text:
Origin of the biochemical term, Pi (inorganic phosphate)
I would like to know when the term Pi (inorganic phosphate) was introduced in the representation of biochemical reactions, how it was originally defined, and the justification given then for using it rather than an individual species of phosphate.
(I would also be interested in the current justification, but that’s probably another question.)
Let me provide some background to my question. Phosphoric acid (H3PO4) has three ionizations, which produce successively the species: dihydrogen phosphate (H2PO4–), monohydrogen phosphate (HPO42–) and orthophosphate (PO43–). At pH 7.4, according to the Wikipedia entry on phosphate, the main species are the mono- and di-hydrogen phosphates (61% and 39% respectively). The term Pi must have been introduced in the 1950s at latest (perhaps before the war), at a time when there would have been little knowledge of the nature of the species involved in reactions involving phosphate — certainly not at the active sites of enzymes.
One of the reasons I am curious to know how the term was introduced is the extent to which it persists in 21st century biochemical text books, where it would seem that many authors either do not know or do not care to explain to their readers why they are still using it at a time when much more is known about the reaction mechanisms. Neither of two well-known texts explain the different ionizations of phosphate, and give only parenthetical definitions in terms of a single species — different in each case: Berg et al. referred to Pi as orthophosphate, whereas Nelson and Cox’s, Lehninger  Principles of Biochemistry referred to it as HPO42–.
Acknowledgement: This question was provoked by the SE-Biology question — Where is the H+ ion in this step of glycolysis coming from?

I think the umbrella term "inorganic phosphate" (Pi) was introduced as a shorthand for "phosphate dissolved in water", precisely because phosphate exists as both HPO4 and H2PO4 forms, as you mention --- it would be inaccurate to use only one formula, and it's inconvenient to have to use both. A similar shorthand is CO2(aq). It may be inaccurate for detailed enzymatic mechanisms, but it's sufficient for describing overall enzymatic reactions in water, and I would guess this is why it's still used. This is just my guess, haven't looking into this in depth ...

@Roland — I had started to do some historic back-tracking when nobody answered, but only got so far. I need to recall old books from the stack of my University library in order to get at the sources and have delayed until I have more time and energy. I'll post an answer to my own question eventually.

I'm voting to close this question as off-topic because  it would be a better fit for history of science and mathematics (hsm.SE)

I thank the person who corrected my spelling of "referred" but have reverted his other gratuitous and unjustified alterations. "When" was italicized for emphasis. It is not unreasonable to do so.  As for the question of whether the full stop (period) in a sentence is inside or outside the parentheses, that is a matter of style. My style is that of The Penguin Handbook — see the accepted answer to a question on SE English Language & Usage. Noli me tangere.

This terminology is at least as old as September 1944 when Enzymatic Synthesis of Acetyl Phosphate Journal of Biological Chemistry
155,  55-70 was published by Lipmann, which says:

Inorganic phosphate, referred to as Pi, was estimated
colorimetrically

See also the definition of "inorganic phosphate" and "orthophosphate" from this 1943 University of Wisconsin Thesis:

Compound:  Inorganic phosphate or orthophosphate
Definition: Phosphate whose calcium salt is insoluble in water-alcohol mixtures under the conditions to be described. E.G. NaH2PO4

In other words, "orthophosphate" was a generic term for mono, di, or tri basic phosphate.  It did not have the narrower meaning attributed in the OP.

Thank you for this piece of information which suggests an answer to the origin of the abbreviation, Pi, for inorganic phosphate. However it is interesting that in this paper Lilpmann does not use Pi in the biochemical equations he presents, but instead uses H.OPO3H2 (i.e H3PO4 — undissociated phosphoric acid). So I suspect that Pi was first used in equations subsequently, perhaps by Lipmann himself. Unless someone does it for me, I'll start to follow this up.

@David ok, start with equations 4 and 6 in this 1953 article: http://www.jbc.org/content/203/1/501.short

How do you find them? That's very interesting because in the list of abbreviations it defines Pi as orthophosphate, which is chemically precise, but ionically incorrect. However this is disguised (as it was for years) by the fact that the equations are "biochemical equations" and do not involve chemical formulae. I'll poke around a little next week in the hope that a comprehensive answer can be constructed.

@David I just searched in Google scholar http://scholar.google.com/ for terms like "inorganic phosphate" and "pi", or "orthophosphate" and "pi".

@David "orthophosphate" was a generic term for PO4---, HPO4--, or H2PO4- .  I clarified this in the answer.

Aaaah. According to the Wikipedia article (which I don't necessarily trust) orthophosphate currently refers to the triply negatively-charged ion, as in the question. I see you are a longstanding contributor to the Chemistry list. Is there a current chemical consensus on the term?

@David I think Wikipedia is just wrong about this and "orthophosphate" is a generic term for phosphoric acid and any salt thereof, but in contrast to metaphosphate, pyrophosphate, and polyphosphate.  "Orthophosphate" has been used in this generic way for at least 150 years.

