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1.  Stochastic Simulations on the Reliability of Action Potential Propagation in Thin Axons 
PLoS Computational Biology  2007;3(5):e79.
It is generally assumed that axons use action potentials (APs) to transmit information fast and reliably to synapses. Yet, the reliability of transmission along fibers below 0.5 μm diameter, such as cortical and cerebellar axons, is unknown. Using detailed models of rodent cortical and squid axons and stochastic simulations, we show how conduction along such thin axons is affected by the probabilistic nature of voltage-gated ion channels (channel noise). We identify four distinct effects that corrupt propagating spike trains in thin axons: spikes were added, deleted, jittered, or split into groups depending upon the temporal pattern of spikes. Additional APs may appear spontaneously; however, APs in general seldom fail (<1%). Spike timing is jittered on the order of milliseconds over distances of millimeters, as conduction velocity fluctuates in two ways. First, variability in the number of Na channels opening in the early rising phase of the AP cause propagation speed to fluctuate gradually. Second, a novel mode of AP propagation (stochastic microsaltatory conduction), where the AP leaps ahead toward spontaneously formed clusters of open Na channels, produces random discrete jumps in spike time reliability. The combined effect of these two mechanisms depends on the pattern of spikes. Our results show that axonal variability is a general problem and should be taken into account when considering both neural coding and the reliability of synaptic transmission in densely connected cortical networks, where small synapses are typically innervated by thin axons. In contrast we find that thicker axons above 0.5 μm diameter are reliable.
Author Summary
Neurons in cerebral cortex achieve wiring densities of 4 km per mm3 by using unmyelinated axons of 0.3 μm average diameter as wires. Many axons (e.g., pain fibers) are thinner. Although, as in computer chips, wire miniaturization economizes on space and energy, it increases the noise introduced by thermodynamic fluctuations in a neuron's “protein transistors,” voltage-gated ion channels. We investigated how well the relatively small number of ion channels found in the membranes of tiny axons propagate the brain's universal signal—the action potential. We built a stochastic model that incorporates the random behavior of individual ion channels and found noise effects much larger than previously assumed, because standard stochastic approximation techniques (Langevin) break down because single channels can produce whole-cell responses. Channel noise destroys information encoded in the timing of action potentials, by randomly varying the speed of conduction, and produces a novel mode of transmission, stochastic microsaltatory conduction. Ion channel populations retain memory of previous activity in the distribution of channel states, causing action potential reliability to vary with context. The effects and general relationships identified here will govern other cell-signaling systems that rely on inherently noisy protein switches to propagate signals, either for intracellular communication (Ca++/cAMP waves) or in nanotechnology.
doi:10.1371/journal.pcbi.0030079
PMCID: PMC1864994  PMID: 17480115
2.  Spikes in Retinal Bipolar Cells Phase-Lock to Visual Stimuli with Millisecond Precision 
Current Biology  2011;21(22):1859-1869.
Summary
Background
The conversion of an analog stimulus into the digital form of spikes is a fundamental step in encoding sensory information. Here, we investigate this transformation in the visual system of fish by in vivo calcium imaging and electrophysiology of retinal bipolar cells, which have been assumed to be purely graded neurons.
Results
Synapses of all major classes of retinal bipolar cell encode visual information by using a combination of spikes and graded signals. Spikes are triggered within the synaptic terminal and, although sparse, phase-lock to a stimulus with a jitter as low as 2–3 ms. Spikes in bipolar cells encode a visual stimulus less reliably than spikes in ganglion cells but with similar temporal precision. The spike-generating mechanism does not alter the temporal filtering of a stimulus compared with the generator potential. The amplitude of the graded component of the presynaptic calcium signal can vary in time, and small fluctuations in resting membrane potential alter spike frequency and even switch spiking on and off.
Conclusions
In the retina of fish, the millisecond precision of spike coding begins in the synaptic terminal of bipolar cells. This neural compartment regulates the frequency of digital signals transmitted to the inner retina as well as the strength of graded signals.
Graphical Abstract
Highlights
► The spike code of vision begins in retinal bipolar cells ► Spikes in bipolar cells phase-lock to visual stimuli with millisecond precision ► Spiking and graded calcium signals can switch on and off at individual synapses ► Spikes in bipolar cells encode a stimulus less reliably than spikes in ganglion cells
doi:10.1016/j.cub.2011.09.042
PMCID: PMC3235547  PMID: 22055291
3.  Temporal Coding by Cochlear Nucleus Bushy Cells in DBA/2J Mice with Early Onset Hearing Loss 
The bushy cells of the anterior ventral cochlear nucleus (AVCN) preserve or improve the temporal coding of sound information arriving from auditory nerve fibers (ANF). The critical cellular mechanisms entailed in this process include the specialized nerve terminals, the endbulbs of Held, and the membrane conductance configuration of the bushy cell. In one strain of mice (DBA/2J), an early-onset hearing loss can cause a reduction in neurotransmitter release probability, and a smaller and slower spontaneous miniature excitatory postsynaptic current (EPSC) at the endbulb synapse. In the present study, by using a brain slice preparation, we tested the hypothesis that these changes in synaptic transmission would degrade the transmission of timing information from the ANF to the AVCN bushy neuron. We show that the electrical excitability of bushy cells in hearing-impaired old DBA mice was different from that in young, normal-hearing DBA mice. We found an increase in the action potential (AP) firing threshold with current injection; a larger AP afterhyperpolarization; and an increase in the number of spikes produced by large depolarizing currents. We also tested the temporal precision of bushy cell responses to high-frequency stimulation of the ANF. The standard deviation of spikes (spike jitter) produced by ANF-evoked excitatory postsynaptic potentials (EPSPs) was largely unaffected in old DBA mice. However, spike entrainment during a 100-Hz volley of EPSPs was significantly reduced. This was not a limitation of the ability of bushy cells to fire APs at this stimulus frequency, because entrainment to trains of current pulses was unaffected. Moreover, the decrease in entrainment is not attributable to increased synaptic depression. Surprisingly, the spike latency was 0.46 ms shorter in old DBA mice, and was apparently attributable to a faster conduction velocity, since the evoked excitatory postsynaptic current (EPSC) latency was shorter in old DBA mice as well. We also tested the contribution of the low-voltage-activated K+ conductance (gKLV) on the spike latency by using dynamic clamp. Alteration in gKLV had little effect on the spike latency. To test whether these changes in DBA mice were simply a result of continued postnatal maturation, we repeated the experiments in CBA mice, a strain that shows normal hearing thresholds through this age range. CBA mice exhibited no reduction in entrainment or increased spike jitter with age. We conclude that the ability of AVCN bushy neurons to reliably follow ANF EPSPs is compromised in a frequency-dependent fashion in hearing-impaired mice. This effect can be best explained by an increase in spike threshold.
