Neuronal noise

Last updated October 26, 2023

Neuronal noise or neural noise refers to the random intrinsic electrical fluctuations within neuronal networks. These fluctuations are not associated with encoding a response to internal or external stimuli and can be from one to two orders of magnitude.^[1] Most noise commonly occurs below a voltage-threshold that is needed for an action potential to occur, but sometimes it can be present in the form of an action potential; for example, stochastic oscillations in pacemaker neurons in suprachiasmatic nucleus are partially responsible for the organization of circadian rhythms.^[2]^[3]

Background

Neuronal activity at the microscopic level has a stochastic character, with atomic collisions and agitation, that may be termed "noise."^[4] While it isn't clear on what theoretical basis neuronal responses involved in perceptual processes can be segregated into a "neuronal noise" versus a "signal" component, and how such a proposed dichotomy could be corroborated empirically, a number of computational models incorporating a "noise" term have been constructed.

Single neurons demonstrate different responses to specific neuronal input signals. This is commonly referred to as neural response variability. If a specific input signal is initiated in the dendrites of a neuron, then a hypervariability exists in the number of vesicles released from the axon terminal fiber into the synapse.^[5] This characteristic is true for fibers without neural input signals, such as pacemaker neurons, as mentioned previously,^[2] and cortical pyramidal neurons that have highly-irregular firing pattern.^[6] Noise generally hinders neural performance, but recent studies show, in dynamical non-linear neural networks, this statement does not always hold true. Non-linear neural networks are a network of complex neurons that have many connections with one another such as the neuronal systems found within our brains. Comparatively, linear networks are an experimental view of analyzing a neural system by placing neurons in series with each other.

Initially, noise in complex computer circuit or neural circuits is thought to slow down^[7] and negatively affect the processing power. However, current research suggests that neuronal noise is beneficial to non-linear or complex neural networks up until optimal value.^[8] A theory by Anderson and colleagues supports that neural noise is beneficial. Their theory suggests that noise produced in the visual cortex helps linearize or smooth the threshold of action potentials.^[9]

Another theory suggests that stochastic noise in a non-linear network shows a positive relationship between the interconnectivity and noise-like activity.^[10] Thus based on this theory, Patrick Wilken and colleagues suggest that neuronal noise is the principal factor that limits the capacity of visual short-term memory. Investigators of neural ensembles and those who especially support the theory of distributed processing, propose that large neuronal populations effectively decrease noise by averaging out the noise in individual neurons. Some investigators have shown in experiments and in models that neuronal noise is a possible mechanism to facilitate neuronal processing.^[11]^[12] The presence of neuronal noise (or more specifically synaptic noise) confers to neurons more sensitivity to a broader range of inputs, it can equalize the efficacy of synaptic inputs located at different positions on the neuron, and it can also enable finer temporal discrimination.^[13] There are many theories of why noise is apparent in the neuronal networks, but many neurologists are unclear of why they exist.

More generally, two types of impacts of neuronal noise can be distinguished: it will either add variability to the neural response, or enable noise-induced dynamical phenomena which cannot be observed in a noise-free system. For instance, channel noise has been shown to induce oscillations in the stochastic Hodgkin-Huxley model.^[14]

Types

Ions exist inside and outside of the neuron and are subject to many bodily conditions. One major source of noise arises from ions or molecules in response to the third law of thermodynamics. This law states that the entropy of a system approaches a constant value as the temperature approaches zero. Since the body maintains temperatures above 0K, the molecules are subjected to increased kinetic energy, or motion. The stochastic, or random, movements give rise to receptor noise produced by the constant bombardment of ions, as described by Brownian motion. Ions are constantly being leaked across the membrane in efforts to equalize the ionic gradient produced by ATPase channels embedded in the membrane. These leaky channels permit the movement of ions across the membrane leading to small fluctuations, or noise, in the membrane potential.^[15]
Synapses are another major source of neural noise. More than often, there is random exocytosis of vesicles containing neurotransmitters, which eventually bind to the postsynaptic membrane, leading to a spontaneous action potential by graded potentials in the postsynaptic neuron.^[16] It is considered the largest-amplitude noise source in the cerebral cortex.^[4]

