Abstract
Classical accounts of biased competition (BC) require an input bias to resolve the competition between neuronal ensembles driving downstream processing. However, flexible and reliable selection of behaviorally-relevant ensembles can occur with unbiased stimulation: striatal D1 and D2 spiny projecting neurons (SPNs) receive balanced cortical input, yet their activity determines the choice between GO and NO-GO pathways in the basal ganglia. We present a corticostriatal model identifying three mechanisms that rely on physiological asymmetries to effect rate- and time-coded BC in the presence of balanced inputs. First, tonic input strength determines which SPN phenotype exhibit higher mean firing rate (FR). Second, low strength oscillatory inputs induce higher FR in D2 SPNs but higher coherence between D1 SPNs. Third, high strength inputs oscillating at distinct frequencies preferentially activate D1 or D2 SPN populations. Of these mechanisms, the latter accommodates observed rhythmic activity supporting rule-based decision making in prefrontal cortex.
Biasing the competition between neuronal ensembles is essential for preferential processing of relevant visual information (1). Two computational principles underlie biased competition, as currently understood. First, stimulus-driven neuronal ensembles having distinct stimulus selectivity suppress each other’s activity via mutual inhibition. Second, an external input preferentially targets one of the competing ensembles, breaking the symmetry of the system. Computational models of biased competition implementing these principles can differ in considering either an asynchronous (2, 3, 4, 5) or a rhythmic (6) input bias, as well as in the impact of the bias on neural circuit dynamics, which may increase firing rate (FR) (2, 3), coherence (4, 5), or both (6).
In this work, we introduce an entirely different set of computational principles for biased competition. In the absence of externally imposed (i.e. input) biases, we will show that biased competition is possible between neuronal ensembles endowed with distinct physiological properties. We use corticostriatal processing as a model system for biased competition in the absence of an input bias, because striatal input-output processing is mediated by competition between two distinct GABAergic populations of spiny projecting neurons (SPNs), preferentially expressing either D1 or D2 dopamine receptors (7, 8, 9), that receive balanced cortical stimulation (10).
The manifold differences between D1 and D2 SPNs span anatomical (11), network (12) and intrinsic properties (13), and the two inhibitory populations interact in complex and asymmetrical ways. Thus, it is difficult to predict which physiological asymmetries enable biased competition, and under which conditions. Consequently, we addressed this question in a neural circuit model of corticostriatal processing (Fig. 1A). In this model, D1 and D2 SPNs (which we think of and refer to as ensembles, respectively representing to execute or hold an action) receive balanced cortical stimulation (10), and exhibit the three main experimentally observed physiological differences: (i) an asymmetric connectivity profile (Fig. 1A), in which there are about five times more connections from D2 to D1 SPNs, than vice-versa (11); (ii) distinct GABAergic dynamics (Fig. 1B), with efferent synapses from D1 SPNs having higher maximum conductance but more rapid depression than those from D2 SPNs (12); and (iii) intrinsic properties (Fig. 1C), such that outward calcium-dependent potassium currents are activated earlier and more strongly in D2 SPNs (13).
Functionally, D1 and D2 SPNs represent the first relay of the direct (GO) and indirect (NO-GO) pathways of the basal ganglia (Fig. 1A). GO and NO-GO pathways compete with each other to either trigger or hold an action (14). Coactivation of D1 and D2 SPNs during action initiation (15) imposes a limitation on winner-take-all competition in the striatum (16). Recent modeling work proves, however, that even weak activity biases strongly influence downstream attractor dynamics subserving routing and decision making (17). Our corticostriatal model is consistent with this view. While the time course of a selected action may depend on complex interactions between basal ganglia nuclei (16, 18), a bias in the activity of D1 and D2 SPNs may be sufficient to determine that selection.
But, how can balanced input enable a flexible biasing of neuronal ensembles–i.e., one that allows the reliable selection of either ensemble through variation in the properties of their common input—, in the first place? We hypothesized, and confirmed in our model, two distinct types of mechanisms, each exploiting a specific neural code based on mean firing rate or on precise spike timing (coherence).