doi:10.1007/s10162-006-0052-9
PMCID: PMC1785302  PMID: 17066341
auditory; spike reliability; entrainment; deafness; endbulb of Held
4.  Temporal Coding by Cochlear Nucleus Bushy Cells in DBA/2J Mice with Early Onset Hearing Loss 
The bushy cells of the anterior ventral cochlear nucleus (AVCN) preserve or improve the temporal coding of sound information arriving from auditory nerve fibers (ANF). The critical cellular mechanisms entailed in this process include the specialized nerve terminals, the endbulbs of Held, and the membrane conductance configuration of the bushy cell. In one strain of mice (DBA/2J), an early-onset hearing loss can cause a reduction in neurotransmitter release probability, and a smaller and slower spontaneous miniature excitatory postsynaptic current (EPSC) at the endbulb synapse. In the present study, by using a brain slice preparation, we tested the hypothesis that these changes in synaptic transmission would degrade the transmission of timing information from the ANF to the AVCN bushy neuron. We show that the electrical excitability of bushy cells in hearing-impaired old DBA mice was different from that in young, normal-hearing DBA mice. We found an increase in the action potential (AP) firing threshold with current injection; a larger AP afterhyperpolarization; and an increase in the number of spikes produced by large depolarizing currents. We also tested the temporal precision of bushy cell responses to high-frequency stimulation of the ANF. The standard deviation of spikes (spike jitter) produced by ANF-evoked excitatory postsynaptic potentials (EPSPs) was largely unaffected in old DBA mice. However, spike entrainment during a 100-Hz volley of EPSPs was significantly reduced. This was not a limitation of the ability of bushy cells to fire APs at this stimulus frequency, because entrainment to trains of current pulses was unaffected. Moreover, the decrease in entrainment is not attributable to increased synaptic depression. Surprisingly, the spike latency was 0.46 ms shorter in old DBA mice, and was apparently attributable to a faster conduction velocity, since the evoked excitatory postsynaptic current (EPSC) latency was shorter in old DBA mice as well. We also tested the contribution of the low-voltage-activated K+ conductance (gKLV) on the spike latency by using dynamic clamp. Alteration in gKLV had little effect on the spike latency. To test whether these changes in DBA mice were simply a result of continued postnatal maturation, we repeated the experiments in CBA mice, a strain that shows normal hearing thresholds through this age range. CBA mice exhibited no reduction in entrainment or increased spike jitter with age. We conclude that the ability of AVCN bushy neurons to reliably follow ANF EPSPs is compromised in a frequency-dependent fashion in hearing-impaired mice. This effect can be best explained by an increase in spike threshold.
doi:10.1007/s10162-006-0052-9
PMCID: PMC1785302  PMID: 17066341
auditory; spike reliability; entrainment; deafness; endbulb of Held
5.  Changing the responses of cortical neurons from sub- to suprathreshold using single spikes in vivo 
eLife  null;2:e00012.
Action Potential (APs) patterns of sensory cortex neurons encode a variety of stimulus features, but how can a neuron change the feature to which it responds? Here, we show that in vivo a spike-timing-dependent plasticity (STDP) protocol—consisting of pairing a postsynaptic AP with visually driven presynaptic inputs—modifies a neurons' AP-response in a bidirectional way that depends on the relative AP-timing during pairing. Whereas postsynaptic APs repeatedly following presynaptic activation can convert subthreshold into suprathreshold responses, APs repeatedly preceding presynaptic activation reduce AP responses to visual stimulation. These changes were paralleled by restructuring of the neurons response to surround stimulus locations and membrane-potential time-course. Computational simulations could reproduce the observed subthreshold voltage changes only when presynaptic temporal jitter was included. Together this shows that STDP rules can modify output patterns of sensory neurons and the timing of single-APs plays a crucial role in sensory coding and plasticity.
DOI: http://dx.doi.org/10.7554/eLife.00012.001
eLife digest
Nerve cells, called neurons, are one of the core components of the brain and form complex networks by connecting to other neurons via long, thin ‘wire-like’ processes called axons. Axons can extend across the brain, enabling neurons to form connections—or synapses—with thousands of others. It is through these complex networks that incoming information from sensory organs, such as the eye, is propagated through the brain and encoded.
The basic unit of communication between neurons is the action potential, often called a ‘spike’, which propagates along the network of axons and, through a chemical process at synapses, communicates with the postsynaptic neurons that the axon is connected to. These action potentials excite the neuron that they arrive at, and this excitatory process can generate a new action potential that then propagates along the axon to excite additional target neurons. In the visual areas of the cortex, neurons respond with action potentials when they ‘recognize’ a particular feature in a scene—a process called tuning. How a neuron becomes tuned to certain features in the world and not to others is unclear, as are the rules that enable a neuron to change what it is tuned to. What is clear, however, is that to understand this process is to understand the basis of sensory perception.
Memory storage and formation is thought to occur at synapses. The efficiency of signal transmission between neurons can increase or decrease over time, and this process is often referred to as synaptic plasticity. But for these synaptic changes to be transmitted to target neurons, the changes must alter the number of action potentials. Although it has been shown in vitro that the efficiency of synaptic transmission—that is the strength of the synapse—can be altered by changing the order in which the pre- and postsynaptic cells are activated (referred to as ‘Spike-timing-dependent plasticity’), this has never been shown to have an effect on the number of action potentials generated in a single neuron in vivo. It is therefore unknown whether this process is functionally relevant.
Now Pawlak et al. report that spike-timing-dependent plasticity in the visual cortex of anaesthetized rats can change the spiking of neurons in the visual cortex. They used a visual stimulus (a bar flashed up for half a second) to activate a presynaptic cell, and triggered a single action potential in the postsynaptic cell a very short time later. By repeatedly activating the cells in this way, they increased the strength of the synaptic connection between the two neurons. After a small number of these pairing activations, presenting the visual stimulus alone to the presynaptic cell was enough to trigger an action potential (a suprathreshold response) in the postsynaptic neuron—even though this was not the case prior to the pairing.