Sources

Noise present in neural system gives rise to the variability in the non-linear dynamical systems, but a black box still exists for the mechanism in which noise affects neural signal conduction. Instead, research has focused more on the sources of the noise present in dynamic neural networks. Several sources of response variability exist for neurons and neural networks:^[17]

Thermal noise: Johnson–Nyquist noise occurs due to the thermal motions of ions and other charge carriers, producing voltage fluctuations proportional to temperature. This source of noise is attributed to the third law of thermodynamics, stating that kinetic energy of molecules increases with a raise in temperature. Thermal noise is the weakest source of noise and can be considered negligible.^[18]
Ionic conductance noise: Ion channels in the membrane undergo spontaneous changes in conformation between different states and can open (or close) due to thermal fluctuations. The transmembrane embedded protein channels are made up of small subunits that undergo conformational changes and are affected by thermal fluctuations. When temperature drops below 33 °C, the rate at which the channel becomes active or inactive decreases. In contrast when the temperature is increased above 33 °C, the rate at which the channel becomes active or inactive increases.^[19]
Ion pump noise: Membrane embedded ATPase ion pumps produce fluctuating potentials by transporting ions against their concentration gradient. The multistep process in which ions are transported across their gradient requires ATP.^[20] The steps involved in active transport have a net forward direction, but small stochastic steps still exist in the conformational process that move backwards.^[20] These backward steps contribute to neuronal noise present in all dynamic neuronal circuits.
Ion channel shot noise: The number of ions that migrate through an open ion channel are discrete and random.^[21] In synapses, the number of calcium ions that enter the postsynaptic side after a spike is on the order of 250 ions,^[17] potentially making potentiation processes noisy. This noise is also associated with thermal fluctuations affecting the protein channels, as previously mentioned. This is not to be confused with shot noise, which is noise produced by the random generation of action potentials in neurons.
Synaptic release noise: Generally, action potentials are transferred down a neuron, which then are converted to either electrical or chemical signals between neurons. Chemical synapses are not deterministic, which means that every action potential produced does not result in the release of neurotransmitters. Rather, the release of vesicles containing neurotransmitters are probabilistic in nature. The number of vesicles released by a single synapse is random in response to a specific input signal and is further influenced by the firing history of the pre- and post-synaptic neurons. This means that neurotransmitters can be released in the absence of an input signal.^[17]
Synaptic bombardment: The large number of incoming spikes add a fluctuating amount of charge to the cell, which depends on the structure of the incoming spike trains and affects the cell's excitability.^[22]
Chaos: Chaotic dynamics can occur in single cells (due to periodic inputs or bursting due to intrinsic currents).^[23] Simple networks of neurons can also exhibit chaotic dynamics.^[24] Even if the chaos is deterministic, it can amplify noise from the other sources to macroscopic levels due to sensitive dependence on initial conditions.
Connectivity noise: Noise that arises from the number of connections and non-uniformity that a neuron has with other neurons within a neuronal network. There is a stronger presence of sub-threshold noise when the interconnectivity is strengthened, or the number of connection to other neurons is increased.^[10] The opposite remains true, too. If the interconnectivity of the neurons is decreased so then is the level of sub-threshold noise.
Environmental stimuli: Noise can be produced on a larger scale due to fluctuations in CO₂, which lead to variations in blood flow.^[25] The level of CO₂ in the blood allows for either vasoconstriction or vasodilation, which can encroach, or expand, into nearby neural networks producing noise.

Recording methods

Global recording

The external noise paradigm assumes "neural noise" and speculates that external noise should multiplicatively increase the amount of internal noise in the central nervous system. It is not clear how "neural noise" is theoretically distinguished from "neural signal." Proponents of this paradigm believe that adding visual or auditory external noise to a stimuli, and measure how it affects reaction time or the subject's performance. If performance is more inconsistent than without the noise, the subject is said to have "internal noise." As in the case of "internal noise," it is not clear on what theoretical grounds researchers distinguish "external noise" from "external signal" in terms of the perceptual response of the viewer, which is a response to the stimulus as a whole.

Electroencephalogram or EEG can be used to measure the brain since the signal-to-noise ratio is poor, so noise produced by the brain can be detected in vivo.
Local field potentials can be used to test the noise present in large neuronal networks. This measure of voltage can be used to determine the interconnectivity by the level of noise.^[10]

Local recording

Local recording has contributed much to discovering many of the new sources of ion channel noise.

