Lotka-Volterra

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I haven't been talking about Sleep: Neurobiology, Medicine, and Society.


I am continually surprised by the flexibility of the Coursera platform for offering massive online open classes (MOOCs).  It seems like every class I take varies at least somewhat, logistically, from all the others.  Flexibility is good.....

One thing that is different about sleep class is that it is intended for two very different audiences.  It's intended for a professional audience, who are updating either their knowledge of sleep, particularly, or their "continuing education" hours.

And it's also intended for "ordinary people" who are interested in sleep.  And the lack thereof -- I suspect the vast majority of "ordinary people" taking this class don't sleep as well as we wish we did..........

The expectation is that the medical people will listen to all the lectures, and take all the quizzes, while the rest of us will skip or skim the science-heavy parts and pay more attention in the "current state of sleep medicine" parts.

I have listened to all of the lectures for the medicos -- dense with neurobio.  Neural anatomy, neural biochemistry, mathematical models of sleep/wake......................  Almost all of it new to me (despite two intro neurobio classes and multiple genetics classes!  The brain is so complex it's hard for me to get my mind around it! ).

I am not into memorization for its own sake; I'm not expecting myself to learn all of that stuff.  Whatever sinks in, sinks in, and whatever doesn't -- oh well.

I did listen to all of it, and in my mind the main take-away point is, as one of the profs said: "Sleep is a whole-animal behavior."

Sleep/wake, and the transitions between those states, are incredibly complex, and are the result of multiple and various networks of systems, all having input into the sleep/wake state of the individual.

No wonder no one knows how to "fix it" when a person can't sleep.................................

Sigh, and alas............


Anyway.

One of the things I have learned about neurons in the last year or so is that (at least in the general case), each neuron takes in info from a bunch of other neurons, and then decides whether or not to fire a signal on to the neurons which are listening to it.

Networks of neurons talk to networks of other neurons.

And another thing I have learned is that some neurons put out inhibitory signals.

So -- each individual neuron is receiving signals from some (potentially very large) number of other neurons.  Some of those other neurons are saying "GO GO GO!", and some are saying "go", and some are saying "no", and some are saying "NO NO NO!"  (And everything in between, no doubt.)

Digression:  Each neuron takes in all of this (probably conflicting) info, and makes a decision about what to tell the neurons that are listening to it.  Any one neuron can say "go" or "no", but, if I understand correctly, not both.  The strength of the signal a neuron sends ("no" or "go") or a stronger ("NO NO NO!" or "GO GO GO!") is a function of how many signals it sends down the line in how much time.  More signals in a given time period is a stronger signal. 
End of Digression.

Ok.

Sometimes there are two populations of neurons that talk back and forth to each other in a little intimate loop.  One population might be saying "GO!" to the other, while hearing "NO!" in response from the other population.  The population hearing "NO!" will be less likely to say anything, while the population hearing "GO!" will be more likely to speak up. 

The point I'm getting to is that someone figured out that the Lotka-Volterra equations, developed for understanding/explaining variations in the populations of predators and prey over time, are used to explain and understand the behavior of this sort of loop between neuronal populations.

I was blown away that A) equations developed for studying the size of populations of predators in relation to the populations of their prey would apply, and B), that anyone would even think of trying to apply such equations to the behavior of neuronal populations.

Until I expressed my amazement to the household statistician.  I learned then that the Lotka-Volterra equations actually have a very wide array of applications, so trying it out to understand neuronal behavior would not be a stretch at all.  Who knew.........


It was still new to me, and I still think it is cool that equations developed for understanding the relationships between the sizes of populations of predators and prey apply to the behavior of different populations of neurons!



And now, for your patience, here is an image.  This is a graph of the Lotka-Volterra equations.  This one is French.  "temps" is time, "proies" is prey (green line), and you can tell that red is predators.  Population size on the Y axis, time on the X axis.

Increases in predator population follow increases in prey population, and crash after the prey population crashes...........

Image from Wikimedia commons. It is in the public domain.

And I still think it's cool that these equations are useful for understanding the behavior of some populations of neurons!


The "current state of sleep medicine" part of Sleep: Neurobiology, Medicine, and Society just started this week.  So if you can't sleep, you might be interested, and you won't have missed any of this part of the course......

(I've only listened to one of these lectures, so far, but it's clear they are aimed at "ordinary people," unlike the previous lectures.  Rather than Lotka-Volterra, it's "Here's how we take a history, for a person who has sleep issues.")

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