Read:: - [ ] Yin et al. (2022) - Oscillation/Coincidence-Detection Models of Reward-Related Timing in Corticostriatal Circuits 🛫2023-09-07 !!2 rd citation todoist Print:: ❌ Zotero Link:: Zotero Files:: attachment Reading Note:: Web Rip:: url:: https://brill.com/view/journals/time/aop/article-10.1163-22134468-bja10057/article-10.1163-22134468-bja10057.xml

TABLE without id
file.link as "Related Files",
title as "Title",
type as "type"
FROM "" AND -"ZZ. planning"
WHERE citekey = "yinOscillationCoincidenceDetectionModels2022" 
SORT file.cday DESC

Abstract

Abstract The major tenets of beat-frequency/coincidence-detection models of reward-related timing are reviewed in light of recent behavioral and neurobiological findings. This includes the emphasis on a core timing network embedded in the motor system that is comprised of a corticothalamic-basal ganglia circuit. Therein, a central hub provides timing pulses (i.e., predictive signals) to the entire brain, including a set of distributed satellite regions in the cerebellum, cortex, amygdala, and hippocampus that are selectively engaged in timing in a manner that is more dependent upon the specific sensory, behavioral, and contextual requirements of the task. Oscillation/coincidence-detection models also emphasize the importance of a tuned ‘perception’ learning and memory system whereby target durations are detected by striatal networks of medium spiny neurons (MSNs) through the coincidental activation of different neural populations, typically utilizing patterns of oscillatory input from the cortex and thalamus or derivations thereof (e.g., population coding) as a time base. The measure of success of beat-frequency/coincidence-detection accounts, such as the Striatal Beat-Frequency model of reward-related timing (SBF), is their ability to accommodate new experimental findings while maintaining their original framework, thereby making testable experimental predictions concerning diagnosis and treatment of issues related to a variety of dopamine-dependent basal ganglia disorders, including Huntington’s and Parkinson’s disease.

Quick Reference

Tasks

Topics

Morris–Lecar neurons tp

Extracted Annotations and Comments

Page 2

From this solid behavioral foundation, more computational models have emerged, some with neurobiological correlates including oscillation/coincidence-detection models (e.g., Buhusi et al., 2016; Gu et al., 2015; Matell & Meck, 2000, 2004; Petter et al., 2016, 2018), drift-diffusion models (e.g., Balcı & Simen, 2014; Luzardo et al., 2013; Emmons et al., 2017; Narayanan, 2016), as well as a variety of state-dependent processes, including population, temporal dynamics, and recurrent neural-network models (e.g., Buonomano, 2014; Goel & Buonomano, 2014; Hardy & Buonomano, 2016; Laje & Buonomano, 2013; Petter & Merchant, 2016; Wang et al., 2018).

Fuck, it’s so many

Page 2

With some defining conditions and caveats, the various types of computational models of interval timing can be logically classified into six interrelated categories, including (1) pacemaker–accumulator, (2) oscillator/coincidence-detection, (3) memory/process-decay, (4) random-process (drift-diffusion/ramping), (5) population clocks, and (6) recurrent neural networks (e.g., Addyman et al., 2016; Buhusi et al., 2018a; Hass & Durstewitz, 2016; Matell & Meck, 2000; Paton & Buonomano, 2018).

Page 2

The current review aims to provide a comprehensive presentation of corticothalamic-basal ganglia (CTBG) timing circuits and oscillatory processes involved in timing and time perception. Ultimately, however, it focuses on the SBF model

Page 3

There is a large and consistent neuropsychological, electrophysiological, and functional neuroimaging literature demonstrating that timing in the milliseconds-tominutes range is based on a core timing network embedded in the motor system comprised of a CTBG timing circuit (e.g., Merchant & Yarrow, 2016; Merchant et al., 2013). This core timing network provides timing pulses (i.e., predictive signals to meaningful stimuli) to the entire brain independent of the temporal-processing context. In addition to this central timing hub, there are a set of distributed satellite regions in the cerebellum, cortex, amygdala, hippocampus, and elsewhere that are selectively engaged in timing depending on the specific sensory, behavioral, and contextual requirements of the task (e.g., Lusk et al., 2016; Meck & Ivry, 2016; Merchant & Yarrow, 2016; Petter et al., 2016; Shi et al., 2013).

Page 8

One of the most comprehensive and extensively studied models of interval timing is the SBF model of reward-related timing which is based, in part, upon the coincidence detection of oscillatory processes in CTBG circuits (e.g., Buhusi & Meck, 2005; Matell & Meck, 2004; Matell et al., 2003; Meck et al., 1998; Van Rijn et al., 2014 − please refer to appendix I for an up-to-date description of the SBF model simulation parameters as well as supporting information provided by Allman & Meck, 2012; Matell & Meck, 2004; Oprisan & Buhusi, 2011).

The appendix He speaks of here is the one found in Allman and Meck 2012

Page 8

The SBF model posits that at the onset of a ‘to-be-timed’ signal, populations of cortical and thalamic neurons reset their phase/synchronize and begin oscillating at their endogenous periodicities, including subthreshold membrane oscillations, spiking, and mixed-mode oscillations (e.g., V-Ghaffari et al., 2016, 2017).

Page 9

The CTBG circuit outlined in Fig. 2 is hypothesized to correspond to the functional components of the SBF model of reward-related timing (Matell & Meck, 2004; Matell et al., 2003; Meck et al., 2008), wherein cortical oscillatory neurons, and reward input from the substantia nigra are integrated by striatal MSNs. These neurons can hold temporal ‘memories’ via DA-facilitated long-term potentiation and long-term depression possibly via AMPA receptor trafficking (Centonze et al., 2001).