Patch clamp technique was crucial to determine shot noise because the use of intercellular recording was not able to show the movement or detection of the few ions escaping at a time.

Related Research Articles

Within a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses - specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. The ability to generate electric signals first appeared in evolution 700 million years ago. 800 million years ago, predecessors of neurons were the peptidergic secretory cells. They eventually gained new gene modules which enabled cells to create post-synaptic scaffolds and ion channels that generate fast electrical signals. The ability to generate electric signals was a key innovation in the evolution of the nervous system.

Chemical synapses are biological junctions through which neurons' signals can be sent to each other and to non-neuronal cells such as those in muscles or glands. Chemical synapses allow neurons to form circuits within the central nervous system. They are crucial to the biological computations that underlie perception and thought. They allow the nervous system to connect to and control other systems of the body.

An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.

In neuroscience, synaptic plasticity is the ability of synapses to strengthen or weaken over time, in response to increases or decreases in their activity. Since memories are postulated to be represented by vastly interconnected neural circuits in the brain, synaptic plasticity is one of the important neurochemical foundations of learning and memory.

An electrical synapse is a mechanical and electrically conductive link between two neighboring neurons that is formed at a narrow gap between the pre- and postsynaptic neurons known as a gap junction. At gap junctions, such cells approach within about 3.8 nm of each other, a much shorter distance than the 20- to 40-nanometer distance that separates cells at chemical synapse. In many animals, electrical synapse-based systems co-exist with chemical synapses.

An inhibitory postsynaptic potential (IPSP) is a kind of synaptic potential that makes a postsynaptic neuron less likely to generate an action potential. IPSPs were first investigated in motorneurons by David P. C. Lloyd, John Eccles and Rodolfo Llinás in the 1950s and 1960s. The opposite of an inhibitory postsynaptic potential is an excitatory postsynaptic potential (EPSP), which is a synaptic potential that makes a postsynaptic neuron more likely to generate an action potential. IPSPs can take place at all chemical synapses, which use the secretion of neurotransmitters to create cell to cell signalling. Inhibitory presynaptic neurons release neurotransmitters that then bind to the postsynaptic receptors; this induces a change in the permeability of the postsynaptic neuronal membrane to particular ions. An electric current that changes the postsynaptic membrane potential to create a more negative postsynaptic potential is generated, i.e. the postsynaptic membrane potential becomes more negative than the resting membrane potential, and this is called hyperpolarisation. To generate an action potential, the postsynaptic membrane must depolarize—the membrane potential must reach a voltage threshold more positive than the resting membrane potential. Therefore, hyperpolarisation of the postsynaptic membrane makes it less likely for depolarisation to sufficiently occur to generate an action potential in the postsynaptic neurone.

In neuroscience, an excitatory postsynaptic potential (EPSP) is a postsynaptic potential that makes the postsynaptic neuron more likely to fire an action potential. This temporary depolarization of postsynaptic membrane potential, caused by the flow of positively charged ions into the postsynaptic cell, is a result of opening ligand-gated ion channels. These are the opposite of inhibitory postsynaptic potentials (IPSPs), which usually result from the flow of negative ions into the cell or positive ions out of the cell. EPSPs can also result from a decrease in outgoing positive charges, while IPSPs are sometimes caused by an increase in positive charge outflow. The flow of ions that causes an EPSP is an excitatory postsynaptic current (EPSC).

An excitatory synapse is a synapse in which an action potential in a presynaptic neuron increases the probability of an action potential occurring in a postsynaptic cell. Neurons form networks through which nerve impulses travels, each neuron often making numerous connections with other cells of neurons. These electrical signals may be excitatory or inhibitory, and, if the total of excitatory influences exceeds that of the inhibitory influences, the neuron will generate a new action potential at its axon hillock, thus transmitting the information to yet another cell.

Synaptogenesis is the formation of synapses between neurons in the nervous system. Although it occurs throughout a healthy person's lifespan, an explosion of synapse formation occurs during early brain development, known as exuberant synaptogenesis. Synaptogenesis is particularly important during an individual's critical period, during which there is a certain degree of synaptic pruning due to competition for neural growth factors by neurons and synapses. Processes that are not used, or inhibited during their critical period will fail to develop normally later on in life.