First, tonic input strength is able to induce a flexible mean firing rate bias, in which each neuronal ensemble is preferentially activated by inputs within a characteristic range of intensities (Fig. 2C). This mechanism applies even though the two ensembles have the same baseline activity (Fig. 2A and B). The fact that the two ensembles are differentially activated by high and low intensity inputs results from a trade-off between inhibition and activity-dependent hyperpolarization: higher GABAergic inhibition targeting D1 SPNs predominates at low input strengths, leading to higher FR in D2 SPNs, whereas higher outward calcium-dependent potassium currents in D2 SPNs reverse this bias at high input strengths (Fig. 1C). This turning point in relative excitability fits with a confidence-based action selection interpretation of corticostriatal computation: low input strengths represent low signal-to-noise ratios, for which triggering NO-GO actions may be behaviorally advantageous. Thus, the NO-GO pathway is favored at low confidence levels, i.e., when SPNs receive asynchronous low strength inputs, whereas the GO pathway is favored at high confidence levels, i.e., when SPNs receive asynchronous high strength inputs. The mechanism is only apparent at the population level, when a sufficiently large proportion of cells are stimulated by the input. In contrast, the turning point disappears under single-cell stimulation (Fig. 2C, inset), because single-cell stimulation barely affects GABAergic dynamics.
Second, an oscillatory input can induce a coherence bias by preferentially activating the resonant properties of a specific neuronal ensemble. In fact, by varying the frequency of a rhythmic cortical input (Fig. 2D), our model reveals two ways in which the resonances of the two SPN ensembles may diverge: At low input strength, D1 and D2 SPN populations both resonate at the same (low beta) frequency, but D1 SPNs are much more strongly synchronized by rhythmic input (Fig. 2E), despite their lower FR. This divergence between rate and coherence relies on synaptic inhibition. Higher inhibition decreases the overall FR, but enhances spiking coherence, since cells are pushed closer to baseline by inhibition and thus exhibit a more uniform state when inhibition wears off (19). At high input strengths, the resonant frequencies of D1 and D2 SPN populations both increase, and diverge from each other (Fig. 2F). The increases in resonant frequency occur because the external input drives SPNs faster than their network frequency in the low beta band (Fig. 2E). As a result, the resonant frequencies of D1 and D2 SPNs shift beyond low beta, respectively to high and middle beta frequencies, following their mean FR (Fig. 2C).
Temporal coordination is, in addition to increased input strength, another mechanism enhancing the signal-to-noise ratio. Thus, while it seems behaviorally advantageous to favor the NO-GO pathway under low strength asynchronous inputs, reliable GO selections can be accomplished for low strength inputs when oscillatory frequency matches the resonant dynamics of SPNs. Furthermore, our results suggest that highly reliable selections of GO and NO-GO actions (in the sense of highest signal-to-noise ratios) occur under rhythmic inputs of high strength, when the oscillatory frequency of the input specifically matches either the resonant frequency of D1 or D2 SPNs.
All together, Figure 2 predicts three types of inputs supporting flexible biased competition under balanced stimulation, confirmed in Figure 3 (top and middle): (i) a rate bias regulated by high vs. low input strength (Fig. 3A and B); (ii) a coherence bias regulated by high strength inputs oscillating at distinct beta bands (Fig. 3D and E); and (iii) coexisting rate and coherence biases in the activity of D2 and D1 SPNs, respectively, resulting from low strength oscillatory inputs at low beta frequency (Fig. 3C). But, how reliable is each bias at driving downstream action selection?
To address this question we ran the model output through two read-out decoders of striatal activity. The first decoder was a spiking activity accumulator, with a slow integration timescale (τ = 100 ms). The second decoder was a coincidence detector, with a fast integration timescale (τ = 5 ms). Our results show that the nature of the striatal bias must fit the timescale of the decoder to guarantee reliable downstream selection (Fig. 3). Thus, only the activity accumulator reliably selects either the GO or the NO-GO pathway from the FR bias between D1 and D2 SPNs (Fig. 3A and B, bottom), while only the coincidence detector flexibly selects either the GO or the NO-GO pathway from the coherence bias between D1 and D2 SPNs (Fig. 3D and E, bottom). When rate and coherence biases coexist, the selection between GO and NO-GO pathways depends on the integration timescale of the decoder. Thus, a coincidence detector reads out the coherence bias of D1 SPNs, whereas an activity accumulator reads out the rate bias of D2 SPNs. Flexible action selection in this case requires adjusting the decoder integration timescale, so it behaves as a coincidence detector or as an activity accumulator. One way to accomplish this may be adjusting the amount of balanced inhibition targeting the decoder, which has been shown to regulate temporal precision (20).
