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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Curr Opin Behav Sci. Author manuscript; available in PMC 2017 April 1.
Published in final edited form as:
PMCID: PMC4797640
NIHMSID: NIHMS764382

Clocks within Clocks: Timing by Coincidence Detection

Abstract

The many existent models of timing rely on vastly different mechanisms to track temporal information. Here we examine these differences, and identify coincidence detection in its most general form as a common mechanism that many apparently different timing models share, as well as a common mechanism of biological circadian, millisecond and interval timing. This view predicts that timing by coincidence detection is a ubiquitous phenomenon at many biological levels, explains the reports of biological timing in many brain areas, explains the role of neural noise at different time scales at both biological and theoretical levels, and provides cohesion within the timing field.

Graphical Abstract

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Introduction

How does one time boiling eggs? One could use a kitchen clock – precise [1], count – less precise [2]**, or do something that takes about the right amount of time – much less precise [3]. Indeed, putative timing mechanisms have traditionally drawn rifts in the timing field. Psychologically, there are many cognitive and behavioral strategies used to time. Physiologically, differences in mechanisms and time scales divided the field into circadian – 24 hour duration, millisecond – or sub-second timing, and interval timing – everything in between [4]**. Theoretically, the many existent models rely on vastly different mechanisms. Here we review these differences, and identify coincidence detection in its most general form as a common thread within models of circadian, millisecond and interval timing. This view has important implications and predictions, and allows for cohesion within the timing field.

Coincidence Detection: from Receptors to Cellular Processes

Receptors as coincidence detectors

Though the term coincidence detection (CD) is rarely used in (neuro)chemistry, neuronal activity required for learning and memory processes is based on CD at the molecular and cellular level. In its simplest form CD means that a substrate is transformed / activated only in the presence of particular chemicals (e.g., ions, small molecules) and only under specific conditions (e.g., membrane depolarization). Only when these molecular complexes are formed and the specific conditions are met, only at that time a particular process takes place (see Fig 1). In this framework, time within a cellular process can be decoded by examining the pattern of activation of various receptors or cellular pathways. For example, receptors, such as the ionotropic NMDA receptor (Fig 1A [5]) or the IP3 receptor [6], act as coincidence detectors at the neuronal level. Synaptic NMDA-dependent long-term potentiation (LTP), a process thought to underlie learning and memory, requires not just glutamate, but also the removal of the Mg2+ block as a result of membrane depolarization, usually provided by AMPA receptor currents [7,8]* (Fig 1A). Moreover, NMDA receptor activation also requires co-activators released by astrocytes, such as D-serine or glycine [9]. Similarly, Purkinje cell LTD, a process underlying cerebellar learning [10], is based on IP3 receptor-dependent Ca2+ release from internal stores; IP3 receptor activation requires both IP3 generated as a result of parallel fiber synaptic activity and Ca2+ influx through voltage-gated channels activated at the climbing fiber synapse [11]**. Given the ubiquitous heterogeneity of synapse structure, the neurotransmitter may reach various receptors with various delays, leading to differences in receptor occupancy, and temporal specificity of activation dynamics at synapse level (Fig 1B [12]).

Figure 1
Coincidence detection at molecular level

Cellular coincidence detection

Since most neurons have complex dendritic arbors, with distinct dendritic domains and a multitude of synaptic inputs from various presynaptic neurons, the firing of the postsynaptic neuron requires CD as well as spatial/temporal integration of multiple dendritic signals. Coincident synaptic input to individual distal dendritic branches produces local spikes that do not propagate reliably to the soma, whereas coincident input to multiple branches can result in larger dendritic spikes that propagate to the soma and thus can trigger an action potential [13]. A recently identified phenomenon, timing-dependent potentiation t-LTP links neuronal activity to maintenance of coincidental synaptic activity at distal dendrites: The action potential back-propagates from the soma to the spines in distal dendrites and contributes, through removal of the Mg2+ block, leading to the coincidental activation of NMDA receptors following post-synaptic depolarization [14]. Interestingly, the NMDA receptor was also shown to be involved in another form of CD – timing-dependent depression t-LTD – involving simultaneous activation of NMDA and cannabinoid CB1 receptors [15]**. Taken together, at cellular level the time code is provided by the coincidental activation of synapses/dendrites (Fig 1B). These phenomena explain the temporal coding in sensory systems such as gustation (Fig 1C [16]).

