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This is an summary of Noise in the nervous system by A. Aldo Faisal, Luc P. J. Selen & Daniel M. Wolpert, Nature Reviews Neuroscience 9, 292-303 (April 2008). All information comes from this source. Article review by Alex Fletcher.


Background

  • Variability is defined as a change in a measurable quantity when external conditions are kept as constant as possible. There are two sources of variability in a given system. The first source is from an inherent variation in the system based on different initial conditions. The second variability source is noise. Noise is defined as random fluctuations that are independent of a given signal. Noise obscures a signal and thus the information contained in the signal.


  • The summarized article focuses on the second source, noise [1]. Noise is present in every level of the central nervous system (CNS). The affect of noise on the nervous system can be divided into three types - sensory, cellular, and motor. The central nervous system deals with these three types of noise in a similar way. The following figure shows an overview of these three sources of noise.


Figure 1: Sensory, Cellular, and Motor Noise. 1


  • While noise is generally considered something to be filtered and reduced, there are some cases where noise can be beneficial. Noise can be helpful if a signal only does something when it passes a certain threshold. Stochastic resonance is a process where a system periodically transmits a signal when it crosses a threshold. With the right level of noise, the signal will reach the threshold with the right period. Too much noise will drown the signal, while too little will result in no transmissions. This process was first discovered in cat visual neurons. [2]


  • Another example of beneficial noise is in neurons that produce spikes. Below the threshold, no spike is produced and nothing happens. This process is inherently nonlinear because the number of spikes will jump from zero to a positive number just past the threshold. Noise will allow some sub-threshold signals to produce spikes, smoothing this nonlinearity.

(for background information on how nerves propagate information please read APPM4390:Traveling Waves in Excitable Media )

Model Category

  • This paper references research that used stochastic modeling to be able to analyze noise propagation and amplification. This model looks at neural networks in humans in both the central nervous system and peripheral nervous system of humans, see Hodgkin-Huxley for nervous system treatments.

Types of Noise

Sensory Noise

  • Sensory noise refers to noise in the signal from our five senses. Taste and smell contain thermodynamic noise. Due to diffusion, molecules randomly hit the receptors. For vision, photons hitting the photoreceptors in our eye follow a Poisson distribution. Refer to APPM4390:Mathematical neuroscience: from neurons to circuits to systems for a bifurcation analysis explaining visual hallucinations.


  • The sensory stage is the first stage of perception, and any noise present in a sensory signal will be passed on to an electrical or chemical signal. An example of a conversion to a chemical signal is photon absorption in the eye, while an example of a conversion to a mechanical signal is the movement of hair in hearing. Amplification often occurs during this conversion.


  • The data-processing inequality theory states that it is impossible to extract any more information from subsequent signal processing than is present at the first stage. Therefore, sensory noise sets a threshold for the detection of a signal. If a sensory signal is small compared to sensory noise, it will never be distinguishable at any further stage. The reduction of noise at the first stage of perception is therefore very important, and is often worth paying a high price in order to reduce this type of noise. The article authors use the example of a fly's photoreceptors, which require one tenth of the energy produced from metabolism and make up one fifth of the fly's weight.

Cellular Noise

  • Action Potentials from stimulated neurons will vary in time on the order of milliseconds, even with perfectly periodic stimulation. The neurons that detect these action potentials can resolve their arrival on the same time scale. The randomness in this process might appear to be noise, but it might also be physiologically meaningful. However, the Shannon theory of information states that the optimal way to transmit information is when the firing is dictated by a random process. Therefore, it is unknown if neurons fire randomly on purpose or if it is just random.


  • The Fano factor defined as the variance of a variable quantity to its mean. No variability in the firing neurons means a Fano factor of zero, while neurons firing like a Poisson distribution have a Fano factor of one. In experiments, there is a large range in the variability of neuron firings. This can depend on the system involved, or the creature in which the process takes place.


  • There are a few sources of noise in neurons. Cellular processing of information will add noise to a signal, just due to inherent randomness. There are many stochastic processes within neurons. A stochastic process is just a random process. Some of these processes are the production of proteins and the opening and closing of ion channels.


  • Electrical noise can be introduced by the membrane potential in cells. Most of this noise is called by channel noise, which is caused by the current produced by opening or closing the ion channels. Channel noise can produce unwanted action potentials. The size of the neuron will affect the severity of the channel noise. Smaller axons become less and less useful for communication for this reason. There is a lower limit on the size of neurons in living species due to this channel noise. Channel noise can also introduce jitters in action potential propagation. (Read APPM4390:Hodgkin-Huxley to find out more about ion channels)


  • There is other sources of electrical noise besides channel noise. Three orders of magnitude lower, there exists both Johnson noise and shot noise caused by the resistance in the membrane. Johnson noise is due to thermal agitation of charge carriers while shot noise occurs when there is a finite number of signal particles such that there are statistically significant random fluctuations. There are also some sources of noise at synapses.