A neural circuit is a population of neurons interconnected by synapses to carry out a specific function when activated. Multiple neural circuits interconnect with one another to form large scale brain networks.

<span class="mw-page-title-main">Neural oscillation</span> Brainwaves, repetitive patterns of neural activity in the central nervous system

Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macroscopic neural oscillations is alpha activity.

Neurotransmission is the process by which signaling molecules called neurotransmitters are released by the axon terminal of a neuron, and bind to and react with the receptors on the dendrites of another neuron a short distance away. A similar process occurs in retrograde neurotransmission, where the dendrites of the postsynaptic neuron release retrograde neurotransmitters that signal through receptors that are located on the axon terminal of the presynaptic neuron, mainly at GABAergic and glutamatergic synapses.

Computational neurogenetic modeling (CNGM) is concerned with the study and development of dynamic neuronal models for modeling brain functions with respect to genes and dynamic interactions between genes. These include neural network models and their integration with gene network models. This area brings together knowledge from various scientific disciplines, such as computer and information science, neuroscience and cognitive science, genetics and molecular biology, as well as engineering.

Neural backpropagation is the phenomenon in which, after the action potential of a neuron creates a voltage spike down the axon, another impulse is generated from the soma and propagates towards the apical portions of the dendritic arbor or dendrites. In addition to active backpropagation of the action potential, there is also passive electrotonic spread. While there is ample evidence to prove the existence of backpropagating action potentials, the function of such action potentials and the extent to which they invade the most distal dendrites remain highly controversial.

In neuroscience and computer science, synaptic weight refers to the strength or amplitude of a connection between two nodes, corresponding in biology to the amount of influence the firing of one neuron has on another. The term is typically used in artificial and biological neural network research.

<span class="mw-page-title-main">Biological neuron model</span> Mathematical descriptions of the properties of certain cells in the nervous system

Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of neurons. In particular, these models describe how the voltage potential across the cell membrane changes over time. In an experimental setting, stimulating neurons with an electrical current generates an action potential, that propagates down the neuron's axon. This spike branches out to a large number of downstream neurons, where the signals terminate at synapses. As many as 85% of neurons in the neocortex, the outermost layer of the mammalian brain, consist of excitatory pyramidal neurons, and each pyramidal neuron receives tens of thousands of inputs from other neurons. Thus, spiking neurons are a major information processing unit of the nervous system.

Synaptic noise refers to the constant bombardment of synaptic activity in neurons. This occurs in the background of a cell when potentials are produced without the nerve stimulation of an action potential, and are due to the inherently random nature of synapses. These random potentials have similar time courses as excitatory postsynaptic potentials (EPSPs) and inhibitory postsynaptic potentials (IPSPs), yet they lead to variable neuronal responses. The variability is due to differences in the discharge times of action potentials.

In neurophysiology, a dendritic spike refers to an action potential generated in the dendrite of a neuron. Dendrites are branched extensions of a neuron. They receive electrical signals emitted from projecting neurons and transfer these signals to the cell body, or soma. Dendritic signaling has traditionally been viewed as a passive mode of electrical signaling. Unlike its axon counterpart which can generate signals through action potentials, dendrites were believed to only have the ability to propagate electrical signals by physical means: changes in conductance, length, cross sectional area, etc. However, the existence of dendritic spikes was proposed and demonstrated by W. Alden Spencer, Eric Kandel, Rodolfo Llinás and coworkers in the 1960s and a large body of evidence now makes it clear that dendrites are active neuronal structures. Dendrites contain voltage-gated ion channels giving them the ability to generate action potentials. Dendritic spikes have been recorded in numerous types of neurons in the brain and are thought to have great implications in neuronal communication, memory, and learning. They are one of the major factors in long-term potentiation.

Nonsynaptic plasticity is a form of neuroplasticity that involves modification of ion channel function in the axon, dendrites, and cell body that results in specific changes in the integration of excitatory postsynaptic potentials and inhibitory postsynaptic potentials. Nonsynaptic plasticity is a modification of the intrinsic excitability of the neuron. It interacts with synaptic plasticity, but it is considered a separate entity from synaptic plasticity. Intrinsic modification of the electrical properties of neurons plays a role in many aspects of plasticity from homeostatic plasticity to learning and memory itself. Nonsynaptic plasticity affects synaptic integration, subthreshold propagation, spike generation, and other fundamental mechanisms of neurons at the cellular level. These individual neuronal alterations can result in changes in higher brain function, especially learning and memory. However, as an emerging field in neuroscience, much of the knowledge about nonsynaptic plasticity is uncertain and still requires further investigation to better define its role in brain function and behavior.