Page 9

Later, when the same signal duration is timed again, these neurons compare the current pattern of cortical activation with the stored ‘memories’; if a matching pattern is detected, then the spiny neurons fire to indicate the target duration has elapsed. This model succeeds at integrating the psychophysical attributes of interval timing with neurobiological underpinnings and is widely used to explain the distortions in time perception and timed performance in psychopathology (Allman & Meck, 2012).

Page 9

Dopamine release from the VTA at the onset of the signal is believed to play a critical role in this resetting function for cortical neurons while also acting as a ‘start gun’ for the initiation of timing behavior. Moreover, DA release from the

Page 10

substantia nigra pars compacta at signal onset works in a similar fashion to ‘reset’ the weights of the synaptic connections in the dorsal striatum via short-term plasticity mechanisms (e.g., Allman & Meck, 2012; Kononowicz, 2015; Matell & Meck, 2004). This results in adjustments of corticostriatal synaptic weights by MSNs in the dorsal striatum, thus tuning the MSNs to specific patterns of coincident oscillatory activity and increasing their likelihood of firing upon similar patterns of cortical activation in the future (Kononowicz & van Rijn, 2014a, 2015).

Page 10

Additional support for the strengthening of the synaptic connections of MSNs (and potentially fast-spiking interneurons) in the formation of duration-based detectors comes from the observation that the acquisition of the ‘Start’ decision threshold for rats learning a temporal procedure is dependent on de novo protein synthesis and is sensitive to inhibition by the protein synthesis inhibitor anisomycin in the dorsal striatum, but not the ventral striatum. Conversely, inhibition of protein synthesis in the ventral striatum, but not the dorsal striatum, impairs the acquisition of the ‘Stop’ decision threshold (MacDonald et al., 2012).

Claims that protein synth is required for encoding of start stim

Page 10

The proposal is that the dorsal and ventral regions of the striatum function as a competitive neural network that encodes the temporal boundaries marking the ‘Start’ and ‘Stop’ times of a response sequence centered around the target duration.

Page 10

Consequently, the proposal is that MSNs act as coincidence detectors for specific cortical oscillatory patterns while multiplexing interval timing and working memory (Buhusi et al., 2016; Gu et al., 2015). These oscillatory patterns can be represented at the level of the MSNs as direct spiking input, a sinusoidal type population signal, or a nearly infinite number of possibilities given the richness of the oscillatory time base (see Matell & Meck, 2004). As an example of this time base flexibility, Xu and Baker (2016) have proposed using population synchrony and

Page 11

spike-time-dependent plasticity derived from oscillatory processes as the time base for the SBF model.

Page 11

They present a variation of the beat-frequency coincidence-detection model (Buhusi & Meck, 2005; Matell & Meck, 2000, 2004; Miall, 1989, 1992, 1996) using noisy oscillators whose timing properties are derived from prior in vivo data (Xu et al., 2014). Their results as well as those of Herrmann et al. (2013) suggest that neural-phase oscillatory patterns are the primary information-bearing elements in the types of neural population coding currently advocated by other investigators (e.g., Paton & Buonomano, 2018).

Page 11

Importantly, Xu and Baker (2016) demonstrate that a large population of resetting oscillators with randomly distributed intrinsic timing parameters and millisecond timescales can be trained to encode specific time intervals in the seconds range using population synchrony and spike-time-dependent plasticity (e.g., Bi & Poo, 1998; Markram et al., 1997).

Seems important

Page 11

Bose et al. (2019) have recently proposed a neuromechanistic model for rhythmic beat generation based on the concept of a gamma counter considering the fact that gamma rhythms (30–90 Hz) are ubiquitous throughout the brain (e.g., Buzsáki & Wang, 2012). Therefore, they modeled 40-Hz gamma oscillations to form two discrete-time clocks that count the number of gamma cycles between specific events. The idea is similar to the pacemaker–accumulator models mentioned above in that they both make use of a counting mechanism. During the development of their beat generation model, Bose et al. (2019) acknowledged that pacemaker–accumulator and oscillator-based models of interval timing are related in a number of important ways. For example, in pacemaker–accumulator models, the accumulator and its reset are equivalent to the integrate-and-fire (IF) class of models, i.e., given regular input, the state variable rises linearly toward a target value for a non-leaky IF model and with a decreasing slope for a leaky IF model (LIF); the accumulator resets once the state variable exceeds the temporal criterion threshold.

Page 11

These IF/LIF models are essentially dynamic system oscillators, and are also nonlinear as a result of the employed reset mechanism. It was noted, however, that the time constant/integration rate required for beat-based situations is reliably slower than in typical applications of IF models for neuronal computations where timescales of 10–30 ms are more common. As a consequence, these models exhibit entrainment and phase-locking properties and show a phase difference among the stimuli.

Page 11

Extended in this way, periodic in time, such a pacemaker–accumulator model can be recast as an entrainment model. As noted by Loehr et al. (2011), differences between the pacemaker–accumulator

Page 12

and the continuous oscillator models are evident under some conditions by adding additional assumptions regarding the reset, phase correction, and/or phase response curves, but are otherwise very similar. This has the advantage of allowing the pacemaker–accumulator model to learn the correct phase and period, allowing the subject to continue to hold on the beat even after resetting (see Gu et al., 2011 for a possible example of this).

Page 12

n the discussion of how their beat generation model fits in with other timing models, Bose et al. (2019) described the features of the SBF model that make it distinctive and set it apart from other models of interval timing. In essence, the SBF model uses neuronal oscillators with different fixed frequencies in an unusual way (see Miall, 1989).

