in real world tasks decision - making and working memory often occur in the context of other complex behaviors , including spatial navigation . for example
, when driving through a city towards a destination , sensory information defining context and place engages memory and decision circuits to plan turns at upcoming intersections .
the posterior parietal cortex ( ppc ) is a prime candidate for the neuronal circuitry combining the cognitive processing elements necessary for such tasks . in primates
the ppc is important for perceptual decision - making and categorization , movement planning , and spatial attention .
studies in rats suggest that the ppc is also important for encoding route progression during navigation . using a virtual reality system for mice and cellular resolution optical imaging methods , we developed a t - maze - based navigation paradigm combining all these cognitive elements and characterized the neuronal circuit dynamics in the ppc , which have not been studied in this combined behavioral context .
neuronal activity patterns in the ppc have been studied using microelectrode recordings during spatial attention , working memory , and perceptual decision tasks .
these studies have commonly found cells with sustained firing rate changes spanning entire task periods ( cue , delay , response periods ) .
for example , cells with persistent activity throughout the delay period of memory - guided saccade / reach tasks have frequently been recorded .
also , studies have identified neurons with ramps of increasing firing rate spanning the accumulation of evidence period in a motion perception task . neurons with sustained activity during the same task period often have similar activity time courses , suggesting the presence of classes of cells ( e.g. delay cells ) and implying that the task - dependent neuronal dynamics are low - dimensional .
the low - dimensional dynamics can be reproduced in recurrent attractor network models , in which each cell s activity is typically an amplitude - scaled version of a prototypical time series .
in contrast , recent analysis of prefrontal cortex activity has identified heterogeneous neuronal activity time courses , in which a neuron s activity can be thought of as the sum of a few activity modes .
in addition , there is growing evidence for sequences of neuronal activation within local circuits , in which each neuron is active for only a fraction of a task period , including during working memory tasks in the prefrontal cortex and the hippocampus and during an object construction task in the ppc .
sequences suggest dynamics that are high - dimensional , without the presence of classes of cells with relatively homogeneous activity time courses .
we explored whether ppc dynamics are best described in terms of cell classes or high - dimensional dynamics . during a navigation - based decision task
the dynamics were high - dimensional : neurons were active in choice - specific sequences in which information moves from one neuronal population to another across time in the task ; although the neuronal activity patterns could be divided into cue , delay , and response groups , sequences were present within each group .
furthermore , exploiting the ability of cellular resolution optical measurements to provide the relative anatomical location of the recorded cells , we found that neurons active during behaviorally - distinct task periods and on trials with different behavioral choices were spatially intermixed over microcircuit length scales .
using a virtual reality system , we trained mice to navigate through a virtual t - maze in a task that incorporated both visual discrimination and a memory - guided response ( methods ; fig .
visual cues present in the initial section of the maze indicated which direction to turn at the t - intersection to receive a water reward ( one set of cues to indicate a right turn and a second set for a left turn ; supplementary fig .
1c ) . between the cue section and the t - intersection , mice ran through a delay maze section that was identical on left and right turn trials ; visual information about the reward location was thus present only in the cue section .
the task resembled traditional delay tasks in its cue - delay - response structure but differed in that ongoing sensorimotor activity was present throughout the task , including the delay period .
mice performed the task with high levels of accuracy ( 83  9% correct , p < 0.0001 vs. 50% , t - test ; fig .
1b ) . within and across trials , individual mice ran at highly consistent speeds ( supplementary fig .
2 ) ; however , running speeds varied between mice and the maze position at which mice began rotating the spherical treadmill to make a right or left turn differed across trials ( turn onset ; fig . 1c ,
3 ; methods ) . to compare behaviorally similar epochs of the task across trials , individual trials were aligned to the time
points when the cue was no longer visible ( cue offset ) , the turn onset , and the end of the trial ; these alignment points formed the boundaries of cue ( trial start to cue offset : 5.1  2.6 s ) , delay ( cue offset to turn onset : 4.2  1.2 s ) , and turn task periods ( turn onset to trial end : 3.0  1.8 s ) . because the location of the mouse ppc has not been characterized , we first performed retrograde and anterograde labeling experiments to locate it anatomically ( methods , supplementary fig .
