Objective:

 

 

1. How is neuronal spike or action potential affected in the presence of noise?
2. What is the variation in spike time-course with the effects of random noise?

 

Is noise useless or has it a role in computation that happens in the brain. Noise in the neuronal network has significant influence on transmission and integration of signals from other neurons as well as alters the firing activity of neurons in population. In this experiment, we address the impact of various types of noises in spiking neurons using electrical analog neuron.

 

Noise and neuronal spike:

 

In vivo recordings of neuronal activity, they are characterized by a high degree of irregularity. The spike train of individual neurons is far from being periodic and relations between the firing patterns of several neurons seem to be random. If the electrical activity picked up by an extra-cellular electrode is made audible by a loudspeaker then we basically hear - noise. The question whether this is indeed just noise or rather a highly efficient way of coding information cannot easily be answered. Listening to a computer modem or a fax machine might also leave the impression that this is just noise. Being able to decide whether we are witnessing the neuronal activity that is underlying the composition of a poem (or the electronic transmission of a love letter) and not just meaningless noise is one of the most burning problems in Neuroscience.

 

The main source of noise in Neuronal networks:

 

The basic definition of neuronal noise is the random influences on the transmembrane voltage of single neurons and by extension the firing activity of neuronal networks. A couple of signals has been proved that it act as noise to the information flow. Important noises are discussed bellow.

 

Noise from Genetic and Metabolic process:

 

Genetic and metabolic noise is a source of variability within the neuron, but its effect on neuron firing has barely been explored.
Researchers have focused on noise sources that act on faster time scales:

 

1. In ion channels and pumps, which control ion flow across the plasma membrane.
2. At synapses, which mediate connections between neurons.
3. In whole neurons, via the summed currents flowing through ion channels.
4. In neural networks, where the noise is related to the activity of all neurons impinging on a given neuron.
5. In brain rhythms, generated by millions of neurons interacting across the large spatial scales.

 

The dominant source is usually synaptic noise, i.e., noise generated by the activity of other neurons. Synaptic strengths also fluctuate because of the different availabilities of neurotransmitter and of components of various biochemical signaling pathways.

 

Noise from Ionic conductance and Ion channel:

 

Conductance fluctuations in ion channels are driven by thermal fluctuations. These protein channels are made up of subunits and complex domains that weave in and out of the cytoplasmic membrane and undergo spontaneous thermally-driven changes in conformations between states. The open state is characterized by a pore that allows specific types of ionic species to migrate through the membrane, under the influence of an electrochemical driving force. Biophysist uses phenomenological kinetic equations to explain the transition rates between the states, and how these rates are modified by the transmembrane potential, the concentration of various ionic species, and the presence of specific ligands such as neurotransmitters.

 

During the time a channel is open, ions migrate in complex ways and varying amounts. The associated fluctuations are termed channel shot noise. This noise is to be distinguished from the shot noise used to describe random spiking of neurons, which leads to random release times of neurotransmitter at synapses, and random currents in the postsynaptic cell. The effect of random noise in AP is discussed in this experiment in detail.

 

Noise from Synaptic activity:

 

Synaptic noise ultimately lies in the molecular events that follow the invasion of a synaptic bouton by an action potential. They release transmitter probabilistically, in response to incoming spikes some time at some low mean rate even without the input threshold. The release probability depends on the history of firing of both the pre- and the postsynaptic neuron: once a neuron fires, it affects every location in the neuron, including receptors at its incoming synapses. Information flow is thus not unidirectional across synapses. Ongoing fluctuations in the mean strength of synaptic connections due to various time-dependent plasticity processes may also contribute noisy currents to a cell.

 

The main component of the noise experienced by a neuron originates in the myriad of synapses made by other cells onto it. Every spike arriving at this synapse contributes a random amount of charge to the cell; the resulting current fluctuations depend on the degree of regularity of these incoming spike trains. This synaptic noise is particularly strong in in vivo recordings, in which the cells receive their normal synaptic input. This noise further increases the mean conductance of the cell - and thus lowers its input resistance - because more ion channels are opened at a given time; this high-conductance state contrasts with the low conductance state characteristic of in vitro recordings.

 

These noises have an influence on the transmission and integration of signals from other neurons as well as alter the firing activity of neurons in isolation. Noise can be generated by electronic devices and it varies greatly by different effects. The total input signal to the system is obtained by a measurement contains two components: one carries the information signal and the other consists of random errors, or noise, that is superimposed on the first component. These random errors are unwanted because they diminish the accuracy and precision of the measurement. In neuroscience, noise-free data can never be obtained in practice due to effects that cannot be avoided during a measurement.

