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. The NFBP consists of responding with neuronal spiking to two of the feature combinations, corresponding to the relevant stimuli (red strawberry and yellow banana), and 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, representing the features of a relevant stimulus, evoke a plateau potential, thus supralinearly exciting the soma. Conversely, co-activation of synaptic clusters for the irrelevant combinations should not evoke plateau potentials.

B: Dendritic Learning: 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 which 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 in Learning: dopaminergic feedback from the midbrain to the striatum (Str) guides the learning process, differentiating between positive feedback for relevant stimuli and negative feedback for irrelevant stimuli. Positive feedback represented by dopamine peaks is necessary for LTP, and negative feedback represented by a dopaminergic pause is necessary for LTD.

D: Signaling pathways underlying synaptic plasticity in dSPNs: Illustrations of molecular components at the corticostriatal synapse that modify synaptic strength (redrawn from Shen et al., 2009). 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 Da triggers LTD (while counteracting the LTP cascade).

Characterization of dendritic plateau behavior in the model.

A: Somatic voltage, spine voltage, NMDA calcium ([Ca]NMDA), and L-type calcium ([Ca]L-type) evoked by a cluster varying in size from 1 to 20 synapses. A plateau potential is evoked after a threshold level of NMDA conductance is exceeded, here set at 10 synapses with a weight of 0.2 each (corresponding to the “baseline” weights in C). The traces for spine voltage, [Ca]NMDA, and [Ca]L-type are averages over all activated spines in the cluster.

B: Schematic of the neuron morphology with an arrow indicating the stimulated dendritic branch in A.

C: Maximal amplitude of the measures shown in A averaged over 10 dendritic locations. The curves represent clusters with different synaptic weights: baseline (0.2), strengthened (0.28) and weakened weights (0.15). Somatic voltages higher than the action potential threshold were set to −50 mV. A synaptic background noise is used in all simulations to elevate the membrane potential to ranges seen in vivo (Reig and Silberberg, 2014).

Example of setup and learning-induced synaptic plasticity

A: Illustration of input configuration. Upper panel shows the arrangement of the features in two dendrites. Each dendrite has synaptic clusters for three features allowing the representation of each of the four feature combinations if seen from the whole neuron’s perspective. Also, the feature combinations allow for only one relevant feature combination per dendrite. The middle panel illustrates the stimulation protocol used in the simulation where stimuli presentation is followed by a dopaminergic feedback signal only if the neuron spikes. The two features representing a stimulus are active within 20 ms, and dopamine feedback, lasting for 50 ms, is delivered 300 ms after the beginning of the stimulus. Two stimuli are spaced 800 ms apart, to allow for the calcium dynamics to reach baseline levels. The bottom panel illustrates the stimulus sequence over the full learning task: all stimuli are equally present in a sequence of 12 stimuli.

B: Example voltage in the soma and the two dendrites before and after learning. Each dendrite stops responding to the irrelevant feature represented by its synaptic clusters.

C: Evolution of synaptic conductances throughout learning. The left panel shows the conductances of the clustered synapses in one of the dendrites (dendrite 1, d1). B, Y and R stand for ‘banana’, ‘yellow’ and ‘red’, respectively. The right panel shows the distributed feature-unspecific synapses. The initial synaptic conductances are set to 0.25 ± 0.05 (around 0.625 nS). The purple trace exemplifies a synapse that is weakened, while the green and blue traces exemplify synapses that are close to the clusters (blue) or by chance (green) have a sufficiently high local NMDA calcium level for LTP to dominate.

D: Peak calcium (dots) and plasticity kernel dynamics (solid lines) during learning. The left panel shows the NMDA calcium of a single ‘banana’ and a single ‘yellow’ synapse that undergo LTP as well as for a single red feature synapse undergoing LTD in dendrite 1 (marked with arrows in the left panel in C). The right panel shows the NMDA calcium for the feature-unspecific synapses identified in the right panel of C.

Impact of feature combinations and synaptic cluster locations on NFBP learning performance

A-C: NFBP configurational analysis. Configurations are categorized based on the number of features per dendrite, those with two or three features (purple traces) and those with all four features on at least one dendrite (light blue traces).

A: Illustration of the setup of the task where two, three or four features are given in two dendritic locations.

B: Performance trajectories for the combinatorial task illustrated in A. Traces of the performance of the model over time for 31 unique feature configurations. Light blue lines show combinations with four features in at least one dendrite, while purple lines show input with maximally 3 input in the local dendritic branches. Right-side histograms display the distribution of the end performance.