This study shows that timing rules known to change the strength of synaptic connections—and proposed to underlie learning and memory—have functional relevance in vivo, and that the timing of single action potentials can change the functional status of a cortical neuron.
DOI: http://dx.doi.org/10.7554/eLife.00012.002
doi:10.7554/eLife.00012
PMCID: PMC3552422  PMID: 23359858
synaptic plasticity; STDP; visual cortex; circuits; in vivo; spiking patterns; rat
6.  Spike-Based Population Coding and Working Memory 
PLoS Computational Biology  2011;7(2):e1001080.
Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.
Author Summary
Most of our daily actions are subject to uncertainty. Behavioral studies have confirmed that humans handle this uncertainty in a statistically optimal manner. A key question then is what neural mechanisms underlie this optimality, i.e. how can neurons represent and compute with probability distributions. Previous approaches have proposed that probabilities are encoded in the firing rates of neural populations. However, such rate codes appear poorly suited to understand perception in a constantly changing environment. In particular, it is unclear how probabilistic computations could be implemented by biologically plausible spiking neurons. Here, we propose a network of spiking neurons that can optimally combine uncertain information from different sensory modalities and keep this information available for a long time. This implies that neural memories not only represent the most likely value of a stimulus but rather a whole probability distribution over it. Furthermore, our model suggests that each spike conveys new, essential information. Consequently, the observed variability of neural responses cannot simply be understood as noise but rather as a necessary consequence of optimal sensory integration. Our results therefore question strongly held beliefs about the nature of neural “signal” and “noise”.
doi:10.1371/journal.pcbi.1001080
PMCID: PMC3040643  PMID: 21379319
7.  Timing Precision in Population Coding of Natural Scenes in the Early Visual System 
PLoS Biology  2008;6(12):e324.
The timing of spiking activity across neurons is a fundamental aspect of the neural population code. Individual neurons in the retina, thalamus, and cortex can have very precise and repeatable responses but exhibit degraded temporal precision in response to suboptimal stimuli. To investigate the functional implications for neural populations in natural conditions, we recorded in vivo the simultaneous responses, to movies of natural scenes, of multiple thalamic neurons likely converging to a common neuronal target in primary visual cortex. We show that the response of individual neurons is less precise at lower contrast, but that spike timing precision across neurons is relatively insensitive to global changes in visual contrast. Overall, spike timing precision within and across cells is on the order of 10 ms. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary to represent the more slowly varying natural environment, we argue that preserving relative spike timing at a ∼10-ms resolution is a crucial property of the neural code entering cortex.
Author Summary
Neurons convey information about the world in the form of trains of action potentials (spikes). These trains are highly repeatable when the same stimulus is presented multiple times, and this temporal precision across repetitions can be as fine as a few milliseconds. It is usually assumed that this time scale also corresponds to the timing precision of several neighboring neurons firing in concert. However, the relative timing of spikes emitted by different neurons in a local population is not necessarily as fine as the temporal precision across repetitions within a single neuron. In the visual system of the brain, the level of contrast in the image entering the retina can affect single-neuron temporal precision, but the effects of contrast on the neural population code are unknown. Here we show that the temporal scale of the population code entering visual cortex is on the order of 10 ms and is largely insensitive to changes in visual contrast. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary in representing the more slowly varying natural environment, preserving relative spike timing at a ∼10-ms resolution may be a crucial property of the neural code entering cortex.
Early neural representation of visual scenes occurs with a temporal precision on the order of 10 ms, which is precise enough to strongly drive downstream neurons in the visual pathway. Unlike individual neurons, the neural population code is largely insensitive to pronounced changes in visual contrast.
doi:10.1371/journal.pbio.0060324
PMCID: PMC2602720  PMID: 19090624
8.  STDP Allows Fast Rate-Modulated Coding with Poisson-Like Spike Trains 
PLoS Computational Biology  2011;7(10):e1002231.
Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (∼10–20 ms) for sufficiently many inputs (∼100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.
Author Summary
In vivo neural responses to stimuli are known to have a lot of variability across trials. If the same number of spikes is emitted from trial to trial, the neuron is said to be reliable. If the timing of such spikes is roughly preserved across trials, the neuron is said to be precise. Here we demonstrate both analytically and numerically that the well-established Hebbian learning rule of spike-timing-dependent plasticity (STDP) can learn response patterns despite relatively low reliability (Poisson-like variability) and low temporal precision (10–20 ms). These features are in line with many experimental observations, in which a poststimulus time histogram (PSTH) is evaluated over multiple trials. In our model, however, information is extracted from the relative spike times between afferents without the need of an absolute reference time, such as a stimulus onset. Relevantly, recent experiments show that relative timing is often more informative than the absolute timing. Furthermore, the scope of application for our study is not restricted to sensory systems. Taken together, our results suggest a fine temporal resolution for the neural code, and that STDP is an appropriate candidate for encoding and decoding such activity.
doi:10.1371/journal.pcbi.1002231
PMCID: PMC3203056  PMID: 22046113
9.  Auditory Frequency and Intensity Discrimination Explained Using a Cortical Population Rate Code 
PLoS Computational Biology  2013;9(11):e1003336.
The nature of the neural codes for pitch and loudness, two basic auditory attributes, has been a key question in neuroscience for over century. A currently widespread view is that sound intensity (subjectively, loudness) is encoded in spike rates, whereas sound frequency (subjectively, pitch) is encoded in precise spike timing. Here, using information-theoretic analyses, we show that the spike rates of a population of virtual neural units with frequency-tuning and spike-count correlation characteristics similar to those measured in the primary auditory cortex of primates, contain sufficient statistical information to account for the smallest frequency-discrimination thresholds measured in human listeners. The same population, and the same spike-rate code, can also account for the intensity-discrimination thresholds of humans. These results demonstrate the viability of a unified rate-based cortical population code for both sound frequency (pitch) and sound intensity (loudness), and thus suggest a resolution to a long-standing puzzle in auditory neuroscience.