Page 12

All the oscillators reset at t = 0; and the differences in the drifting frequencies of convergent units will eventually result in a near-coincidence (the so-called ‘beating phenomenon’ of non-identical oscillators) at a duration that as a result of reinforcement learning (strengthening of synapses onto coincidence-detector units) can match the target duration (Petter et al., 2018).

what does this mean, especially the part about RL

Page 12

As Bose et al. (2019) note, the uniqueness and applicability of this model have not been lost on others as it has been extended to the periodic case and considered for rhythmic prediction/reproduction by a number of investigators interested in the calculation of rate, time, and numbers due to it offering a more general case than the pacemaker–accumulator account of the phenomena (e.g., Brighouse et al., 2014; Hartcher-O’Brien et al., 2016; Teki et al., 2012 – in addition to Gu et al., 2011).

Page 12

3.2. Oscillatory Properties of the Time Base There are potentially significant advantages of having an oscillatory time base composed of regularly repeating patterns of oscillation that are widely observed in the cortex and striatum. One is that such regulatory activity is an important aspect of sensory processing and interval timing that allows synchronization of information-processing in different brain areas, including the types of resource allocation underlying dynamic attending and working memory (e.g., Breska & Deouell, 2017; Cravo et al., 2013; Gu et al., 2015; Haegens & Golumbic, 2018; Henry & Herrmann, 2014; Herbst & Landau, 2016; Kösem et al., 2014; Meck & Benson, 2002; Teki et al. (2017) − but see Breska & Deouell, 2016 for an example of when synchronizing to distracting rhythms is detrimental to shifting attention, and van Ede et al., 2018 for a cautionary note on whether neural oscillations contained within certain frequency ranges are best viewed as sustained rhythms or transient burst events). These synchronized oscillations allow the time base to change in a systematic fashion as a function of time, thus proving additional temporal information in the repeated subsets (phase harmonics) of the oscillating time base. Consequently, even though cortical firings occur in the millisecond range, the summation of these firings provides an oscillatory pattern (time base) from which subjects can discriminate target durations in the seconds-to-minutes-to-hours

Page 13

range through the coincidence-detection mechanism previously described, while at the same time having access to the harmonics of these target durations (Matell & Meck, 2004, p. 165). These harmonics potentially provide a rich source of temporal information supporting concepts such as less than (shorter) or greater than (longer) − see Cordes & Meck (2014), Coull & Droit-Volet (2018), and Droit-Volet (2016).

Page 13

As noted above, the concepts of ‘shorter’ and ‘longer’ can be readily obtained from the SBF model by tracking the harmonics derived from primary coincidence detection of the entrained target duration (see Matell & Meck, 2004, fig. 3a). These harmonics in neural activity occur at fractions and multiples of the target duration and are specifically filtered by a ‘threshold’ in the SBF model with reference to the sharpening of responses to the target durations as temporal discriminations are acquired (see Matell & Meck, 2004, p. 165).

Page 13

Likewise, the behavioral training procedures typically used in animal timing studies would be designed to inhibit responses by subjects that are not associated with the response requirements for earning reinforcement, i.e., responding too early or too late. Nevertheless, subjects could theoretically be sensitive to these harmonics and reveal them in behavior not regimented by the reinforcement contingencies. Consequently, the harmonic information in the time base could be used by subjects to make a number of different temporal judgments, including halving or doubling of the interval.

Page 14

if the underlying time base were thus constructed, subjects would be able to continue a rhythmic cycle based on the target duration even in the absence of the ‘to-be-timed’ signal, which would typically be during the inter-trial interval when there is no opportunity for subjects to earn reinforcement.

Page 14

Under standard training conditions, this would only be possible if the rhythmical behavior were to occur in an ancillary response not directly related to the reinforcement contingencies. For example, if rats’ lever pressing were the reinforced response, food cup checking would be an ancillary response that the animals might make in anticipation of food delivery that would not directly be shaped by the reinforcement contingencies and hence might reveal uninhibited patterns of rhythmical behavior entrained to the target duration. Additionally, even if rhythmical patterns of responding for the reinforced response are inhibited by the reinforcement contingencies, they may be revealed by pharmacological treatments with dopaminergic drugs, such as quinpirole, known to remove inhibition from motor systems.

Page 14

A study by Gu et al. (2011) was designed to address the possibility that rhythmical behaviors (reflecting an underlying oscillatory time base) that are normally inhibited by the reinforcement contingencies can be disinhibited within the context of a model for obsessive/compulsive behavior (see Corbit et al., 2019). The primary findings reported by Gu et al. (2011) were that rhythmical patterns of responding were indeed observed in an ancillary response (food cup checking) as well as in the reinforced response (lever pressing) following the administration of quinpirole to rats trained on a 40-s peak interval (PI) procedure of the type used to establish the fundamental properties of interval timing (see Church et al., 1994; Yin et al., 2017). Taken together, these data provide strong support for an oscillatory time base underlying interval timing as currently implemented in the SBF model.

Page 14

3.3. Entrainment of the Oscillatory Time Base In line with the oscillatory time base, the SBF model of reward-related timing was extended to include the encoding of information in working memory. This version of the SBF timing model utilizes a type of resource allocation of working memory that proposes that memory resources can be flexibly distributed among several items such that the precision of working memory decreases with the number of items to be encoded (Gu et al., 2015). This type of hybrid model is consistent with human performance in working-memory tasks based on visual, auditory as well as temporal stimulus patterns. At the neural-network level, a coupled excitatory/inhibitory oscillation (EIO) feature was added to the SBF model to show how interval timing and working memory can originate from the same oscillatory processes but differ in terms of which dimension of the neural oscillation is utilized for item extraction, temporal order, and duration information.

