Classically, single neurons in the nervous system have been thought to operate as simple linear integrators such that the nonlinearity of dendrites can be neglected (McCulloch and Pitts, 1943). Based on this simplification, powerful artificial neural systems have been created that outperform humans on multiple tasks (Silver et al., 2018). However, in recent decades, it has been shown that active dendritic properties shape neuronal output and that dendrites display nonlinear integration of input signals (Antic et al., 2010). These dendritic nonlinearities enable a neuron to perform sophisticated computations (Tran-Van-Minh et al., 2015; Gidon et al., 2020), expanding its computational power beyond what is available with the somatic voltage threshold and making it similar to a multilayer artificial neural network (Poirazi et al., 2003).
A dendritic nonlinearity common among projection neurons in several brain areas is the NMDA-dependent plateau potential (Oikonomou et al., 2014). Plateau potentials are regenerative, all-or-none, supralinear voltage elevations triggered by spatiotemporally clustered glutamatergic input (Schiller et al., 2000; Polsky et al., 2004; Losonczy and Magee, 2006; Major et al., 2008; Larkum et al., 2009; Lavzin et al., 2012; Xu et al., 2012). Such plateaus require that nearby spines are coactivated, but the spatial requirement is somewhat loose as even single dendritic branches have been proposed to act as computational units (Branco and Häusser, 2010; Losonczy and Magee, 2006). Nevertheless, multiple so-called hotspots, preferentially responsive to different input values or features, are known to form with close dendritic proximity (Jia et al., 2010; Chen et al., 2011; Varga et al., 2011). Such functional synaptic clusters are present in multiple species, developmental stages, and brain regions (Kleindienst et al., 2011; Takahashi et al., 2012; Winnubst et al., 2015; Wilson et al., 2016; Iacaruso et al., 2017; Scholl et al., 2017; Niculescu et al., 2018; Kerlin et al., 2019; Ju et al., 2020). Hence, multiple features are commonly clustered in a single dendritic branch, indicating that this could be the neural substrate where combinations of simple features into more complex items occur.
Combinations of features in dendritic branches further provide single neurons with the possibility to solve linearly non-separable tasks, such as the nonlinear feature binding problem (NFBP) (Tran-Van-Minh et al., 2015; Gidon et al., 2020). In its most basic form, the NFBP involves discriminating between two groups of feature combinations. This problem is nonlinear because the neuron must learn to respond only to specific feature combinations, even though all features contribute equally in terms of synaptic input. A commonly used example involves two different shapes combined with two different colors, resulting in four total combinations. Out of these, the neuron should respond only to two specific feature combinations (exemplified in Figure 1A and B).
Learning mechanisms in direct-pathway striatal projection neurons (dSPNs) for the nonlinear feature binding problem (NFBP).
(A) Inputs and assumed supralinearity that could solve the NFBP: The NFBP is represented with an example from visual feature binding. In the simplest form of the NFBP, a stimulus has two features, here shape and form, each with two possible values: strawberry and banana, and red and yellow, respectively. In the NFBP, the neuron should learn to respond by spiking to two of the feature combinations, representing the relevant stimuli (red strawberry and yellow banana), while remaining silent for the other two feature combinations which represent the irrelevant stimuli (yellow strawberry and red banana). Assuming that each feature is represented with locally clustered synapses, a solution of the NFBP can be achieved when the co-active clusters on a single dendrite, corresponding to a relevant stimulus, evoke a plateau potential, thus superlinearly exciting the soma. Conversely, co-activation of synaptic clusters for the irrelevant combinations should not evoke plateau potentials. (B) Synaptic clustering in dendrites: Illustration of how synaptic plasticity in SPNs may contribute to solving the NFBP for a pre-existing arrangement of synaptic clusters on two dendrites. A plasticity rule that strengthens only synaptic clusters representing relevant feature combinations so that they produce robust supralinear responses, while weakening synapses activated by irrelevant feature combinations, could solve the NFBP. (C) Dopamine (Da) feedback: Dopaminergic inputs from the midbrain to the striatum (Str) guide the learning process, differentiating between positive feedback for relevant stimuli and negative feedback for irrelevant stimuli. Positive feedback, represented by a dopamine peak, is necessary for long-term potentiation (LTP), and negative feedback, represented by a dopamine pause, is necessary for long-term depression (LTD). (D) Signaling pathways underlying synaptic plasticity in dSPNs: illustrations of signaling components at the corticostriatal synapse that modify synaptic strength (redrawn from Shen et al., 2008). NMDA calcium influx, followed by stimulation of D1 dopamine receptors (D1Rs), triggers LTP (while inhibiting the LTD cascade). L-type calcium influx and activation of metabotropic glutamate receptors (mGluRs) when D1Rs are free of dopamine triggers LTD (while counteracting the LTP cascade).