Author Summary
A widely held view among auditory scientists is that the neural code for sound intensity (or loudness) involves temporally coarse spike-rate information, whereas the code for sound frequency (or pitch) requires more fine-grained and precise spike timing information. One problem with this view is that neurons in auditory cortex do not produce precisely time-locked responses to higher frequencies within the pitch range, suggesting that a transformation to a rate code must occur. However, because cortical neurons exhibit relatively broad tuning to frequency and correlated spike counts, it is unclear whether a cortical population code based on spike rates alone can support the remarkably precise pitch-discrimination ability of humans. Here we show that a relatively small population of virtual neurons with frequency-tuning and spike-count correlation characteristics consistent with those of actual neurons in the primary auditory cortex of primates, can account for both the smallest frequency- and intensity-discrimination thresholds measured behaviorally in humans. These results suggest a resolution to a long-standing puzzle in auditory neuroscience.
doi:10.1371/journal.pcbi.1003336
PMCID: PMC3828126  PMID: 24244142
10.  Long-Term Temporal Imprecision of Information Coding in the Anterior Cingulate Cortex of Mice with Peripheral Inflammation or Nerve Injury 
The Journal of Neuroscience  2014;34(32):10675-10687.
Temporal properties of spike firing in the central nervous system (CNS) are critical for neuronal coding and the precision of information storage. Chronic pain has been reported to affect cognitive and emotional functions, in addition to trigger long-term plasticity in sensory synapses and behavioral sensitization. Less is known about the possible changes in temporal precision of cortical neurons in chronic pain conditions. In the present study, we investigated the temporal precision of action potential firing in the anterior cingulate cortex (ACC) by using both in vivo and in vitro electrophysiological approaches. We found that peripheral inflammation caused by complete Freund's adjuvant (CFA) increased the standard deviation (SD) of spikes latency (also called jitter) of ∼51% of recorded neurons in the ACC of adult rats in vivo. Similar increases in jitter were found in ACC neurons using in vitro brain slices from adult mice with peripheral inflammation or nerve injury. Bath application of glutamate receptor antagonists CNQX and AP5 abolished the enhancement of jitter induced by CFA injection or nerve injury, suggesting that the increased jitter depends on the glutamatergic synaptic transmission. Activation of adenylyl cyclases (ACs) by bath application of forskolin increased jitter, whereas genetic deletion of AC1 abolished the change of jitter caused by CFA inflammation. Our study provides strong evidence for long-term changes of temporal precision of information coding in cortical neurons after peripheral injuries and explains neuronal mechanism for chronic pain caused cognitive and emotional impairment.
doi:10.1523/JNEUROSCI.5166-13.2014
PMCID: PMC4122801  PMID: 25100600
chronic pain; cingulate cortex; cortex; mice; synaptic transmission; temporal precision
11.  Neural Coding of Natural Stimuli: Information at Sub-Millisecond Resolution 
PLoS Computational Biology  2008;4(3):e1000025.
Sensory information about the outside world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion-sensitive neurons of the fly visual system as a test case. Our experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight. New mathematical methods allow us to draw more reliable conclusions about the information content of neural responses even when the set of possible responses is very large. We find that significant amounts of visual information are represented by details of the spike train at millisecond and sub-millisecond precision, even though the sensory input has a correlation time of ∼55 ms; different patterns of spike timing represent distinct motion trajectories, and the absolute timing of spikes points to particular features of these trajectories with high precision. Finally, the efficiency of our entropy estimator makes it possible to uncover features of neural coding relevant for natural visual stimuli: first, the system's information transmission rate varies with natural fluctuations in light intensity, resulting from varying cloud cover, such that marginal increases in information rate thus occur even when the individual photoreceptors are counting on the order of one million photons per second. Secondly, we see that the system exploits the relatively slow dynamics of the stimulus to remove coding redundancy and so generate a more efficient neural code.
Author Summary
Neurons communicate by means of stereotyped pulses, called action potentials or spikes, and a central issue in systems neuroscience is to understand this neural coding. Here we study how sensory information is encoded in sequences of spikes, using a combination of novel theoretical and experimental techniques. With motion detection in the blowfly as a model system, we perform experiments in an environment maximally similar to the natural one. We report a number of unexpected, striking observations about the structure of the neural code in this system: First, the timing of spikes is important with a precision roughly two orders of magnitude greater than the temporal dynamics of the stimulus. Second, the fly goes a long way to utilize the redundancy in the stimulus in order to optimize the neural code and encode more refined features than would be possible otherwise. This implies that the neural code, even in low-level vision, may be significantly context dependent.
doi:10.1371/journal.pcbi.1000025
PMCID: PMC2265477  PMID: 18369423
12.  Spectral Analysis of Input Spike Trains by Spike-Timing-Dependent Plasticity 
PLoS Computational Biology  2012;8(7):e1002584.
Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron “sees” the input correlations. We thus denote this unsupervised learning scheme as ‘kernel spectral component analysis’ (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a “linear” response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.
Author Summary
Tuning feature extraction of sensory stimuli is an important function for synaptic plasticity models. A widely studied example is the development of orientation preference in the primary visual cortex, which can emerge using moving bars in the visual field. A crucial point is the decomposition of stimuli into basic information tokens, e.g., selecting individual bars even though they are presented in overlapping pairs (vertical and horizontal). Among classical unsupervised learning models, independent component analysis (ICA) is capable of isolating basic tokens, whereas principal component analysis (PCA) cannot. This paper focuses on spike-timing-dependent plasticity (STDP), whose functional implications for neural information processing have been intensively studied both theoretically and experimentally in the last decade. Following recent studies demonstrating that STDP can perform ICA for specific cases, we show how STDP relates to PCA or ICA, and in particular explains the conditions under which it switches between them. Here information at the neuronal level is assumed to be encoded in temporal cross-correlograms of spike trains. We find that a linear spiking neuron equipped with pairwise STDP requires additional mechanisms, such as a homeostatic regulation of its output firing, in order to separate mixed correlation sources and thus perform ICA.
doi:10.1371/journal.pcbi.1002584
PMCID: PMC3390410  PMID: 22792056
13.  Fast Coding of Orientation in Primary Visual Cortex 
PLoS Computational Biology  2012;8(6):e1002536.
