Abstract
The brain’s functionality is developed and maintained through synaptic plasticity. As synapses undergo plasticity, they also affect each other. The nature of such ‘co-dependency’ is difficult to disentangle experimentally, because multiple synapses must be monitored simultaneously. To help understand the experimentally observed phenomena, we introduce a framework that formalizes synaptic co-dependency between different connection types. The resulting model explains how inhibition can gate excitatory plasticity while neighboring excitatory–excitatory interactions determine the strength of long-term potentiation. Furthermore, we show how the interplay between excitatory and inhibitory synapses can account for the quick rise and long-term stability of a variety of synaptic weight profiles, such as orientation tuning and dendritic clustering of co-active synapses. In recurrent neuronal networks, co-dependent plasticity produces rich and stable motor cortex-like dynamics with high input sensitivity. Our results suggest an essential role for the neighborly synaptic interaction during learning, connecting micro-level physiology with network-wide phenomena.
Main
Synaptic plasticity is thought to be the brain’s fundamental mechanism for learning1,2,3. Based on Hebb’s postulate and early experimental data, theories have focused on the idea that synapses change based solely on the activity of their presynaptic and postsynaptic counterparts4,5,6,7,8,9,10, defining synaptic plasticity as predominantly a synapse-specific process. However, experimental evidence11,12,13,14,15,16,17,18,19,20 has pointed toward learning mechanisms that act locally at the mesoscale, taking into account the activity of multiple synapses and synapse types nearby. For example, excitatory synaptic plasticity (ESP) has long been known to rely on intersynaptic cooperativity by way of elevated calcium concentrations from multiple presynaptically active excitatory synapses15,16,17,18. Interestingly, GABAergic, inhibitory synaptic plasticity (ISP) has also been shown to depend on the activation of neighboring excitatory synapses: ISP is blocked when nearby excitatory synapses are deactivated11,12, and the magnitude of the changes depends on the ratio between local excitatory and inhibitory currents (EI balance)11. Moreover, the absence of inhibitory currents can either flip the direction13,14 or maximize ESP21,22,23. The amplitude of long-term potentiation (LTP) at excitatory synapses also depends on the history of nearby excitatory LTP induction, revealing temporal and distance-dependent effects24. Finally, Hebbian LTP can also trigger long-term depression (LTD) at neighboring synapses19 through a heterosynaptic plasticity mechanism—that is, without the need of presynaptic activation. There is currently no unifying framework to incorporate these experimentally observed interdependencies at the mesoscopic level of synaptic plasticity.
Existing models typically aim to explain, for example, how cell assemblies are formed and maintained9,25. In these studies, synapse-specific plasticity rules are typically complemented with global processes, such as normalization of excitatory synapses25 or modulation of inhibitory synaptic plasticity by the average network activity9, for stability. Moreover, intricate spatiotemporal dynamics, such as the activity patterns observed in motor cortex during reaching movements26, can be reproduced only when inhibitory connections are optimized (that is, hand tuned) by iteratively changing the eigenvalues of the connectivity matrix toward stable values27,28 or learned by non-local supervised algorithms, such as FORCE29,30. However, models that rely on connectivity changes triggered by non-local quantities are usually based on the optimization of network dynamics27,28,29,30 and often do not reflect biologically relevant mechanisms (but see ref. 31).
To fill the theoretical gap in mesoscopic, yet local, synaptic plasticity rules, we introduce a new model of ‘co-dependent’ synaptic plasticity that includes the direct interaction between different neighboring synapses. Our model accounts for a wide range of experimental data on excitatory plasticity and receptive field plasticity of excitatory and inhibitory synapses and makes predictions for future experiments involving multiple synaptic stimulation. Furthermore, it provides a mechanistic explanation for experimentally observed synaptic clustering and for how dendritic morphology can facilitate the emergence of single (clustered) or mixed (scattered) feature selectivity. Finally, we show how naive recurrent networks can grow into strongly connected, stable and input-sensitive circuits showing amplifying dynamics.
Results
We developed a general theoretical framework for synaptic plasticity rules that accounts for the interplay between different synapse types during learning. In our framework, excitatory and inhibitory synapses change according to the functions ϕE(E, I; PRE, POST) and ϕI(E, I; PRE, POST), respectively (Fig. 1a). The signature of the co-dependency between neighboring synapses—that is, synapses that are within each others’ realm of physical influence—is given by E and I, which describe the recent postsynaptic activation of nearby excitatory and inhibitory synapses. The activity of the synapses’ own presynaptic and postsynaptic neurons—that is, the local synapse-specific activity—is described by the variables PRE and POST. We modeled E and I as variables that integrate neighboring synaptic currents: calcium influx through N-methyl-D-aspartate (NMDA) channels for E and chloride influx through γ-aminobutyric acid type A (GABAA) channels for I. The implementation of excitatory and inhibitory plasticity rules varies slightly, as follows below.
Co-dependent excitatory plasticity model
The rule ϕE(E, I; PRE, POST) by which excitatory synaptic efficacy change is constructed similarly to classic spike-timing-dependent plasticity (STDP) models15,32: pre-before-post spike patterns may elicit potentiation (details below), whereas post-before-pre elicits depression (Fig. 1b). Synaptic changes are also modulated by ‘neighboring’ excitatory and inhibitory activity (Fig. 1a). Initially, we defined an explicit distance-dependent term so that the influence between two neighboring synapses decays with their separation (Methods). In later models, we assumed, for simplicity, that all synapses onto a dendritic compartment or postsynaptic neuron contribute equally to the variables E and I, such that all synapses onto a dendritic compartment or postsynaptic neuron are neighbors with each other.
In addition to the STDP component, the learning rate for potentiation increases linearly with the magnitude of neighboring (including the synapse’s own) NMDA currents15,16,18 (Fig. 1c, green line). This destabilizing positive feedback, in which potentiation leads to bigger excitatory currents, which, in turn, leads to more potentiation, is counterbalanced by introducing a heterosynaptic term9 that weakens a synapse via a quadratic dependency on its neighboring (including the synapse’s own) NMDA currents (Fig. 1c, orange line). This term is based on experimentally observed heterosynaptic weakening of excitatory synapses neighboring other synapses undergoing LTP19. Together, potentiation and heterosynaptic weakening form a fixed point in the dynamics of synaptic weights. As a result, weak to intermediate excitatory currents elicit strengthening, whereas strong currents induce weakening (Fig. 1c, gray line). In addition to neighboring excitatory–excitatory effects, we constructed the model such that elevated inhibition blocks excitatory plasticity: only when synapses are disinhibited can excitatory plasticity change their efficacies (Fig. 1d). Inhibition thus directly modulates excitatory plasticity in our model, complementing the indirect influence of inhibition on excitatory plasticity via the direct influence of inhibition on the postsynaptic neurons’ membrane potential and spike times. This direct control of inhibition over excitatory plasticity allows for rapid, one-shot-like learning33 during periods of disinhibition34 in behavioral timescales—that is, when multiple presynaptic excitatory spikes coincidentally activate a postsynaptic neuron, because the effective learning rate can vary wildly (through rapid intermittent disinhibition) without compromising the stability of the network. At all other times—when inhibition is strong enough to effectively block excitatory plasticity—excitatory weights cannot drift due to ongoing presynaptic and postsynaptic activity….
