[MURG] - emulation difficulties

[digfarenough]

"Joseph J. Strout" <joe at strout.net> wrote:


Well, neuroscience has advanced quite a bit since Hodgkin and Huxley; 
neuron models today are quite a bit more complex than that. But this 
is the right basic idea.


Oh? In all the simulations I've ever done we used basically the same old HH formalism, with an extra channel here and there or so. Of course it only covers dynamics, you need separate equations for LTP and that kind of thing...


No it won't. If your integration method is poor and your time step 
is too large, then yes, the system will become unstable and fly apart 
(this is always fun to watch if you're doing a physics simulation!). 
But this is a problem that has long been solved. With even a poor 
integration method, you can always take time steps sufficiently small 
that it remains stable; and there are more advanced integration 
methods that allow you to take a much larger timestep.


Granted, I don't know a lot about diff eq, I just worked through a few chapters of a textbook to get some idea of how they work, some time I should take a real class in them. But there's a relationship between timestep and instability, right? Personally, I'd want my upload to last forever, who's to say the end of the universe is as far as we'll make it? There's at least one theory (based on some older models, may no longer work) of a way for us to escape, and we can always hope for infinite computation... hey, it may be a long shot, but I want to be prepared. So I'm not sure if I'd be comfortable with a system that could allow this slowly growing instability (but I'll take it if it's the only option, but those last millenia of dementia won't be fun:).


Error is different from instability. It's unlikely that minor errors 
in the simulation will have any noticeable impact on the working of 
the mind. Neurons work in a very chaotic environment, and if they 
were sensitive to small errors, the whole system would fall apart. 
Instead, there are numerous feedback loops everywhere you look, which 
result in the emergent behavior being very robust to a wide variety 
of influences. Only extreme, systematic errors caused by things such 
as drugs or ischemia are able to disrupt the system behavior.


I may have used the wrong word in choosing "error." What I meant is that with each timestep, the difference between the numeric solution and the exact solution increases. "Errors" of this sort would be systemic, they would apply to every computation done to emulate the mind. One idea that has occured to me is a separate group of calculations that watch the effects of the simulation and somehow nerf the effect... if done gradually it might work, if done system wide all at once the resulting brain hiccup could be fatal.


That's not true; even the equations governing individual ion channels 
are differential. So are individual atoms, for that matter. 
Basically, all the universe works on differential equations. But 
this is not a serious problem.


No, basically all the universe can be described by different equations, that doesn't mean it works on them. Above the quantum level, everything seems to work by nice deterministic equations (although I recall Penrose showing a few exceptions). At the quantum level things may or may not be deterministic (I read a paper, but have forgotten the foreign name, of a physicist who offered a deterministic quantum theory based on information loss). But I may be getting off topic...


The first way you outlined above (with the caveat that an accurate 
compartmental model is a great deal more complex than just the HH 
equations) will work.


Right, I had intended on biologically realistic models, perhaps with a number of compartments that'd put De Schutter's Purkinje cell model to shame... (and boy would I hate to have to program those models... luckily, there are undergrads).


If you want to experiment with this sort of thing yourself, check out 
one of the neuron modeling libraries such as GENESIS, NEURON, or my 
own CONICAL.


I've done simulations in both GENESIS and NEURON, and seem to be in the minority in thinking that GENESIS is the superior program, despite its occasional... unwelcome features.

 -Eric


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