 

To understand the impact of noise we use a remote setup to generate action potentials with noise.

 

Gaussian noise:

 

Gaussian noise is a very good approximation of noise that occurs in many practical cases. It is similar to white noise, but confined to a narrower range of frequencies. A Gaussian noise is a type of statistical noise in which the amplitude of the noise follows that of a Gaussian distribution. Here the precession frequency of the input signal will increase so in the output signal noise effects will be very high. Statistical noise is the colloquialism for recognized amounts of unexplained variation in a sample. Gaussian noise is statistical noise that has a probability density function of the normal distribution. In probability theory, a probability density function or just density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point in the observation space. In probability theory and statistics, the normal distribution or Gaussian distribution is an absolutely continuous probability distribution with zero cumulants of all orders higher than two. The cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.

 

Gaussian function is given by,

 

 

where μ and σ2 are the mean and the variance of the distribution. The Gaussian distribution with μ = 0 and σ2 = 1 is called the standard normal distribution.

 

Given that the probability density function, f(x), of the Gaussian-distributed Gaussian noise Pattern is,

 

 

Where s is the absolute value of the specified standard deviation, and that you can compute the expected values, E{•}, using the formula,

 

 

Then the expected mean value, μ, and the expected standard deviation value, σ, of the pseudorandom sequence are,

 

 

 

Modeling of biological neuron as electronic analog neuron:

 

As we explained the biological neuron modeled as equivalent electric circuit in experiment - I. In this experiment we are studying the effect of noise and the variation in spike time-course in electronic analog neuron.

 

We have designed an analog neuron model using Resistors, transistors, capacitors and externally input voltage. These all are some basic electronic components which will make analog neuron to behave like biologically realistic neuron.

 

• Resistance represents the difficulty a particle experiences while moving in a medium. It is measured in ohms. The inverse of resistance is conductance. Conductance is the ease at which a particle can move through a medium. It is measured in Siemens. Because they are inversely related, high conductance are correlated to low resistance, and vice versa. It is important to note that generally speaking resistance and conduction in the neuron are dealing with the ability of ions to cross the membrane. Thus it often referred to as membrane resistance or membrane conductance. As such, when the majority of ion channels are closed, few ions cross the membrane, and membrane resistance is said to be high.

 

•  The capacitor is a passive electronic components consisting of pair of conductors separated by an insulator. The cell membrane is also said to act as a capacitor, and has a property known as capacitance. A capacitor consists of two conducting regions separated by an insulator. A capacitor works by accumulating a charge on one of the conducting surfaces. As this charge builds, it creates an electric field that pushes like charges on the other side of the insulator away. This causes an induced current known as a capacitive current. It is important to realize that there is no current between the conducting surfaces of the capacitor. Capacitance may be defined two ways as ,1) an ability to store and separate charge, or 2) as the quantity of charge required to create a given potential difference between two conductors. Thus given a set number of charges on each side of the membrane, a higher capacitance results in a lower potential difference. In a cellular sense, increased capacitance requires a greater ion concentration difference across the membrane.

 

•  Transistor is an active semiconductor device commonly used to amplify (strengthen) or switch electronic signal. Here we are using 3 transistors, two NPN and one PNP transistor. Transistor has mainly three terminals. Emitter (E), Base (B) and Collector(C). Transistor T1 and T3 are NPN transistor and T2 is a PNP transistor. For an NPN transistor collector voltage is more positive than emitter. So current flows from collector to emitter. For a PNP transistor emitter voltage is more positive than collector. So current flows from emitter to collector.

 

 

 

When the input signal with noise is given the membrane capacitance Cm begins to charge, when the voltage across the capacitor reaches more than cut in voltage of transistor T1, the transistor turns on and the current flows from collector to emitter. Then the base voltage of transistor T2 becomes less and T2 also turns on and current flows from emitter to collector. The energy for it provided by an electrical gradient of Na⁺ across the membrane ,here it is modelled as E_Na.

 

This makes the capacitor C1 to charge. When the voltage across the capacitor C1 reaches more than cut in voltage of transistor T3, the transistor turns. By this time membrane capacitor Cm becomes fully charged and begins to discharge i.e., when the capacitor voltage drops transistor T1 turn off, consequently T2. As a result capacitor C1 begins to discharge and transistor T3 turn which leads potassium current to stop flow. Thus the repolarising phse of an action potential.