Coincidence Detection: from Neurons to Circuits

Millisecond timing

The prototypical CD circuit is involved in sound localization based on interaural time differences (Fig 2A). Though important differences have been reported across species [17]*, in this instance, location is determined by coincidental activation of midbrain neurons by delay lines from the left and right cochlear nuclei. As discussed above, cerebellar learning prominently involved in motor control [10] is based on IP3 acting as a coincidence detector of activity in parallel fibers and climbing fibers [11]**. However, emerging evidence suggests a role for multiple forms of plasticity in the granular and molecular layers and cerebellar cortex operating synergistically in a temporally and spatially distributed manner [1820].

Figure 2
Coincidence detection at neuronal and circuit level

Circadian timing

The circadian timing system is virtually composed of as many clocks as there are cells in the body. At the cellular level (Fig 2B [21]**), circadian timing is based on two transcriptional-translational feedback loops relying on molecular CD: In the positive feedback loop, only when transcriptional activator BMAL dimerizes with CLOCK they bind the promoter elements of clock-controlled genes PER and CRY, whose mRNA is translated in the cytoplasm. In the negative loop, only when the PER/ CRY proteins enter the nucleus and bind to the BMAL/CLOCK complex they inhibit their own transcription. The coincidental activation of the positive and negative loops is detected by nuclear receptors ROR/REV-ERB that are transcriptionally regulated by the positive loop and, in turn, activate or inhibit the transcription of BMAL and CLOCK. Posttranslational modifications of proteins regulate their subcellular localization and degradation, regulating the function and speed of the circadian clock [21] (Fig 2B). At the systems level, the multitude of cellular clocks are synchronized through electrical and endocrine pathways [22]; on top of the hierarchy is the suprachiasmatic nucleus (SCN), which receives light information from the retina and entrains the circadian system to the environmental light-dark cycle through induction of immediate-early genes and clock genes in SCN neurons [2325]**.

Interval timing

Prototypical interval timing CD neurons have large dendritic arbors that allow them to collect information from many different inputs and at the same time be very selective to the timing of these inputs. Indeed, brain regions like the striatum, the cortex, the hippocampus and the cerebellum all have such neurons, all have been suggested to be involved in CD [13,26,27], and all have been shown to be involved in timing [2830]. With many dendrites and spines (e.g., 10–30,000 afferents) it is not surprising that striatal medium spiny neurons (MSNs) are thought to act as coincidence detectors by firing only when specific input patterns are coincidental (Fig 2C) [1,31]. The general structure of a striatal beat frequency model is also shown in Fig 2C to emphasize that CD neurons (in this case MSNs) are embedded in larger networks, which may lead to emergent properties, as discussed in the next section. Though the model has been recently extended to apply to multiple events [32], to address pharmacological treatments [33], and to incorporate larger networks [34,35], it has not reached the yet level of complexity to address complex associative paradigms, or the effect of retention intervals or distractors [32,36,37], as the spectral timing model shown in Fig 2D [38].

Molecular, neural and circuit heterogeneity

As discussed above, at network level (or rather behavioral or cognitive levels) each node can be sought of as being engaged in CD in regard to its inputs. However, with increasing complexity at each level – molecular, cellular, circuit – the number of inputs, variables, or processes increases, such that “neural noise” – natural heterogeneity of various receptors, synapses, and cells – results in more errors. While interfering with timing, neural noise may be the unexpected source of emergent network properties, such as scalar timing. The scalar property is the phenomenon by which errors in timing increase proportionally with the timed duration [39]. Most models add specific assumptions to deal with scalar property, as the classic scalar expectancy model does [39], a model in which timing is done by accumulating pacemaker pulses in one counter (stopwatch). Notably, three models went the extra mile to incorporate noise in the fabric of time [2,27,4042]**.

Rather than counting pulses with a stopwatch [39], imagine using a digital clock (Fig 3A). When each counter (seconds, minutes, hours) is noiseless, this amounts to perfect counting/timing. However, when counters exhibit small errors, errors accumulate and result in larger errors in upper units, all in a self-scaling fractal manner [2,42]**. Similarly, when pulses used for timing are neural spikes, as in the striatal beat frequency model, not only timing emerges from CD (as shown in the previous section) but scalar property also emerges without no apparent extra assumptions [27,40]*, from the heterogeneity of various receptors, synapses, and neurons [27,43,44]**. Finally, in the model in Fig 3C, time is coded by the coincidental activation of multiple units which decay at different rates. Though variability (error) is assumed to be similar in size for all clocks, the combined output exhibits scalar property [41]. Taken together, these models suggest that when CD is coupled with the heterogeneity of various receptors, synapses, and cells in a network, allows scalar timing to emerge with no extra assumptions.