we identified a region consistent with the rat and primate ppc based on the set of areas from where it received axonal projections , the areas to which it sent projections , and its location relative to other cortical regions ( anterior to visual cortex and posterior to somatosensory cortex ) .
we therefore considered this area to be the mouse ppc . to test if the ppc was required for the behavioral task , we inactivated it using bilateral injections of the gabaa receptor agonist muscimol .
muscimol reversibly decreased behavioral performance from high levels of accuracy in control sessions to near chance levels , but did not affect the rate of trials performed ( fraction correct : no injections 87  7% , saline 85  5% , muscimol 54  5% p
< 0.0001 vs. no injections , t - test ; trials per minute : no injections 3.2  0.5 , muscimol 3.1  0.3 , p > 0.8 , t - test ; fig .
in contrast , ppc inactivation did not significantly affect performance on a visually - guided task in which a visual cue was present at the reward site and visible throughout the trial , indicating that the decrease in performance on the memory - guided task was unlikely due to a major visual or motor deficit ( no injections : 90  5% , muscimol : 87  5% , p > 0.2 , t - test ; fig . 1e , supplementary fig .
we used two - photon microscopy to image layer 2/3 ppc neurons expressing the genetically - encoded calcium indicator gcamp3 , which increases in fluorescence intensity in response to action potential firing ( methods ) . on average , we imaged ~65 cells simultaneously within a ~300 m by ~150 m area ( range : 3794 cells ) .
nearly all imaged cells showed statistically significant ca transients during the behavioral session ( 96% of cells had > 0.2 transients per minute ; methods ) .
of the cells with high levels of activity ( > 2 ca transients per minute on average ; supplementary fig .
5 ) , ~73% had significant increases in their mean fluorescence intensity traces ( f / f , averaged across trials ) during a specific time in the trial or inter - trial interval ( task - modulated cells ; fig .
these task - modulated cells had ca transients for only short time intervals on individual trials ( 11  8% of time points in trials with a transient ) such that only a small fraction of neurons was active simultaneously ( fig .
2b  e , supplementary figs . 8 , 9a ) ; cells with prolonged activity patterns covering a large fraction of the trial were not observed .
the majority ( ~71% ) of task - modulated cells had significantly different levels of activity on correct right and left choice trials ( choice - specific cells ) .
similar choice - specific , task - modulated activity patterns were observed in extracellular electrophysiological recordings ( supplementary figs .
cells were also active on error trials , such that neurons active during the cue period tended to be correlated with the cue identity , and neurons active during the turn period in general were correlated with the behavioral response ( supplementary fig
. only a small fraction of cells had obvious reward - related signals ( ~2% of active cells with p < 0.01 , t - test , comparing f / f values within ~0.6 s after the reward was given on correct trials or missed on error trials ) . when the activity patterns of all the choice - specific , task - modulated cells were ordered according to the time profile of their ca transients , the active periods across cells were staggered relative to one another in time forming a sequence of neuronal activation covering the entire trial length ( fig . 2c  d , supplementary fig .
different sequences of neurons were activated on left and right trials ( fig . 2c  d and absence of activity in fig .
although these plots of sequences combined cells from different experiments and averaged across trials , similar properties were observed when considering only the cells imaged in a single mouse and on individual trials ( fig .
sequences were also apparent in the ~29% of task - modulated cells that did not have choice - specific activity ; these cells participated in the sequences for both right and left choice trials ( supplementary fig .
sequences similar to those during the task were not observed in shuffled versions of the dataset , demonstrating that the sequences were not an artifact created by ordering the data ( supplementary fig . 14a 
because previous studies of the ppc have categorized cells into classes with cue , delay , or response period activity , we examined if neurons in the sequence were grouped based on behavioral periods .
the distribution of activity times of all cells in the population ( calculated for each cell as the center - of - mass ( com ) in time of the mean f / f during the trial , tcom ) had three peaks corresponding to the cue , delay , and turn periods , suggesting a possible grouping by behavioral period ( fig .
consistently , principal component analysis ( pca ) on the mean f / f traces for all cells revealed three intermixed groups , with each group mostly containing cells preferring the same behavioral period ( fig .
although the population of neurons could be divided into groups , the temporal activity patterns within each individual period were heterogeneous and formed sequences ( fig .
cells within their preferred period were active for only a fraction of the period ( 35  16% of time points in preferred periods with a ca transient ) with different cells active at different times . although cells with activity covering a large fraction of the period were occasionally observed ( e.g. fig .
