Temporal Order Detection and Coding in ... - MIT Press Journals

LETTER

Communicated by Danko Nikolic

Temporal Order Detection and Coding in Nervous Systems Klaus M. Stiefel [email protected]

Jonathan Tapson [email protected]

Andr´e van Schaik [email protected] University of Western Sydney, MARCS Institute, Bioelectronics and Neuroscience Penrith, NSW 2751, Australia

This letter discusses temporal order coding and detection in nervous systems. Detection of temporal order in the external world is an adaptive function of nervous systems. In addition, coding based on the temporal order of signals can be used as an internal code. Such temporal order coding is a subset of temporal coding. We discuss two examples of processing the temporal order of external events: the auditory location detection system in birds and the visual direction detection system in flies. We then discuss how somatosensory stimulus intensities are translated into a temporal order code in the human peripheral nervous system. We next turn our attention to input order coding in the mammalian cortex. We review work demonstrating the capabilities of cortical neurons for detecting input order. We then discuss research refuting and demonstrating the representation of stimulus features in the cortex by means of input order. After some general theoretical considerations on input order detection and coding, we conclude by discussing the existing and potential use of input order coding in neuromorphic engineering. 1 Introduction Events in the external physical world occur in a temporal order, and hence the signals these events emit arrive at an animal’s sense organ in a temporal order. Detection of the temporal order of such events will thus convey a significant adaptive advantage. Animals have evolved sophisticated mechanisms for temporal order detection. Furthermore, the temporal order of neural signals (spikes) is a potential candidate for the internal code of neural signaling. The order of spikes in different neurons could represent a wider range of variables unrelated to the temporal order of external events. Spikes from one input arriving before those from another could signify a value related to network computation (such as the deviation from a desired firing rate) or the presence or absence Neural Computation 25, 510–531 (2013)

c 2013 Massachusetts Institute of Technology 

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of a threat, reward, or noxious stimulus. They could also represent a property of the external world not akin to temporal order. In all of these cases, mechanisms already evolved for processing temporal order in the external world could have been adapted for use in processing an internal temporal order code. In this letter, we first discuss several neural mechanisms for temporal order detection in the sensory systems of animals. These mechanisms are from the auditory location detection system in birds and the visual direction of motion detection system in flies. We then discuss several experimentally demonstrated temporal order detection mechanisms in mammalian cortical neurons that have not yet been connected to any behavioral phenomena. These include mechanisms involving synaptic plasticity, notably spike-time-dependent plasticity. Next, we discuss experimental support for the existence of such a code in the mammalian cortex. Given this context, we revisit theoretical work on temporal order and detection and elaborate on possible advantages and disadvantages of an internal temporal order code. We conclude with some thoughts on the existing and potential use of temporal order coding in neuromorphic engineering. Temporal order coding is a subset of temporal coding. In its purest form, the only thing that represents information is which spike occurs before the other. This will always be limited to a certain time window, since the biophysical processes involved have limiting upper and lower time constants. Spikes too temporally distant from each other simply will not have an overlapping influence on the states of the nervous system. Furthermore, coding and detection of temporal order can be broadly or finely tuned to a specific time difference between the first and the following spike. In broadly tuned temporal order coding, only the order of inputs is relevant. In the case of fine tuning, the exact timing difference between the spikes represents information just as their temporal order does, and the difference between input order coding and general temporal coding is a gradual one. In this letter, we use the terms temporal order coding and detection in a wider sense. We refer to it as coding schemes and readout mechanisms that depend, though not necessary exclusively, on the temporal order of spikes. The classic concept for comparing the timing of two neural signals is the Reichardt detector, first proposed by Werner E. Reichardt (1961). In such a Reichardt detector, two photoreceptors receive signals from a moving stimulus passing from one side to the other (see Figure 1A). The photoreceptors are hence activated in a temporal order as determined by the direction of the moving stimulus and with an interval determined by the speed of the stimulus. The two signals then pass through two different delay lines before converging at a multiplicative unit. Only when the delays offset the temporal interval of the photoreceptor activation will the inputs converge at the multiplicative unit coincidentally, and hence activate it maximally. The photoreceptors can be generalized as any sensory receptor, the delay lines can be generalized as a low-pass filter, and the multiplicative unit

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Figure 1: Input order detection in sensory systems. (A) The principle of the Reichardt-detector. Signals from two receptors converge at a nonlinear unit— one directly, the other after passing trough a delay or low-pass filter. The shadings code for these three elements is maintained in the other panels. (B) Barn owl auditory location system (adapted from Carr & Konishi, 1988). Axons act as delay lines. The spiking dynamics of the postsynaptic nucleus laminaris neurons (not shown in the anatomical reconstruction) acts as a nonlinearity. (C) Fly visual motion detection system (adapted from Higgins et al., 2004). This motion detection system contains two sets of delay lines: the amacrine-T1 neuron path and the downstream Tm1-Tm9 neuron path. The shunting inhibition acting on the T5 cells comprises the nonlinearity.