Network of human nervous system comprises nodes that are connected by links. The connectivity may be viewed anatomically, functionally, or electrophysiologically. These are presented in several Wikipedia articles that include Connectionism, Biological neural network, Artificial neural network, Computational neuroscience, as well as in several books by Ascoli, G. A. (2002), Sterratt, D., Graham, B., Gillies, A., & Willshaw, D. (2011), Gerstner, W., & Kistler, W. (2002), and Rumelhart, J. L., McClelland, J. L., and PDP Research Group (1986) among others. The focus of this article is a comprehensive view of modeling a neural network. Once an approach based on the perspective and connectivity is chosen, the models are developed at microscopic, mesoscopic, or macroscopic (system) levels. Computational modeling refers to models that are developed using computing tools.

References

↑ Jacobson, G. A. (2005). "Subthreshold voltage noise of rat neocortical pyramidal neurones". J Physiol. 564 (Pt 1): 145–160. doi:10.1113/jphysiol.2004.080903. PMC 1456039 . PMID 15695244.
1 2 Ko, C. H. (2010). "Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker". PLOS Biology. 8 (10): e1000513. doi: 10.1371/journal.pbio.1000513 . PMC 2953532 . PMID 20967239.
↑ Mazzoni, E. O. (2005). "Circadian Pacemaker Neurons Transmit and Modulate Visual Information to Control a Rapid Behavioral Response". Neuron. 45 (2): 293–300. doi: 10.1016/j.neuron.2004.12.038 . PMID 15664180. S2CID 9568853.
1 2 Destexhe, A. (2012). Neuronal noise. New York: Springer.
↑ Stein, R. B. (2005). "Neuronal variability: noise or part of the signal?". Nature Reviews Neuroscience. 6 (5): 389–397. doi:10.1038/nrn1668. PMID 15861181. S2CID 205500218.
↑ Softky, W. R.; Koch, C. (1993). "The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs" (PDF). J Neurosci. 13 (1): 334–350. doi:10.1523/JNEUROSCI.13-01-00334.1993. PMC 6576320 . PMID 8423479.
↑ McDonnell, Mark D. (2011). "The Benefits Of Noise In Neural Systems: Bridging Theory And Experiment". Nature Reviews Neuroscience. 12 (7): 415–426. doi:10.1038/nrn3061. PMID 21685932. S2CID 1699918.
↑ Parnas, B. R. (1996). "Noise and neuronal populations conspire to encode simple waveforms reliably". IEEE Trans Biomed Eng. 43 (3): 313–318. doi:10.1109/10.486289. PMID 8682544. S2CID 8594684.
↑ Anderson, J. S. (2000). "The contribution of noise to contrast invariance of orientation tuning in cat visual cortex". Science. 290 (5498): 1968–1972. Bibcode:2000Sci...290.1968A. doi:10.1126/science.290.5498.1968. PMID 11110664. S2CID 15983514.
1 2 3 Serletis, D. (2011). "Complexity in neuronal noise depends on network interconnectivity". Ann Biomed Eng. 39 (6): 1768–1778. doi:10.1007/s10439-011-0281-x. PMID 21347547. S2CID 25516931.
↑ Mysterious 'Neural Noise' Primes Brain for Peak Performance. rochester.edu (November 10, 2006)
↑ Ma, B. (2006). "Bayesian inference with probabilistic population codes" (PDF). Nature Neuroscience. 9 (11): 1432–1438. doi:10.1038/nn1790. PMID 17057707. S2CID 11562994.
↑ See the "High-conductance state" article in Scholarpedia.
↑ Wainrib, Gilles; Thieullen, Michèle; Pakdaman, Khashayar (2011). "Reduction of stochastic conductance-based neuron models with time-scales separation". Journal of Computational Neuroscience. 32 (2): 327–346. doi:10.1007/s10827-011-0355-7. PMID 21842259. S2CID 17271489.
↑ Randall, D. J., et al. (2002). Eckert animal physiology: mechanisms and adaptations. New York, W.H. Freeman and Co.
↑ Fatt, P.; Katz, B. (1952). "Spontaneous subthreshold activity at motor nerve endings". J Physiol. 117 (1): 109–128. doi:10.1113/jphysiol.1952.sp004735. PMC 1392564 . PMID 14946732.
1 2 3 KochChristoph (1999) Biophysics of Computation. Oxford University Press, New York.
↑ Manwani A, Koch C (1999) "Signal detection in noisy weakly active dendrites", in Kearns MS, Solla SA, Cohn DA (eds.) Advances in Neural Information Processing Systems 11. MIT Press, Cambridge, MA.
↑ Cao, X. J.; Oertel D. (2005). "Temperature affects voltage-sensitive conductances differentially in octopus cells of the mammalian cochlear nucleus". J Neurophysiol. 94 (1): 821–832. doi:10.1152/jn.01049.2004. PMID 15800074. S2CID 9141608.
1 2 Lauger, P. (1984). "Current noise generated by electrogenic ion pumps". Eur Biophys J. 11 (2): 117–128. doi: 10.1007/BF00276627 . PMID 6100543. S2CID 35431682.
↑ Brunetti, R. (2007). "Shot noise in single open ion channels: A computational approach based on atomistic simulations". Journal of Computational Electronics. 6 (1): 391–394. doi:10.1007/s10825-006-0140-4. S2CID 51896278.
↑ Ho N, Destexhe A (2000). "Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons". J. Neurophysiol. 84 (3): 1488–96. doi:10.1152/jn.2000.84.3.1488. PMID 10980021. S2CID 3133375.
↑ Longtin, A (1997). "Autonomous stochastic resonance in bursting neurons". Phys. Rev. E. 55 (1): 868–876. Bibcode:1997PhRvE..55..868L. doi:10.1103/PhysRevE.55.868. S2CID 7256148.
↑ Li, C., Yu, J., & Liao, X. (2001). "Chaos in a three‐neuron hysteresis hopfield‐type neural networks". Physics Letters A. 285 (5–6): 368–372. Bibcode:2001PhLA..285..368L. doi:10.1016/S0375-9601(01)00381-4.{{cite journal}}: CS1 maint: multiple names: authors list (link)
↑ Birn, R. M. (2012). "The role of physiological noise in resting-state functional connectivity". NeuroImage. 62 (2): 864–70. doi:10.1016/j.neuroimage.2012.01.016. PMID 22245341. S2CID 20590747.