Figure 3
Heterogeneity of intrinsic biophysical properties of the mechanisms involved in coincidence detection leads to scalar timing

Conclusions

We reviewed a number of biological and theoretical mechanisms and models, few of which originally were described in terms of CD. Yet, at each level – molecular, cellular, circuit – we identified CD as a naturally occurring mechanism. As each level builds on the lower one, the complexity and flexibility of the system increases but its precision decreases (Fig 4). Indeed, the differences in precision between circadian, millisecond and interval timing may not reflect solely differences in timing mechanism, but rather their level of complexity and heterogeneity. The circadian clock involves relatively few elements, thus it is the least heterogeneous and the most precise. Millisecond timing involves relatively small circuits, thus it involves more heterogeneity than that of the circadian clock, while interval timing relies on larger circuits. Yet, as soon as enough elements are involved, neural noise compounds and scalar property emerges in the system. This view predicts that timing and the scalar property are phenomena shared at its deepest core by many (if not all) brain regions. Indeed, all biochemical processes in all neurons involve gene expression / translation mechanisms, if not similar in detail to, yet similar in its most general principle – CD – with circadian timing. Also, many brain regions have neurons with large dendritic arbors, both suggestive of exquisite CD, and supportive of timing, such as striatum, hippocampus, and cerebellum, though it is unclear that they would have to be extensive to support scalar timing. For example, the models discussed in Fig 3 exhibit robust scalar property at only tens-to-hundreds of units/synapses [2,40,41], suggesting that scalar timing does not necessarily require extremely large dendritic arbors, though probably accurate timing might. Finally, CD provides a unifying window to many (if not all) timing models, and cohesion to the growing, diverse field of biological and theoretical timing [4547].

Figure 4
Clocks within clocks: coincidence detection at various biological levels (left) is accomplished by specific heterogeneous mechanisms (center) that result in increasing timing error

Highlights

  • reviews circadian, millisecond and interval timing both at biological and theoretical levels
  • identifies coincidence detection in its most general form as a common mechanism
  • predicts timing by coincidence detection as an ubiquitous phenomenon at all biological levels
  • explains reports of biological timing in many brain areas
  • provides a cohesive view of the timing field.

Acknowledgments

This work was supported by NIH grant MH073057 to CVB, NSF-CAREER award 1054914 to SAO, and NIH grant NS090283 to MB.