As a task, the NFBP is relevant to brain regions which perform integration of multimodal input signals, or signals representing different features of the same modality (Roskies, 1999). It is usually illustrated with examples from the visual system, as in Figure 1A; Roskies, 1999; von der Malsburg, 1999; Tran-Van-Minh et al., 2015. A region that integrates multimodal inputs, such as sensory information and motor-related signals, is the input nucleus of the basal ganglia, the striatum (Reig and Silberberg, 2014; Johansson and Silberberg, 2020), and this system will be used in the present modeling study. Here, however, we will continue to illustrate the NFBP with the more intuitive features borrowed from the visual field, although for the dorsal striatum these features would rather map onto different sensory- and motor-related features. Plateau potentials and some clustering of input have been demonstrated in striatal projection neurons (SPNs) (Plotkin et al., 2011; Oikonomou et al., 2014; Du et al., 2017; Hwang et al., 2022; Day et al., 2024; Sanabria et al., 2024).
In addition to integrating converging input from the cortex and the thalamus, the striatum is densely innervated by midbrain dopaminergic neurons which carry information about rewarding stimuli (Schultz, 2007; Matsuda et al., 2009; Surmeier et al., 2010). As such, the striatum is thought to be an important site of reward learning, associating actions with outcomes based on neuromodulatory cues. In this classical framework, peaks in dopamine signify rewarding outcomes and pauses in dopamine represent the omission of expected rewards (Schultz et al., 1997). Dopamine signals further control the synaptic plasticity of corticostriatal synapses on the SPNs (Figure 1C). In direct pathway SPNs (dSPNs) expressing the D1 receptor, a dopamine peak together with significant calcium influx through NMDA receptors triggers synaptic strengthening (long-term potentiation [LTP]). Conversely, when little or no dopamine is bound to the D1 receptors, as during a dopamine pause, and there is significant calcium influx through L-type calcium channels, synaptic weakening occurs (long-term depression [LTD], see Figure 1D; Shen et al., 2008; Fino et al., 2010; Plotkin et al., 2013).
The ability to undergo LTP or LTD is itself regulated (Huang et al., 1992), a concept termed metaplasticity (Abraham and Bear, 1996). Metaplasticity refers to changes in synaptic plasticity driven by prior synaptic activity (Frey et al., 1995) or by neuromodulators (Moody et al., 1999), effectively making plasticity itself adaptable. Metaplasticity can further regulate synaptic physiology to shape future plasticity without directly altering synaptic efficacy, acting as a homeostatic mechanism to keep synapses within an optimal dynamic range (Abraham, 2008). Previous theoretical studies have demonstrated the essential role of metaplasticity in maintaining stability in synaptic weight distributions (Bienenstock et al., 1982; Fusi et al., 2005; Clopath et al., 2010; Benna and Fusi, 2016; Zenke and Gerstner, 2017).