Understanding how populations of neurons encode sensory information is a major goal of systems neuroscience. Attempts to answer this question have focused on responses measured over several hundred milliseconds, a duration much longer than that frequently used by animals to make decisions about the environment. How reliably sensory information is encoded on briefer time scales, and how best to extract this information, is unknown. Although it has been proposed that neuronal response latency provides a major cue for fast decisions in the visual system, this hypothesis has not been tested systematically and in a quantitative manner. Here we use a simple ‘race to threshold’ readout mechanism to quantify the information content of spike time latency of primary visual (V1) cortical cells to stimulus orientation. We find that many V1 cells show pronounced tuning of their spike latency to stimulus orientation and that almost as much information can be extracted from spike latencies as from firing rates measured over much longer durations. To extract this information, stimulus onset must be estimated accurately. We show that the responses of cells with weak tuning of spike latency can provide a reliable onset detector. We find that spike latency information can be pooled from a large neuronal population, provided that the decision threshold is scaled linearly with the population size, yielding a processing time of the order of a few tens of milliseconds. Our results provide a novel mechanism for extracting information from neuronal populations over the very brief time scales in which behavioral judgments must sometimes be made.
Author Summary
How can humans and animals make complex decisions on time scales as short as 100 ms? The information required for such decisions is coded in neural activity and should be read out on a very brief time scale. Traditional approaches to coding of neural information rely on the number of electrical pulses, or spikes, that neurons fire in a certain time window. Although this type of code is likely to be used by the brain for higher cognitive tasks, it may be too slow for fast decisions. Here, we explore an alternative code which is based on the latency of spikes with respect to a reference signal. By analyzing the simultaneous responses of many cells in monkey visual cortex, we show that information about the orientation of visual stimuli can be extracted reliably from spike latencies on very short time scales.
doi:10.1371/journal.pcbi.1002536
PMCID: PMC3375217  PMID: 22719237
14.  Spike Timing and Reliability in Cortical Pyramidal Neurons: Effects of EPSC Kinetics, Input Synchronization and Background Noise on Spike Timing 
PLoS ONE  2007;2(3):e319.
In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Δt) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (≤2.45 ms) in response to synchronous compounds of EPSCs with fast rise and decay kinetics. Compounds with slow EPSC kinetics (decay time constants>6 ms) triggered spikes at lower temporal precision (≥6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.
doi:10.1371/journal.pone.0000319
PMCID: PMC1828624  PMID: 17389910
15.  Temporal Correlation Mechanisms and Their Role in Feature Selection: A Single-Unit Study in Primate Somatosensory Cortex 
PLoS Biology  2014;12(11):e1002004.
How neurons pay attention Top-down selective attention mediates feature selection by reducing the noise correlations in neural populations and enhancing the synchronized activity across subpopulations that encode the relevant features of sensory stimuli.
Studies in vision show that attention enhances the firing rates of cells when it is directed towards their preferred stimulus feature. However, it is unknown whether other sensory systems employ this mechanism to mediate feature selection within their modalities. Moreover, whether feature-based attention modulates the correlated activity of a population is unclear. Indeed, temporal correlation codes such as spike-synchrony and spike-count correlations (rsc) are believed to play a role in stimulus selection by increasing the signal and reducing the noise in a population, respectively. Here, we investigate (1) whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature, (2) the interplay between spike-synchrony and rsc during feature selection, and (3) whether feature attention effects are common across the visual and tactile systems. Single-unit recordings were made in secondary somatosensory cortex of three non-human primates while animals engaged in tactile feature (orientation and frequency) and visual discrimination tasks. We found that both firing rate and spike-synchrony between neurons with similar feature selectivity were enhanced when attention was directed towards their preferred feature. However, attention effects on spike-synchrony were twice as large as those on firing rate, and had a tighter relationship with behavioral performance. Further, we observed increased rsc when attention was directed towards the visual modality (i.e., away from touch). These data suggest that similar feature selection mechanisms are employed in vision and touch, and that temporal correlation codes such as spike-synchrony play a role in mediating feature selection. We posit that feature-based selection operates by implementing multiple mechanisms that reduce the overall noise levels in the neural population and synchronize activity across subpopulations that encode the relevant features of sensory stimuli.
Author Summary
Attention can select stimuli in space based on the stimulus features most relevant for a task. Attention effects have been linked to several important phenomena such as modulations in neuronal spiking rate (i.e., the average number of spikes per unit time) and spike-spike synchrony between neurons. Attention has also been associated with spike count correlations, a measure that is thought to reflect correlated noise in the population of neurons. Here, we studied whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature. Simultaneous single-unit recordings were obtained from multiple neurons in secondary somatosensory cortex in non-human primates performing feature-attention tasks. Both firing rate and spike-synchrony were enhanced when attention was directed towards the preferred feature of cells. However, attention effects on spike-synchrony had a tighter relationship with behavior. Further, attention decreased spike-count correlations when it was directed towards the receptive field of cells. Our data indicate that temporal correlation codes play a role in mediating feature selection, and are consistent with a feature-based selection model that operates by reducing the overall noise in a population and synchronizing activity across subpopulations that encode the relevant features of sensory stimuli.
doi:10.1371/journal.pbio.1002004
PMCID: PMC4244037  PMID: 25423284
16.  Low-noise encoding of active touch by layer 4 in the somatosensory cortex 
eLife  null;4:e06619.
Cortical spike trains often appear noisy, with the timing and number of spikes varying across repetitions of stimuli. Spiking variability can arise from internal (behavioral state, unreliable neurons, or chaotic dynamics in neural circuits) and external (uncontrolled behavior or sensory stimuli) sources. The amount of irreducible internal noise in spike trains, an important constraint on models of cortical networks, has been difficult to estimate, since behavior and brain state must be precisely controlled or tracked. We recorded from excitatory barrel cortex neurons in layer 4 during active behavior, where mice control tactile input through learned whisker movements. Touch was the dominant sensorimotor feature, with >70% spikes occurring in millisecond timescale epochs after touch onset. The variance of touch responses was smaller than expected from Poisson processes, often reaching the theoretical minimum. Layer 4 spike trains thus reflect the millisecond-timescale structure of tactile input with little noise.
