Insights on memory storage and recall: the importance of sparseness in CA3 and DG

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Phase precession and spatial encoding during motion

During motion, temporal compression is allowed by the concomitance of two factors: the overlap between nearby place elds and a mechanism called phase precession, reported for the rst time in [12] and characterized in a detailed way in [13]. To understand this mechanism the rst point to make is that since nearby place elds largely overlap with each other, the spike trains of the respective place cells are actually intermingled at a time-scale faster than the time needed to run the distance between the centers of the place elds. The activation order in each compressed sequence is maintained constant thanks to a precise phase relationship between place cell spikes and the hippocampal theta rhythm, a strong neural oscillation with a frequency of 6{10 Hz, observed especially during active behavior in the hippocampus and many other brain structures (see 1.3). In particular, as the rat moves through a place eld, the corresponding place cell assembly discharges earlier and earlier in successive theta cycles (see Fig. 1.2), and the theta phase of a place cell assembly at a particular time represents distance travelled through the place eld [14]. Indeed, at faster running speeds the phase shift from one cycle to the next one is larger, suggesting that hippocampal place cell assemblies may be speed-controlled oscillators [15]. This phase precession, the underlying mechanism of which is still debated, enables  activation within each theta cycle of an ordered sequence of place cell assemblies, representing a segment of trajectory centered at the current location. Interestingly, the number of assemblies that can nest in each theta cycle (7, see Fig. 1.2) re ects the number of gamma cycles (faster neural oscillations) per theta period [16, 17]. This is a sign of the central role of brain rhythms in coordinating the activity of populations of neurons and in dening the syntax of cell assembly organization [7]. The number of cell assemblies that can be contained in a given theta cycle determines the spatial resolution of neuronal representations (about 5 cm/theta cycle). Phase precession also implies that
during multiple theta cycles several overlapping cell assembly sequences are encountered, each one diering from the previous one by one cell assembly only: it is this repetition of largely overlapping, time-compressed sequences that is thought to be crucial for the initial formation during behaviour of an episodic (spatial) memory trace.

Encoding of a exible and multimodal cognitive map of the environment

Cell assemblies in the hippocampus can also represent future trajectories in navigational tasks. In [45], the authors have observed that in a spatial alternation task on a W-track, synchronous neural activity during SWRs is stronger before correct, as compared to incorrect, trials and this coordinated activity represents both correct and incorrect possible future trajectories. This observation suggests another potential function of hippocampal cell assemblies: place cell sequences activated during awake SWRs may support memoryguided decision making, by recapitulating all possible choices at the decision point. Similar forward shifted trajectories on a spatial decision task have been observed in [46]; however in this case future paths represented at the decision point turns out to be concomitant with theta and gamma oscillations rather than SWRs, which seems to indicate that also other brain states may support activation of this kind of cell assemblies. In agreement with the hypothesis of a function in navigational planning, representations of future paths were found at locations where the rat paused and re-oriented, and their amount and content varied according to task demand. Another experiment reported in [26] shows that, during SWRs activity, trajectories representing routes towards a remembered goal location are more represented compared to random trajectories and they predict immediate future behaviour, while trajectories towards locations that are known to be unrewarded are even less represented than random trajectories. Interestingly, these goal-directed trajectories do not start at the animal current location and they can not be interpreted as replay events triggered by local inputs, while they may represent a non-trivial mechanism to help the construction of a task dependent cognitive map of the environment and to guide behaviour. Activation of sequences representing trajectories leading to (and away from) the goal has been observed also during sleep, when goal location is visible but inaccessible and therefore unexplored in the previous behavioural phase [47]. Such pre-activation of new trajectories, which will be explored in the future, is called preplay. Some experiments also report completely ‘de novo’ preplay of trajectories that have not even been seen during previous behaviour [48]: the explanation for the ‘de novo’ preplay is still debated, but it has been proposed that a new experience can engage cell assemblies that are, at least partially, pre-congured in the place cell synaptic matrix, in such a way that the new sensory cues in the environment will be bound to those cell assemblies and encoded in them. However in [47] preplay is restricted to trajectories that the animal has already seen and associated with reward, and preplay seems to re ect thinking and planning of the future rewarded route. In [31] it is suggested that preplay of trajectories not yet experienced may be important for learning and maintaining a cognitive map of the entire environment.

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Brain rhythms and global cell assemblies

Brain rhythms are oscillations observed in the local eld potential (LFP), that is the electric potential recorded (typically using micro-electrodes) in the extracellular brain tissues, re ecting the sum of the local synaptic currents. Brain rhythms, both during behaviour and during sleep, are thought to play and important role in orchestrating the activity of cell assemblies in spatially widespread brain structures.

