Biological neuron models and simulated data


by uetmathematics
Tags: biological, data, models, neuron, real application, simulated
gravenewworld
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#19
Feb2-14, 09:04 AM
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Quote Quote by Pythagorean View Post
Another thought: experimentalists are usually only reporting neurons that produce robust results. So if a neuron is varying a bunch (and not as a mechanism of something they're studying) then they won't use that neuron. When experimentalists do produce robust kinetics (which is generally what gets published) they match the basic assumptions of Hodgkin-Huxley quite well: a single cell withstands several voltage clamp treatments, maintaining a robust response in terms of activation/inactivation parameters. And these activation and inactivation functions allow the model to reproduce the output given a particular input, confirming the empirical physical assumptions about ion flow and electrochemistry across a capacitive membrane with a Boltzmann distribution of channel sensitivities.

Many (most) cells, of course, receive some modulatory effects and interested experimentalists will isolate those and characterize them and characterize their effects on the kinetics as a function of concentration in some microdomain near the channel (like calcium channels are often near other channels with calcium targets like calmodulin).

Then, if that's the phenomena the modeler is interested in, they will try to fit their activation constants as functions of concentration and introduce a new variable that models the concentration as a function of activity. If the concentration changes come from a completely different system that you're not interested in studying, and has no functional dependence on the state of the neuron you're studying, then you just model it in an algorithmic matter (there's really nothing else you can do).

If you're actually interested in the mechanics of the protein system, you're getting more into modeling proteomic and genomic dynamics than neuron dynamics. As a neuron modeler, I might draw on models from proteomics if I think it's necessary, but I wouldn't do all the tinkering to model a proteomic system myself.

There's actually a book called "Computational Neurogenetics" that has treatments whereby you consider networks of neurons, but each neuron in the network is really a network of genetic/protein processes. So you have a network of networks:

http://www.springer.com/engineering/...-0-387-48353-5


Hmm interesting, I may really check this book out. Thanks!
Pythagorean
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Feb2-14, 09:36 AM
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Quote Quote by gravenewworld View Post
That's my point I guess, is that there are explainable mechanisms through which each channel in a neuron could have different conductance and through which the number of channels on the same neuron can change with time based on the way it is modified with glycans. It's almost impossible to predict how an ion channel would be glycosylated at a moment in time. Could the H-H include a component so that the overall electrical activity of a single neuron changes with time? When you study the H-H model, what kind of environment is your neuron in? Can you test it with say one concentration of insulin and then also test it with say a different concentration of insulin? Could you test a neuron in different concentrations of sugars? Then check to see if electrical activity has a measurable change?

Now what happens when you connect a billion neurons together? Where each neuron has its own electrical identity. This identity of each neuron could also change in time, because something like glycosylation responds to environmental stress and cue. How can one include the fact that each neuron in a network is just slightly different and the identity of each is constantly changing? What I'm getting at is, is it possible to take into account the dynamic nature of an in vivo system? Hormonal cues are constantly changing, responding to stress, and responding differently in different parts of the body. It could be another way to fine tune electrical activity through a network of neurons so that the behavior of different parts of a neural network are different. Who knows, maybe it could be important for learning or storing memory? I have no idea for what other purposes dynamically changing regulatory mechanisms that fine tune electrical activity of ion channels(like glycosylation) may be important for, but nature is likely doing it for a reason.
So channels are already considered stochastically. The activation function is based on a maxwell boltzmann distribution of channel sensitivities. If glyocsylation was pervasive (I have no idea of how common it is) it could be a part of that distribution.

So we can't (and don't try) to predict individual channels deterministically, but we predict the group behavior of the channels as a statistical ensemble. The processes that go into determining each channel's individual state could have glycosylation involved for all I know.

People do distinguish heterogenous networks form homogenous ones (all the same neuron in a network vs. a distribution of neurons) and can find different dynamics in each case. That's a common topic in complexity sciences in many models besides neurons.