C: Outcome results split on stimuli for configurations where maximally three features in one dendritic location (C1) or at least one dendrite has all four features present in a single dendrite (C2).

D and E: End performance in a three-feature configuration as a function of cluster location. D illustrates the location of the inputs, and E shows end performance in the three-pattern configuration as a function of somatic distance of the synapse clusters. Initial synaptic weight is 0.25 ± 0.05 in all the simulation experiments.

Effects of inhibitory inputs on performance

A: Dendritic input configuration with inhibitory synapses added. Illustrations depict two dendritic branches, each with synaptic connections from three excitatory and four inhibitory features, but the general setup is the same as in Fig. 4.

B: Displays average performance for configurations with varying pattern configurations as a comparison between the setup with (orange) and without inhibitory plasticity (blue).

C: Shows task-specific performances for dendritic locations of the clustered synapses, with individual dots and curves representing fitted performance curves with (solid) and without plastic inhibition (dashed).

D: Synaptic conductance changes during learning. Left panel shows excitatory synaptic conductances in dendrite 1 during learning. The right panel shows the inhibitory synaptic conductances. B, Y, R and S stands for ‘banana’, ‘yellow’, ‘red’ and ‘strawberry’.

E: Peak calcium (dots) and plasticity thresholds dynamics (lines) over the learning. The left panel shows examples of the postsynaptic calcium amplitude of the clustered spines in dendrite 1 (marked with arrows on the left panel in D). The right panel tracks calcium levels at inhibitory synapses. The Upper threshold (Tmax) captures peak calcium levels while the lower threshold (Tmin) identifies the next highest. Stability achieved at both thresholds enhances contrast between the activity levels and makes the dendrites respond preferentially to one relevant feature combination at that dendritic site.

Performance analysis of learning using distributed synaptic inputs

A: Example illustration of synaptic distribution before (top) and after learning (bottom) of the 200 excitatory and 60 inhibitory inputs.

B: Learning performance with two spillover models, branch-specific thresholded and accumulative, without (left) and with plasticity of inhibitory synapses (right).

C: Performance trends of 31 distributions with branch-specific thresholded spillover and inhibitory plasticity.

D: Example of summed synaptic conductances (left) and voltage (right) in the soma, and four example dendrites (d1-d4) of one model following successful learning of the NFBP. The sums of both excitatory (Ex) and inhibitory (Inh) inputs are shown.

Synaptic Plasticity Rules: Calcium and Dopamine Interactions in Synaptic Weight Modification

A: Synaptic weight updates during a dopamine peak. (Left) LTP kernel is a bell-shaped curve which determines an optimal [Ca]NMDA region in which synaptic weight is increased. (Right) A wider bell-shaped kernel, i.e. the metaplasticity kernel, determines how the LTP kernel (the optimal region for plasticity) slides along the calcium level ([Ca]NMDA) axis following a Da peak.

B: Synaptic weight updates during LTD. (Left) The LTD plasticity kernel. This kernel is constant. The LTD threshold is constant and set at 70 nM (Right). Metaplasticity describes how the LTP kernel slides along the calcium axis following a Da pause.

C: A schematic of how the LTP kernel window is updated following a dopamine peak. As NMDA calcium levels increase following activation of the strengthened synapse due to a dopamine peak (illustrated with the red circle jumping to the blue circle), the LTP kernel slides down and in this example the strengthened synapse (blue circle) stabilizes, and doesn’t increase in strength even though additional rewards arrive.

D: A schematic showing the update of the LTP window following a dopamine pause leading to that synaptic weight and calcium response decrease as a function of L-type Ca (illustrated with the red circle jumping to the blue one). Here, the LTP kernel slides up towards higher NMDA calcium levels, and thus the weakened synapse (blue circle) is more unlikely to be recruited into the LTP window (unless it in the future is activated with Da peaks more regularly than with Da dips).

E: Depicts the inhibitory plasticity rule. (Left) Changes in synaptic weight for active (orange) and inactive (blue) synapses based on voltage dependent calcium levels in the dendritic shaft at the location of the inhibitory synapse, and minimum (Tmin) and maximum (Tmax) threshold. (Right) Functions for sliding the minimum and maximum thresholds with voltage dependent calcium level. The asterisk denotes the semi-stable zero level where the curves for active and inactive synapses meet.

Excitatory Plasticity Parameters

Inhibitory Plasticity Parameters