Correlation Across Environments Encoded by Hippocampal Place Cells
CCorrelation Across Environments Encoded by Hippocampal Place Cells
Bhav Jain ([email protected])
Department of Brain and Cognitive SciencesMassachusetts Institute of Technology, Cambridge, MA 02139, USA
Sean Elliott ([email protected])
Department of MathematicsMassachusetts Institute of Technology, Cambridge, MA, 02139, USA
Abstract
The hippocampus is often attributed to episodic memory for-mation and storage in the mammalian brain; in particular,Alme et al. showed that hippocampal area CA3 forms sta-tistically independent representations across a large number ofenvironments, even if the environments share highly similarfeatures. This lack of overlap between spatial maps indicatesthe large capacity of the CA3 circuitry. In this paper, we sup-port the argument for the large capacity of the CA3 network.To do so, we replicate the key findings of Alme et al. andextend the results by perturbing the neural activity encodingswith noise and conducting representation similarity analysis(RSA). We find that the correlations between firing rates arepartially resistant to noise, and that the spatial representationsacross cells show similar patterns, even across different envi-ronments. Finally, we discuss some theoretical and practicalimplications of our results.
Keywords: hippocampus; place cells; CA3 network
Introduction
Episodic memory consists of long-term memory associatedwith specific events, situations, and experiences, and muchresearch has explored the encoding, formation, and storage ofthese memories. Of particular importance are the neural net-work properties of hippocampal area CA3, which has richerinternal connectivity between neurons compared to other hip-pocampal regions (Cherubini et al., 2015). With regardsto encoding particular environments, CA3 place cells storehighly unique neural representations of different locations,implying minimal overlap in spatial mapping and maximalpotential for storage of experiences (Muller, 1996).To better probe the storage capacity and representation en-coding of episodic memory in CA3 place cells, previous workhas focused on validating the statistical independence of mapsbetween pairs of environments (Leutgeb et al., 2004). As anextension, Alme et al. (2014) confirmed that place cell firingpatterns remain unique when the number of environments isincreased from 2 to 11 (and correspondingly, the number ofenvironment pairs is increased from 1 to 55).Although the upper bound of this capacity has yet tobe solved, these results indicate that the large capacity forepisodic memory in part arises from the lack of correlationbetween CA3 representations. Understanding the robustnessof this memory, as well as whether this large memory capac-ity is present in other regions of the mammalian brain, couldhave implications on our understanding of the principles ofneural encoding of sensory information and gradual conver-sion into long-term memories. As such, this paper focuses on replicating the results re-ported in Alme et al., followed by an extension to test therobustness of these encodings by influencing the system withnoise. In addition, we generated correlation matrices betweencells for a given environment and computed the similarity be-tween these correlation matrices through a method referred toas representational similarity analysis (RSA) (Kriegeskorte etal., 2008). These results will indicate the extent to which CA3spatial representations are highly structured and sensitive toperturbations, as well as reveal one more level of correlationbeyond that done in traditional statistical analyses.
Preliminaries
This study uses the same dataset as that employed in Alme etal., which consists of EEG recordings over two consecutivedays from CA3 pyramidal cells in the dorsal hippocampusfrom seven rats across 11 rooms. Ten of these rooms werenovel to the rats, while one was highly familiar. The taskinvolved chasing food crumbles in square boxes, and eachenvironment had distinct physical features. A total of 342isolated CA3 cells are included in the dataset, of which 210are active in at least one environment. To ensure stabilityof firing fields over time, Alme et al. measured the spatialcorrelation between trials in the familiar room on differentdays.
Methods
We start by explaining the steps involved in extracting theAlme et al. dataset for statistical analysis. Then, we providebrief descriptions of the noise perturbation and Representa-tion Similarity Analysis (RSA) methods used to better un-derstand the robustness of memory in CA3 and the extent towhich spatial representations are highly structured. Finally,we will discuss the methods relating to the portions of Almeet al. that we replicated.