When you study the H-H model, what kind of environment is your neuron in? Can you test it with say one concentration of insulin and then also test it with say a different concentration of insulin? Could you test a neuron in different concentrations of sugars? Then check to see if electrical activity has a measurable change?
This would be a similar extension to the model, but the canonical model doesn't contain that machinery. You'd need experimental data to augment the Hodgkin Huxley model. As above, the experimentalist would have to measure the effects on the kinetics of the electrophysiology and then the modeler would fit that data to a function that replaces a constant in the HH model.
gravenewworld
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Feb3-14, 04:46 PM
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Quote Quote by Pythagorean View Post
So channels are already considered stochastically. The activation function is based on a maxwell boltzmann distribution of channel sensitivities. If glyocsylation was pervasive (I have no idea of how common it is) it could be a part of that distribution.

So we can't (and don't try) to predict individual channels deterministically, but we predict the group behavior of the channels as a statistical ensemble. The processes that go into determining each channel's individual state could have glycosylation involved for all I know.

People do distinguish heterogenous networks form homogenous ones (all the same neuron in a network vs. a distribution of neurons) and can find different dynamics in each case. That's a common topic in complexity sciences in many models besides neurons.



This would be a similar extension to the model, but the canonical model doesn't contain that machinery. You'd need experimental data to augment the Hodgkin Huxley model. As above, the experimentalist would have to measure the effects on the kinetics of the electrophysiology and then the modeler would fit that data to a function that replaces a constant in the HH model.

So what would be the advantages of having subceullar prediction for ion channel activity? Instead of using stochastic models, what would you need to have a deterministic model?

Glycosylation is everywhere, in every single cell. If you look at the glycome of the heart--that is the entire network of glycosylation enzymes that are expressed and all of the patterns of glycans that they can produce---there are different but non-random patterns of glycans on ion channels depending on which portion you are in of the heart. People believe that the glycome is tuning patterns glycosylation on ion channels in a non-random manner to tightly control electrical current through heart tissue. There's likely a high probability that the brain is the same.

I sort of remember stochastic processes from my undergrad when we went over brownian motion, which made the assumption of random walks to be able to apply stochastic models to describe motion of the particles. What if in this case ion channel activity was not random based on glycosylation of ion channels, that is inherently linked to a cell's metabolic state? A neuron may be non-randomly selecting for a specific population of ion channels to tune electrical response just like heart tissues seem to be doing.

I'm assuming that HH experiments are done in tightly controlled conditions? How big are the gaps between in vitro HH experiments and how neurons behave in vivo in a dynamically changing environments?
Pythagorean
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Feb3-14, 07:18 PM
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I don't know the details of glyosylation interactions, but most chemical systems have models based on mass action. But other dynamics are used, depending on the cooperativity or competitiveness of all the participating molecules. The variables/dimensions of the system are the concentrations of each participating molecule. A generic model of complex chemical interactions is the Grey Scott model:

http://groups.csail.mit.edu/mac/proj...ous/GrayScott/

The advantages/disadvantages depend on the specific question you're asking. Because of that previously mentioned problem of generality vs. specificity in modelling, you want to build your models to answer specific questions and not try to make a catch all. So such a model would be advantageous in predicting how glyosylation contributes to the kinetic state of individual channels the way you're framing it currently.

If you want to ask about whether the high frequency gamma oscillations in the hippocampus can be explained by axo-axonic gap junctions, you probably don't want to bother with the details of glycosylation.

I'm assuming that HH experiments are done in tightly controlled conditions? How big are the gaps between in vitro HH experiments and how neurons behave in vivo in a dynamically changing environments?
Yes, HH-type modeling is based off intracellular recordings. In Vivo experiments are more likely to be extracellular: measuring field potentials. Dynamically changing environments are modeled as "bath applications" or "volume transmission". It's basically just modeling more channels (extra-synaptic ones) and again, adding a new variable that represents the concentration of some ligand in the region.

You could do spatial extensions too, so that your ligands can diffuse and can have sources and sinks in 3D space and your "spherical cow" neurons would have a spatial designation and each neuron in the region of ligand would have channels reacting to it. I don't know if anyone actually does this, but I have a framework for how I'd model it. This kind of complexity is a lot of pieces to put together though, lots of experiments, lots of model tweaking, lots of abstractions. It would be a chore and you never know whether you're going to get an answer out of it or not so you have to pick your battles and work your way up to this kind of complexity carefully.


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