Synaptic scaling in combination with many generic plasticity mechanisms stabilizes circuit connectivity

Abstract

Synaptic scaling is a slow process that modifies synapses, keeping the firing rate of neural circuits in specific regimes. Together with other processes, such as conventional synaptic plasticity in the form of long term depression and potentiation, synaptic scaling changes the synaptic patterns in a network, ensuring diverse, functionally relevant, stable, and input-dependent connectivity. How synaptic patterns are generated and stabilized, however, is largely unknown. Here we formally describe and analyze synaptic scaling based on results from experimental studies and demonstrate that the combination of different conventional plasticity mechanisms and synaptic scaling provides a powerful general framework for regulating network connectivity. In addition, we design several simple models that reproduce experimentally observed synaptic distributions as well as the observed synaptic modifications during sustained activity changes. These models predict that the combination of plasticity with scaling generates globally stable, input-controlled synaptic patterns, also in recurrent networks. Thus, in combination with other forms of plasticity, synaptic scaling can robustly yield neuronal circuits with high synaptic diversity, which potentially enables robust dynamic storage of complex activation patterns. This mechanism is even more pronounced when considering networks with a realistic degree of inhibition. Synaptic scaling combined with plasticity could thus be the basis for learning structured behavior even in initially random networks.

Time scales of memory, learning, and plasticity

“…plast. (Song et al 2000)ẇ i j = μ e − t/τ+ for t ≥ 0 −λ e t/τ− for t < 0 τ ± : decay times; t: spike-time difference (7) Synaptic scaling (Tetzlaff et al 2011)…”

“…First, a change in the wiring is possible only if both of the connected neurons are active and, thus, correlated (Oja 1982;Bienenstock et al 1982). The second interpretation is that a change should depend only on information that is locally available, that is, the activity of the two neurons and the weight itself (Gerstner and Kistler 2002;Tetzlaff et al 2011). For instance, for weight normalization (Rochester et al 1956; von der Malsburg 1973) a process that takes into account weights of neighboring neurons is thus not possible for the latter.…”

“…A synaptic plasticity mechanism that seems to work on a longer time scale than minutes to hours is synaptic scaling (Turrigiano et al 1998;Turrigiano and Nelson 2004;Rabinowitch and Segev 2006;Tetzlaff et al 2011). Here, the synaptic efficiency of all inputs to a neuron increases/ decreases if the activity of this neuron is lower/higher than a target activity (Davis 2006).…”

“…Mathematically this can be described as shown in Table 1-7 with a weight dependence added for generality. It can be shown mathematically that adding synaptic scaling with quadratic weight dependence to generic plasticity rules stabilizes weight development (Tetzlaff et al 2011). …”

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

“…This question has been repeatedly addressed by theorists and modellers, and their work typically indicates that without some form of stabilization of firing rates or synaptic weights, network models that can store memory patterns in recurrent synaptic strength become unstable, typically in the direction of activity being too high [1][2][3][4]. These runaway increases in activity emerge from the fact that most Hebbian strengthening mechanisms are dependent on coincident firing between the pre-and post-synaptic neurons, and this process involves a positive feedback loop: namely, the more frequent coincident activity in a group of neurons is, the more likely that synapses connecting these neurons are strengthened.…”