Fig 1.
A mechanistic basis for systems memory consolidation.
(A) Circuit motif for the parallel pathway theory. Cue-response associations are initially stored in an indirect synaptic pathway (blue) and consolidated into a parallel direct pathway (red). (B) Hippocampal connectivity. The entorhinal cortex projects to CA1 through an indirect pathway via DG-CA3 and the Schaffer collaterals (SC, blue arrow), and through the direct perforant path (PPCA1, red arrow). (C) Model of consolidation through STDP. Left: before consolidation, a strong SC input (middle, blue vertical bar) causes a large EPSP and triggers a spike in CA1 (bottom, black vertical bar). A weak PPCA1 input (top, red) that precedes the SC input is potentiated by STDP. Right: after consolidation through STDP, the PPCA1 input (top) can trigger a spike in CA1 by itself (bottom). (D-E) Consolidation in a single integrate-and-fire CA1 cell receiving 1000 PPCA1 and 1000 SC excitatory inputs. (D) PPCA1 activity consists of independent poisson spike trains; the SC activity is an exact copy of the PPCA1 activity, delayed by 5 ms. (E) Consolidation of a synaptic weight pattern from non-plastic SC synapses to plastic PPCA1 synapses. Left and middle: normalized synaptic weights before and after consolidation. Right: time course of correlation between SC and PPCA1 weight vectors during consolidation (mean ± SEM for 10 trials). (F) Failure of consolidation of a synaptic weight pattern from non-plastic PPCA1 to plastic SC synapses; panels as in E.
Fig 2.
Interaction of temporal correlations and the STDP learning window.
The weight dynamics of the direct path [Eq (6)] is driven by inputs from the direct and indirect paths: weight changes are determined by the integrated products of the STDP learning window L with the autocorrelation f [Eq (4)] and the cross-correlation g [Eq (5)], respectively. (A) Examples of a learning window L(τ) and an autocorrelation f(τ), both plotted as a function of the “relative timing” τ. For separable statistics, f is symmetric. If the learning window L has a stronger negative part for τ < 0 and a weaker positive part for τ > 0, the coefficient A ≔ ∫dτ L(τ)f(τ) is typically negative. (B)–(D) Learning window L as in (A) and three example cross-correlations g. (B) The indirect path primarily induces potentiation in the direct path if B ≔ ∫dτ L(τ)g(τ − D) > 0. This is the case if (i) the delay D between the paths is positive, (ii) the learning window is positive for positive delays, and (iii) the time scale of the decay of cross-correlations g is shorter than the delay D and the width of the learning window L. These three conditions favor consolidation. (C) If the cross-correlation g decays on a time scale that is much longer than the width of the learning window and the delay D, the indirect path can drive both potentiation and depression, and consolidation is weaker (i.e., the coefficient B is smaller) than for shorter correlations. (D) If the delay D between the direct and the indirect paths is longer than the width of the learning window L, the indirect path cannot induce systematic changes in the weights of the direct path (coefficient B ≈ 0), and consolidation is ineffective.
Fig 3.
Consolidation of spatial representations.
(A) Replay of PPCA1 and SC activity during sleep. 500 PPCA1 inputs and 2500 SC inputs are spatially tuned on a linear track with periodic grid fields (top, red) and place fields (bottom, blue). Spiking activities are independent Poisson processes (10 spikes/s) inside place/grid fields, otherwise silent. SC activity is delayed by 5 ms. (B) Multi-compartmental model of a reconstructed CA1 pyramidal neuron (see Methods). PPCA1 and SC inputs project to distal apical tuft dendrites (red dots) and proximal apical and basal dendrites (blue dots). (C) Active neuron properties. Top: somatic sodium spike (black) propagates to the distal tuft and initiates a dendritic calcium spike (red) and further sodium spikes. Bottom: dendritic calcium spike leads to bursts of somatic spikes. (D) Spatial tuning before consolidation. SC provides place field-tuned input to the CA1 cell (left, blue), which yields spatially tuned spiking activity (right, blue); PPCA1 input is not spatially tuned (left, red), and (alone) triggers low and untuned spiking activity (right, red). (E) Somatic and dendritic activity during consolidation. During replay, SC input generates backpropagating sodium spikes (black vertical lines) that generate dendritic calcium spikes (red). (F) After consolidation. Spatial tuning is consolidated from the indirect SC pathway into the direct PPCA1 pathway. Left: spatial tuning of total PPCA1 input (red) approaches theoretically derived PPCA1 input tuning (magenta; see Methods). Right: CA1 output is place field-tuned through either SC or PPCA1 input alone. (G) Evolution of correlation between actual and optimal PPCA1 input tuning (see F) for replay speeds corresponding to hippocampal replay events (black) and real-time physical motion (grey). Position in D, E, and F normalized to [0, 1].