can be conceptualized as any type of nonlinearity. Real neurons can act explicitly as multiplicative coincidence detectors, as proposed by Reichardt (Srinivasan & Bernard, 1976). Equally, there are many ways of biologically implementing low-pass filters and nonlinearities. The Reichardt detector is hence a general concept for temporal order detection, albeit not a meaninglessly general one (Haag, Denk, & Borst, 2004). Here, we first look at the implementation of temporal order detection in more detail in two wellstudied systems: the avian auditory localization system and the fly motion detection system. 2 Avian Auditory Location Detection Barn owls (Tyto alba) are nocturnal predators that rely on their audition to capture prey. For this purpose, they have developed sophisticated neural circuitry to detect the location of a sound source. The sound waves emitted from the prey animal arrive at the two ears of the owl with a time difference corresponding to the lateral offset of the prey’s position. Sound from a

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mouse located to the right of the bird will first reach the right ear and activate the cochlea of that ear. In this way, the temporal order of neural activation represents the relative position of the prey animal (Carr & Konishi, 1988, 1990). This temporal order of neural activation is maintained during the first stages of auditory processing, the nucleus cochlearis and the nucleus magnocellularis. Temporal order detection, and hence detection of the soundemitting object, is then performed in the neurons of the nucleus laminaris (see Figure 1B). In this nucleus, axonal delay lines coming from the nucleus magnocellularis are calibrated so that their conduction delays compensate for the temporal offset caused by the spatial displacement of the sound source. While in the chicken, a less specialized bird, only the contralateral axons act as delay lines, in the owl both the ipsi- and contralateral axons act as such (Carr & Friedman, 1999). The individual nucleus laminaris neurons are activated most effectively by coincident activation of inputs from both ears. When the axonal delays equal the difference in auditory signal arrival times, such coincident activation takes place, and the neurons are firing output spikes. For each range of auditory signal arrival time differences, and hence lateral sound displacements, a set of axonal delay lines compensates. Hence, the nucleus laminaris contains an array of neurons responsive to sound locations represented as auditory signal arrival time differences in their inputs. This arrangement of axons creates an array of neurons, each specialized for a specific frequency band and a specific interaural time (phase) difference. Such a mechanism was first proposed by Jeffress (1948), as has since been elucidated in a variety of experimental studies. The relevant time differences in this system are small, ranging from 0 μs (coincidence) to 200 μs. Hence, the readout process is improved by several cellular specializations. First, the inputs from the two different ears arrive on two different dendrites. This provides a useful separation of the inputs, which leads to their electrotonic isolation. In this way, the summation of signals from the two different sources is improved, and the domination of the signal by the stronger dendrite is prevented. This mechanism is expressed in a more pronounced fashion in the auditorily unspecialized chicken than in the owl, and more so in low-frequency-responsive neurons (Carr, Iyer, Soares, Kalluri, & Simon, 2005). Second, dendritic potassium conductances sharpen the waveform of the postsynaptic potentials, leading to improved temporal precision (Oertel, 1999; Trussell, 1999). Third, the synapses in the nucleus laminaris (Carr & Friedman, 1999) are enlarged and therefore have increased reliability and precision of synaptic transmission. These larger subcellular structures have large numbers of ion channel proteins and neurotransmitter vesicles, which will even out the stochastic nature of the channel opening and transmitter release. As a consequence of these cellular specializations, only near-coincident inputs originating from both ears will cause the nucleus laminaris neurons

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to fire. As a consequence of the axonal delay lines delivering this input to the nucleus laminaris, only inputs with a very specific temporal order and delay will arrive coincidentally (see Grau-Serrat, Carr, & Simon, 2003, for a simulation study of this system). In summary, the direction of the sound source is initially represented as a temporal order. The precise amount of lateral displacement is represented by the temporal delay between the signals originating from the two ears. This temporal order code is preserved in the first stages of auditory processing, then read out by an array of coincidence detectors receiving input from finely tuned delay lines. From then on, position information is encoded as a place code or labeled-line activity level. Hence, in the avian auditory system, we are looking at a neural system where input order coding and detection play a significant role at an early stage. 3 Fly Visual Motion Detection Another well-studied system in which temporal order is used to represent properties of the real world at one stage is the blowfly (Phaenicia sericata) visual direction of motion detection system. This system processes visual information initially received in the omatidial eyes of the fly. An ecologically highly relevant environmental feature for a flying organism is the direction of the visual flow. The task of determining the visual flow is equivalent to detecting the temporal order of visual activation of spatially offset photoreceptors. When a stimulus is moving across the visual field of the fly, the photoreceptors in the surround are activated before those in the center. This is what the fly motion detection system exploits. The neurons in the initial part of the fly visual system—the retina, lamina, medulla, and outer lobula—carry out this computation. The temporal delays between photoreceptor activation at realistic motion velocities will be larger than the interaural delays processed by the owl brain. Axonal delay lines would need to be much longer to compute these delays. Additionally, the fly brain is orders of magnitude smaller than the owl brain. Hence, axonal delay lines are not an option for offsetting delays. In fact, all the neurons involved in this computation are nonspiking. In the fly, evolution has produced an analog version of the Reichhardt detector (see Figure 1C). Initially, light activates the photoreceptors in the retina, which are organized in groups of seven (visual sampling units) in the fly. They form histaminergic synaptic connections with L2 transmedullary neurons and amacrine cells in the lamina. Amacrine cells form engulfing α processes around several photoreceptors, and amacrine-to-amacrine crosstalk widens their receptive fields. In contrast, L2 neurons sample only locally from photoreceptors directly above. In the next downstream stage, the medula and amacrine cells make glutamatergic synaptic connections onto T1 neurons. These T1 neurons

