Modeling the Dynamic Interaction of Hebbian and Homeostatic Plasticity

Abstract

Summary Hebbian and homeostatic plasticity together refine neural circuitry, but their interactions are unclear. In most existing models, each form of plasticity directly modifies synaptic strength. Equilibrium is reached when the two are inducing equal and opposite changes. We show that such models cannot reproduce ocular dominance plasticity (ODP) because negative feedback from the slow homeostatic plasticity observed in ODP cannot stabilize the positive feedback of fast Hebbian plasticity. We propose a new model in which synaptic strength is the product of a synapse-specific Hebbian factor and a postsynaptic-cell-specific homeostatic factor, with each factor separately arriving at a stable inactive state. This model captures ODP dynamics and has plausible biophysical substrates. We experimentally confirm model predictions that plasticity is inactive at stable states and that synaptic strength overshoots during recovery from visual deprivation. These results highlight the importance of multiple regulatory pathways for interactions of plasticity mechanisms operating over separate timescales.

The dialectic of Hebb and homeostasis

“…There is a potentially trivial explanation: sleep-induced changes in the lymphatic system designed to wash away metabolites and toxins [51] might also wash away some extracellular factor that is essential for the induction of homeostatic plasticity. One candidate might be tumor necrosis factor alpha (TNFa), which is clearly essential for the homeostatic recovery of activity during prolonged MD [33,35]; however, our in vitro data suggest that synaptic scaling is only impaired by loss of TNFa signalling after many (approx. 24) hours [55], whereas the gating we observe by sleep and wake occurs on a timescale of many minutes [14].…”

“…However, this slowness may be a critical issue for another proposed function of synaptic scaling, which is to prevent the positive feedback nature of Hebbian mechanisms from producing runaway potentiation or depression [34]. This problem arises because most homeostatic mechanisms that have been identified within neocortical circuits are slow relative to the rapid changes that can be induced by in vitro LTP or LTD protocols, and in theoretical models if the time constants of Hebbian and homeostatic mechanisms are not well-matched then Hebbian positive feedback cannot be kept in check by homeostatic negative feedback [35]. On the other hand, fast rstb.royalsocietypublishing.org Phil.…”

“…Obviously, homeostatic mechanisms must be slow relative to the fluctuations in firing that carry information [4]. A second issue with having homeostatic and Hebbian mechanisms operate at close to the same timescale is the development of oscillations that prevent the system from reaching steady state [35,36]. A third interesting possibility is that activity may be too constrained under conditions where homeostatic negative feedback can always perfectly compensate for Hebbian plasticity.…”

“…Postsynaptically expressed LTP and synaptic scaling involve changes in the accumulation of synaptic glutamate receptors, so these two forms of plasticity are in some sense competing for control over the number of a-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) at synapses. Under some conditions, this situation-much like a mismatch in timescales-can cause oscillations in synaptic weights as LTP and synaptic scaling compete with each other to control synaptic strength [35]. In addition to sharing a final common output, these various forms of plasticity also share some elements of the complex signalling networks within neurons that couple changes in activity to the regulation of synaptic strength [5,43].…”

Integrating Hebbian and homeostatic plasticity: the current state of the field and future research directions

“…What characteristics of the circuit are being stabilized by these mechanisms that make this process homeostatic? There is experimental evidence for three balance parameters: firing rate homeostasis, subthreshold activity homeostasis, and synaptic weight homeostasis, and any of these three parameters, when incorporated into the appropriate theoretical model, may stabilize the network to prevent pathological neuronal dynamics or learning [1,3,4,[47][48][49][50][51][52][53][54][55][56][57][58]. First, firing rate homeostasis was initially described with the first experimental evidence of synaptic scaling [5], and altering cellular [59] and network firing rate has consistently evoked a response of the induction of homeostatic mechanisms [5,7,11,12,29,60].…”