If dopamine peaks are associated with the relevant feature combinations in the NFBP and dopamine pauses with the irrelevant ones, they trigger LTP in synapses representing the relevant feature combinations and LTD in those representing irrelevant combinations. If, after learning, the relevant feature combinations have strong enough synapses so they can evoke plateau potentials, while the irrelevant feature combinations have weak enough synapses so they don’t evoke plateaus, the outcome of this learning process should be a synaptic arrangement that could solve the NFBP (Figure 1B; Tran-Van-Minh et al., 2015). In line with this, it has been demonstrated that the NFBP can be solved in abstract neuron models where the soma and dendrites are represented by single electrical compartments and where neuronal firing and plateau potentials are phenomenologically represented by instantaneous firing rate functions (Legenstein and Maass, 2011; Schiess et al., 2016). Good performance on the NFBP has also been demonstrated with biologically detailed models (Bicknell and Häusser, 2021). This solution used a multicompartmental model of a single pyramidal neuron, including both excitatory and inhibitory synapses and supralinear NMDA depolarizations. Synapses representing different features were randomly dispersed throughout the dendrites, and a phenomenological precalculated learning rule – dependent on somatic spike timing and high local dendritic voltage – was used to optimize the strength of the synapses. The solution did, however, depend on a form of supervised learning as somatic current injections were used to raise the spiking probability of the relevant feature combinations.
In this study, we ask whether – and under what conditions – the theoretical solution to the NFBP can be achieved in a biophysically detailed model of an SPN using only local, biologically-grounded learning rules. We frame this paper around two questions: First, can a single dSPN equipped with only calcium- and dopamine-dependent excitatory plasticity solve the NFBP when the relevant features are pre-clustered on one dendritic branch? Second, if that mechanism is insufficient – as with randomly distributed or very distal inputs – does adding inhibitory plasticity restore plateau-based nonlinear computation and spiking?
To answer these questions, we adopt an approach that relies on the following key mechanisms:
A local learning rule: We develop a learning rule driven by local calcium dynamics in the synapse and by reward signals from the neuromodulator dopamine. This plasticity rule is based on the known synaptic machinery for triggering LTP or LTD at the corticostriatal synapse onto dSPNs (Shen et al., 2008). Importantly, the rule does not rely on supervised learning paradigms, and no separate training and testing phase is required.
Robust dendritic nonlinearities: According to Tran-Van-Minh et al., 2015, sufficient supralinear integration is needed to ensure that, e.g., two inputs (one feature combination in the NFBP, Figure 1A) on the same dendrite generate greater somatic depolarization than if those inputs were distributed across different dendrites. To accomplish this, we generate dendritic plateau potentials using the approach of Trpevski et al., 2023.
Metaplasticity: Our simulations demonstrate that metaplasticity is necessary for synaptic weights to remain stable and within physiologically realistic ranges, regardless of their initial values.
We first demonstrate the effectiveness of the proposed learning rule under the assumption of pre-existing clustered synapses for each individual feature, as suggested by Tran-Van-Minh et al., 2015. These clustered synapses are trained to a degree where they can reliably evoke robust plateau potentials for the relevant feature combinations required to solve the NFBP, while synapses representing irrelevant features are weakened (illustrated in Figure 1B).
We then extend the analysis by applying the learning rule to more randomly distributed synapses, which initially exhibit minimal local supralinear integration. However, when incorporating the assumption that branch-specific plasticity mechanisms are at play, supralinear integration emerges within distinct dendritic branches. This suggests that branch-specific plasticity could play a critical role in enabling single neurons to solve nonlinear problems. Furthermore, we explore an activity-dependent rule for GABAergic plasticity and demonstrate its potential importance in shaping dendritic nonlinearities. This mechanism may thus further enhance computational capabilities by refining and stabilizing the integration of inputs across dendritic branches.
Although brain systems like the striatum, which integrate multimodal inputs, somehow solve nonlinear problems at the network or systems level, it remains unclear whether individual neurons in the brain regularly solve the NFBP. Our investigation suggests, however, that single SPNs possess the computational capacity to address linearly non-separable tasks. This is achieved by leveraging the organism’s performance feedback, represented by dopamine peaks (success) and dopamine pauses (failure), in combination with their ability to generate dendritic plateau potentials. Since the mechanisms used in the rule are general to the brain, this capability may also extend to other projection neurons capable of producing dendritic plateaus, such as pyramidal neurons. However, the specific feedback mechanisms, represented here by dopamine, would need to be associated with alternative neuromodulatory signals depending on the type of neuron and synapse involved.