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in turn make glutamatergic synaptic connections (involving the NMDA receptor) to a neuron termed Tm1. The L2 cells also make glutamatergic synapses onto Tm1. Thus, at Tm1, the amacrine-T1 and the L2 pathways converge. The visual input arrives directly via the L2 neuron, but delayed by an extra synapse and by cellular low-pass filter properties via the amacrine and T1 neurons. Hence, we have the convergence of signals from different areas (small center–large surround) with different delays—the classic first stage of a Reichardt detector. The second stage of a Reichardt detector is the nonlinear interaction of converging inputs. In the fly motion detection system, this is implemented by dual projections from the Tm1 neuron to the next downstream stage, the outer lobula. The lobular neurons receiving input from the Tm1 cells are the T5 neurons. Tm1 neurons project directly to the T5 neurons below them via cholinergic synapses. They also project to laterally offset T5 neurons via the Tm9 GABAergic inhibitory neuron. For computing visual motion, this serves two purposes. First, the mainly shunting GABAergic inhibition constitutes a nonlinear interaction, as is necessary for the second stage of the Reichardt detector. Second, the low-pass filtering intrinsic to the Tm9 cell and the added synaptic relay cause a second convergence of signals with different delays—a duplicate first Reichardt detector stage. In contrast to the first delay line (amacrine—Tm1 neurons), this one introduces orientation selectivity, since it compares adjacent visual areas, not center and surround. The GABAergic inhibitory IIIN further sharpens the direction selectivity by providing lateral inhibition between adjacent T5 neurons. (See Sinakevitch & Strausfeld, 2004, and Higgins, Douglass, & Strausfeld, 2004, for a detailed description and numerical model of this neural circuit.) The output of this neural circuit, via the T5 cells, constitutes the input in the well-studied lobula plate wide-field motion integration system, which computes the global motion direction from the local motion information supplied by T5 cells (Single & Borst, 1998; Borst & Haag, 2002). In conclusion, in the fly visual system, we have another example of temporal order coding. Temporal order of the inputs to the T5 neurons represents visual motion direction, and the length of the time interval between the input spikes represents the speed of the visual flow. The circuit decoding this information is significantly different from the owl auditory localization system—analog instead of digital and using cellular filter properties instead of axonal delays. 4 Temporal Order Coding in the Human Somatosensory Periphery In the examples already noted, the temporal order of neural activation represents the temporal order of events in the external world (sound or light arriving at spatially offset receptors). In the human peripheral nervous system, the temporal order of spikes codes for a quantity unrelated to the order of external events. Johansson and Birznieks (2004) and Birznieks et al.