External links

Neuronal Noise article in Scholarpedia
High-Conductance State article in Scholarpedia

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[jacobson-1] Jacobson, G. A. (2005). "Subthreshold voltage noise of rat neocortical pyramidal neurones". J Physiol. 564 (Pt 1): 145–160. doi:10.1113/jphysiol.2004.080903. PMC 1456039 . PMID 15695244.

[ko-2] 1 2 Ko, C. H. (2010). "Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker". PLOS Biology. 8 (10): e1000513. doi: 10.1371/journal.pbio.1000513 . PMC 2953532 . PMID 20967239.

[maz-3] Mazzoni, E. O. (2005). "Circadian Pacemaker Neurons Transmit and Modulate Visual Information to Control a Rapid Behavioral Response". Neuron. 45 (2): 293–300. doi: 10.1016/j.neuron.2004.12.038 . PMID 15664180. S2CID 9568853.

[des-4] 1 2 Destexhe, A. (2012). Neuronal noise. New York: Springer.

[stein-5] Stein, R. B. (2005). "Neuronal variability: noise or part of the signal?". Nature Reviews Neuroscience. 6 (5): 389–397. doi:10.1038/nrn1668. PMID 15861181. S2CID 205500218.

[koch2-6] Softky, W. R.; Koch, C. (1993). "The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs" (PDF). J Neurosci. 13 (1): 334–350. doi:10.1523/JNEUROSCI.13-01-00334.1993. PMC 6576320 . PMID 8423479.

[mcdon-7] McDonnell, Mark D. (2011). "The Benefits Of Noise In Neural Systems: Bridging Theory And Experiment". Nature Reviews Neuroscience. 12 (7): 415–426. doi:10.1038/nrn3061. PMID 21685932. S2CID 1699918.

