from the time when speed plateaus to pause onset , gaussian approximation ) . in order to assess whether a second peak in an apparently uniform distribution was significant ,
first , the distribution histogram was fitted using an ad hoc uniform function ( log - normal in our case ) and a least - squares fit algorithm ( lsqcurvefit function in matlab ) .
second , the probability distribution for the value of each bin was calculated by computing random samples ( n = 10 samples ) using the fitted distribution .
third , a significance curve was defined by applying the same percentile to all bins ( equiprobability ) .
the value of the percentile was chosen so that the probability of having at least one peak bigger than the significance curve was 5% ( see figure s4 )
. this statistical test was robust against binning phase  and size as long as the peak was not split between two bins ( see figures s4f 
 we detected the onset and offset of its mean fluorescence transient over all sequences ; the onset being the time when the fluorescence transient reached 10% of its maximum value and the offset the time when the trace derivative reached its minimum value .
this gave an estimate of the firing duration for each cell ; the distance field was defined as the product of the median speed and the firing duration thus calculated .
 summarythe hippocampus is essential for spatiotemporal cognition . 
 sequences of neuronal activation provide a substrate for this fundamental function . at the behavioral timescale 
 , these sequences have been shown to occur either in the presence of successive external landmarks or through internal mechanisms within an episodic memory task . in both cases , 
 activity is externally constrained by the organization of the task and by the size of the environment explored . 
 therefore , it remains unknown whether hippocampal activity can self - organize into a default mode in the absence of any external memory demand or spatiotemporal boundary . 
 here we show that , in the presence of self - motion cues , a population code integrating distance naturally emerges in the hippocampus in the form of recurring sequences . 
 these internal dynamics clamp spontaneous travel since run distance distributes into integer multiples of the span of these sequences . 
 these sequences may thus guide navigation when external landmarks are reduced . 
Introduction
Results
Discussion
Experimental Procedures
Author Contributions