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(2010) found that the response of afferents projecting from touch receptors in the fingertips carried significant information in the relative timing of the first spike. In both awake humans and anesthetized monkeys, the relative first spike timing was superior, compared to a rate code, as a predictor of stimulus quantities such as the force direction, shape, or torque. These studies did not directly show that a spike-time order code is used more centrally to decode this information, but based on the fast processing times known from the somatosensory system, a utilization of fast neural codes is likely. 5 Temporal Order Detection in Mammalian Cortical Neurons The owl auditory system and fly visual system examples use temporal order as a representation for a quality of the external world, relative sound source location, and optic flow direction. The primate peripheral somatosensory system represents stimulus properties as spike temporal order and possibly uses this information farther downstream. To a large degree, we understand the behavioral meaning of the neural signals in these systems, as well as their internal representation and their processing. Our understanding has not reached that depth for a number of central circuits and cell types capable of temporal order detection. Work in in vitro neurophysiology has demonstrated the capability of neurons of the mammalian cerebral cortex to act as temporal order detectors. These studies show that cortical neurons can detect the temporal order of signals; however, it is not clear if they actually perform temporal order detection in vivo. There is considerable uncertainty as to what information is precisely contained in their inputs. While we understand that the neural activity in the somatosensory cortex increases with touch to the body surface of the animal, we do not exactly comprehend what each of the several thousands of synapses that impinge on the cortical neuron conveys. The reason is that only some synapses transmit feedforward signals from the thalamus; a large number of synapses also convey lateral excitation or inhibition from the same or different cortical regions, and fast or neuromodulatory signals from extracortical areas. This diversity and multiplicity of different inputs to cortical neurons cause difficulties in understanding exactly what neural signals represent in more central systems. In contrast, the systems discussed above are closer to the sensory receptors, and we have a better understanding what their inputs represent and what input patterns they receive. Despite these uncertainties, cortical neurons have been shown to have astonishing capabilities for reacting to the temporal order of incoming signals, and we have to consider these capabilities potentially relevant. We now review some of these capabilities. A study that showed the capability of the dendrites of cortical layer V pyramidal neurons to detect the temporal order of inputs was conducted by Larkum, Zhu, and Sakmann (1999). By establishing multiple patch clamp

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recordings from the dendrites and soma of the same neuron, the authors could record the electrical activity in several locations of the neuron. An axosomatic Na+ -current-based action potential propagated back into the distal apical dendrites. Paired with an EPSP-shaped depolarization to the dendrites, this backpropagating action potential evoked a dendritic Ca2+ spike, which then propagated to the axosomatic compartment, where it evoked more Na+ -action potentials. A time interval of 5 ms between the somatic and dendritic current injections was optimal for evoking this dendritic regenerative event. At a time interval of about 20 ms, the backpropagating action potential was no more effective in evoking dendritic Ca2+ spikes than dendritic current pulses alone. Here we have a case of temporal order detection at the level of a large (several 100 μm) dendritic tree, implemented by the interaction of dendritic morphology and electrogenesis. Another cellular mechanism, capable of reacting to the temporal order ¨ of spikes, is spike-time-dependent plasticity (Markram, Lubke, Frotscher, & Sakmann, 1997; Bi & Poo, 1998). In spiketime-dependent plasticity, the order of neural activation determines the polarity of synaptic plasticity. A spike of the presynaptic neuron, followed by a spike of the postsynaptic neuron, will lead to a strengthening of the synapse, and the inverse temporal order will lead to a weakening of the synapse. The action potentials need to follow each other in a time window encompassing tens of milliseconds for the induction of such spike-time-dependent plasticity. The expression of this type of plasticity can last for hours (the duration of in vitro experiments) and presumably even longer. A recent study that demonstrated temporal order detection by cortical neurons was carried out by Branco, Clark, and H¨ausser (2010; see Figure 2). By using laser-guided uncaging of glutamate, they could stimulate postsynaptic glutamate receptors with high temporal and spatial precision, stimulating dendrites in a temporal and spatial sequence along a stretch of dendrite. Progressing in time along the dendrite from the distal section to the soma, depolarization was maximal. Reversing the spatial order—going from the soma-proximal to the distal stimulation sites—also reversed the temporal order of stimulation and led to a minimal voltage response. This mechanism therefore occurs at the scale of a single dendritic branch (several 10 μm). It involves impedance mismatch and is NMDA receptor dependent. In the case of spike-time-dependent plasticity, the comparison is not between different input spike times but between an input and an output spike. The output spike can be caused partially by the input spike, and this possible causal connection has contributed much to the popularity of spike-time-dependent plasticity among brain theorists. However, the small amplitude of synaptic potentials in the cortex (typically a fraction of the distance from threshold) means that a single synaptic potential is rarely enough to cause an output spike. Spike-time-dependent plasticity can equally be understood as a temporal order detection mechanism. What

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Figure 2: Temporal order sensitive physiological mechanisms in mammalian cortical neurons. (A) Temporal order sensitive interaction of backpropagating action potentials and distal dendritic inputs in cortical layer V pyramidal neurons (from Larkum et al., 1999). Top: Action potential and distal input offset by 3, 7, and 11 ms. Note the dendritic Ca2+ spike and subsequently evoked additional somatic action potentials seen only at t = 7 ms. Bottom: Recording configuration and relationship between t somatic-dendritic current injection and Ca2+ spike threshold. Peak synergy occurs when the somatic current injection precedes the five dendritic injections by ms. Note the temporally asymmetric shape of this curve. (B) Temporal and spatial order selectivity of dendritic branches (from Branco et al., 2010). Top: II/III pyramidal neuron dendrite, with the glutamate uncaging sites indicated. Center: Schematic representation of the two stimulation protocols. Bottom: Resultant depolarization in response to the stimulation in the outward and inward directions.