Page 14

The main idea behind the EIO–SBF model is that different ranges of frequency bands are related to different cognitive functions. For example, the gamma oscillators entrained in

Page 15

the theta rhythm can encode items to be maintained in working memory, and the theta oscillators entrained in delta rhythms can encode time. This model uses a Gaussian distribution of oscillator frequencies (e.g. mean 6.5 Hz with 0.2-Hz SD, allowing variation between 6 and 7 Hz) and hypothesizes that these thetaexcitatory oscillators can produce delta oscillations (mean 0.5 Hz with 0.2-Hz SD) through an interaction with synchronized theta inhibitory inputs. As a consequence, the resulting coincident pattern of delta oscillators functions as the time base

Page 15

The EIO–SBF model has been successful in accounting for a variety of experimental findings including the observation that the cerebellum and the striatum represent core areas for representing temporal information in working memory (Teki et al., 2016, 2017). In addition, multiple studies showed the increase of neural oscillations with interval timing (Emmons et al., 2016; Gu et al., 2015; Suzuki & Tanaka 2019). For example, low-frequency oscillations including theta and delta oscillations were increased during the encoding and comparison of duration information in the corticostriatal circuits (Gu et al., 2018).

Page 15

Excitatory/inhibitory oscillation models of temporal processing such as the EIO–SBF model developed by Gu and colleagues (Gu et al., 2015; Teki et al., 2017) provide an alternative solution for solving the unbounded accumulator problem.

Page 15

Unlike the original STT model, which postulates the accumulation of pacemaker pulses, multi-frequency EIO-based neurons oscillate over time, allowing a unique phase pattern to be observed at any given time (e.g., occurrence of a salient event). The phase pattern is essentially a timestamp, that can be represented by a relatively small number of EIO neurons and easily stored in memory (e.g., Gu et al., 2015).

How, what does this mean?

Page 15

Thus, the unbounded accumulator problem of STT-like models is nonexistent in the EIO model. Furthermore, in order to maintain the computational accessibility offered by the STT model, the phase pattern (i.e., timestamp) of the EIO model is not arbitrary, but rather a combinatorial coding for any given time. Using combinatorial coding as timestamps, the signal onset problem is also solved and the scalar property naturally emerges when the EIO oscillators are allowed to have Gaussian variation. As a consequence, duration estimation based on combinational coding provides a straightforward solution for solving the computational accessibility problems encountered by other models, as well as the unbounded accumulator and biological plausibility concerns outlined above (Shi et al., 2022).

Page 15

In coupled systems, variances are reduced in two ways: (1) the oscillators are tied together by network-recurrent inhibitory feedback, so the relation between one theta oscillator’s frequency variation and the population activity does not actually change very much, e.g., a spike phase locked to theta population activity (LFP), which is a common empirical observation; and also by (2) applying slower oscillators (delta instead of theta) to the simulation which also matches experimental findings.

Page 15

According to the first point, time can speed up or slow down because the synchronized inhibitory delta envelope feedback shifts to faster or

Page 16

slower frequencies (meaning that the variance across time in population activity only changes the speed of the clock, not the precision of the time representation). However, by adding different amounts of variance to each oscillator independently, it allows a change in oscillator precision within a constrained limit considering that they are in a network receiving feedback. Taken together, this leads to a systematic relation between frequency bands and time representation − a type of chronotropy.

Page 16

In addition, the EIO model can explain not only an interval duration in the suprasecond range, but also multiple subsecond durations maintained in working memory (Teki et al., 2017). For example, a triggering event (e.g., light or sound) can drive various frequencies of excitatory oscillators in the beta frequency range across a cell population (desynchronized) with relatively synchronized inhibitory oscillators. The excitatory and inhibitory inputs produce beta rhythms entrained in delta or a slower frequency, and this pattern can be maintained during subsecond durations. As noted above, in the EIO–SBF model, the coincident firing pattern of a relevant neuronal group encodes the duration information for a time interval. For example, the 0.4-s time cells are a neuronal group showing a firing peak around 0.4 s and their population firing produces beta rhythms whose power peaks at 0.4 s. Other groups of time cells represent different durations in a similar fashion (Gu et al., 2015).

Page 16

although a variety of computational models have been proposed to account for time perception and timed performance (e.g., Buonomano, 2014; Hass & Durstewitz, 2014; Paton & Buonomano, 2018; van Rijn et al., 2014), relatively few of them are based on the known electrophysiological properties of neural networks (e.g., Bakhurin et al., 2017; Hardy & Buonomano, 2016; Hass & Durstewitz, 2016) or are able to account for the psychophysical properties of interval timing behavior (Allman et al., 2014).

Page 16

For example, there are various reports of neural ramping that are put forward as candidates for a putative timing

Page 17

mechanism (e.g., Emmons et al., 2017; Jazayeri & Shadlen, 2015; Kim et al., 2017; Narayanan, 2016; Parker, 2015; Parker et al., 2014). The primary concern here is that ramping functions are typically unable to account for the scalar property of interval timing or the continued ability to keep track of time for multiple durations after they resolve following the first target duration (Kononowicz & Penney, 2016; van Rijn et al., 2011).

Page 17

Moreover, as cautioned by Kononowicz and colleagues (Kononowicz & van Rijn, 2011, 2014b; Kononowicz et al., 2018) as well as Paton & Buonomano (2018), the properties of ramping activity are often more accurately described as representing activity in a brain area that is monitoring some unspecified time signal emanating from another area of the brain, rather than the locus of a timing mechanism or clock, i.e., the generator of the time base. In many instances, however, the use of the term ‘ramping’ likely functions as a descriptive label that means little more than something that is increasing monotonically as a function of time; whereas for how long it will last and how it will eventually resolve are not usually known unless appropriate probe trials are used, which is often not the case.

Page 17

Unfortunately, this tends to lead to more complicated instances in which one has to conclude that despite whatever assurances the authors might initially provide, they rapidly transit to using the term ‘ramping’ in a way that implies a mathematically formal relationship with the data without providing the appropriate justification for doing so.

Page 17

This error then multiplies itself by being extended to multiple brain areas and is ultimately used to make unsupported claims about the specific types of formal ramping models when in fact it is doing nothing of the sort. The inclusion of appropriate control conditions and/or further examination of the data should be able to determine whether a stepping-dynamics model provides a better description of the observed neural activity than any sort of ramping dynamics model (e.g., Bakhurin et al., 2017; Latimer et al., 2015; Zoltowski et al., 2019).