2c top panel ) , these cells were rare ( 4% of cells with activity lasting for > 60% of the period ; supplementary fig .
9b ) ; the distribution of epoch coverage by an individual neuron s activity was similar during the delay and cue or turn periods ( p > 0.1 , ks test ) .
furthermore , pearson s correlations between the non - averaged f / f traces for cell pairs with the same trial - type and behavioral period preferences varied widely , with a large fraction of pairs having low correlation coefficients ( supplementary fig .
the low correlation coefficients could be due to activity at different times in the period , as expected for sequences , or activity at the same time in the trial except on different trials .
however , the probability that both cells in these pairs had ca transients or both cells did not have transients on the same trial during their preferred epoch was generally high ( supplementary fig .
16b ) , suggesting that the diversity primarily resulted from differences in the activity times of cells within trials .
together these data indicate that classes of cells with homogeneous activity patterns were not present .
rather , choice - specific sequences of neurons were activated in all behavioral periods , with a lower density of cells in the sequence at the borders between periods . to further examine the sequential neuronal activation on individual trials , we calculated correlations between the activity patterns of cells using the non - averaged f / f time series .
cells that were active at similar time points in the trial on average ( measured as the difference in tcom values on correct trials , tcom ) had , on correct trials and in their preferred behavioral periods , highly correlated f / f traces and peaks in their cross correlation at a lag approximately equal to tcom ( supplementary fig .
h ) ; these relationships in the non - averaged f / f time series provide further evidence for sequential activity on individual trials .
cells that were active at similar times on correct trials were also highly correlated on error trials and in non - preferred periods ( supplementary fig . 16c 
f ) . additionally , cells that were sequentially activated during their preferred behavioral period on correct trials were sequentially active with similar lags during error trials and other time points in the task ( supplementary fig .
the choice - specific activity could result if mice experienced different visual stimuli and running patterns on right and left trials and if ppc activity was modulated by those differences . to examine this
, we first performed a multiple regression analysis to determine the potential effects of the parameters defining the mouse s running trajectory on the fluorescence changes during the delay period ( supplementary table 1 ) .
these parameters could not explain the choice - specific activity patterns , suggesting that any differences in running trajectories between right and left trials did not trigger the activity we observed .
in addition , we performed two sets of experiments to further examine whether the maze visual stimuli alone or the mouse s running patterns triggered ppc activity .
in the first experiments , movies of simulated left and right turn runs through the t - maze , which closely approximated real runs , were played to mice that passively viewed the visual scenes ( open - loop experiments ; supplementary fig . 17a 
mice were trained on a virtual linear track to perform a simple running back and forth task ( run to one end for a reward , turn around , run to the other end for the next reward ) .
the linear track had several visual patterns on the walls , all of which were the same as patterns in portions of the t - maze ( supplementary fig .
the task required similar running and turning behaviors to the t - maze , except that turns were not memory - guided based on visual cues and a delay period and there was not a two - alternative forced - choice structure .
the overall levels of activity during the simulated t - maze runs or during the linear track task were much lower than when mice actively performed the t - maze task ( supplementary figs .
17c  d , 18c  d ) . also , only a small fraction of neurons had significant increases in activity at specific locations in the maze , either during the simulated t - maze runs or in the linear track , suggesting that cells were not activated robustly by location - specific visual scenes or running patterns ( simulated runs : 1.3% , linear track : 5.8% , t - maze : 32.3% ; supplementary figs .
these results suggest that ppc neurons in the t - maze were not activated only by the visual information or by the running patterns of the mouse .
the heterogeneous and sequential neuronal activity patterns during the t - maze task indicated that we should consider the dynamics of the population rather than classes of cells .
we therefore analyzed the dynamics as a trajectory through a state space of neuronal population activity ( neuronal circuit trajectory ) . at each time point , the activity state of the circuit containing n simultaneously imaged neurons was defined as a point in an n - dimensional space , with each dimension representing the activity ( f / f values ) of a single neuron .
different trajectories ( visualized using factor analysis for dimensionality reduction ) were traversed for trials with different behavioral choices ( fig .
the trajectories for correct right and left choice trials began the trial at similar positions , gradually diverged to reach a peak separation near the time of the behavioral choice , and converged to the starting point in the inter - trial interval ( fig .