distinguishes it from the mechanisms discussed above is that it connects the tens of millisecond timescales of its induction (10−2 s) with the longer timescales of its expression over many hours (>104 s). Any mechanism bridging six orders of temporal magnitude will inevitably contribute to the complexity of a system. 6 Internal Temporal Order Codes in the Mammalian Cortex We have now established that temporal order codes are used in some sensory systems and that cortical neurons have cellular mechanisms that intrinsically give them the capability of distinguishing the temporal order of

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spikes. So is the mammalian central nervous system using temporal order coding? In particular, is this type of code used in the mammalian cortex? This question is conflated with the general discussion about temporal coding in the cortex (pro: Singer, 1999; contra: Shadlen & Newsome, 1994), but there are some interesting points more specific to temporal order coding. Experimental studies have both confirmed and rejected the idea of temporal order coding in the cortex. In a study by Rolls, Franco, Aggelopoulos, and Jerez (2006) of the macaque (Macaca mulatta) inferior temporal visual cortex, the authors found no indication of temporal order coding. During a task involving visual fixation followed by the perception of a series of natural and geometrical images, they recorded from two to nine neurons simultaneously. As compared to the number of spikes in a brief (20 ms) window, they found no excess information in either the timing of the first spikes or their order of arrival. In contrast, Fries, Reynolds, Rorie, and Desimone (2001) found that the jitters to the first spike in neurons of the primary visual cortex of the anesthetized cat (Felix lybica) and the awake macaque monkey in response to a visual stimulus are highly correlated. The temporal order of arrival times was highly conserved. This correlation was higher during episodes of gamma band (40–70 Hz) oscillatory activity. The correlation was also more pronounced between pairs of neurons with overlapping visual receptive fields or shared orientation preferences, suggesting a functional role. Interestingly, Havenith and colleagues (2011; see Figure 3) found that relative spike delays in the cat visual cortex are reproducible and transitive. The relative delay between spikes from different neurons was typically less than 10 ms and clustered at the peak of the gamma cycle. The order of spiking and the amount of delay was very similar from trial to trial and stable over several hours. In addition, the delays added in a transitive manner. In an example, when neuron A was spiking 3.73 ms ahead of neuron B and neuron B 1.74 ms ahead of neuron C, the A-to-C delay was 5.65 ms, only 0.18 ms different from the sum of the component delays (0.25 ms average discrepancy). This would be a trivial statement if every cell was spiking in every trial, but since this is not the case, this is an impressive demonstration of submillisecond precision in the cortex. This ordering of inputs also generalized to groups larger than pairs or triplets and allowed the compilation of systematic temporal order graphs. This temporal arrangement of spikes was conserved within one stimulus condition, and when the stimulus (a moving grating) was altered, the temporal order arrangement also changed to a new, stable set. This precise and stimulusdependent arrangement spike temporal order suggests a role for spike order in coding. We can also consider the timing of a spike relative not to another single spike but to the network oscillation. The gamma band oscillations in the

Figure 3: Experimental testing of temporal order coding in the mammalian cortex. (A) Temporal order relationships between multiple neurons responding to one stimulus in the cat visual cortex in vivo (from Havenith et al., 2011). The arrows and associated quantities denote the temporal relationships and time delays between pairs of neurons. The cross-correlatiograms for some pairs are shown. (B) Translativity of the measured delays. (C) Relationship between stimulus orientation, neuronal firing rate, and firing time relative to the gamma phase in the monkey visual cortex in vivo (from Vinck et al., 2010).

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cortex are caused by an inhibitory interneuron network (Buhl, Tam´as, & Fisahn, 1998), which imposes its rhythm on the pyramidal neurons. A temporal relationship of a spike to the phase of the gamma oscillations is hence equivalent to a relationship to the average spiking of the interneuronal population. Vinck et al. (2010) showed that spikes in the monkey primary visual cortex occur at a delay relative to the gamma cycle conserved on a trial-to-trial basis. This delay was also dependent on the orientation of the visual stimulus used to evoke the neural response. Again, both the precision and the representative nature of the temporal order suggest a functional role. The work on relative spike timing in gamma band oscillations is in line with that by O’Keefe and colleagues in the hippocampus. In this brain structure, theta oscillations (5–12 Hz) occur due to a combination of external oscillatory forcing and intrinsic resonance. The source of the forcing is found in the enthorhinal cortex, the dorsal raphe, nucleus reticularis pontis oralis, and the supramammillary region (Leranth, Carpi, Buzsaki, & Kiss, 1999; Buzs´aki, 2002). In rodents, the hippocampus encodes the spatial location the animal is currently in by the activity of the place cells, each active in a specific place field. The spiking activity of these neurons is locked to the hippocampal rhythm in an interesting way: the phase at which a spike appears codes for the location of the animal in a place field (O’Keefe & Recce, 1993; O’Keefe & Burgess, 1996). This arrangement has interesting consequences; for instance, the relative spike timing of two place cells encodes the beginning and end of the rat’s journeys (Shapiro & Ferbinteanu, 2006). What can explain the discrepancy between the studies supporting and rejecting temporal order coding? We believe that the difference lies in the different species and brain regions investigated, as well as in the sensory paradigm and data analysis method used. It is imprecise to speak of coding in “the cortex”; the macaque inferior temporal visual cortex is a structure with a different structure, function, and input from the cat primary visual cortex. Based on these studies, we can speculate that cortical regions closer to the primary sensory input could employ a coding scheme more optimized for temporal coding, and hence employ temporal order coding. Alternatively, or in addition, the fact that these studies challenged the animals with different tasks could be of importance. Finally, the difference in the level of gamma oscillations during the recordings could influence the importance of temporal order coding (Havenith et al., 2011). With the proposed role of gamma oscillations as a carrier frequency for a temporal code, increased gamma power should lead to an increase in the role of temporal, and input-order, coding. A number of factors could influence the amount of gamma power present during an experiment, among them the experimental animal, cortical region, anesthesia, task, presented sensory input, and amount of attention required versus overlearning by the experimental animal.