DOI: http://dx.doi.org/10.7554/eLife.06619.001
eLife digest
Cells called neurons connect to form large networks that process information in the brain. A region of the brain called the cerebral cortex receives information about touch from sensors in the skin. A series of neurons relay the touch information to the cerebral cortex as patterns of electrical activity called ‘spike trains’. Understanding how these spike trains represent information about the world around us is one of the greatest challenges facing neuroscience.
At first glance, the number and timing of the individual spikes within the trains appear to be random. It is possible that the irregularity within spike trains is ‘noise’ that is generated within the cortex itself. This noise could represent uncertainty about the nature of the stimulus from the sensors, or random fluctuations in brain activity. However, other findings have challenged this view and argued that these erratic spike trains actually carry hidden information.
Hires et al. investigated this possibility by recording how neurons within a region of the mouse brain called the somatosensory cortex responded to sensory information coming from the mouse's whiskers. Mice sweep their whiskers across objects to locate and identify them, much like how humans feel objects with their fingertips. Here, the mice used their whiskers to judge the location of an object by touch alone, while the electrical activity of the neurons was measured using electrodes. Importantly, the movements of the whiskers and contact with the object were tracked to one millisecond precision.
Similar to previous studies, sensory information from the whiskers triggered irregular spike trains in neurons within the somatosensory cortex. Hires et al. found that the apparently irregular spikes coincided precisely with the timing of when the whiskers contacted the object. Other spikes aligned perfectly with the movement of whiskers into particular positions. Furthermore, the patterns of electrical activity in the spike trains precisely predicted when and how the object was contacted, and which whisker was involved.
These findings suggest that the timing of individual spikes within spike trains carries important information to the brain. Future studies will develop our understanding of how the brain interprets and responds to the rich data contained in these spike trains to identify objects and decide how to interact with them.
DOI: http://dx.doi.org/10.7554/eLife.06619.002
doi:10.7554/eLife.06619
PMCID: PMC4525079  PMID: 26245232
sensory coding; somatosensation; barrel cortex; noise; mouse
17.  Analysis of Slow (Theta) Oscillations as a Potential Temporal Reference Frame for Information Coding in Sensory Cortices 
PLoS Computational Biology  2012;8(10):e1002717.
While sensory neurons carry behaviorally relevant information in responses that often extend over hundreds of milliseconds, the key units of neural information likely consist of much shorter and temporally precise spike patterns. The mechanisms and temporal reference frames by which sensory networks partition responses into these shorter units of information remain unknown. One hypothesis holds that slow oscillations provide a network-intrinsic reference to temporally partitioned spike trains without exploiting the millisecond-precise alignment of spikes to sensory stimuli. We tested this hypothesis on neural responses recorded in visual and auditory cortices of macaque monkeys in response to natural stimuli. Comparing different schemes for response partitioning revealed that theta band oscillations provide a temporal reference that permits extracting significantly more information than can be obtained from spike counts, and sometimes almost as much information as obtained by partitioning spike trains using precisely stimulus-locked time bins. We further tested the robustness of these partitioning schemes to temporal uncertainty in the decoding process and to noise in the sensory input. This revealed that partitioning using an oscillatory reference provides greater robustness than partitioning using precisely stimulus-locked time bins. Overall, these results provide a computational proof of concept for the hypothesis that slow rhythmic network activity may serve as internal reference frame for information coding in sensory cortices and they foster the notion that slow oscillations serve as key elements for the computations underlying perception.
Author Summary
Neurons in sensory cortices encode objects in our sensory environment by varying the timing and number of action potentials that they emit. Brain networks that ‘decode’ this information need to partition those spike trains into their individual informative units. Experimenters achieve such partitioning by exploiting their knowledge about the millisecond precise timing of individual spikes relative to externally presented sensory stimuli. The brain, however, does not have access to this information and has to partition and decode spike trains using intrinsically available temporal reference frames. We show that slow (4–8 Hz) oscillatory network activity can provide such an intrinsic temporal reference. Specifically, we analyzed neural responses recorded in primary auditory and visual cortices. This revealed that the oscillatory reference frame performs nearly as well as the precise stimulus-locked reference frame and renders neural encoding robust to sensory noise and temporal uncertainty that naturally occurs during decoding. These findings provide a computational proof-of-concept that slow oscillatory network activity may serve the crucial function as temporal reference frame for sensory coding.
doi:10.1371/journal.pcbi.1002717
PMCID: PMC3469413  PMID: 23071429
18.  Temporal Encoding in a Nervous System 
PLoS Computational Biology  2011;7(5):e1002041.
We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.
Author Summary
The information coding schemes used within nervous systems have been the focus of an entire field within neuroscience. An unresolved issue within the general coding problem is the determination of the neural “symbols” with which information is encoded in neural spike trains, analogous to the determination of the nucleotide sequences used to represent proteins in molecular biology. The goal of our study was to determine if pairs of consecutive action potentials contain more or different information about the stimuli that elicit them than would be predicted from an analysis of individual action potentials. We developed linear and non-linear coding models and used likelihood analysis to address this question for sensory interneurons in the cricket cercal sensory system. Our results show that these neurons' spike trains can be decomposed into sequences of two neural symbols: isolated single spikes and short-interval spike doublets. Given the ubiquitous nature of similar neural activity reported in other systems, we suspect that the implementation of such temporal encoding schemes may be widespread across animal phyla. Knowledge of the basic coding units used by single cells will help in building the large-scale neural network models necessary for understanding how nervous systems function.
doi:10.1371/journal.pcbi.1002041
PMCID: PMC3088658  PMID: 21573206
19.  Encoding and decoding amplitude-modulated cochlear implant stimuli—a point process analysis 
Cochlear implant speech processors stimulate the auditory nerve by delivering amplitude-modulated electrical pulse trains to intracochlear electrodes. Studying how auditory nerve cells encode modulation information is of fundamental importance, therefore, to understanding cochlear implant function and improving speech perception in cochlear implant users. In this paper, we analyze simulated responses of the auditory nerve to amplitude-modulated cochlear implant stimuli using a point process model. First, we quantify the information encoded in the spike trains by testing an ideal observer’s ability to detect amplitude modulation in a two-alternative forced-choice task. We vary the amount of information available to the observer to probe how spike timing and averaged firing rate encode modulation. Second, we construct a neural decoding method that predicts several qualitative trends observed in psychophysical tests of amplitude modulation detection in cochlear implant listeners. We find that modulation information is primarily available in the sequence of spike times. The performance of an ideal observer, however, is inconsistent with observed trends in psychophysical data. Using a neural decoding method that jitters spike times to degrade its temporal resolution and then computes a common measure of phase locking from spike trains of a heterogeneous population of model nerve cells, we predict the correct qualitative dependence of modulation detection thresholds on modulation frequency and stimulus level. The decoder does not predict the observed loss of modulation sensitivity at high carrier pulse rates, but this framework can be applied to future models that better represent auditory nerve responses to high carrier pulse rate stimuli. The supplemental material of this article contains the article’s data in an active, re-usable format.
