Stochastic Nature of Neuronal Behavior

 

Stochastic nature of neuronal behavior

Because single neurons have small and uncertain effects on other neurons, the cortical description must be carried out in terms of neuronal populations rather than at the level of individual cells. (Stevens; Cortical Theory, 242)

Neurons exhibit stochastic variability.  Even for repeated presentations of a fixed stimulus, a neuron's spike response cannot be predicted with certainty. (Doya, et al.; Bayesian Brain, 53)

The random nature of synaptic transmission makes neuronal behavior uncertain; networks of neurons must be described probabilistically. (Stevens; Cortical Theory, 241)

The reliability of spike transmission increases steeply for approximately 20 to 40 synchronous thalamic inputs in a time window of 5 milliseconds, when the reliability per spike is most energetically efficient. The optimal range of synchronous inputs is influenced by the balance of background excitation and inhibition in the cortex, which can gate the flow of information into the cortex. Ensuring reliable transmission by spike synchrony in small populations of neurons may be a general principle of cortical function.  (Spike Synchrony in Small Populations of Neurons)

 

Synaptic Transmission a Stochastic Process

Synaptic transmission is a stochastic process. Neurotransmitter is released at axon terminals in packets—called quanta (not to be confused with ‘quantum’ in quantum physics; they are completely unrelated)—so that the total effect of a nerve impulse arrival is an integral multiple of the smallest effect, the one produced by a single quantum. The quanta are released probabilistically according to a Poisson process. (Stevens; Cortical Theory, 240)

Many neuronal pathways arising via synaptic efficacies are spatially intertwined in sparse, distributed patterns in the neuronal network. Many synapses along any active pathway flicker on or off from moment to moment resulting from stochastic synaptic effects.

Probability of release of a packet quantum at an individual synapse is generally very low, about 0.1 to 0.5. (Stevens; Cortical Theory, 241)

Any particular neuron generally seems to receive only one or two synapses from any other neuron. (Stevens; Cortical Theory, 241)

When a pair of cells is connected, the communication link between them is quite unreliable for pulse arrival, although it is predictable in a statistical sense. (Stevens; Cortical Theory, 241)

The effect of one neuron on another is generally small and uncertain. (Stevens; Cortical Theory, 241)

A single input has only a relatively small effect on its target. (Stevens; Cortical Theory, 241)

The random nature of synaptic transmission makes neuronal behavior uncertain; networks of such neurons must be described probabilistically. (Stevens; Cortical Theory, 241)

Probabilistic descriptions are not required for all neurons in the brain. For Purkinje cells in the cerebellum, for example, in which one neuron makes thousands of synapses on its target cell, statistical fluctuations in synaptic strength are very small. (Stevens; Cortical Theory, 241)

Stochastic nature of individual neuron behavior

An individual neuron does not fire in a deterministic fashion. The thousands of synaptic inputs on the dendritic tree of a neuron function on a population basis to result in a probabilistic influence on the neuron’s firing. Assemblies of perhaps ~1000 neurons  within a volume of ~0.1 mm³ may be sufficiently correlated to comprise a physiologically meaningful neural signal.

The behavior of cortex at a particular point is described by the firing in a population of neurons. The total firing that represents this population would be determined by a weighted average of the appropriate neurons in the cortical region that surrounded the point, perhaps with weights that are described by a spatial Gaussian. (Stevens; Cortical Theory, 243)

 

 

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