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Many daily activities that we perform are result of inbuilt oscillatory circuits in our body. For example walking, breathing, heart beat, blinking, etc. The coding and decoding of stored memory also happen via controlled oscillations. The link http://en.wikipedia.org/wiki/Neural_oscillation contains information about neural oscillations. It says in here that a single neuron, an ensemble of neurons and activity of brain may exhibit synchronised oscillations. It is also said that these oscillatory circuits can control all the parameters of oscillations i.e. frequency, phase and amplitude.While above are true for neurons as a part of bigger systems, my question is related to study of isolated neurons.

There are many instances of studies of artificial neural circuitary created on a customized substrate(Micro Electrode Array) by masking techniques. Also there are loads of ongoing research to study the simple neural circuits in temporal and spatial domain by electrical interfacing of semiconductor and nerve cells using Field Effect Transistor(FET).

I want to know if these kind of oscillations are unique to some special kinds of neuron? Is the control of oscillation parameter possible in every neurons and isolated neurons? Can a neuron or any other cell exhibit change in action potential independently? Do other cells except neuron and pacemaker cells exhibit oscillation? Can a single neuron exhibit memory?
Can a simple circuit like below generate oscillations?
Suppose I culture the neurons on a substrate in a controlled way such that one neuron is connected to only one other neuron in a linear fashion and the last neuron is connected to first. Assuming we supply the ions if there is loss, can a clock pulse of varying frequencies be generated, where the frequency is the function of the no. of intermediate neurons and their length.

It would be a great help if somebody can provide information about softwares to simulate simple neural circuits (If available).

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    $\begingroup$ What is your analysis on this? Theoretically you can build a continuously oscillating system but there will always be some loss. If the neuron never runs out of energy then it would keep firing. The period of the oscillation and the nature of the steady states depend on system parameters. Your question is broad and you have not made any effort to find an answer to the question. Therefore I am voting to close this. $\endgroup$ – WYSIWYG Apr 28 '15 at 11:08
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    $\begingroup$ I wanted to know about generating clock pulse using neurons by giving its own signal as feedback $\endgroup$ – 9Heads Apr 28 '15 at 12:17
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    $\begingroup$ Suppose for example I culture the neurons on a substrate in a controlled way such that one neuron is connected to only one other neuron in a linear fashion and the last neuron is connected to first. Assuming we supply the ions if there is loss, can a clock pulse of varying frequencies can be generated, where the frequency depends on the no. of intermediate neurons $\endgroup$ – 9Heads Apr 28 '15 at 12:20
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    $\begingroup$ I vote to re-open this (edited) question. At least there are some theoretical studies on such systems, and also relation to how such constructions can't explain the scalar property. $\endgroup$ – Memming Apr 28 '15 at 15:55
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    $\begingroup$ I'm voting to close this question as off-topic because OP did not provide any work on answering question. This might be asked in chat room, rather than Bio@SE. Although, I might be wrong $\endgroup$ – Oct18 is day of silence on SE Apr 29 '15 at 1:19
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Short answer
A single pacemaker neuron can generate oscillatory behavior.

Background
Given our exchange in the comments, I will focus on single neurons with intrinsic oscillatory behavior. For example, thalamocortical relay neurons and inferior olive neurons have intrinsic oscillatory properties, mainly through the interaction of a hyperpolarization-activated cation current (Ih) and a low-threshold activated Ca2+ current (IT) (McCormick & Huguenard, 1992, and Fig. 1).

Model for an oscillatory inferior olive neuron
Fig. 1 Model for an oscillatory inferior olive neuron. Source: Bal & McCormick (1997)

Rhythmic burst firing is created through generation of a low-threshold Ca2+ current (IT), which activates fast action potentials mediated by Na+, K+, and Ca2+ currents (INa, IK, and ICa, respectively). Entry of Ca2+ in the cell during fast action-potential firing and low-threshold Ca2+ spiking result in after-hyperpolarization through activation of a Ca2+-activated K+ current. This afterhyperpolarization activates Ih. Combined activation of Ih and decrease of a Ca2+ activated K+ current (IK,Ca) results in depolarization of neuron, which activates another low-threshold Ca2+ spike. In this manner, Ih modulates frequency of oscillation. In addition, tonic activation of Ih also contributes to average membrane potential, and therefore to presence, strength, and frequency of oscillation in these neurons.

Regarding the series of sub-questions - these are quite varied. Perhaps it is better to generate another one or two focused, well-formulated questions on this. For now, I will answer them curtly below. Further, the papers I linked contain a wealth of information, and the McCormick & Huguenard (1992) paper is a detailed modeling study. Both papers are awesome and the authors are three of my all-time favorites so far.

I want to know if these kind of oscillations are unique to some special kinds of neuron?
Answer: Yes quite unique, because Ih channels are quite unique (they have been called "funny currents") and they are not present in every cell.

Is the control of oscillation parameter possible in every neurons and isolated neurons?
Answer: No, as the molecular machinery such as Ih channels may be lacking in most other cells.

Can a neuron or any other cell exhibit change in action potential independently?
Answer: That depends whether the cells are coupled through synapses or other means.

Do other cells except neuron and pacemaker cells exhibit oscillation?
Answer: Yes, some cells start to oscillate, for example in the degenerated retina (modeling work only) and there are non-neural cells that when cultured spontaneously start to oscillate.

Can a single neuron exhibit memory?
Answer: Yes, through long-term potentiation or depression.

References
- Bal & McCormick, J Neurophysiol (1997); 77:3145-56
- McCormick & Huguenard, J Neurophysiol (1992), 68(4): 1384-1400

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