Synchronization during wakefulness

As already mentioned in par. 1.1, during active behaviour (and also during REM sleep) hippocampal activity is entrained by theta waves, oscillations with a frequency range of 6{10 Hz, which are probably driven by extrinsic generators (burst ring patterns of cells) located in the medial septum and in the EC [85, 86], together with intrinsic generators in the CA1 region of the hippocampus [87]. EC layers 2 and 3 feed input to the CA3 and CA1 regions of the hippocampus respectively (Fig. 1.1), where the ring preferences of place cells move towards phases which are earlier and earlier in the theta cycle compared to the ring phase of the EC neurons, as the animal crosses each place eld [29]: therefore hippocampal ring dynamics seems to be initiated by entorhinal inputs and to lately evolve independently from them through mechanisms, like phase precession, which are closely related to the theta rhythm. Together with cell assembly sequences built up through phase precession, groups of strongly synchronized neurons, possibly carrying non-sequential information, have also been observed in the hippocampus [18], as previously noticed: these Hebbian-like cell assemblies repeatedly activate at the troughs of theta cycles, on times-scales (30 ms, corresponding to a gamma period) shorter than those typical of place cell sequences (which typically span 7 gamma periods). Timing of activity in medial prefrontal cortex can also be biased by theta rhythm. A signicative example is illustrated in [3]: in a task in which a rule has to be learned in a Y-maze, theta-coherence between mPFC and hippocampus peaks at the decision point and after learning; interestingly, during these high theta-coherence periods, pyramidal neurons in mPFC shift their ring phase towards the troughs of the theta cycle, probably
due to increased ecacy of interneurons. As a result, highly synchronized cell assemblies emerge in mPFC cortex, which match the theta phase of Hebbian cell assemblies observed (in other experiments) in the hippocampus. This nding suggests that hippocampal theta rhythm may play a central role in coordinating activity in cortical structures, and in generating global, inter-structure cell assemblies, which re ect multiple features of episodic memories (see also par. 1.4).

Table of contents :

1 Cell assemblies and memory 
1.1 Hippocampal cell assemblies
1.1.1 Phase precession and spatial encoding during motion
1.1.2 Replay of past trajectories
1.1.3 Encoding of a exible and multimodal cognitive map of the environment 
1.2 Cell assemblies in other brain areas
1.3 Brain rhythms and global cell assemblies
1.3.1 Synchronization during wakefulness
1.3.2 Synchronization during sleep
1.4 Towards a unifying theory of learning and memory
1.4.1 The two-stage model
1.4.2 The hippocampal memory index theory
1.4.3 Insights on memory storage and recall: the importance of sparseness in CA3 and DG
1.4.4 The standard consolidation theory
1.4.5 The transformation hypothesis
2 Methods for the study of neuronal networks 
2.1 Descriptive statistics of correlations
2.2 Model-based methods
2.2.1 Maximum-entropy models
2.2.2 Inference of ME models
2.2.3 Generalized linear models
2.2.4 State-space models
2.3 Methods to identify cell assemblies and replay
2.3.1 Some introductory examples
2.3.2 Template matching for hippocampal cell assemblies
2.3.3 PCA-based methods and community detection techniques
3 A new method to study cell assemblies 
3.1 Eective network model for the neuronal activity
3.2 Inference and validation of the model
3.3 Choice of the time-bin width t
3.4 Comparison of the coupling networks across the epochs
3.5 Null model for the coupling adjustment
3.6 Simulations of the inferred model
3.7 Coactivation of the `putative cell assemblies’
3.8 Possible scenarios for cell assemblies across sessions
3.9 Comparison with PCA{based methods
3.10 Quantitative estimates of the replay
3.10.1 A statistical interpretation of the replay
3.10.2 Comparison with previous interpretations
3.10.3 Replay as a function of time in session A
3.10.4 Session-wide replay
3.10.5 Null model for the replay
3.11 Insights on sessions A, B, C, D, E, F, G
3.11.1 Session A (181014)
3.11.2 Session B (200208)
3.11.3 Session C (181021)
3.11.4 Session D (150720)
3.11.5 Session E (190228)
3.11.6 Session F (181012)
3.11.7 Session G (200209)
4 Simulations of the models in the presence of noise 
4.1 Results at T = 0 on slightly modied datasets
4.1.1 Non-uniform inputs in the model of Sleep Post activity
4.2 Simulations at T = 1
4.2.1 Description of the method
4.2.2 Study of the susceptibility maxima and minima
4.2.3 Localized stimulation in the model of Sleep Post activity
4.3 From T = 0 to T = 1
4.3.1 Neuron susceptibilities on varying T
4.3.2 Local susceptibility peaks vs. conditional average variations
4.4 Discussion on the meaning of the method
4.4.1 Is inference of the Ising model necessary to predict rare coactivation events?
4.4.2 What does drive H represent?
4.4.3 Properties of coactivating neurons
5 Inference and sampling of a Bernoulli-GLM 
5.1 Model inference and goodness-of-t
5.2 Interactions and spatio-temporal patterns
6 Correlation analysis of optogenetic cultures 


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