Neural coding: Difference between revisions

Revision as of 10:30, 2 December 2008

Revision as of 10:51, 2 December 2008

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== Overview ==

Neurons are remarkable among the [[cells (biologybilology)]] of the body in their ability to propagate signals rapidly over large distances. They do this by generating characteristic electrical pulses called [[action potentials]] or, more simply, spikes that can travel down nerve fibers. Sensory neurons change their activities by firing sequences of action potentials in various temporal patterns, with the presence of external sensory stimuli, such as [[light]], [[sound]], [[taste]], [[smell]] and [[touch]]. It is known that information about the stimulus is encoded in this pattern of action potentials and transmitted into and around the brain. It is also discovered that [[muscles]] are activated by action potentials and that [[motor neurons]] serve to convert action potentials generated by the brain into muscle movements that allow animals to interact with the environment, often in response to sensory stimuli they receive from it.

Although action potentials can vary somewhat in [[duration]], [[amplitude]] and [[shape]], they are typically treated as identical stereotyped events in neural coding studies. If the brief duration of an action potential (about 1ms) is ignored, an action potential sequence, or spike train, can be characterized simply by a series of all-or-none point events in time <ref name="Gerstner">Gerstner, W. and Kistler, W. 2002. ''Spiking Neuron Models: Single Neurons, Populations, Plasticity''. Cambridge University Press, Cambridge</ref>. The lengths of interspike intervals (ISIs[[ISI]]s) between two successive spikes in a spike train often vary, apparently randomly, both within and across trials <ref name="Stein">Stein, R., Gossen, E. and Jones, K. 2005. Neuronal variability: noise or part of the signal? ''Nature Reviews Neuroscience'' 6:389–397</ref>. The study of neural coding, involves measuring and characterizing how stimulus attributes, such as light or sound intensity, or motor actions, such as the direction of an arm movement, are represented by neuron action potentials or spikes. In order to describe and analyze neuronal firing, [[statistical methods]] and methods of [[probability theory]] and stochastic [[stochasticpoint process|point processes]] have been widely applied.

== Encoding and Decoding ==

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== Coding schemes ==

A sequence, or 'train', of spikes may contain information based on different coding schemes. In motor neurons, for example, the strength at which an innervated muscle is flexed depends solely on the '[[firing rate]]', the average number of spikes per unit time (a '[[rate code]]'). At the other end, a complex '[[temporal code]]' is based on the precise timing of single spikes. They may be locked to an external stimulus such as in the [[auditory system]] or be generated intrinsically by the neural circuitry <ref name="Gerstner97">GERSTNER. 1997. Neural codes: Firing rates and beyond. ''Proceedings of the National Academy of Sciences of the United States of America'' 94:12740-12741</ref>.

Whether neurons use rate coding or temporal coding is a topic of intense debate within the neuroscience community, even though there is no clear definition of what these terms mean.

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=== Rate Coding ===

Rate coding is a traditional coding scheme, assuming that most, if not all, information about the stimulus is contained in the firing rate of the neuron. Because the sequence of action potentials generated by a given stimulus varies from trial to trial, neuronal responses are typically treated statistically or probabilistically. They may be characterized by firing rates, rather than as specific spike sequences. In most sensory systems, the firing rate increases, generally non-linearly, with increasing stimulus intensity <ref name="Kandel">Kandel, E., Schwartz, J. and Jessel, T.M. 1991. ''Principles of Neural Science''. Elsevier, New York</ref>. Any information possibly encoded in the temporal structure of the spike train is ignored. Consequently, rate coding is inefficient but highly robust with respect to the ISI '[[noise]]' <ref name="Stein"/>.

The concept of firing rates has been successfully applied during the last 80 years. It dates back to the pioneering work of ED Adrian who showed that the firing rate of stretch [[receptor]] neurons in the muscles is related to the force applied to the muscle<ref name="Adrian"> Adrian ED and Zotterman Y. 1926. The impulses produced by sensory nerve endings: Part II: The response of a single end organ. ''Journal of Physiology'' 61: 151-71</ref>. In the following decades, measurement of firing rates became a standard tool for describing the properties of all types of sensory or [[cortical]] neurons, partly due to the relative ease of measuring rates experimentally. However, this approach neglects all the information possibly contained in the exact timing of the spikes. During recent years, more and more experimental evidences have suggested that a straightforward firing rate concept based on temporal averaging may be too simplistic to describe brain activity <ref name="Stein"/>.

During rate coding, precisely calculating firing rate is very important. In fact, the term “firing rate” has a few different definitions, which refersrefer to different averaging procedures, such as an average over time or an average over several repetitions of experiment.

==== Spike-Count Rate ====

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The Spike-count rate, also referred to a temporal average, is obtained by counting the number of spikes that appear during a trial and dividing by the duration of trial. The length T of the time window is set by experimenter and depends on the type of neuron recorded from and the stimulus. In practice, to get sensible averages, several spikes should occur within the time window. Typical values are T = 100 ms or T = 500 ms, but the duration may also be longer or shorter.

The spike-count rate can be determined from a single trial, but at the expense of losing all temporal resolution about variations in neural response during the course of the trial. Temporal averaging can work well in cases where the stimulus is constant or slowly varying and does not require a fast reaction of the [[organism]] - and this is the situation usually encountered in experimental protocols. Real-world input, however, is hardly stationary, but often changing on a fast time scale. For example, even when viewing a static image, humans perform [[saccades]], rapid changes of the direction of gaze. The image projected onto the retinal [[photo receptors]] changes therefore every few hundred milliseconds.

