Pattern separation in the hippocampus: distinct circuits under different conditions

Abstract

Pattern separation is a fundamental hippocampal process thought to be critical for distinguishing similar episodic memories, and has long been recognized as a natural function of the dentate gyrus (DG), supporting autoassociative learning in CA3. Understanding how neural circuits within the DG-CA3 network mediate this process has received much interest, yet the exact mechanisms behind remain elusive. Here, we argue for the case that sparse coding is necessary but not sufficient to ensure efficient separation and, alternatively, propose a possible interaction of distinct circuits which, nevertheless, act in synergy to produce a unitary function of pattern separation. The proposed circuits involve different functional granule-cell populations, a primary population mediates sparsification and provides recurrent excitation to the other populations which are related to additional pattern separation mechanisms with higher degrees of robustness against interference in CA3. A variety of top-down and bottom-up factors, such as motivation, emotion, and pattern similarity, control the selection of circuitry depending on circumstances. According to this framework, a computational model is implemented and tested against model variants in a series of numerical simulations and biological experiments. The results demonstrate that the model combines fast learning, robust pattern separation and high storage capacity. It also accounts for the controversy around the involvement of the DG during memory recall, explains other puzzling findings, and makes predictions that can inform future investigations.

Appendices

Appendix: Implementational details

Our model includes networks for the DG and CA3 regions of the hippocampus (Fig. 2). The cell numbers are scaled down to approximately 1/1000 the size of the rat hippocampus (West et al. 1991; Witter 2010): 1000 PPGC, 120 HGC and 120 MC in the DG; 300 PPCA3 and 50 HCA3 in CA3; and external inputs are provided by 200 neurons in the EC. The simulated neurons are simple points with continuous firing rates. The postsynaptic activity is computed as a function of the neuron’s membrane potential which evolves according to the sum of all excitatory and inhibitory synaptic inputs the neuron receives. The computations proceed in discrete time steps during which the activity of a homogeneous population of neurons is updated synchronously.

The DG network

All inputs from the EC cells to a PPGC_i are summed up to a membrane potential, V _i :

$${V_i}(t)=\mathop \sum \limits_{j} {W_{ij}}{\text{E}}{{\text{C}}_j}(t) - {I_{{\text{PPGC}}}}$$

where EC _j is the activity of the jth EC cell; W _ij refers to the synaptic weights between EC and PPGC; I_PPGC is the amount of tonic inhibition in the DG which has been held constant at 0.75. At the beginning of each simulation run, W _ij are initialized as random values drawn from a normal distribution with a mean of 1 and a standard deviation of 0.05 and are further normalized onto each PPGC.

Within each cluster, PPGC compete among themselves and only those receiving maximal excitation are driven to fire. The firing rate is given by:

$$PPG{C_i}(t)=\left\{ {\begin{array}{*{20}{l}} {\tanh\big( {\sigma {V_i}\left( t \right)} \big),~}&{{\text{if}}\;{V_i}\left( t \right)=\mathop {\arg \hbox{max} }\limits_{{k \in C}} \big( {{V_k}\left( t \right)} \big)} \\ {0,}&{{\text{otherwise}}} \end{array}} \right.$$

with σ is a constant defining the slope of the hyperbolic function and set to 0.1 for all PPGC, k is the index that labels PPGC belonging to the same cluster C as PPGC _i .

In the hilus, the membrane potential of a MC_i depends upon its two main inputs. The influence of PPGC input is computed in a way similar to that described for associative memories with binary neurons (Willshaw et al. 1969; Knoblauch et al. 2010):

$$V_{{\text{i}}}^{{{\text{(PPGC)}}}}(t)= \left\{\begin{aligned} &{V_i}=\mathop \sum \limits_{j} {W_{ij}}{\text{PPG}}{{\text{C}}_j}(t),&{\text{if}}\;{V_i} \geqslant \mathop \sum \limits_{j} {\text{PPG}}{{\text{C}}_j}(t) \\ &0,&\text{otherwise} \end{aligned} \right.$$

The weights of synapses that connect PPGC and MC are initially set to zero, and updated during learning according to the “clipped” Hebbian learning (Willshaw et al. 1969; Knoblauch et al. 2010), which means that W _ij is changed from 0 to 1 when both presynaptic and postsynaptic cells are simultaneously active (MC _i  > 0 and PPGC _j  > 0) while further co-activations do not induce further changes.