Page 17

Historically, two empirical phenomena have been interpreted as support for the claim that climbing neural activity, irrespective of its neuronal source, reflects interval timing. Firstly, a climbing neural activity-like pattern of behavior has been shown to be present across a broad range of intervals and brain regions. Secondly, the slope of the climbing neural activity is typically a function of the length of the interval, suggesting that the mechanisms underlying the climbing neural activity are sensitive to the intended target duration (Mita et al., 2009), a phenomenon usually referred to as temporal scaling or time scale invariance (Gibbon et al., 1997). Interestingly, beside this ‘classical’ climbing neural activity trace that superficially resembles an accumulating or ramping pattern, Merchant and colleagues were able to demonstrate that at the level of individual spiking neurons a much richer spectrum of neural activity patterns can be observed (Merchant et al., 2011, 2014).

Page 17

This work identified four main types of neural activity embedded in the so-called climbing (ramping) neural activity patterns: (a) motor control/velocity cells; (b) absolute time cells; (c) relative time cells; and d) temporal

Page 18

accumulator cells, thus demonstrating that the globally observed climbing neural activity is composed of a broader range of phenomena than previously thought.

Page 18

Matell et al. (2011) also reported a similar heterogeneity of firing patterns in the medial agranular cortex of rats performing in 10-s and 20-s PI procedures. These firing patterns in rats were similar to those identified by Merchant et al. (2011) in monkeys and included ramps, peaks, and dips − all with different slopes, directions, and times at which maxima or minima occurred during a single trial. Based on these findings, Matell et al. (2011) advocated for the formal modeling of these different sources and forms of neural activity under the assumption that the utilization of the full range of different temporal markers (e.g., positive and negative ramps, U-shaped functions, and peaks with independent slopes and minimal/ maximal firing rates at different times within a single trial) would lead to an improvement in temporal prediction and therefore increase temporal accuracy and precision.

Page 18

Matell et al. (2003) entertained a similar idea for analyzing the ensemble recording data obtained from rats trained on 10-s and 40-s PI procedures. Interestingly, the ensemble analysis provided relatively little improvement in temporal accuracy or precision over individual neurons that tracked the durations by producing Gaussian-shaped neural firing patterns centered around the target durations with the form of the response and the maximal response rates (peak rates) held nearly constant for the two target durations. The importance of individual neurons to the observed reward-related timing behavior contributed to the implementation of individual neuron ‘perceptron-like’ duration detectors in the SBF model of reward-related timing, and leading to similar conclusions while also documenting these results, theoretical work has proposed the idea that these neuronal patterns that are typically interpreted as evidence of accumulation can also serve as a threshold mechanism that could be distinguished from more gradual accumulator-like activations (Moutard et al., 2015; Simen, 2012).

Page 18

Additionally, recent evidence also challenged the notion that climbing neural activity exhibited by individual neurons is directly linked to time accumulation (e.g., Cook & Pack, 2012; Goel & Buonomano, 2014; Schneider & Ghose, 2012; Simen, 2012). Interestingly, Schneider and Ghose (2012) demonstrated that at the level of individual spiking neurons, time judgments are just as likely to be associated with a decrease of the spiking rate (see Kojima & Goldman-Rakic, 1982).

Page 18

Moreover, although ramping and population-clock models can account for temporal scaling, population and recurrent neural-network models may be better suited to account for complex spatiotemporal patterns, such as those that underlie speech perception or Morse code (Hardy & Buonomano, 2016). Interestingly, CTBG timing mechanisms have been previously implicated in speech perception due to their ability to provide a beat-frequency framework for extracting not only individual syllable durations (e.g., mora), but also patterned input involving relative relationships among elements in a sequence (Schirmer, 2004; Ullman, 2006; Yi et al., 2016). Admittedly, this is not an area of application that the SBF model

Page 19

has been challenged to deal with up to this point in time, but see Miall, 1989, 1992, 1996 for potentially fruitful extensions.

Page 19

Coincidence detection − the integration of simultaneous activation of multiple inputs − currently seems to be the best solution for explaining how the brain detects the durations of multisecond events using millisecond-scale neural processes (e.g., Allman & Meck, 2012; Buhusi et al., 2016).

Page 19

Coordination of Direct and Indirect Striatal Pathways Due to the morphological and electrophysiological dichotomies observed in striatal MSNs reviewed above, it is reasonable to consider a modified version of the SBF model that can incorporate these phenomena in the model.

Page 19

In this modified version of the SBF model illustrated in Fig. 4, the to-be-timed duration is still encoded by D1R-mediated ‘dopamine-stamped’ coincidental cortical inputs into dorsal striatal synapses and decoded by a matching pattern of cortical inputs.

Page 19

The difference is that the expression of the timing signal, i.e., the decision threshold, is now determined by the summation of D1R direct-pathway MSNs and D2R indirect-pathway MSNs, rather than the summation of single MSN outputs.

Page 19

The summation of two independent pathways is likely achieved at the level of the substantia nigra pars reticulata (SNpR), as this nucleus is the major ‘waystation’ where two basal ganglia (BG) pathways converge, although the internal segment of the globus pallidus (GPi) can also be a potential ‘second-level integrator’ (Surmeier et al., 2011). Because the D2R MSNs are more excitable than D1R MSNs, they tend to fire earlier, but with smaller amplitudes in response to synchronized cortical inputs, potentiating the indirect pathway. As time progresses, the D1R MSNs are activated by a matching pattern of cortical input with large amplitudes, potentiating the direct pathway (Kitano et al., 2002). The net effects of D1R MSNs and D2R MSNs at BG output is computed by either SNpr or GPi, and if the difference surpasses a threshold, the BG output is initiated, providing a ‘Go’ signal that can be regarded as the ‘Start’ time in timing tasks such as the PI procedure (e.g., MacDonald et al., 2012).