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Figure 4: Morphological features of neurons optimized for input-order detection. Best-performing neurons from four optimization runs for six different t. Shown (columns from left to right) are passive neurons and neurons containing IKA , ICaT , and IKA and ICaT . The blue and red circles represent the left and right synapses. Conductance densities are coded by shade (IKA , left, 0–0.22 pS mm2 , ICaT , right, 0–0.0022 pS mm2 ). (From Torben-Nielsen & Stiefel, 2009.)

7 Theoretical Considerations Regarding Temporal Order Detection and Coding With the wealth of empirical information we have described, two main questions present themselves for the brain theoretician: What kind of neural temporal order detectors are possible in principle and which of these are implemented in nature, and For which purposes can temporal order coding be used by the nervous system. We have recently used a computational method to find multicompartmental models of neurons optimized for input-order detection (Stiefel & Sejnowski, 2007; Torben-Nielsen & Stiefel, 2009, 2010). The idea of this approach is to compare these artificial model neurons optimized for functions to gain insight into the role of real neurons with functions that so far are unknown. By using a genetic algorithm, we obtained multicompartmental models that functioned as high-performing input-order detectors. A placement on a semianalytically determined fitness landscape for input-order detection showed that the models were at least close to truly optimal. The morphology of these model neurons was conserved, with one or more thin dendrites carrying the synapses activated first and a thick dendrite carrying the synapses activated second in the preferred order (see Figure 4). As a result of this arrangement, the synaptic potential activated first is strongly filtered, and its peak is delayed. The following synaptic

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potential then rises from the delayed peak of the first synaptic potential, leading to optimal summation. When the synaptic potentials are evoked in the inverse, nonpreferred order, the geometry of the synaptic potentials leads to minimal summation. Hence we have a single cell version of the Reichardt detector where thin (electrotonically long) dendrites act as delay lines. We also found stereotypical distributions of ionic conductances in the optimized input-order detector model neurons. The hyperpolarizing A-type K+ conductance was present in spatially increasing gradients only on the thick dendrites. The depolarizing T-type Ca2+ conductance was present mostly on the thin dendrites, concentrated around the sites of synaptic contact. This mirrors the distributions found in many types of real neurons (Migliore & Shepherd, 2002). One possibility is that these neurons are tuned for temporal coding or, more specifically, temporal order coding, just as our model neurons optimized for this task. While we cannot exclude that this arrangement of conductances (in concert with additional conductances) evolved for different or additional reasons, the convergence is nevertheless striking. The optimized model neurons we obtained were using dendrites as input-order detectors, and they operate on the 10−2 to 10−3 s (10s of ms to ms) scale. As we have seen, input-order detectors based on axonal delays operate on the faster 10−4 s (100 us) scale. Even faster input-order detectors would have to use ion channel protein conformational dynamics, while slower inputorder detectors would have to take advantage of biochemical cascades. We predict that the nervous system will use the appropriate mechanism, or combinations thereof, to match the specific needs of different computations. Another question brain theoreticians have addressed is if and how temporal order coding can be used by the brain. What would the advantages and disadvantages of temporal order coding be? In the literature, different theoreticians have investigated different variants and possible roles of temporal order coding. Thorpe and Gautrais (1997) and Van Rullen and Thorpe (2001) argue that neurons should be reinterpreted as analog-to-delay converters, not as analog-to-digital converters. They show in simulations of a simplified model of the visual system that this gives rise to a fast and efficient coding scheme. Delorme (2003) proposes a similar coding scheme to account for orientation selectivity and gain control in the visual cortex. In his model, he places a significant importance on feedforward inhibition, which reduces the response to later spikes. In a modeling study, Delorme and Thorpe (2001) used temporal order coding in a cortical network model to decode faces. A significant result they achieve is a resistance of the code against image noise. Taking all this work into consideration, we see that in contrast to rate coding, the advantages of temporal order coding are clear and similar to those of temporal coding in general: more information can be represented