These mechanisms impose predictions that can be tested experimentally. According to the rate bias mechanism, action release must functionally correlate with higher mean FR of D1 over D2 SPNs (Fig. 3B). According to the coherence bias mechanism, action release must functionally correlate with a peak in spike-field coherence at either high (Fig. 3D) or low (Fig. 3C) beta frequencies. Note that mean rate and coherence biases may both be present at once (e.g., Fig. 3D). In this context, a contrast between correct vs. error trials, and/or between short vs. long response time trials, may help to identify the ultimate mechanism supporting BC. Thus, in Figure. 3D, we expect that the amplitude of the peak in spike-field coherence is more strongly correlated with behavior than the mean rate difference between D1 and D2 SPNs.
We have focused so far on the situation in which D1 and D2 SPN ensembles compete for the power to trigger or hold isolated actions, but most frequently goal-directed behaviors require selecting the proper action from multiple available sensory-motor associations, such as in rule-based decision tasks. Rule, category and stimulus selective neural activities have been reported in prefrontal cortex (PFC) (21, 22, 23, 24) and striatum (25, 26), with coactivation of competing ensembles in PFC, coactivating, in turn, competing pathways in the basal ganglia (27). Modeling studies have proposed connectionist and rate coding mechanisms to describe routing of sensory-motor responses according to rule biases (28, 29, 17); however, recent experimental evidence highlights the central role of temporal dynamics. In particular, rhythmic activity at high beta frequencies is observed in the interaction between PFC and striatum during category learning (30), as well as within PFC while performing a rule-based decision task (31), where beta phase-locking was higher for the neuronal ensemble encoding relevant information than for its irrelevant competitors. In the same rule-based decision task, alpha-band prefrontal activity was suggested to mediate suppression of ensembles processing the dominant sensory-motor responses during non-dominant trials, i.e., when these representations were irrelevant (31).
Our model sheds light on how high beta and alpha rhythms might affect downstream processing in the basal ganglia during this task, suggesting a coherence bias as a mechanistic explanation for rule-based action selection based on stronger high beta synchronization of relevant ensembles in PFC. We hypothesize that while D1 and D2 SPN ensembles representing the same categorical action receive balanced input, SPNs representing relevant categorical actions receive more synchronized input at high beta frequency than SPNs representing irrelevant categorical actions (Fig. 4A top). Higher input synchrony produces more coherent striatal firing (Fig. 4A middle), a bias that can be reliably read-out by a coincidence detector, but not by an activity accumulator because the mean FR is the same for relevant and irrelevant SPN ensembles (Fig. 4A middle and bottom). Thus, higher beta coherence in PFC is able to bias relevant over irrelevant GO pathways of the basal ganglia. Importantly, neither of the other two biased competition mechanisms present in our model favored the relevant GO pathway (Fig. S3B and supplementary text).
In the basal ganglia, inhibitory control is mediated by the indirect (NO-GO) pathway. For an alpha rhythm in PFC to play a role in downstream inhibitory control, it would have to bias the activity of D2 over D1 SPNs. This is the case for the coherence bias mechanism: a balanced cortical input oscillating at alpha frequencies (Fig. 4B top) leads to more coherent firing in D2 SPNs (Fig. 2F and Fig. 4B middle), which can be reliably read-out by a coincidence detector (Fig. 4B bottom). An activity accumulator, on the contrary, does not support an alpha oscillatory input as an inhibitory control mechanism, since it reads out the higher mean FR of D1 SPNs (Fig. 4B bottom). Thus, our model suggests a manner by which cortical inputs oscillating at alpha frequencies synchronize the activity of D2 SPNs more strongly than that of D1 SPNs, hence favoring the selection of the NO-GO pathway. Neither of the other two biased competition mechanisms favored the NO-GO pathway (Fig. S3A and supplementary text).