Despite its shortcomings, the concept of a spike-count rate code is widely used not only in experiments, but also in models of [[neural networks]]. It has led to the idea that a neuron transforms information about a single input variable (the stimulus strength) into a single continuous output variable (the firing rate).

==== Time-dependent Firing Rate ====

The time-dependent firing rate is defined as the average number of spikes (averaged over trials) appearing during a short interval between times t and t+Δt, divided by the duration of the interval. It works for stationary as well as for time-dependent stimuli. To experimentally measure the time-dependent firing rate, the experimenter records from a neuron while stimulating with some input sequence. The same stimulation sequence is repeated several times and the neuronal response is reported in a [[Peri-Stimulus-Time Histogram]] (PSTH). The time t is measured with respect to the start of the stimulation sequence. The Δt must be large enough (typically in the range of one or a few milliseconds) so there are sufficient number of spikes within the interval to obtain a reliable estimate of the average. The number of occurrences of spikes n_K(t;t+Δt) summed over all repetitions of the experiment divided by the number K of repetitions is a measure of the typical activity of the neuron between time t and t+Δt. A further division by the interval length Δt yields time-dependent firing rate r(t) of the neuron, which is equivalent to the spike density of PSTH.

For sufficiently small Δt, r(t)Δt is the average number of spikes occurring between times t and t+Δt over multiple trials. If Δt is small, there will never be more than one spike within the interval between t and t+Δt on any given trial. This means that r(t)Δt is also the [[fraction]] of trials on which a spike occurred between those times. Equivalently, r(t)Δt is the [[probability]] that a spike occurs during this time interval.

As an experimental procedure, the time-dependent firing rate measure is a useful method to evaluate neuronal activity, in particular in the case of time-dependent stimuli. The obvious problem with this approach is that it can not be the coding scheme used by neurons in the brain. Neurons can not wait for the stimuli to repeatedly present in an exactly same manner before generating response.

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=== Temporal Coding ===

When precise spike timing or high-frequency firing-rate [[fluctuations]] are found to carry information, the neural code is often identified as a temporal code <ref name="Dayan">Dayan P and Abbott LF. 2001. ''Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems''. Cambridge, Massachusetts: The MIT Press</ref>. A number of studies have found that the temporal resolution of the neural code is on a millisecond time scale, indicating that precise spike timing is a significant element in neural coding <ref name="Daniel">Daniel A. Butts, Chong Weng, Jianzhong Jin, Chun-I Yeh, Nicholas A. Lesica1, Jose-Manuel Alonso and Garrett B. Stanley. 2007. Temporal precision in the neural code and the timescales of natural vision. ''Nature'' 449, 92-95</ref>.

Temporal codes employ those features of the spiking activity that cannot be described by the firing rate. For example, time to first spike after the stimulus onset, characteristics based on the second and higher statistical moments of the ISI [[probability distribution]], spike randomness, or precisely timed groups of spikes (temporal patterns) are candidates for temporal codes <ref name="Kostal">Kostal L, Lansky P, and Rospars JP. 2007. Neuronal coding and spiking randomness. ''Europen Journal of Neuroscience''. 26:2693-701</ref>. As there is no absolute time reference in the nervous system, the information is carried either in terms of the relative timing of spikes in a population of neurons or with respect to an ongoing BRAINbrain OSCILLATIONoscillation <ref name="Stein"/>.

The temporal structure of a spike train or firing rate evoked by a stimulus is determined both by the dynamics of the stimulus and by the nature of the neural encoding process. Stimuli that change rapidly tend to generate precisely timed spikes and rapidly changing firing rates no matter what neural coding strategy is being used. Temporal coding refers to temporal precision in the response that does not arise solely from the dynamics of the stimulus, but that nevertheless relates to properties of the stimulus. The interplay between stimulus and encoding dynamics makes the identification of a temporal code difficult.

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Population coding is a method to represent stimuli by using the joint activities of a number of neurons. In population coding, each neuron has a distribution of responses over some set of inputs, and the responses of many neurons may be combined to determine some value about the inputs.

From the theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet, is simple enough for theoretic analysis <ref name="Wu">S Wu, S Amari, and H Nakahara. 2002. Population Coding and Decoding in a Neural Field: A Computational Study. ''Neural Computation'' 14: 999-1026</ref>. Experimental studies have revealed that this coding paradigm is widely used in the sensor and motor areas of the brain. For example, in the visual area [[middle temporal]] (MT), neurons are tuned to the moving direction <ref name="Maunsell">Maunsell, J. H. R., and Van Essen, D. C. 1983. Functional properties of neurons in middle temporal visual area of the Macaque monkey. I. Selectivity for stimulus direction, speed, and orientation. ''Journal of Neurophysiology'' 49:1127–1147</ref>. In response to an object moving in a particular direction, many neurons in MT fire, with a [[noise-corrupted]] and [[bell-shaped]] activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron’s signal.

Population coding has a number of advantages, including reduction of uncertainty due to neuronal [[variability]] and the ability to represent a number of different stimulus attributes simultaneously. Population coding is also much faster than rate coding and can reflect changes in the stimulus conditions nearly instantaneously <ref name="Hubel">Hubel, D. H. and Wiesel, T. N.. 1959. Receptive fields of single neurons in the cat's striate cortex. ''ournal of Physiology'' 148:574-591</ref>. Individual neurons in such a population typically have different but overlapping selectivities, so that many neurons, but not necessarily all, respond to a given stimulus.

== References ==