Motor Noise

  • In order to move our body, the central nervous system must relay a signal to motor neurons. This signal is converted into forces on the corresponding muscle fibers. The force of a motor neuron is proportional to the number of fibers that it can stimulate. Small signals affect neurons that stimulate a small number of muscle fibers. This is Henneman's size principle.


  • Motor neurons fire at different rates. Neurons that stimulate the smallest number of muscles fibers fire fastest. At low firing rates, muscles twitches are separated in time. A continuous contraction results from high firing rates. The motor neuron that fires slowest will affect the most fibers, and variability in movement is caused by these types of neurons.


  • There are three sources for the variability of movement in muscles. Slow firing neurons that fire periodically will produce a periodic force on the muscles. Also, these motor neurons are still affected by any cellular noise. Finally, each twitch have variability in duration and amplitude from any previous noise source.


  • Human movement (limbs, eyes, etc) will be attempted in a way that minimized movement variability due to noise. This is discussed further in the following section.


Management of Noise in the Central Nervous System

  • Many experimental results suggest that the central nervous system acts in a way that reduces the effect of noise on subsequent actions. The body cannot remove noise but it can minimize its negative effects. The central nervous system manages noise in two ways: averaging and prior knowledge. Both of these methods resemble techniques used in signal and image processing.


Averaging

  • When the same signal is sent multiple times, the noise can be reduced. Noise is by definition independent of signal, and redundant signals will have different additive noise. If the noise is uniform, each redundancy will, on average, reduce the noise by a factor of the square root of two. This process is common in sensory noise. Hair cells are coupled so they move together, producing redundant signals. Similarly, photoreceptors in the eye overlap so visual input is averaged over several photoreceptors. When one neuron sends a signal over many different noisy axons, these signals can be averaged at their destination to reduce noise.


Prior Knowledge

  • Prior knowledge assumes the structure of the signal is known beforehand, in order to better separate it from noise. This concept is known as a matched filter, and the same idea can be applied in image processing. Averaging and prior knowledge can be combined to further reduce noise. Prior knowledge of the signal leads to weighted averaging, where more reliable signals are given a larger weight in averaging.


Examples

  • The motor system uses weighted averaging. If two muscles can perform the same action, they are both activated in order to minimize variabililty.


  • Averaging can occur over time as well. If the nervous system needs to know the current state of our limbs, the motor commands and the sensory feedback from the limbs (which are both noisy) are combined into a prediction. This is called Kalman filtering.


  • If the central nervous system has a task to perform (for example, moving an arm), there are many different routes to achieve this goal. This becomes a cost minimization problem, with the costs being energy, time, error, etc. It has been suggested that humans move in a way that reduces the effect of noise.


  • Sometimes we move in a manor that does not minimize the effect of noise. For example, if there is a high accuracy constraint on a certain movement then humans will contract different muscles at the same time, which increases motor noise and thus is expected to increases the variability in movement. However, the increase in joint stiffness balances the increase in movement variability in such a situation.

Application

Noise in the nervous system is being hypothesized as having an important role in perception, which is discussed by Gustave Deco and Ranulfo Romo.[3]. This review paper discusses some of the research that is being directed towards understanding how perception occurs. One interesting hypothesis is that the sensory nerves have a bistable system, where one stability point means "no stimuli" and the other means "stimulus detected". If the noise in the system is great enough then the system can be pushed from the default stable point of "no stimuli" over to the "stimulus detected" stable point. This would be referred to as a "False positive" and can occur trying to percieve stimuli near the perception limit. This review also suggests that the fluctuations in the nervous system is necessary to perceive stimuli that may be slightly below the detection limit.

Other Applications

References

  1. A. Aldo Faisal, Luc P. J. Selen & Daniel M. Wolpert. "Noise in the nervous system" Nature Reviews Neuroscience 9, 292-303 (April 2008)
  2. Alonso JM, Martinez LM (1998) Functional connectivity between simple cells and complex cells in cat striate cortex. Nat Neurosci 1:395-403.
  3. Gustave Deco and Ganulfo Romo. "The Role of Fluctuations in Perception". Trends in Neurosciences. Volume 31, Issue 11, November 2008, Pages 591-598