, we used a classifier based on the distance from an individual trial trajectory to the mean right and left choice trajectories at single time points .
it was possible , from the activity of a small population of neurons located in close anatomical proximity ( ~65 neurons separated by < 250 m ) , to predict the mouse s choice on single correct trials at better than chance levels during the cue , delay , and turn periods ( methods ; fig . 4e , supplementary fig .
the activity in the ppc can therefore be considered as divergent , choice - specific trajectories through a state space of neuronal population activity .
some trajectories began close to the correct choice trajectory during the cue period and transitioned toward the error choice trajectory later in the trial ; such transitions occurred at a wide range of points in the trial ( gray traces in fig . 4f , supplementary fig .
the error trial trajectories were more similar to the correct choice trajectory during the cue period and closer to the error choice trajectory during the turn period ( cue offset : trajectory selectivity index = 0.13  0.22 , p < 0.001 vs. 0 , t - test ; trial end : trajectory selectivity index = 0.18  0.15 , p < 0.001 vs. 0 ; fig .
therefore , individual trajectories transitioned between the mean correct right and left choice trajectories at many time points during trials , but most frequently switched during the delay period .
to determine how the cells implementing the activity dynamics were anatomically organized , we first examined if cells with different response preferences , such as activity peaks at different times in the trial or different preferences for right and left choice trials , were present in the same regions of the ppc or separated into different areas .
each ~250 m by ~125 m area ( i.e. field - of - view with simultaneously imaged cells ) contained both right and left choice - preferring cells of approximately equal numbers and cells with activity peaks at a wide range of times in the trial ( fig .
next , within each imaged area we compared the activities of pairs of neurons as a function of the distance between the neurons cell bodies .
the difference in the trial - type selectivity for cells in a pair did not depend significantly on the distance between cells , indicating that left and right choice - preferring cells were intermixed (  = 0.04 , spearman s correlation , p > 0.05 ; fig .
tcom for a cell pair did not differ with the distance between the cells , indicating that cells active during different periods of the task were intermingled (  = 0.01 , p > 0.6 ; fig .
however , cells that were separated by less anatomical distance had f / f traces that were significantly more correlated than cell pairs further apart , but the relationship between the correlation coefficient and distance was weak ( all pairs of active cells :  = 0.16 , p < 0.001 ; pairs with the same trial - type and behavioral period preference :  = 0.22 , p < 0.001 fig .
this weak relationship could be due to overlapping fluorescence changes , such as from dendritic signals , or could reflect an actual , weak spatial organization .
regardless , cells with highly different activity patterns were intermixed over short length scales , and an anatomical separation of the response properties we measured was not present .
the choice - specific sequences of ppc neuronal activation we report here add to the growing list of studies that have identified cortical sequences of activity states during working memory tasks . furthermore , because we demonstrated that ppc activity was necessary only for the memory - guided task , the sequences of activation were likely important at least for the memory aspect of the task .
sequence - based dynamics may therefore be a common framework for circuit function during memory and decision tasks , including during navigation behaviors .
such dynamics could potentially be implemented using feedforward architectures or liquid state machines related to those that have been proposed for working memory .
our results also offer a way to unite previous work on neural coding in the ppc .
navigation , memory , and choice information may be combined in the sequences such that the identity of the active sequence reflects choice - related information for working memory and movement planning and the currently active cell within the sequence reflects spatial or temporal progression through the task , which were highly correlated in our task ( supplementary fig .
it seems unlikely that ppc neurons only provided location information in a context - dependent manner , like hippocampal place cells , because unlike place cells ppc neurons did not encode spatial location during a linear track task ( supplementary fig .
a possible explanation for heterogeneity and sequences in our experiments versus stereotypy and low - dimensional dynamics , which have been emphasized in previous recordings and models of ppc activity , is that the ppc adopts different dynamics depending on the demands of the behavioral task . because traditional delayed saccade tasks , for example , have one spatiotemporal component during the delay period ( fixation before making a response ) , the ppc may adopt sustained activity patterns .
in contrast , during tasks that involve many spatial and temporal components , as are common in natural behaviors and during navigation , the ppc may utilize sequences of activation .
alternatively , sequences of activity may be present in the primate ppc during traditional tasks but have yet to be identified , consistent with emerging evidence for heterogeneous temporal response properties .