Page 19

The determination of the ‘Stop’ times is less clear in this model. Nevertheless, one could speculate that thalamic gating of glutamatergic signaling pathways may also play a role (e.g., Ding et al., 2010).

Page 20

Briefly speaking, thalamic bursts, in response to a salient stimulus such as a reward or reward omission, efficiently drive cholinergic interneurons and generate a burst-pause firing pattern, which transiently releases acetylcholine that can suppress release probability at corticostriatal synapses formed on both D1R and D2R MSNs. In addition, activation of nicotinic acetylcholine receptors (nAChRs) on FSIs can also lead to a transient postsynaptic inhibition of both types of MSNs.

Page 20

A pause in the cholinergic activity generated by recurrent collateral or neighboring interneuron activation of dopaminergic terminals provides a time window in

Page 21

which D2R MSNs are strongly biased toward a second repertoire of cortical activations, the result of which is to enhance the indirect-pathway outputs in order to pass the threshold that determines the ‘Stop’ time (Ding et al., 2010).

Page 21

Indeed, during steady-state performance, the striatal neurons are known to fire in a pattern that ‘chunks’ action repertoires (e.g., Barnes et al., 2005). Since the regulation of ‘Stop’ times in this way is determined by the responsivity of D2R as well as D1R MSNs to cortical inputs, manipulations on dopaminergic or cholinergic systems could, in theory, modulate the ‘Stop’ times in accordance with, or independent of the regulation of the ‘Start’ time, depending on the nature of the manipulations on the temporal dynamics of dopaminergic and cholinergic systems (see De Corte et al., 2019).

Page 21

Variations of ‘Start’ and ‘Stop’ response thresholds in the ‘double-summation’ (DS) extension of the SBF model come from three levels: the variations in coincidental cortical inputs, variations in the states of D2R MSNs regulated by extracellular DA fluctuations and complex feedback and feed-forward striatal microcircuits, and the variations in the states of the ‘second-level integrator’ regulated by modulations on the GABAergic efferent or the glutamatergic afferent (e.g., Betarbet & Greenamyre, 2004; Ibanez-Sandoval et al., 2011; Lee et al., 2017).

Page 21

Now that a ‘double-summation’ extension of the SBF model has been outlined, it would be beneficial to test whether this SBF-DS model can account for previously observed effects of pharmacological modulations on interval timing.

Page 21

Remarkably, this ‘double-summation’ model can clearly explain the effects of D2R agonists (e.g., quinpirole, see Gu et al., 2011), D2R antagonists (e.g., haloperidol − MacDonald & Meck, 2005; Meck, 1983, 1986; and raclopride − MacDonald & Meck, 2006), DAT blockers (e.g., cocaine − Cheng et al., 2006, 2007a) and DA release enhancers (e.g., methamphetamine − Cheng et al., 2007b) on interval timing without major difficulties (see Fig. 4, panels B–D).

Page 22

It is known that basal muscarinic tone suppresses the excitability of D2R MSNs (Shen et al., 2004), therefore, the pattern of cortical inputs is ‘stamped’ earlier than it should be, resulting in a change in the memory translation constant K* (see Meck, 1983, 1996, 2002 for an explanation of K*). For example, K* < 1 represents an increase in memory storage speed for physostigmine and K* > 1 represents a decrease in memory storage speed for atropine. This effect gradually emerges as a function of repeated training sessions, at which point it stabilizes and is maintained by continued drug administrations, lesions, degeneracy and/or or aging (Lewis & Meck, 2012; Meck, 1996, 2002; Oprisan & Buhusi, 2011; Yin & Meck, 2014).

Page 24

Summary and Future Directions The SBF model remains one of the most successful computational models of interval timing in terms of explaining the neural correlates of behavior across a broad range of timing procedures. The model continues to serve as an important guidepost for interpreting current data and directing future research involving neural oscillations and their entrainment (e.g., Grabot et al., 2019; Gupta & Chen, 2016; Hashimoto & Yotsumoto, 2015, 2018; Iversen & Balasubramaniam, 2016; Kononowicz & van Wassenhove, 2016; Kononowicz et al., 2018; Wiener & Kanai, 2016), dopaminergic mechanisms (e.g., Farrell, 2011; Oprisan & Buhusi, 2011; Soares et al., 2016), BG functions (e.g., Gu et al., 2018; Harrington & Jahanshahi, 2016; Jahanshahi et al., 2006; Jones & Jahanshahi, 2014; Teki et al., 2011; Toda et al., 2017; van Rijn et al., 2011), and strengthening of cortical–striatal synaptic connections as a function of the amount of training in duration discriminations (e.g., Dallérac et al., 2017; Doyère & El Massioui, 2016)

Page 24

Indeed, the power of a theoretical approach lies not only in its explanatory and predictive power, but also in its flexibility to adapt to different situations without the need to change the foundational framework of the model. In accordance with the apparent dichotomy in D1R-direct and D2R-indirect dorsal striatal MSNs, the current review presents a proposal of how the SBF model can be modified in order to account for new behavioral and neurobiological findings.

Page 24

This does not suggest that the newly proposed SBF-DS model is better or worse than the original SBF model, but it provides a way in which different lines of research can be incorporated into the same logical framework. Indeed, the SBF-DS model is still under development and lacks several important features in order to fully account for timing behavior, such as the source of the scalar property, the variability of the ‘Start’ and ‘Stop’ decision thresholds, as well as the middles and spreads of the ‘high’ response state observed in the PI procedure (Church, 2003; Church et al., 1994).

