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Noise in the Nervous System REVIEWS Noise in the nervous system A. Aldo Faisal, Luc P. J. Selen and Daniel M. Wolpert Abstract | Noise — random disturbances of signals — poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise’s potential benefits. Noise Variability is a prominent feature of behaviour. Variability In this Review, we begin by considering the nature, Random or unpredictable in perception and action is observed even when exter- amount and effects of noise in the CNS. As the brain’s fluctuations and disturbances nal conditions, such as the sensory input or task goal, purpose is to receive and process information and act in that are not part of a signal. are kept as constant as possible. Such variability is also response to that information (FIG. 1), we then examine how 1–4 Spike observed at the neuronal level . What are the sources of noise affects motor behaviour, considering the contribu- An action potential interpreted this variability? Here, a linguistic problem arises, as each tion of noise to variability at each level of the behavioural as a unitary pulse signal (that field has developed its own interpretation of terms such loop. Finally, we discuss the strategies that the nervous is, it either is or is not present), as variability, fluctuation and noise. In this Review, we use system uses to counter, compensate for or account for the timing of which determines the term variability to refer to changes in some measur- noise in perception, decision making and motor behaviour. its information content. Other properties of the action able quantity, such as spike timing or movement duration. Given the many levels and systems that are spanned, we potential, such as its shape or Importantly, the term variability does not indicate that a cannot provide a comprehensive Review, but instead depolarization levels, are particular mechanism has generated the variability, and we pick out specific examples that reflect in a more general ignored. does not suggest whether the variability is beneficial or manner the constraints and limitations that noise sets in Trial-to-trial variability BOX 1 Trial-to-trial variability detrimental. can arise from two dis- the CNS; the benefits of noise are discussed in . The differences between tinct sources. The first source is from the deterministic responses that are observed properties of the system. For example, the initial state Sensory noise when the same experiment is of the neural circuitry will vary at the start of each trial, External sensory stimuli are intrinsically noisy because repeated in the same specimen leading to different neuronal and behavioural responses. they are either thermodynamic or quantum mechanical (for example, in the same neuron or in the same subject). The variability in the response will be exacerbated if the in nature. For example, all forms of chemical sensing system’s dynamics are highly sensitive to the initial con- (including smell and gustation) are affected by thermo- ditions. The second source of variability is noise, which dynamic noise because molecules arrive at the receptor at is defined in the Oxford English Dictionary as ‘random random rates owing to diffusion and because receptor or irregular fluctuations or disturbances which are not proteins are limited in their ability to accurately count part of a signal [ … ] or which interfere with or obscure the number of signalling molecules7,8. Similarly, vision a signal or more generally any distortions or additions involves the absorption of photons that arrive at the which interfere with the transfer of information’. photoreceptor at a rate governed by a Poisson process. Computational and Biological Learning Lab, Department of Whereas previous reviews have focused on neuronal This places a physical limit on contrast sensitivity in Engineering, University of variability in general, we focus here on work directly relat- vision, which is reduced at low light levels — when fewer Cambridge, Trumpington ing to noise. Noise permeates every level of the nervous photons arrive at the photoreceptor9. Street, Cambridge, system, from the perception of sensory signals to the gen- At the first stage of perception (FIG. 1a), energy in the CB2 1PZ, UK. eration of motor responses, and poses a fundamental prob- sensory stimulus is converted into a chemical signal Correspondence to A.A.F. 5,6 e-mail: [email protected] lem for information processing . In recent years the extent (through photon absorption or ligand-binding of odour doi:10.1038/nrn2258 to which noise is present and how noise shapes the struc- molecules) or a mechanical signal (such as the movement Published online 5 March 2008 ture and function of nervous systems have been studied. of hair cells in hearing). The subsequent transduction 292 | APRIL 2008 | VOLUME 9 www.nature.com/reviews/neuro © 2008 Nature Publishing Group REVIEWS a Sensory noise b Cellular noise Electrical noise Sensory transduction and amplification Receptor Excitable membrane Network of neurons neuron Voltage-gated ion channel Synaptic noise c Motor noise Muscle Ca2+ Spinal cord Motor neuron Figure 1 | Overview of the behavioural loop and the stages at which noise is present in the nervous system. a | Sources of sensory noise include the transduction of signals. This is exemplified here by a photoreceptorNature Reviews and| Neur itsoscienc signal-e amplification cascade. b | Sources of cellular noise include the ion channels of excitable membranes, synaptic transmission and network interactions (see BOX 2). c | Sources of motor noise include motor neurons and muscle. In the behavioural task shown (catching a ball), the nervous system has to act in the presence of noise in sensing, information processing and movement. process amplifies the sensory signal and converts it into variability is on the order of milliseconds or lower14,15,20–25 an electrical one, either directly or indirectly through but because cortical neurons can detect the coincident second-messenger cascades. Any sensory noise that is arrival of APs on millisecond timescales26,27, this order of already present or that is generated during the ampli- timing precision might well be physiologically relevant. fication process (transducer noise10) will increase trial- Indeed, the precision of single-neuron AP timing on the to-trial variability. Therefore, noise levels set perceptual milli- and sub-millisecond scale has been shown to be thresholds for later stages of information processing, as behaviourally relevant in perception28,29 and movement30. signals that are weaker than the noise cannot be distin- To what extent this neuronal variability contributes to guished from it after amplification11. This is rigorously meaningful processing (as opposed to being meaning- underpinned by the data-processing inequality theorem12, less noise) is the fundamental question of neural cod- which states that subsequent stages of processing (even if ing4,19,31–33. A key issue is that neuronal activity might they are noise free) cannot extract more information than look random without actually being random. is present at earlier stages. Therefore, to reduce noise, Neuronal variability (both in and across trials) can organisms often pay a high metabolic and structural exhibit statistical characteristics (such as the mean price at the first stage of processing (the sensory stage). and variance) that match those of random processes. Poisson process A random process that For example, a fly’s photoreceptors account for 10% of its However, even when neuronal-firing statistics match generates binary (yes or no) resting metabolic consumption and its eye’s optics make those of a random process, it does not necessarily fol- events for which the probability up over 20% of the flight payload13. low that the firing is generated by random processes. of occurrence in any small time In fact, we know from Shannon’s theory of informa- interval is low. The rate at Cellular noise tion5,12 that when optimal encoding is used to maximize which events occur completely determines the statistics of the If neurons are driven with identical time-varying information transmission, neural signals will look ran- 31 events. Poisson processes have stimuli over repeated trials, the timing of the resultant dom . Furthermore, neuronal variability is not equal a Fano factor of 1. action potentials (APs) varies across the trials3,14–19. This in all neurons. The Fano factor is a simple measure of NATURE REVIEWS | NEUROSCIENCE VOLUME 9 | APRIL 2008 | 293 © 2008 Nature Publishing Group REVIEWS Box 1 | Benefits of noise protein production and degradation, the opening and closing of ion channels, the fusing of synaptic vesicles Noise is not only a problem for neurons: it can also be a solution in information- and the diffusion and binding of signalling molecules to processing. Several strategies have been adopted to use noise in this fashion. For receptors. It is often implicitly assumed that averaging example, stochastic resonance is a process by which the ability of threshold-like large numbers of such stochastic elements effectively systems to detect and transmit weak (periodic) signals can be enhanced by the presence of a certain level of noise85,173. At low noise levels, the sensory signal does not eliminates the randomness of individual elements. cause the system to cross the threshold and few signals are detected. For large noise However, this assumption requires reassessment. levels, the response is dominated by the noise.
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