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in the same time span. A more subtle question is what the possible advantages of temporal order coding are over other forms of temporal coding. As we have seen, processing speed and coding efficiency have been proposed. Increased robustness is also a possible advantage: the temporal order of spikes will be conserved in the face of small jitter in the times of individual spikes. In fact, the sensitivity to jitter is asymmetric. A spike-time change will strongly increase the coding error when it moves the spike across 0 and, hence, reverses the temporal order of spikes. In contrast, spike-time jitter preserving the temporal order of spikes will change the error signal only mildly (see Figure 5A). In this sense, input order detection is a hybrid code: very time sensitive when crossing the t = 0 mark but less so (see the shallow slope in Figure 5A) when the spike-time order is preserved. Two situations come to mind in which such a coding scheme could be advantageous: (1) the high-background-activity state of neurons in the wakeful cortex and (2) the functioning of the brains of poikilothermic animals at different temperatures. It is well established that neurons in the mammalian cortex during active wakefulness are exposed to high-rate, synchronized background activity (see Figure 5B; Steriade et al., 2001; Destexhe, Rudolph, & Par´e, 2003). This background activity leads to large-amplitude voltage fluctuations (σ > 2 mV) and a roughly 20-fold increase in input conductance. The functional role of these fluctuations is not completely understood yet, and stochastic resonance and providing a contextual input have been suggested (Rudolph & Destexhe, 2001). These fluctuations represent either a contextual signal or noise, with only their statistical distributions mattering. In any case, they will introduce a significant spike-time jitter that will be different for successive perceptual acts. A neural code based on precise coincidences would possibly degrade in the presence of such fluctuations, while a temporal code based on input order would be more robust. A second situation in which a temporal order code could be beneficial is in the brains of poikilothermic animals. These are the majority of animals other than birds and mammals that do not maintain a constant body (and brain) temperature. Under such circumstances, the neuronal ion channel kinetics vary, depending on the current temperature. These kinetics approximately double in speed when the temperature increases by 10◦ C; however, the exact change (called the q10 ) varies among channels (Hille, 2001). As a consequence, with changing temperature, a neuron’s spike threshold, firing frequency, and adaptation also change. Spikes that were emitted coincidentally at one temperature will be temporally offset at a different temperature, and a neural code based on strict coincidences might fail at this point. In contrast, a neural code based on input order detection could be robust in the face of temperature-induced excitability changes. Experimentally, rhythms with a spike order preserved at different temperatures have been observed in the stomatogastric ganglion of Cancer borealis (see Figure 5C; Tang et al., 2010).

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Figure 5: (A) Schematic plot showing the error = (1-firing probability) in temporal order detectors and coincidence detectors as a function of t between spikes. Note that the error for the temporal order detector is temporally asymmetric, with strict timing dependence only when the order of spikes is reversed. (B) Intracellular membrane potential recording from a pyramidal neuron of an awake cat showing high spontaneous activity. (From Steriade, Timofeev, & Grenier, 2001.) (B) Lobster stomatogastric ganglion neurons firing at different temperatures. Note that while the firing speeds up at higher temperatures, the relative spike times remain conserved (from Tang et al., 2010).

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We believe that further study of the specific advantages and downsides of different forms of temporal coding will be a major challenge in computational neuroscience in the near future. But even with our current understanding, temporal order coding seems to be a computationally attractive and biologically realistic coding scheme. 8 Temporal Order Coding in Neuromorphic Engineering We have seen that temporal order coding is used in the nervous systems of animals, and theoretical work has indicated useful properties of this coding scheme. It is therefore obvious that brain-inspired engineering (neuromorphic engineering) would take advantage of temporal order coding. Indeed, in neuromorphic engineering, one of the first recognized advantages of spike-based computation was the ease with which spike coincidences could be detected. This was quickly followed by the realization that if two spike trains are highly correlated but not coincident (e.g., two identical spike trains with one delayed by a fixed amount from the other), the introduction of an appropriate delay to one of the two spike trains would again lead to easily detected coincidences. Thus, the neural systems in which temporal order coding was first hypothesized—sound localization in the barn owl and visual motion detection in the fly—were also among the first to be implemented by neuromorphic engineers as integrated circuits. Neuromorphic engineering was started as a research field by Mead (1989) after the realization that there were clear similarities between transistors in integrated circuits and ion channels in neurons. The first electronic implementations in the field were a silicon neuron, a silicon retina, and a silicon cochlea. Lazzaro and Mead (1989a) used a pair of silicon cochleae with copies of the neuron circuit to generate spikes as the output of both cochleae. The addition of delay lines and coincidence detectors within each cochlear frequency band completed an electronic model of sound localization in the barn owl. Lazzaro and Mead (1989b) also used this architecture to implement Licklider’s model of pitch perception (Licklider, 1951). By comparing the current output spikes from the silicon cochlea with the past output spikes of that cochlea, traveling along hypothesized axonal delay lines, correlations between the spikes will be found for a periodic signal, at a delay that is inversely proportional to the period of the signal, as well as at integer multiples of that delay. In 1989, Licklider’s model was still considered a physiological model of pitch perception in humans, but no evidence has been found for the hypothesized axonal delay lines in physiological experiments of pitch perception. A variant of Licklider’s model without axonal delay lines (van Schaik, 2001) uses the fact that sound pressure waves cause the basilar membrane in the cochlea to display a traveling wave along its length. The same is true in the silicon cochlea. In such a traveling wave, the phase delay of a periodic signal increases from base to apex. Different sections of the cochlea