Page 24

Our goal is to be able to provide a sufficiently detailed model in order to support quantitative mathematical simulations of future pharmacological and optogenetic studies based on studies similar to those of Soares et al. (2016) and Toda et al. (2017). It has been recently observed, for example, that sequences of neural activity in the striatum exhibit the ability to temporally rescale their dynamics, dilating or contracting the sequence duration by up to a factor of five in proportion to the intervals being timed in order to earn a reward (Mello et al., 2015).

Page 25

a successful SBF model should have the ability to dynamically rescale its activity, while at the same time coordinating the chronotopic mapping of durations spanning from at least 0.2 to 3 s in the SMA to be in agreement with the findings recently reported by Protopapa et al. (2019).

Page 25

Given the close anatomical correspondence between the dorsal striatum and the SMA (e.g., Haber, 2016; Heilbronner et al., 2016) it would be expected that if the same relative duration comparisons were maintained (e.g., ratio of short to long anchor durations in a duration bisection task), there would be positive transfer of temporal discriminations with the same relative degree of generalization without requiring the entire reconfiguration of the synaptic weights for MSNs or the reordering of the interconnected DS and SMA (and possibly pre-SMA) maps each time a transition to different target durations occurs (Murray & Escola, 2017).

Page 25

Such chronotopic mapping could possibly account for the recent observation of moving ‘bumps’ of cell firing in the striatum and SMA/preSMA during the timing of a series of durations (e.g., Gámez et al., 2019; Mello et al., 2015; Merchant et al., 2015).

Page 25

Hardy & Buonomano (2016) have recently proposed that the brain encodes time in dynamic patterns of neural activity that are referred to as population clocks. In support of this proposal, they demonstrated that recurrent neural-network models of interval timing can account for temporal scaling while capturing the Weber-speed effect where temporal precision improves at faster speeds of motor reproduction of temporal patterns (e.g., Hardy et al., 2018; Mello et al., 2015; Wang et al., 2018). One issue here is that population codes based on neurons that have a Poisson distribution of spike probabilities generate behavioral and computational properties that can be understood in terms of the tuning properties of individual cells in a manner very similar to that specified by the SBF model and consistent with the Poisson properties of STT (e.g., Averbeck et al., 2006; Gibbon, 1992; Sanger, 2003).

Hmmm so they don’t especially like recurrent models

Page 25

As indicated above, the contribution of the dopaminergic system to timing and time perception has been extensively studied (see Marinho et al., 2018 for a review). Unfortunately, the methods and techniques used thus far have lacked the specificity required for identifying the precise neuronal underpinnings supporting interval timing. As a consequence, Toda, Lusk, and colleagues recently developed a novel version of the standard peak interval procedure using fixed-time rather than fixed-interval trials for studying interval timing in head-fixed mice using a licking response to obtain liquid rewards (Toda et al., 2017).

Peak Interval procedure variation

Page 25

This task utilizes the optogenetic stimulation of recently identified GABAergic nigrotectal projections that coordinate drinking behavior (Rossi et al., 2016). In this fixed-time task, head-fixed mice are trained to lick in order to obtain a liquid reward at specified target durations during which the temporal control of this behavior can be studied using a variety of optogenetic stimulation techniques (Toda et al., 2017).

Page 25

This procedure makes it possible to identify the principal elements of timing behavior

Page 26

independently from the complex behavioral sequences observed in freely moving rodents.

Page 26

The optogenetic stimulation findings reported by Toda et al. (2017) implicate the presence of an oscillatory process generated outside of the nigrotectal pathway that was being stimulated, e.g., the CTBG circuit specified by the SBF model of interval timing.

Page 26

As a consequence, the ability to time target duration depends on neural circuits that generate slow oscillatory cycles with variable speed, amplitude, and phase. The period of this oscillator, perhaps responsible for ‘clock speed’, is adjusted according to the relevant perceptual inputs. Given the regular occurrence of rewards at 7.5-, 10-, and 15-s intervals as used by Toda et al. (2017), the oscillator can be adjusted to have a comparable period, thus allowing striatal MSNs to rescale in the manner of Mello et al. (2015).

Page 26

In addition, the amplitude of the cycle appears to be proportional to the lick rate or behavioral vigor. This parameter is modulated by the motivational state, and appears to set decision thresholds for the initiation of bouts of licking. When the accumulated value of inputs or synchronization of the neuronal activities exceeds the threshold, licking will be initiated. When the relevant motivational signal is high, e.g., when mice are thirsty, the licking on probe trials is initiated earlier and terminates later, resulting in greater variance.

Page 26

Finally, the phase of the oscillation can be adjusted by reward feedback as well as descending motor commands to initiate licking. When such signals are interrupted by canceling licking behavior, as achieved with photostimulation of the nigrotectal pathway, the authors were able to pause and/or reset the timing mechanism in a frequency-dependent manner.

Page 26

One possible explanation of these results is that the BG not only modulate the motor commands for licking movement, but also provide efferent copies to higher levels. The areas that receive the efferent copies, which could include the CTBG circuit and the thalamus, can adjust the oscillatory cycle based on this type of internal feedback signal.

Page 26

The command of the licking bout initiation itself is used as the pause or reset of the signal that adjusts the phase of the oscillator.

Page 26

dopaminergic signaling has been strongly implicated by the SBF model of reward-related timing (Agostino & Cheng, 2016; Cheng et al., 2016; Coull et al., 2011; Gu et al., 2016). Future work will be needed to examine the generation of oscillatory cycles for interval timing and how their phase can be reset by BG output and reward feedback.