Footnotes

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References

1. Miall RC. The storage of time intervals using oscillating neurons. Neural Comput. 1989;1:359–371.
2. Killeen PR, Taylor TJ. How the propagation of error through stochastic counters affects time discrimination and other psychophysical judgments. Psychol Rev. 2000;107:430–459. [PubMed] ** describes the emergence of fractal scalar property in a stochastic counter.
3. Killeen PR, Fetterman JG. A behavioral theory of timing. Psychol Rev. 1988;95:274–295. [PubMed]
4. Buhusi CV, Meck WH. What makes us tick? Functional and neural mechanisms of interval timing. Nat Rev Neurosci. 2005;6:755–765. [PubMed] ** comprehensive review of biological and theoretical timing.
5. Hasan MT, Hernandez-Gonzalez S, Dogbevia G, Trevino M, Bertocchi I, Gruart A, Delgado-Garcia JM. Role of motor cortex NMDA receptors in learning-dependent synaptic plasticity of behaving mice. Nat Commun. 2013;4:2258. [PMC free article] [PubMed]
6. Ogasawara H. The calcium kinetics and inositol trisphosphate receptor properties shape the asymmetric timing window of coincidence detection. J Neurosci. 2008;28:4293–4294. [PubMed]
7. Tabone CJ, Ramaswami M. Is NMDA receptor-coincidence detection required for learning and memory? Neuron. 2012;74:767–769. [PubMed]
8. Miyashita T, Oda Y, Horiuchi J, Yin JC, Morimoto T, Saitoe M. Mg(2+) block of Drosophila NMDA receptors is required for long-term memory formation and CREB-dependent gene expression. Neuron. 2012;74:887–898. [PubMed] * demonstrates the requirement of the NMDA Mg2+ for long-term memory.
9. Mothet JP, Le Bail M, Billard JM. Time and space profiling of NMDA receptor co-agonist functions. J Neurochem. 2015;135:210–225. [PubMed]
10. Freeman JH. Cerebellar learning mechanisms. Brain Res. 2015;1621:260–269. [PMC free article] [PubMed]
11. Sarkisov DV, Wang SS. Order-dependent coincidence detection in cerebellar Purkinje neurons at the inositol trisphosphate receptor. J Neurosci. 2008;28:133–142. [PubMed] * identifies IP3 receptor as an order-dependent coincidence detector and describes its role in LTD induction in Purkinje cells.
12. Grossberg S, Schmajuk NA. Neural dynamics of adaptive timing and temporal discrimination during associative learning. Neural Net. 1989;2:79–102.
13. Spruston N. Pyramidal neurons: dendritic structure and synaptic integration. Nat Rev Neurosci. 2008;9:206–221. [PubMed] ** discusses coincidence detection by pyramidal neurons.
14. Hao J, Oertner TG. Depolarization gates spine calcium transients and spike-timing-dependent potentiation. Curr Opin Neurobiol. 2012;22:509–515. [PubMed]
15. Sjostrom PJ, Turrigiano GG, Nelson SB. Neocortical LTD via coincident activation of presynaptic NMDA and cannabinoid receptors. Neuron. 2003;39:641–654. [PubMed] ** reports a novel form of coincidence detection: timing-dependent LTD involving simultanous activation of NMDA and CB1 receptors.
16. Buhusi CV. The across-fiber pattern theory and fuzzy logic: a matter of taste. Physiol Behav. 2000;69:97–106. [PubMed]
17. Vonderschen K, Wagner H. Detecting interaural time differences and remodeling their representation. Trends Neurosci. 2014;37:289–300. [PubMed] * reviews current knowledge about coincidence detection in auditory systems of various species.
18. Gao Z, van Beugen BJ, De Zeeuw CI. Distributed synergistic plasticity and cerebellar learning. Nat Rev Neurosci. 2012;13:619–635. [PubMed]
19. Thurling M, Kahl F, Maderwald S, Stefanescu RM, Schlamann M, Boele HJ, De Zeeuw CI, Diedrichsen J, Ladd ME, Koekkoek SK, et al. Cerebellar cortex and cerebellar nuclei are concomitantly activated during eyeblink conditioning: a 7T fMRI study in humans. J Neurosci. 2015;35:1228–1239. [PubMed]
20. Rahmati N, Owens CB, Bosman LW, Spanke JK, Lindeman S, Gong W, Potters JW, Romano V, Voges K, Moscato L, et al. Cerebellar potentiation and learning a whisker-based object localization task with a time response window. J Neurosci. 2014;34:1949–1962. [PubMed]
21. Albrecht U. Timing to perfection: the biology of central and peripheral circadian clocks. Neuron. 2012;74:246–260. [PubMed] ** reviews current knowledge on the circadian clock system.
22. Coomans CP, Ramkisoensing A, Meijer JH. The suprachiasmatic nuclei as a seasonal clock. Front Neuroendocrinol. 2015;37:29–42. [PubMed]
23. Ramkisoensing A, Meijer JH. Synchronization of biological clock neurons by light and peripheral feedback systems promotes circadian rhythms and health. Front Neurol. 2015;6:128. [PMC free article] [PubMed]
24. Golombek DA, Rosenstein RE. Physiology of circadian entrainment. Physiol Rev. 2010;90:1063–1102. [PubMed]