Fig 4.
Consolidation of place-object associations in multiple hippocampal stages.
(A) Structure of the extended model. PPSUB: perforant path to the subiculum. Each area (EC, DG-CA3, CA1, SUB) contains object-coding and place-coding populations. Open arrows: all-to-all connections between these areas. (B) Decoding of consolidated associations. Top: The location of a platform in a circular environment is stored as an object-place association in the SC (thick diagonal arrows in A, right). Middle: Platform position probability maps given the platform object cue, inferred from the CA1 output resulting from SC or PPCA1 alone, at different times during consolidation (see section “Consolidation of place-object associations in multiple hippocampal stages” in Methods). Bottom: Platform-in-quadrant probabilities (±SEM) given PPCA1 input alone during consolidation. Quadrant with correct platform position (target quadrant) in orange. (C) Consolidation from SC to PPCA1 and to PPSUB over four weeks. Each day, a new association is first stored in SC and then partially consolidated. An association on day 0 is monitored in SC, PPCA1, and PPSUB. Panels as in B. (D) Effects of PPCA1 lesions on memory consolidation, model and experiment (data with permission from [27]). Histograms of time (±SEM) spent in quadrants at different delays after memory acquisition (“probe”). Dashed lines at 25% are chance levels. T: target quadrant; Left, Right: adjacent quadrants; O: opposite quadrant. Top: Control without lesion. Middle: Lesion before memory acquisition. Bottom: Lesion 21 days after memory acquisition.
Fig 5.
Consolidation from hippocampus into neocortex by hierarchical nesting of consolidation circuits.
(A) Schematic of the hierarchical model. The hippocampal formation (HPC) is connected to cortical input circuit 1 and output circuit 1. Increasing numbers indicate circuits further from the HPC and closer to the sensory/motor periphery. Each direct connection at one level (e.g., dark blue arrow between input 1 and output 1) is part of the indirect pathway of the next level (e.g., for pathways from input 2 to output 2). Learning rates of the direct connections decrease exponentially with increasing level (i.e., from blue to red). (B) Memories gradually propagate to circuits more distant from the HPC. The correlation of the initial HPC weights with the direct pathways is shown as a function of time and reveals a memory wave from HPC into neocortex. The maximum of the output circuits follows approximately a power-law (black curve). Noise level indicates chance-level correlations between pathways. (C) Consolidated memories yield faster responses (from sensory periphery, e.g., Input 8, to system output) because these memories are stored in increasingly shorter synaptic pathways.
Table 1.
Parameters for simulations shown in Fig 4.
Table 2.
Parameters for simulations in Fig 5.
Fig 6.
Mathematical analysis of the hierarchical consolidation network.
(A) The mathematical analysis is performed for a network consisting of N + 1 input and N + 1 output layers. All output layers (except output layer 0) weight the input from the previous layer with a factor α and the input via the shortcut pathway with a factor 1 − α, to ensure that activity does not rise as increasingly many pathways converge onto the output layers. Input layer i is hence connected to output layer i through a shortcut connection with weight matrix (1 − α)Wi (except for the bottom-most layers i = 0, for which no factor 1 − α is required). All connections between input layers are set to the identity matrix I, and all connections between output layers are set to αI, for notational simplicity in the derivations. The math can be generalized to arbitrary connection matrices, as long as the network is linear. Each connection introduces a synaptic delay of D. The multi-synaptic pathway from input layer i to output layer i via shortcut connection j ≠ i has a total delay of (2(i − j) + 1) ⋅ D, so the difference in delays between the pathway through shortcut i and shortcut j is Dij = 2(i − j) ⋅ D. (B) The similarity Oi of the weight matrix W0 (in which memory traces are initially stored) and the shortcut connection Wi as a function of the time elapsed after storage (colored lines), and their maximum (black line). Simulations shown for D = 2 ms, α = 0.8, ηi = 2−i and STDP time constant τSTDP = 40 ms.