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respond best to different frequency ranges, but it can be shown that for a given frequency, a phase delay of 2π (i.e., a full period) can be obtained between two sections along the cochlea that both respond strongly to that frequency. Thus, by requiring coincident spiking activity between these two sections of the cochlea, only frequencies for which the phase delay is very close to 2π will be detected. While again no physiological evidence for this model has been found, van Schaik notes that this system offers a distinct engineering advantage over standard electronic filters. In filter theory, it is well known that one cannot increase frequency resolution by making a filter more selective without reducing the temporal resolution of that filter proportionally. However, when detecting coincident spikes a single period apart, the system will always respond after a delay of one period, but the system can be made arbitrarily selective by generating spikes only at a single phase in the waveform, such as at a zero crossing of the signal, and by narrowing the time window over which spikes are considered coincident. This architecture therefore can respond to a periodic signal quickly while at the same time being exquisitely selective in frequency. The axonal delay line architecture of Lazzaro and Mead (1989a) was also adapted for use with a 1D retina for visual motion detection by Horiuchi, Lazzaro, Moore, and Koch (1991). While a change in sensor, from cochlea to retina, is straightforward, and both implementations displayed decent performance, to our knowledge, a visual system using the same strategy as the barn owl sound localization system for motion detection does not exist in nature. An attempt at a silicon implementation of the Reichardt motion detector was first reported by Andreou, Strohbehn, and Jenkins (1991) for a 1D system, and the first functional 2D version was reported by Delbruck (1993). These early publications on the electronic implementation of Reichardt detectors were the inspiration for one of us (A.vS) to design a motion-detecting retina in a clocked system, where spatial derivatives of the intensity at one pixel are compared with the spatial derivatives of the neighboring pixels at the previous time step. This implementation became the first commercially successful neuromorphic engineering application (Arreguit, van Schaik, Bauduin, Bidiville, & Raeber, 1996), in an optical trackball. The early electronic Reichardt detectors were followed by several variants of this approach to motion (e.g., Etienne-Cummings, Van der Spiegel, & Mueller, 1997; Kramer, Sarpeshkar, & Koch, 1997; Higgins et al., 1999). The neuromorphic implementation of the EMD was eventually perfected in Harrison and Koch (2000). 9 Conclusion We have seen that nervous systems have evolved sophisticated mechanisms for detecting the temporal order of events at a very short (< ms) timescale. The role of these mechanisms in several sensory neural circuits is well understood. In cortical neurons, a number of temporal order sensitive cellular

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mechanisms have been demonstrated. These include order-sensitive electrophysiological and synaptic plasticity-related mechanisms. The cells and circuits in the mammalian cerebral cortex did not evolve independently from the more peripheral sensory systems of the nervous system. It is therefore reasonable to assume that temporal order, so expertly decoded in the neural periphery, is a part of the coding scheme in the cortex as well. Experimental studies partially confirm and partially contradict this assumption, with good evidence for temporal order coding in the primary visual cortex and during gamma oscillations. In neuromorphic engineering, the first electronic implementations that used temporal order coding were the same as those for which temporal order coding was found to be relevant in biology: barn owl sound localization and the Reichardt motion detector. These architectures were then extended to process sensory signals using temporal order coding in different ways from those found in biology, such as for the detection of periodicity. Using delays and coincident activity to detect periodicity has also proven to be able to perform operations that were not possible using standard analog or digital engineering techniques, by exhibiting an arbitrarily selective response while responding rapidly. The strength of temporal order coding is also demonstrated by the fact that the first commercial application of a neuromorphic engineering system used temporal order coding based on Reichardt motion detection. Acknowledgments We thank Ben Torben-Nielsen for helpful discussion and the reviewers for valuable feedback on the first version of this letter.

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Received April 19, 2012; accepted August 31, 2012.