Figures

Figure

Page 9

Figure 2

Figure 2. Striatal-beat-frequency (SBF) model of reward-based timing. (A) In this model, intervals are timed neurons that have patterns of activity that fire with different frequencies and converge onto spiny neurons, as illustrated. At the beginning of an interval, these oscillating neurons are synchronized and the status level of the spiny neurons reset by phasic dopaminergic input from the ventral tegmental area and substantia nigra pars compacta, respectively. The delivery of reinforcement at the target duration produces a pulse of dopamine, thereby strengthening the synapses in the striatum that are activated as a result of the beat frequency pattern of these cortical neurons at that specific point in time. In this manner, mechanisms of long-term potentiation and long-term depression are used to strengthen and weaken synaptic weights in order to produce a record in memory of the target duration. Later, when the same signal duration is timed again, neostriatal GABAergic spiny neurons compare the current pattern of activation of these cortical neurons with the pattern stored in memory in order to determine when the target duration has been reached. (B) When the clock and memory patterns match as determined by coincidence detection, the spiny neurons fire to indicate that the interval has elapsed (adapted from Allman and Meck, 2012; Matell and Meck, 2004).

Figure 2. Striatal-beat-frequency (SBF) model of reward-based timing. (A) In this model, intervals are timed neurons that have patterns of activity that fire with different frequencies and converge onto spiny neurons, as illustrated. At the beginning of an interval, these oscillating neurons are synchronized and the status level of the spiny neurons reset by phasic dopaminergic input from the ventral tegmental area and substantia nigra pars compacta, respectively. The delivery of reinforcement at the target duration produces a pulse of dopamine, thereby strengthening the synapses in the striatum that are activated as a result of the beat frequency pattern of these cortical neurons at that specific point in time. In this manner, mechanisms of long-term potentiation and long-term depression are used to strengthen and weaken synaptic weights in order to produce a record in memory of the target duration. Later, when the same signal duration is timed again, neostriatal GABAergic spiny neurons compare the current pattern of activation of these cortical neurons with the pattern stored in memory in order to determine when the target duration has been reached. (B) When the clock and memory patterns match as determined by coincidence detection, the spiny neurons fire to indicate that the interval has elapsed (adapted from Allman and Meck, 2012; Matell and Meck, 2004). Page 9

Figure 2

Figure

Page 13

Figure 3.

Figure 3. Outline of parallel timing circuits involving corticostriatal and corticocerebellar pathways. The corticostriatal and the corticocerebellar pathways are connected to each other, the thalamus, and the pre-SMA/SMA (supplementary motor area) through multiple loops (adapted from Allman et al., 2014; Teki et al. 2012).

Figure 3. Outline of parallel timing circuits involving corticostriatal and corticocerebellar pathways. The corticostriatal and the corticocerebellar pathways are connected to each other, the thalamus, and the pre-SMA/SMA (supplementary motor area) through multiple loops (adapted from Allman et al., 2014; Teki et al. 2012). Page 13

Figure 3

Figure

Page 20

Figure 4

Figure 4. The double summation (DS) extension of the striatal-beat-frequency (SBF) model of reward-related timing. (A) The baseline situation. Coincidental cortical inputs activate both D1R direct pathway MSNs and D2R indirect pathway MSNs. Because the D2R MSNs are more excitable, they can be activated by a less similar pattern of activation or simply by extracellular dopamine (DA). D1R MSNs depend more on a matching pattern of coincidental glutamatergic inputs. Therefore, D2R MSNs have smaller time constants than D1R MSNs. The net effects at basal ganglia (BG) outputs are the summation of the direct and the indirect pathway, and the decision threshold corresponds to the ‘Start’ time. (B) The D2R agonist suppresses D2R MSNs but also suppresses D1R MSNs via reduction of cholinergic tone (Wang et al., 2006; Wang et al., 2013; Zhang et al., 2019), resulting in relatively unchanged ‘Start’ time. (C) The D2R antagonist disinhibits D2R MSNs, therefore produces a rightward shift of ‘Start’ time. The degree of shift should be correlated to the D2R affinity of the drug used. Chronic blockade of D2Rs would lead to homeostatic upregulation of D2Rs, normalizing the effect. (D) A DAT blocker (e.g., cocaine and methamphetamine) increases extracellular DA, and thus activates D2Rs that suppresses D2R MSNs without causing LTD at D1R MSNs, resulting in a leftward shift of ‘Start’ time. Chronic elevation of extracellular dopamine leads to downregulation of D2Rs, normalizing the effect.

Figure 4. The double summation (DS) extension of the striatal-beat-frequency (SBF) model of reward-related timing. (A) The baseline situation. Coincidental cortical inputs activate both D1R direct pathway MSNs and D2R indirect pathway MSNs. Because the D2R MSNs are more excitable, they can be activated by a less similar pattern of activation or simply by extracellular dopamine (DA). D1R MSNs depend more on a matching pattern of coincidental glutamatergic inputs. Therefore, D2R MSNs have smaller time constants than D1R MSNs. The net effects at basal ganglia (BG) outputs are the summation of the direct and the indirect pathway, and the decision threshold corresponds to the ‘Start’ time. (B) The D2R agonist suppresses D2R MSNs but also suppresses D1R MSNs via reduction of cholinergic tone (Wang et al., 2006; Wang et al., 2013; Zhang et al., 2019), resulting in relatively unchanged ‘Start’ time. (C) The D2R antagonist disinhibits D2R MSNs, therefore produces a rightward shift of ‘Start’ time. The degree of shift should be correlated to the D2R affinity of the drug used. Chronic blockade of D2Rs would lead to homeostatic upregulation of D2Rs, normalizing the effect. (D) A DAT blocker (e.g., cocaine and methamphetamine) increases extracellular DA, and thus activates D2Rs that suppresses D2R MSNs without causing LTD at D1R MSNs, resulting in a leftward shift of ‘Start’ time. Chronic elevation of extracellular dopamine leads to downregulation of D2Rs, normalizing the effect. Page 20

Figure 4

🤖🧠 Michael 4.0

Explorer

@yinOscillationCoincidenceDetectionModels2022

Quick Reference

Tasks

Further Reading

Topics

Morris–Lecar neurons tp

Extracted Annotations and Comments

Figures

Graph View

Table of Contents

Backlinks