doi:10.1007/s10827-010-0224-9
PMCID: PMC2898280  PMID: 20177761
Point process model; Cochlear implant; Auditory nerve; Amplitude modulation; Neural coding
20.  A stimulus-dependent spike threshold is an optimal neural coder 
A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.
doi:10.3389/fncom.2015.00061
PMCID: PMC4451370  PMID: 26082710
neural coding; coding fidelity; energy-efficient coding; dynamic threshold; spike-timing; source coding; spike-threshold
21.  Inhibition does not affect the timing code for vocalizations in the mouse auditory midbrain 
Many animals use a diverse repertoire of complex acoustic signals to convey different types of information to other animals. The information in each vocalization therefore must be coded by neurons in the auditory system. One way in which the auditory system may discriminate among different vocalizations is by having highly selective neurons, where only one or two different vocalizations evoke a strong response from a single neuron. Another strategy is to have specific spike timing patterns for particular vocalizations such that each neural response can be matched to a specific vocalization. Both of these strategies seem to occur in the auditory midbrain of mice. The neural mechanisms underlying rate and time coding are unclear, however, it is likely that inhibition plays a role. Here, we examined whether inhibition is involved in shaping neural selectivity to vocalizations via rate and/or time coding in the mouse inferior colliculus (IC). We examined extracellular single unit responses to vocalizations before and after iontophoretically blocking GABAA and glycine receptors in the IC of awake mice. We then applied a number of neurometrics to examine the rate and timing information of individual neurons. We initially evaluated the neuronal responses using inspection of the raster plots, spike-counting measures of response rate and stimulus preference, and a measure of maximum available stimulus-response mutual information. Subsequently, we used two different event sequence distance measures, one based on vector space embedding, and one derived from the Victor/Purpura Dq metric, to direct hierarchical clustering of responses. In general, we found that the most salient feature of pharmacologically blocking inhibitory receptors in the IC was the lack of major effects on the functional properties of IC neurons. Blocking inhibition did increase response rate to vocalizations, as expected. However, it did not significantly affect spike timing, or stimulus selectivity of the studied neurons. We observed two main effects when inhibition was locally blocked: (1) Highly selective neurons maintained their selectivity and the information about the stimuli did not change, but response rate increased slightly. (2) Neurons that responded to multiple vocalizations in the control condition, also responded to the same stimuli in the test condition, with similar timing and pattern, but with a greater number of spikes. For some neurons the information rate generally increased, but the information per spike decreased. In many of these neurons, vocalizations that generated no responses in the control condition generated some response in the test condition. Overall, we found that inhibition in the IC does not play a substantial role in creating the distinguishable and reliable neuronal temporal spike patterns in response to different vocalizations.
doi:10.3389/fphys.2014.00140
PMCID: PMC3997027  PMID: 24795640
spike timing; mouse IC; inhibition; selectivity; information; neural coding
22.  Coding and Decoding with Adapting Neurons: A Population Approach to the Peri-Stimulus Time Histogram 
PLoS Computational Biology  2012;8(10):e1002711.
The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a ‘quasi-renewal equation’ which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.
Author Summary
How can information be encoded and decoded in populations of adapting neurons? A quantitative answer to this question requires a mathematical expression relating neuronal activity to the external stimulus, and, conversely, stimulus to neuronal activity. Although widely used equations and models exist for the special problem of relating external stimulus to the action potentials of a single neuron, the analogous problem of relating the external stimulus to the activity of a population has proven more difficult. There is a bothersome gap between the dynamics of single adapting neurons and the dynamics of populations. Moreover, if we ignore the single neurons and describe directly the population dynamics, we are faced with the ambiguity of the adapting neural code. The neural code of adapting populations is ambiguous because it is possible to observe a range of population activities in response to a given instantaneous input. Somehow the ambiguity is resolved by the knowledge of the population history, but how precisely? In this article we use approximation methods to provide mathematical expressions that describe the encoding and decoding of external stimuli in adapting populations. The theory presented here helps to bridge the gap between the dynamics of single neurons and that of populations.
doi:10.1371/journal.pcbi.1002711
PMCID: PMC3464223  PMID: 23055914
23.  The Neural Code for Motor Control in the Cerebellum and Oculomotor Brainstem†‡  
eNeuro  2014;1(1):ENEURO.0004-14.2014.
Our paper evaluates the nature of the neural code under conditions where we can understand the details of trial-by-trial neural variation and its relationship to behavior. We demonstrate that a single extra spike in the activity of a neuron can predict impending motor behavior.
Abstract
Spike trains are rich in information that can be extracted to guide behaviors at millisecond time resolution or across longer time intervals. In sensory systems, the information usually is defined with respect to the stimulus. Especially in motor systems, however, it is equally critical to understand how spike trains predict behavior. Thus, our goal was to compare systematically spike trains in the oculomotor system with eye movement behavior on single movements. We analyzed the discharge of Purkinje cells in the floccular complex of the cerebellum, floccular target neurons in the brainstem, other vestibular neurons, and abducens neurons. We find that an extra spike in a brief analysis window predicts a substantial fraction of the trial-by-trial variation in the initiation of smooth pursuit eye movements. For Purkinje cells, a single extra spike in a 40 ms analysis window predicts, on average, 0.5 SDs of the variation in behavior. An optimal linear estimator predicts behavioral variation slightly better than do spike counts in brief windows. Simulations reveal that the ability of single spikes to predict a fraction of behavior also emerges from model spike trains that have the same statistics as the real spike trains, as long as they are driven by shared sensory inputs. We think that the shared sensory estimates in their inputs create correlations in neural spiking across time and across each population. As a result, one or a small number of spikes in a brief time interval can predict a substantial fraction of behavioral variation.
doi:10.1523/ENEURO.0004-14.2014
PMCID: PMC4596133  PMID: 26464956
abducen; floccular complex; population coding; rate code; smooth pursuit eye movements; temporal code
24.  A thesaurus for a neural population code 
eLife  null;4:e06134.