25. Fuhr L, Abreu M, Pett P, Relogio A. Circadian systems biology: When time matters. Comput Struct Biotechnol J. 2015;13:417–426. [PubMed] ** reviews experimental methodologies, bioinformatics and theoretical models used in exploring circadian timing.
26. Kawato M, Kuroda S, Schweighofer N. Cerebellar supervised learning revisited: biophysical modeling and degrees-of-freedom control. Curr Opin Neurobiol. 2011;21:791–800. [PubMed]
27. Oprisan SA, Buhusi CV. What is all the noise about in interval timing? Philos Trans R Soc Lond B Biol Sci. 2014;369:20120459. [PubMed] ** mathematical proof or the emergence of scalar property in the striatal beat frequency model from neural noise.
28. Matell MS, Meck WH, Nicolelis MA. Interval timing and the encoding of signal duration by ensembles of cortical and striatal neurons. Behavioral Neuroscience. 2003;117:760–773. [PubMed] * dissociates motor coding from timing by striatal neurons.
29. Eichenbaum H. Time cells in the hippocampus: a new dimension for mapping memories. Nat Rev Neurosci. 2014;15:732–744. [PubMed] ** reviews experimental data on hippocampal time cells.
30. Spencer RM, Zelaznik HN, Diedrichsen J, Ivry RB. Disrupted timing of discontinuous but not continuous movements by cerebellar lesions. Science. 2003;300:1437–1439. [PubMed] ** dissociates the role of cerebelllum in discontinuous but not in continuous movements.
31. Matell MS, Meck WH. Cortico-striatal circuits and interval timing: coincidence detection of oscillatory processes. Cog Brain Res. 2004;21:139–170. [PubMed] * describes the biological assumptions of the striatal beat frequency model.
32. Oprisan SA, Dix S, Buhusi CV. Phase resetting and its implications for interval timing with intruders. Behav Processes. 2014 [PubMed]
33. Oprisan SA, Buhusi CV. Modeling pharmacological clock and memory patterns of interval timing in a striatal beat-frequency model with realistic, noisy neurons. Front Integr Neurosci. 2011;5:52. [PMC free article] [PubMed]
34. Gu BM, van Rijn H, Meck WH. Oscillatory multiplexing of neural population codes for interval timing and working memory. Neurosci Biobehav Rev. 2015;48:160–185. [PubMed]
35. Akam T, Kullmann DM. Oscillatory multiplexing of population codes for selective communication in the mammalian brain. Nat Rev Neurosci. 2014;15:111–122. [PMC free article] [PubMed]
36. Buhusi CV, Matthews AR. Effect of distracter preexposure on the reset of an internal clock. Behav Processes. 2014 [PMC free article] [PubMed]
37. Matthews AR, He OH, Buhusi M, Buhusi CV. Dissociation of the role of the prelimbic cortex in interval timing and resource allocation: beneficial effect of norepinephrine and dopamine reuptake inhibitor nomifensine on anxiety-inducing distraction. Front Integr Neurosci. 2012;6:111. [PMC free article] [PubMed]
38. Buhusi CV, Schmajuk NA. Timing in simple conditioning and occasion setting: A neural network approach. Behav Process. 1999;45:33–57. [PubMed] ** to our knowledge, the only timing model of asociative learning capable of addressing both simple conditioning, compound conditioning, and occasion setting with coincidence detection at multiple levels.
39. Gibbon J. Scalar expectancy theory and Weber's law in animal timing. Psychol Rev. 1977;84:279–325.
40. Buhusi CV, Oprisan SA. Time-scale invariance as an emergent property in a perceptron with realistic, noisy neurons. Behav Process. 2013;95:60–70. [PMC free article] [PubMed] * a good introduction to the emergence of scalar property in the striatal beat frequency model.
41. Dragoi V, Staddon JE, Palmer RG, Buhusi CV. Interval timing as an emergent learning property. Psychol Rev. 2003;110:126–144. [PubMed] ** to our knowledge, the first timing model in which scalar property emerges from noise / variability.
42. Killeen PR, Taylor TJ. A stochastic adding machine and complex dynamics. Nonlinearity. 2000;13:1889–1903. [PubMed] * mathematical proof of the emergence of a fractal from a stochastic Markov chain.
43. Oprisan SA, Buhusi CV. How noise contributes to time-scale invariance of interval timing. Phys Rev E Stat Nonlin Soft Matter Phys. 2013;87:052717. [PubMed]
44. Oprisan SA, Buhusi CV. Why noise is useful in functional and neural mechanisms of interval timing? BMC Neurosci. 2013;14:84. [PMC free article] [PubMed]
45. Tucci V, Buhusi CV, Gallistel R, Meck WH. Towards an integrated understanding of the biology of timing. Philos Trans R Soc Lond B Biol Sci. 2014;369:20120470. [PMC free article] [PubMed]
46. Merchant H, Harrington DL, Meck WH. Neural basis of the perception and estimation of time. Annu Rev Neurosci. 2013;36:313–336. [PubMed]
47. Allman MJ, Teki S, Griffiths TD, Meck WH. Properties of the internal clock: first- and second-order principles of subjective time. Annu Rev Psychol. 2014;65:743–771. [PubMed]