Models of Metaplasticity: A Review of Concepts

Abstract

Part of hippocampal and cortical plasticity is characterized by synaptic modifications that depend on the joint activity of the pre- and post-synaptic neurons. To which extent those changes are determined by the exact timing and the average firing rates is still a matter of debate; this may vary from brain area to brain area, as well as across neuron types. However, it has been robustly observed both in vitro and in vivo that plasticity itself slowly adapts as a function of the dynamical context, a phenomena commonly referred to as metaplasticity. An alternative concept considers the regulation of groups of synapses with an objective at the neuronal level, for example, maintaining a given average firing rate. In that case, the change in the strength of a particular synapse of the group (e.g., due to Hebbian learning) affects others' strengths, which has been coined as heterosynaptic plasticity. Classically, Hebbian synaptic plasticity is paired in neuron network models with such mechanisms in order to stabilize the activity and/or the weight structure. Here, we present an oriented review that brings together various concepts from heterosynaptic plasticity to metaplasticity, and show how they interact with Hebbian-type learning. We focus on approaches that are nowadays used to incorporate those mechanisms to state-of-the-art models of spiking plasticity inspired by experimental observations in the hippocampus and cortex. Making the point that metaplasticity is an ubiquitous mechanism acting on top of classical Hebbian learning and promoting the stability of neural function over multiple timescales, we stress the need for incorporating it as a key element in the framework of plasticity models. Bridging theoretical and experimental results suggests a more functional role for metaplasticity mechanisms than simply stabilizing neural activity.

Keywords: Hebbian learning; STDP; homeostasis; metaplasticity; synaptic plasticity.

Figure 1

Intrinsic timescale of Hebbian learning. (A) The classical STDP pairing protocols widely used in the literature. (B) Synaptic modification for one pair of pre- and post-synaptic spikes, as a function of their relative timing. (C) Evolution as a function of time of a single synaptic weight, after an STDP protocol, for various papers taken from the literature, both for LTP of LTD protocols [dash-dotted thin black line is the null-line for Sjöström et al. (2001)]. (D) Adapted from Keck et al. (2013), Normalized mEPSC amplitude in a layer 5 cell in the mice visual cortex following a lesion in the retina. (E) Adapted from Huang et al. (1992), Prior synaptic activity triggered during the red shaded area (LTP priming, red curve) reduces LTP in CA1 hippocampus compared to control without pre-activation (black curve). (F) Adapted from Mockett et al. (2002), Low frequency stimulation (LFS, red shaded areas) influences non-linearly the amount of LTD in CA1 hippocampus: black curve, (control with only one LFS), red curve (two consecutive LFS).

Figure 2

Interplay between Hebbian and homeostatic timescales for pairwise STDP. (A) Evolution of the weight w and the running estimate θ of the post-synaptic firing rate as function of time, for τ_Hebb = τ_homeo = 10 min and various gain α for the heterosynaptic scaling. Insets shows the trajectory in the phase space (w, θ). (B) Same as (A) with a slower homeostatic scaling: τ_homeo = 10 τ_Hebb = 100 min.

Figure 3

Interplay between Hebbian and homeostatic timescales for different learning rules and homeostatic forces. (A) Pairwise STDP with weight dependent modification in Equation (19). Left column: convergence in the phase space (w, θ) for a fast homeostatic force (τ_Hebb = τ_homeo = 10 min, upper row), or for a slow homeostatic force (τ_homeo = 10τ_Hebb, lower row). Right column is the same, but with a stronger drive α = 1 for the homeostatic force. (B) Same as (A) for the triplet learning rule (Pfister and Gerstner, 2006), see Equation (20).

Figure 4

Competition for several plasticity rules with different timescales for Hebbian and homeostatic forces. (A) Pairwise STDP with weight-independent update. Convergence of two synaptic weights w_1∕2 with different correlation inputs and the estimate of the post-synaptic firing rate, θ as function of time, for a fast homeostatic force (τ_Hebb = τ_homeo = 10 min, top row), for a slow homeostatic force (τ_homeo = 10τ_Hebb, middle row), or for a slow and stronger homeostatic force (α = 0.5). (B) Same as A for the weight-dependent STDP learning rule (van Rossum et al., 2000). (C) Same as (A) for triplet learning rule (Pfister and Gerstner, 2006).

Figure 5

Interplay between Hebbian and homeostatic timescales for the BCM learning rule. (A) Upper row: evolution of the weight and the running estimate Ψ of the post-synaptic firing rate as function of time, for τ_Hebb = τ_homeo = 10 min. Lower row: same but in the phase space (w, θ). (B) Same as (A) with τ_homeo = 2τ_Hebb.

Figure 6

Convergence of metaplastic learning rules. (A) Convergence in the phase space (w, θ) of a classical STDP plasticity, either for a fast homeostatic time constant (τ_homeo = τ_Hebb, upper row) or for a slow one (τ_homeo = 10 τ_Hebb, lower row). (B) Same as (A) for a metaplastic learning rule combining the triplet learning rule and scaling of the LTD term (Zenke et al., 2013). (C) Same as (A) for a non-linear metaplastic learning rule including thresholds (El Boustani et al., 2012).

Figure 7

Memory retention problem and timescales. (A) Illustration of metaplastic thresholds stabilizing the learning. Synapses are stable at in the ongoing regime, then a “plasticity trace” builds up during presentation of new sensory inputs, but this will eventually be stopped by a sliding activation threshold, allowing the synapse to adapt to those novel stimuli. (B) Illustration of the multiple timescales involved in plasticity, from the membrane time constant τ_m to the homeostatic one τ_homeo, ranging from ms to days.