Data Processing
To begin, we wrote a Python script to read the mouse po-sition data and spike times and extract spike positions overtime for each cell. This approach was based on the MATLABscript provided in the dataset, and required using a k-d tree tofind the closest position data to associate with a given spiketime. An example of position data and corresponding spikesis shown in Figure 1. a r X i v : . [ q - b i o . N C ] D ec igure 1: Blue: position of mouse over time. Red: locationsof spikes recorded over a 15 min window.We then discretized the space of the rooms into a 20 x 20grid and transformed the spike positions into 20 x 20 matricesrepresenting the firing rates for a given cell, as done in Almeet al. An example of such a matrix is shown in Figure 2 as aheat map.Figure 2: Heat map of normalized firing rates across dis-cretized space. Noise Perturbation
For a given vector of firing rates (cid:126) r , we can perturb the en-semble firing activity by creating a new vector (cid:126) r noise = (cid:126) r + (cid:126) z ,where (cid:126) z ∼ N ( , σ ) . While the net effect of the noise vec-tor in expectation is zero for linear functions, the choice of σ can impact the ”power” of the noise perturbation, as mea-sured by signal-to-noise ratio: SNR = A signal σ noise , where A signal isthe amplitude of the firing pattern. This can have an effect onstatistics such as the correlations between trials, as we stud-ied. Representation Similarity Analysis
Representation Similarity Analysis (RSA) is a method devel-oped by Kriegeskorte et al. (2008), in which similarity or dis-similarity matrices are compared, thereby abstracting awayfrom the firing patterns themselves to understand whether theCA3 place cells exhibit underlying connectivity that manifestin consistent activity across environments. Since there are11 environments in the Alme et al. dataset, RSA providesa powerful means by which to quantify consistency of localsub-ensembles of place cells across 55 pairs of environments.Table 1 provides a schematic of a given environment’s cor-relation matrix, indicating the correlation between all pairs ofplace cells. Cell 1 Cell 2 Cell 3 · · ·
Cell 1 r(C1,C1) r(C1,C2) r(C1,C3) · · ·
Cell 2 r(C2,C1) r(C2,C2) r(C2,C3) · · ·
Cell 3 r(C3,C1) r(C3,C2) r(C3,C3) · · · ... ... ... ... . . .Table 1: Correlation matrix for a given environmentThe pseudocode below illustrates how we performed RSA.One of the primary challenges we faced in implementing eachof our computations was the lack of complete data present inthe dataset. That is, given two environments, there are somecells that fired in one environment but not the other. Thus,whenever we computed similarities between correlation ma-trices, we had to find the cells that fired in both environments.
Algorithm 1
Representation Similarity Analysis for environment in environments do Compute correlation matrix c i between all place cells end for for environment a , environment b in environment pairs do Find I = { i : cell i fires in c a and c b } . Compute cross-correlation between c a [ I ] and c b [ I ] end for Mean Activation Vector
As described in Alme et al., a mean activation vector must becomputed for each environment in order to compute overlapsbetween spatial representations. The mean activation vectorconsists of the mean activity of each recorded CA3 place cellacross the environment. The firing rate is extracted from EEGdata, and each component of the vector corresponds to theaverage firing rate in the neural signal for a particular cell.Once the mean activation vectors are computed for eachenvironment, overlap is calculated as the normalized dotproduct between the mean activation vectors −−→
MAV a and −−→ MAV b in two rooms: Overlap = −−→ MAV a · −−→ MAV b c , where c isthe number of non-zero entries across both vectors (i.e., thedot product is only normalized by the number of cells withnon-zero firing activity in both environments).s with RSA, we faced the challenge that the cells thatfired in one environment may not fire in another. When com-puting the dot product, we only looked at the cells that firedin each environment. We had to keep track of the numberof such cells in order to normalize by the correct number.As shown in the Results section, we reproduced the result inAlme et al. that the overlap between mean activation vectorsfrom different trials in the same room is greater than the over-lap between between mean activation vectors from differentrooms. Location-Specific Population Vector
Since the computed mean activation vectors are not location-specific within a particular environment, a population vectorcan be computed as well. In this case, the environment isdiscretized into 20 x 20 spatial bins, and the firing rate ofeach place cell in each spatial bin is normalized by that placecell’s maximal firing rate across all environments and loca-tions. Thus, an environment’s population representation con-sists of a three-dimensional matrix, in which the first dimen-sion corresponds to a place cell and the second/third dimen-sions correspond to the spatial bin (see Figure 2).As before, we can compute overlap between twopopulation vectors by calculating, for each place cell,the quantity
Cell Similarity ( i , A , B ) = Mean ( A i (cid:12) B i ) . Cell Similarity ( i , A , B ) effectively averages the place cell’sdot product between the two rooms A and B over location.Then, we compute the environment similarity by calculating Overlap ( A , B ) = n ∑ ni = Cell Similarity ( i , A , B ) , where i in-dexes the place cell, to average the cell similarities over allplace cells in the two environments. Results
Overlap Between Mean Activation Vectors
We first reproduced one of the results from Alme et al. asa way of checking our data processing. Namely, we com-puted the overlaps between mean activation vectors, first fortwo trials in the same room, and then for two trials in differ-ent rooms. The values are shown in a cumulative frequencyplot in Figure 3. We found that the correlations tended to behigher for trials in the same environment, as expected. In-deed, applying Welch’s t -test, we concluded that overlaps be-tween vectors from the same environment have greater meanthan those from different environments ( p < . ) . Figure 3: Overlap between mean activation vectors. Blue:two trials from the same environment. Orange: two trialsfrom different environments. Correlation Between Perturbed Population Vectors