in addition , different regions or layers of the ppc may have differing activity dynamics , or the dynamics of rodent and primate ppc circuits may differ . because cells that were active at distinct time points in the task and that participated in different choice - specific sequences were spatially intermingled ,
this extends previous work in sensory cortex , motor cortex , and the hippocampus showing spatial intermixing of heterogeneous response properties in cells encoding qualitatively similar types of information ( e.g. orientation selectivity in visual cortex ) or cells with activity during similar task epochs .
these findings differ from the predictions of models that have emphasized the spatial clustering of similar response patterns , as in functional columns , and that propose connectivity defined by axonal - dendritic overlap without fine - scale specificity .
rather , our results support a model in which microcircuits are formed by highly specific synaptic connectivity and are comprised of neuronal motifs , such as those identified in brain slice recordings in sensory cortices and amongst visual cortical neurons with the same orientation selectivity .
our results showing that cell pairs that were sequentially active during their preferred periods on correct trials had similar activity relationships even during error trials and the inter - trial interval suggest the presence of such motifs ( supplementary fig .
we note however that activity trajectories occasionally switched during a trial between the prototypical correct left and right choice trajectories , including frequently on error trials , suggesting that the mouse s decision was not necessarily irreversibly reached immediately after a trial s start ( trajectory selectivity switch during the delay period or last 1 s of the cue period : 63% of error trials , 20% of correct trials ; fig .
sequences may therefore play a role in some aspect of decision - related processes , but further experiments will be necessary to assess this possibility .
our results motivate consideration of a conceptual framework for decision - making and working memory in which sensory information used for the decision activates a neuronal sequence of activity .
the sequence begins in a choice - independent state , which could be mediated by neurons that are not choice - specific ( supplementary fig .
7b ) , and then moves toward a choice - specific trajectory and away from other trajectories in a manner dependent on the incoming information .
a decision is proposed to be reached when the sequence of activity intersects a choice - specific trajectory ; different decisions involve intersections with different trajectories . upon reaching a decision ,
changing decisions would occur through transitions between trajectories , but as time progresses in the task , the state space distance between trajectories increases , in effect creating a larger barrier to change . in this view , decision - making and working memory utilize an ordered progression through a sequence in which information moves from one population of neurons to another over time .
the framework we propose is an extension of a point - of - view first considered in describing the dynamics underlying behavioral choices in the leech nervous system .
it has both some similarities and differences from drift / diffusion - to - bound , race , and recurrent network models of decision - making implemented as neuronal integrator winner - take - all circuits .
these models are similar to the trajectory - based view in that different decisions correspond to a divergence in state space surrounding a separatrix .
however , these models differ from the sequence framework in that decisions are reached when the activity approaches a choice - specific fixed point with working memory maintained as stable activity at that point . thus , although these circuits can demonstrate divergent trajectories to reach the fixed points associated with different choices , the trajectories are defined by relatively homogeneous changes in the activity of the population , and the same set of neurons participate in all stages of the decision - making and working memory process .
a complete description of the experimental methods and data analysis is available in the supplementary information .
 the posterior parietal cortex ( ppc ) plays an important role in many cognitive behaviors ; however , the neural circuit dynamics underlying ppc function are not well understood . 
 here we optically imaged the spatial and temporal activity patterns of neuronal populations in mice performing a ppc - dependent task that combined a perceptual decision and memory - guided navigation in a virtual environment . 
 individual neurons had transient activation staggered relative to one another in time , forming a sequence of neuronal activation spanning the entire length of a task trial . 
 distinct sequences of neurons were triggered on trials with opposite behavioral choices and defined divergent , choice - specific trajectories through a state space of neuronal population activity . 
 cells participating in the different sequences and at distinct time points in the task were anatomically intermixed over microcircuit length scales ( < 100 micrometers ) . during working memory decision tasks 
 the ppc may therefore perform computations through sequence - based circuit dynamics , rather than long - lived stable states , implemented using anatomically intermingled microcircuits . 
Introduction
A PPC-dependent navigation-based decision task for head-restrained mice
Imaging sequences of neuronal activity
Choice-specific neuronal circuit trajectories
Anatomical micro-organization of PPC dynamics
Discussion
Methods summary
Supplementary Material