# Hodgin-Huxley model for a single neuron

• Topologia
In summary, the Hodgin-Huxley model is a model for channel kinetics that is based on a plausible mechanistic interpretation. However, the actual channel mechanisms should primarily be thought of as phenomenological models or "good curve fits."
Topologia
I am viewing (through https://www.edx.org/course ) an introduction course to computational neuroscience. In the second lecture, the Hodgin-Huxley model is considered. I am going over some of the questions and have encountered a problem with one of them (a picture of the exercise is attached below). I have a strong background in mathematics, but my background in biology is yet very poor. I am having a hard time connecting the biology to the math. Can anyone help with this question:

http://www.upf.co.il/preview/930650464/ea89d08e9d2bec2a0ddbefc1c860d757.html
http://www.upf.co.il/preview/730918148/54449c4d3938eb4de89a02a072d8159e.html

Thank you!

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http://www.upf.co.il/preview/930650464/ea89d08e9d2bec2a0ddbefc1c860d757.html
http://www.upf.co.il/preview/730918148/54449c4d3938eb4de89a02a072d8159e.html%5b/img

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Are you asking why the correct answer is that gion is the maximal conductance?

My problem is that I don't know how to even start this question..
The formal answer of the course is that all the answers are correct except number 2.
My original answer was that 1,5,7 are correct.
But, basically, I have a problem understanding what considerations I should use..
http://www.upf.co.il/preview/146130318/61dd63a379862f86de55863ed4935eb7.html

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I wouldn't worry about it too much. I don't think the answer is necessarily correct, but it is conventional. The form of a Hodgkin-Huxley type model is certainly guessed based on having a plausible mechanistic interpretation. However, with respect to the actual channel mechanisms, they should primarily be thought of as phenomenological models or "good curve fits" rather than mechanistic models.

But let me explain the reasoning behind the formal answer of the course. The form of the equation is:

current = conductance * (potential difference from reversal potential).

The reversal potential is the thermodynamic equilibrium potential so it is the potential at which no net current flows. So we know that current flow must be some function of the potential difference from the reversal potential, and we guess that the function is linear for each conformation of the channel. The channel conformation determines the conductance.

The conductance (g * rn1 * sn2) is determined by the channel conformation. The terms rn1 and sn2 vary between 0 and 1, so they are fractions, and g is the maximal conductance. The terms ro and so determine what r and s will tend to. When the membrane potential is increased, the curves how that ro increases towards 1 and so will decrease towards 0. So r will tend to open the channel, which is why it represents activation, and s will tend to close the channel which is why it represents inactivation. The time constant for r must be shorter than the time constant for s if the channel is to open before it closes (or more technically is inactivated).

(It's really a question of physical chemistry, since the form is motivated by thermodynamics and common mathematical forms for chemical kinetics.)

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Topologia
Topologia
I see.. will think about it a little further.

## What is the Hodgkin-Huxley model for a single neuron?

The Hodgkin-Huxley model is a mathematical model that describes the behavior of a single neuron. It was developed in the 1950s by Alan Lloyd Hodgkin and Andrew Huxley and is based on experiments conducted on the giant squid axon. The model describes how ion channels in the neuron's membrane open and close to generate and propagate electrical signals.

## What are the key components of the Hodgkin-Huxley model?

The key components of the Hodgkin-Huxley model are the membrane capacitance, membrane conductance, and ion currents. The membrane capacitance represents the ability of the neuron's membrane to store electrical charge, while the membrane conductance represents the ease with which ions can flow in and out of the neuron. The ion currents are the movement of ions through channels in the membrane, which generate the electrical signals in the neuron.

## How is the Hodgkin-Huxley model used in neuroscience research?

The Hodgkin-Huxley model is used to study the electrical activity of neurons and how they generate and propagate signals. It has been crucial in understanding the mechanisms of action potentials, the role of ion channels in neuronal signaling, and the effects of drugs and diseases on neuronal function. The model is also used to develop and test new treatments for neurological disorders.

## What are the limitations of the Hodgkin-Huxley model?

While the Hodgkin-Huxley model is a valuable tool in neuroscience research, it has some limitations. It is a simplified model that does not take into account the complex signaling pathways and interactions between neurons. It also does not consider the effects of glial cells, which play a crucial role in supporting and regulating neuronal function. Additionally, the model is based on experiments conducted on the giant squid axon and may not accurately reflect the behavior of all types of neurons.

## How has the Hodgkin-Huxley model influenced our understanding of the nervous system?

The Hodgkin-Huxley model has greatly influenced our understanding of the nervous system by providing a framework for studying the electrical activity of neurons. It has helped us understand the underlying mechanisms of action potentials and how they are generated and propagated in neurons. The model has also been used to develop and test treatments for neurological disorders and has led to further research and advancements in the field of neuroscience.

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