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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.
How does one time boiling eggs? One could use a kitchen clock – precise , count – less precise **, or do something that takes about the right amount of time – much less precise . 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 **. 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.
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 ) or the IP3 receptor , 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 . Similarly, Purkinje cell LTD, a process underlying cerebellar learning , 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 **. 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 ).
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 . 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 . 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 **. 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 ).
The prototypical CD circuit is involved in sound localization based on interaural time differences (Fig 2A). Though important differences have been reported across species *, 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  is based on IP3 acting as a coincidence detector of activity in parallel fibers and climbing fibers **. 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 [18–20].
The circadian timing system is virtually composed of as many clocks as there are cells in the body. At the cellular level (Fig 2B **), 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  (Fig 2B). At the systems level, the multitude of cellular clocks are synchronized through electrical and endocrine pathways ; 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 [23–25]**.
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 [28–30]. 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 , to address pharmacological treatments , 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 .
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 . Most models add specific assumptions to deal with scalar property, as the classic scalar expectancy model does , 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 [2,27,40–42]**.
Rather than counting pulses with a stopwatch , 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 . 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.
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 [45–47].
This work was supported by NIH grant MH073057 to CVB, NSF-CAREER award 1054914 to SAO, and NIH grant NS090283 to MB.
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