Information is carried in the brain by the joint spiking patterns of large groups of noisy, unreliable neurons. This noise limits the capacity of the neural code and determines how information can be transmitted and read-out. To accurately decode, the brain must overcome this noise and identify which patterns are semantically similar. We use models of network encoding noise to learn a thesaurus for populations of neurons in the vertebrate retina responding to artificial and natural videos, measuring the similarity between population responses to visual stimuli based on the information they carry. This thesaurus reveals that the code is organized in clusters of synonymous activity patterns that are similar in meaning but may differ considerably in their structure. This organization is highly reminiscent of the design of engineered codes. We suggest that the brain may use this structure and show how it allows accurate decoding of novel stimuli from novel spiking patterns.
DOI: http://dx.doi.org/10.7554/eLife.06134.001
eLife digest
Our ability to perceive the world is dependent on information from our senses being passed between different parts of the brain. The information is encoded as patterns of electrical pulses or ‘spikes’, which other brain regions must be able to decipher. Cracking this code would thus enable us to predict the patterns of nerve impulses that would occur in response to specific stimuli, and ‘decode’ which stimuli had produced particular patterns of impulses.
This task is challenging in part because of its scale—vast numbers of stimuli are encoded by huge numbers of neurons that can send their spikes in many different combinations. Furthermore, neurons are inherently noisy and their response to identical stimuli may vary considerably in the number of spikes and their timing. This means that the brain cannot simply link a single unchanging pattern of firing with each stimulus, because these firing patterns are often distorted by biophysical noise.
Ganmor et al. have now modeled the effects of noise in a network of neurons in the retina (found at the back of the eye), and, in doing so, have provided insights into how the brain solves this problem. This has brought us a step closer to cracking the neural code. First, 10 second video clips of natural scenes and artificial stimuli were played on a loop to a sample of retina taken from a salamander, and the responses of nearly 100 neurons in the sample were recorded for two hours. Dividing the 10 second clip into short segments provided a series of 500 stimuli, which the network had been exposed to more than 600 times.
Ganmor et al. analyzed the responses of groups of 20 cells to each stimulus and found that physically similar firing patterns were not particularly likely to encode the same stimulus. This can be likened to the way that words such as ‘light’ and ‘night’ have similar structures but different meanings. Instead, the model reveals that each stimulus was represented by a cluster of firing patterns that bore little physical resemblance to one another, but which nevertheless conveyed the same meaning. To continue on with the previous example, this is similar to way that ‘light’ and ‘illumination’ have the same meaning but different structures.
Ganmor et al. use these new data to map the organization of the ‘vocabulary’ of populations of cells the retina, and put together a kind of ‘thesaurus’ that enables new activity patterns of the retina to be decoded and could be used to crack the neural code. Furthermore, the organization of ‘synonyms’ is strikingly similar to codes that are favored in many forms of telecommunication. In these man-made codes, codewords that represent different items are chosen to be so distinct from each other that even if they were corrupted by noise, they could be correctly deciphered. Correspondingly, in the retina, patterns that carry the same meaning occupy a distinct area, and new patterns can be interpreted based on their proximity to these clusters.
DOI: http://dx.doi.org/10.7554/eLife.06134.002
doi:10.7554/eLife.06134
PMCID: PMC4562117  PMID: 26347983
neural code; information; noise; entropy; natural stimuli; metric; retina; salamander
25.  The Temporal Winner-Take-All Readout 
PLoS Computational Biology  2009;5(2):e1000286.
How can the central nervous system make accurate decisions about external stimuli at short times on the basis of the noisy responses of nerve cell populations? It has been suggested that spike time latency is the source of fast decisions. Here, we propose a simple and fast readout mechanism, the temporal Winner-Take-All (tWTA), and undertake a study of its accuracy. The tWTA is studied in the framework of a statistical model for the dynamic response of a nerve cell population to an external stimulus. Each cell is characterized by a preferred stimulus, a unique value of the external stimulus for which it responds fastest. The tWTA estimate for the stimulus is the preferred stimulus of the cell that fired the first spike in the entire population. We then pose the questions: How accurate is the tWTA readout? What are the parameters that govern this accuracy? What are the effects of noise correlations and baseline firing? We find that tWTA sensitivity to the stimulus grows algebraically fast with the number of cells in the population, N, in contrast to the logarithmic slow scaling of the conventional rate-WTA sensitivity with N. Noise correlations in first-spike times of different cells can limit the accuracy of the tWTA readout, even in the limit of large N, similar to the effect that has been observed in population coding theory. We show that baseline firing also has a detrimental effect on tWTA accuracy. We suggest a generalization of the tWTA, the n-tWTA, which estimates the stimulus by the identity of the group of cells firing the first n spikes and show how this simple generalization can overcome the detrimental effect of baseline firing. Thus, the tWTA can provide fast and accurate responses discriminating between a small number of alternatives. High accuracy in estimation of a continuous stimulus can be obtained using the n-tWTA.
Author Summary
Considerable experimental as well as theoretical effort has been devoted to the investigation of the neural code. The traditional approach has been to study the information content of the total neural spike count during a long period of time. However, in many cases, the central nervous system is required to estimate the external stimulus at much shorter times. What readout mechanism could account for such fast decisions? We suggest a readout mechanism that estimates the external stimulus by the first spike in the population, the tWTA. We show that the tWTA can account for accurate discriminations between a small number of choices. We find that the accuracy of the tWTA is limited by the neuronal baseline firing. We further find that, due to baseline firing, the single first spike does not encode sufficient information for estimating a continuous variable, such as the direction of motion of a visual stimulus, with fine resolution. In such cases, fast and accurate decisions can be obtained by a generalization of the tWTA to a readout that estimates the stimulus by the first n spikes fire by the population, where n is larger than the mean number of baseline spikes in the population.
doi:10.1371/journal.pcbi.1000286
PMCID: PMC2633619  PMID: 19229309

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