The results reported in this work reveal novel computational principles underlying preferential processing in support of goal-directed behaviors, such as action selection in the striatum. These mechanisms extend previous approaches that only considered unbalanced inputs as the source of the bias between competing neuronal ensembles. In the context of corticostriatal processing, such an approach (32) is challenged by the evidence of balanced cortical input to SPNs (10). In contrast, our model predicts, to our knowledge for the first time, that flexibly biasing basal ganglia dynamics toward activation of either the direct or the indirect pathway can be accomplished by tuning either the strength or the spectral properties of a balanced cortical input. Of the alternative mechanisms supporting BC under balanced input, only the coherence bias mechanism is consistent with observed rhythmic activity in PFC in the context of rule-based decisions (31). In fact, our model of corticostriatal processing suggests a mechanistic explanation for how alpha and high beta rhythms in PFC support, respectively, inhibitory control and rule-based action selection in the basal ganglia.
An attractive, if speculative, hypothesis is that the three BC mechanisms play a role at different learning stages. Dopamine release increases the firing rate of rule-selective neural ensembles in the PFC (33), and these very same ensembles synchronize at high beta frequency (31), which is expected to build-up through training. Based on these observations, we suggest that corticostriatal inputs grow in signal-to-noise ratio, both in strength and coherence, through practice. Thus, at early learning stages, cortical inputs are presumably of weak intensity, for which NO-GO activation may be the default mode (Fig. 3A), unless inputs to SPNs temporally coordinate at low beta frequency (Fig. 3C). Later on, through continuous learning, cortical inputs are expected to grow in mean drive, increasing the signal to noise ratio and then biasing the preferential selection toward the GO pathway further and further (Fig. 3B). At this point the task is mastered, so that cortical inputs are strong enough to dissociate the resonant frequency of SPNs (Fig. 3D vs. 3E), so that alpha vs. high beta inputs are able to reliably activate top-down triggered inhibitory control (Fig. 4B) vs. rule-based action selection (Fig. 4A).
The validity of these computational principles may extend beyond corticostriatal processing. Thus, a rate bias may arise wherever a difference in relative excitability exists between competing neuronal ensembles (34), and a coherence bias may be induced whenever competing neuronal ensembles resonate at distinct frequencies (35). For the two biases to exist simultaneously, there must be a trade-off between FR and coherence. In our model, this trade-off relies on competing neuronal ensembles receiving different amounts of inhibition, internally generated within the striatal microcircuit, despite balanced cortical input. We suspect that the FR-coherence trade-off may also be present when competing ensembles have different AMPA to NMDA conductance ratios, resulting in different synaptic decay timescales: while more AMPA excitation may enhance coherent dynamics (6), less NMDA excitation reduces the overall excitability and, hence, decreases mean FR.
We analyzed biased competition between distinct neuronal ensembles receiving the same inputs, the inverse condition of “classical” biased competition, where identical ensembles receive unbalanced inputs. In general, however, biased competition may occur between competing neuronal ensembles that differ both physiologically and in their input. While this situation is more complex (e.g., cooperation vs. competition between internal and external biased competition mechanisms), it may also be more ubiquitous in the brain and, hence, important to consider systematically. Our work provides a foundation upon which to start addressing this challenge.
Acknowledgments
This research was supported by ARO Grant W911NF-12-R-0012-02. N.K. and S.A. were also supported by NSF Grant DMS-1042134. M.M.M. was supported by CRCNS NIH Grant CRCNS 1R01NS081716. S.A. designed research; N.K. supervised research; All authors contributed to guide research in regular discussions; S.A. implemented the model, with contributions from M.M.M. and J.S.S.; S.A. ran the simulations, analyzed data, prepared the figures and wrote the manuscript; All authors contributed to edit and revise the text. We thank T. Womels-dorf for helpful suggestions on the manuscript.