The influence of CA3 backprojection on MC membrane potential is approximated by the summed activity of the whole population of PPCA3:

$$V_{i}^{{\left( {{\text{PPCA3}}} \right)}}\left( t \right)=G\Big( {\tanh\big( {\sigma \mathop \sum \limits_{j} {W_{ij}}{\text{PPCA}}{{\text{3}}_j}\left( t \right)} \big)} \Big)$$

Here, we assume a fully connected projection from PPCA3 to MC with all synaptic weights, W _ij , are set to 1; σ is set to 0.1; and G(.) is a dual-thresholding function which implicitly defines the influence of PPCA3 on MC. Specifically, G(V _i ) causes one of the high-threshold mossy cells, MC_h, to be active if V _i  > θ_h; or activates one of the low-threshold mossy cell, MC_l, if θ_l < V _i  ≤ θ_h; otherwise, CA3 backprojection has no influence on MC. This function also assigns 1/0 binary states to free vs. already recruited MC to ensure that a MC would be recruited only if it is not part of other previously-established memory traces. The default values for MC thresholds, θ_l and θ_h, are set to 0.1 and 0.5, respectively.

The firing rate of a MC_i is then given by:

$${\text{M}}{{\text{C}}_i}\left( t \right)=\tanh\Big( {\sigma \big( V_{i}^{{\left( {{\text{PPGC}}} \right)}}\left( t \right)+V_{i}^{{\left( {{\text{PPCA3}}} \right)}}\left( t \right)}\big) \Big)$$

with σ is set to 10. The synaptic weights between MC and HGC are set to 1 and HGC are assumed to show equal responses as their presynaptic partners (HGC _i (t) = MC _i (t)).

The CA3 network

The activity of PPCA3 cells is driven by multiple excitatory and inhibitory inputs. During learning, PPGC mossy fiber inputs function as detonators for their PPCA3 targets provided that the latter are not under active inhibition from HGC/HCA3. The firing rate of a PPCA3 _i is given by:

$${\text{PPCA}}{{\text{3}}_i}(t)=\left\{ {\begin{aligned} &{\tanh\big( {\mathop \sum \limits_{j} {W_{ij}}{\text{PPG}}{{\text{C}}_j}(t)} \big),~}&{{\text{if}}\;{I_i}=0} \\ & {0,}&{{\text{otherwise}}} \end{aligned}} \right.$$

With

$${I_i}=\mathop \sum \limits_{j} {Q_{ij}}{\text{HG}}{{\text{C}}_j}(t)+\mathop \sum \limits_{j} {Z_{ij}}{\text{HCA}}{{\text{3}}_j}(t)$$

Here, W _ij refers to the synaptic weights of mossy fibers which are all equal to 1; I _i refers to the summed inhibitory action that HGC and HCA3 might trigger onto PPCA3; all the weights of inhibitory synapses between HGC and PPCA3, Q _ij , are initiated at 1, while the weights of inhibitory synapses between HCA3 and PPCA3, Z _ij , are all initiated and maintained at 1. Learning occurs in CA3 by modifying the synaptic weights of EC-PPCA3 and PPCA3-PPCA3 connections according to clipped Hebbian learning and by setting the synaptic weights of the inhibitory connections between co-active HGC and PPCA3 cells to zero.

During recall, PPGC inputs are disabled. PPCA3 receive excitatory drives from the perforant path and recurrent projections, but may also undergo strong inhibition from local interneurons; HCA3 are only responsive to drive from HGC:

$${\text{PPCA}}{{\text{3}}_i}(t)=\left\{ { \begin{aligned} &\tanh \Big( \sigma \big( \mathop \sum \limits_{j} W_{{ij}}^{{{\text{PP}}}}{\text{E}}{{\text{C}}_j}(t) &\\ &+\mathop \sum \limits_{k} W_{{ik}}^{{{\text{RC}}}}{\text{PPCA}}{{\text{3}}_k}(t - 1)- {I_{{\text{PPCA3}}}}(t) \big) \Big), & \quad{{\text{if}}\;{I_i}=0} \\ &{0,~}&\quad{{\text{otherwise}}} \end{aligned}} \right.$$

with

$${I_{{\text{PPCA3}}}}=\mu \big( {\mathop \sum \limits_{j} {\text{E}}{{\text{C}}_j}(t)+\mathop \sum \limits_{k} {\text{PPCA}}{{\text{3}}_k}(t - 1)} \big)$$

and

$${\text{HCA}}{{\text{3}}_i}(t)={\text{HG}}{{\text{C}}_i}(t)$$

Again, I _i refers to the amount of inhibition arising from HGC/HCA3 on PPCA3 _i ; $W_{{ij}}^{{{\text{PP}}}}$ and $W_{{ik}}^{{{\text{RC}}}}$ are respectively the synaptic weights of EC-PPCA3 and PPCA3-PPCA3 connections; I_PPCA3 is the amount of inhibition that depends on incoming activity from the EC and CA3 itself; µ is a constant which has been set to 0.2. The activity of PPCA3 is computed repeatedly until the network settles into a steady state or until a maximum of 10 iterations is reached.