Next, we analyzed the correlations between population vec-tors after applying Gaussian noise to the firing rates. We trieddifferent values for the parameter σ and found that values onthe order of 0 . Representational Similarity Analysis
After constructing correlation matrices for each trial, we ap-plied Representational Similarity Analysis to each pair of tri-als from the same environment (shown in Figure 5), as well asacross all pairs of trials from different environments (shownin Figure 6). In general, we found a nontrivial level of sim-ilarity in both cases. We also used Welch’s t -test to test thenull hypothesis that both distributions had the same mean, butould not reject the null hypothesis ( p = . Discussion
We successfully replicated the core methods in Alme et al.,such as the overlap between mean activation vectors (see Fig-ure 3) and correlation between population vectors (see Fig-ure 4) in different environments.Through our extension of the findings in Alme et al., wediscovered novel and interesting implications. Namely, thelocation-specific population vector encodings appear to bepartially, but not fully, robust to noisy perturbations. Whennoise with a relatively high signal-to-noise ratio (low vari-ance) is used to change the place cell firing patterns, the popu-lation vector dot products are of similar magnitude and struc- ture as the original (see Figure 4). On the other hand, whennoise with low signal-to-noise ratio (high variance) perturbsthe firing patterns, the population vector dot products appearsignificantly different in magnitude and structure. The pre-cise threshold for signal-to-noise ratio at which the structureof the population vector encoding degrades is unclear, butthese results provide insight into the general scale of noisyfluctuations commonplace in hippocampal area CA3.Additionally, the RSA results provide an additional layeronto the results that Alme et al. previously reported. Alme etal. showed that the activity of place cells across environmentsis statistically insignificant, supporting a model in which dif-ferent environments have highly unique encodings. How-ever, their analysis did not conclude whether certain groupsof place cells may together exhibit similarly high/low firingrates in different environments – that is, whether place cellscould be grouped into activity-related clusters. The distribu-tion of similarity across correlation matrices obtained in theRSA analysis (see Figures 5 & 6) support the existence ofactivity-related clusters of place cells. These results are per-haps unexpected when situated in the context of Alme et al.,which emphasized the lack of statistical correlation for placecells across different environments. Instead, comparisons be-tween place cells across multiple trials in the same environ-ment exhibited non-distinguishable similarity between corre-lation matrices compared to those of place cells across dif-ferent environments. This may indicate non-random connec-tivity between hippocampal place cells, contrary to currentmodels of the CA3 network. Indeed, hippocampal place cellsmay form precise connections to each other during develop-ment that are not organized around common locations/spatialfields, but rather another organizational pattern that is not yetwell understood.Overall, our results provide support for several of the find-ings in Alme et al., while qualifying other conclusions. Mostimportantly, these results support the statistical independenceof firing patterns for different environments, but highlightsthe possibility for hippocampal ”hyper-structure.” Such ahighly organized hippocampus suggests that the statistical in-dependence results from Alme et al. are applicable at thelocal level only.
Future Work
Our results demonstrate the partial robustness of the CA3 net-work to noise and statistical correlation of groups of placecells across different environments, but further research isneeded to fully understand the significance of these findingsin the context of storage capacity, memory formation, anddifferent disease states.Although both Alme et al. and our results demonstrate thehigh storage capacity of the CA3 network, it is currently un-clear what the upper bound of storage for this region is. Stud-ies exposing animals to a large number of environments maybe necessary to arrive at a mathematically tractable answer tothis question.dditionally, the experimental setup in Alme et al. can-not differentiate between short-term and long-term mem-ory. Since these forms of memory manifest on differenttimescales, it is plausible that they are encoded differently inneural representations. Studies examining the robustness tonoise and representational similarity of these sub-categoriesof memory would be another interesting avenue to approachthis question.Lastly, understanding the impact of disease states such asdementia and Alzheimer’s disease on the neural representa-tions of episodic memory in the CA3 area (as well as otherhippocampal regions) would be useful towards developingbetter models of the changes that occur in the brain associatedwith pathology. Ultimately, reversing these changes could bea mechanism of treatment.
Contributions
Bhav and Sean worked on pre-processing the EEG datafrom the Alme et al. dataset. Following this, Sean pri-marily focused on implementing the mean activation vector,population vector, and RSA methods. Bhav implementedthe noise perturbation method and directed the writing ofthe manuscript and presentation slides. Both members de-bugged/tested the model and contributed to the paper.
Acknowledgments
We would like to thank Professor Ila Fiete and Tho Tran at theMassachusetts Institute of Technology for granting us accessto the Alme et al. dataset, reviewing our project proposal, andproviding us with feedback on our methods.
References
Alme, C. B., Miao, C., Jezek, K., Treves, A., Moser, E. I.,& Moser, M.-B. (2014). Place cells in the hippocampus:eleven maps for eleven rooms.
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