[parnas-8] Parnas, B. R. (1996). "Noise and neuronal populations conspire to encode simple waveforms reliably". IEEE Trans Biomed Eng. 43 (3): 313–318. doi:10.1109/10.486289. PMID 8682544. S2CID 8594684.

[anderson-9] Anderson, J. S. (2000). "The contribution of noise to contrast invariance of orientation tuning in cat visual cortex". Science. 290 (5498): 1968–1972. Bibcode:2000Sci...290.1968A. doi:10.1126/science.290.5498.1968. PMID 11110664. S2CID 15983514.

[serletis-10] 1 2 3 Serletis, D. (2011). "Complexity in neuronal noise depends on network interconnectivity". Ann Biomed Eng. 39 (6): 1768–1778. doi:10.1007/s10439-011-0281-x. PMID 21347547. S2CID 25516931.

[11] Mysterious 'Neural Noise' Primes Brain for Peak Performance. rochester.edu (November 10, 2006)

[12] Ma, B. (2006). "Bayesian inference with probabilistic population codes" (PDF). Nature Neuroscience. 9 (11): 1432–1438. doi:10.1038/nn1790. PMID 17057707. S2CID 11562994.

[13] See the "High-conductance state" article in Scholarpedia.

[14] Wainrib, Gilles; Thieullen, Michèle; Pakdaman, Khashayar (2011). "Reduction of stochastic conductance-based neuron models with time-scales separation". Journal of Computational Neuroscience. 32 (2): 327–346. doi:10.1007/s10827-011-0355-7. PMID 21842259. S2CID 17271489.

[eckert-15] Randall, D. J., et al. (2002). Eckert animal physiology: mechanisms and adaptations. New York, W.H. Freeman and Co.

[fatt-16] Fatt, P.; Katz, B. (1952). "Spontaneous subthreshold activity at motor nerve endings". J Physiol. 117 (1): 109–128. doi:10.1113/jphysiol.1952.sp004735. PMC 1392564 . PMID 14946732.

[koch-17] 1 2 3 KochChristoph (1999) Biophysics of Computation. Oxford University Press, New York.

[manwani-18] Manwani A, Koch C (1999) "Signal detection in noisy weakly active dendrites", in Kearns MS, Solla SA, Cohn DA (eds.) Advances in Neural Information Processing Systems 11. MIT Press, Cambridge, MA.

[cao-19] Cao, X. J.; Oertel D. (2005). "Temperature affects voltage-sensitive conductances differentially in octopus cells of the mammalian cochlear nucleus". J Neurophysiol. 94 (1): 821–832. doi:10.1152/jn.01049.2004. PMID 15800074. S2CID 9141608.

[lauger-20] 1 2 Lauger, P. (1984). "Current noise generated by electrogenic ion pumps". Eur Biophys J. 11 (2): 117–128. doi: 10.1007/BF00276627 . PMID 6100543. S2CID 35431682.

[brunetti-21] Brunetti, R. (2007). "Shot noise in single open ion channels: A computational approach based on atomistic simulations". Journal of Computational Electronics. 6 (1): 391–394. doi:10.1007/s10825-006-0140-4. S2CID 51896278.

[22] Ho N, Destexhe A (2000). "Synaptic background activity enhances the responsiveness of neocortical pyramidal neurons". J. Neurophysiol. 84 (3): 1488–96. doi:10.1152/jn.2000.84.3.1488. PMID 10980021. S2CID 3133375.

[23] Longtin, A (1997). "Autonomous stochastic resonance in bursting neurons". Phys. Rev. E. 55 (1): 868–876. Bibcode:1997PhRvE..55..868L. doi:10.1103/PhysRevE.55.868. S2CID 7256148.

[24] Li, C., Yu, J., & Liao, X. (2001). "Chaos in a three‐neuron hysteresis hopfield‐type neural networks". Physics Letters A. 285 (5–6): 368–372. Bibcode:2001PhLA..285..368L. doi:10.1016/S0375-9601(01)00381-4.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[Birn-25] Birn, R. M. (2012). "The role of physiological noise in resting-state functional connectivity". NeuroImage. 62 (2): 864–70. doi:10.1016/j.neuroimage.2012.01.016. PMID 22245341. S2CID 20590747.

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