OK. You get the money. I'll try to do a little more on this and perhaps post a summary.


text:
Homogeneous and complex nuclei
In the Wikipedia article on nuclei one reads:

"The neurons in one nucleus usually have roughly similar connections
  and functions."

I read this as "a nucleus usually is roughly homogenous", i.e. contains a small number of neuron types, distributed roughly equally and with a roughly homogenous connectivity pattern.
But it is also stated:

"A nucleus may itself have a complex internal structure, with multiple
  types of neurons arranged in clumps (subnuclei) or layers."

What I would like to know:

Is my reading correct?
Are there really more nuclei of the more simple (homogeneous) type than of the more complex type?
Which are prototypical examples of both of the types (more simple and more complex)?
Which are the greatest nuclei of "the" simple type (with respect to volume or number of neurons, taking "simple" with a grain of salt)?

I think you are reading too much into that statement. The proper reading of that statement is to add on the implied "..compared to other nuclei." That is, what defines a nucleus, in most cases, is some shared similarity in connectivity. That does not mean homogeneity.

I also think your reading of the second statement is incorrect; it does not suggest that there are "simple and complex" nuclei as two distinct categories, rather it is indicating that "complexity" varies, and gives a couple examples; essentially, it is exactly saying that you should not assume homogeneity.

I don't think it makes much sense to think in terms of "number" of nuclei, and anyways, nuclei can be somewhat arbitrary. For example, take the auditory thalamus: the medial geniculate nucleus (MGN). The MGN is typically divided into three parts: the dorsal, ventral, and medial divisions. Someone chose to call them all the medial geniculate nucleus, based on gross appearance, but with more functional understanding we can classify each part separately. Should this be one nucleus or three? It really doesn't matter, it's just semantics and terminology to get people talking about the same structure. In one context, it makes sense to talk about the whole MGN, in other cases it makes sense to differentiate between MGv, MGm, and MGd. You could call them subnuclei, or nuclei, or whatever you want. Most people choose to just be consistent with the terminology used in their field for historical reasons because it doesn't matter.
I don't really think it makes sense to think of in terms of prototypes; nuclei are different from each other.
Again, you'd have to first define simple and complex. I don't think there is meaningful dichotomous distinction.

I am aware that there is no strict dichotomy between "simple" and "complex" but a continuum. Maybe I should have pointed this out.

Okay - your questions #2 and #4 don't work if that is true. #3 maybe but I think it's still a problematic; the simple/complex continuum is also not one-dimensional (i.e., there are different potential types/definitions for complexity).

You are right! But why do you say "the simple/complex continuum is also not one-dimensional"? Isn't this at the very heart of the problem? Given this "problem": How could one ever approach it?

Exactly - in my opinion it's an ill-posed problem. So, the issue isn't trying to approach the problem, but deciding not to. I think it's more helpful to appreciate and embrace the diversity of nuclei; the same approach is important in biology in general. It's much harder to reduce biological concepts to strict rules the way other fields sometimes strive for. If you pick any two nuclei, and claim one is simpler than the other, I can almost guarantee someone can make an argument for the inverse based on a different definition of complexity.

Nevertheless, there is possibly some truth in the dichotomy (as in most dichotomies). And why throw the baby out with the bathwater?

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text:
Does opening of ion channels alter the membrane potential directly?
Does the opening of a voltage-gated ion channel (i.e. the change of configuration of the protein) by an appropriate local change of the membrane potential directly and significantly alter the membrane potential in turn? Like the influx of ions that was caused by the opening of the channel does directly alter the local membrane potential?
(Assume there were no ions going through the channel: would there nevertheless be a significant change of the membrane potential by the mere opening of the channel?)

Why are you interested in this question? How can you imagine a channel opening but no ions passing through? Even if we could somehow experimentally isolate this effect, why would you expect it to matter enough compared with the voltage changes due to ion flow?

I added "significant" in my question. Because I am not a biophysicist and my physical intuition is not strong enough, I only guess that there might be a significant change. If you say the effect is negligible ("doesn't matter enough"), that's already a valid answer.

Like others said before: if there was such an effect, you would have heard of it. Does this apply here, too?

BTW: Of course I can imagine a channel opening but no ions passing (because there aren't any around). But not under normal circumstances, that's true.

Not in any substantial way from the perspective of the overall membrane potential; it could be possible to measure the charge moving as a way to study channel gating, but that's a completely separate issue (and the scale of measurement would have to be incredibly precise, way more precise than is relevant for neural function).
Although very few ions have to move across the membrane to change the membrane potential, this "very few" is in relationship to the total number of ions present in a solution, which is massive and difficult to imagine. A single ion channel can flux millions of ions per second.

That's the explicit answer I hoped for (and expected) but couldn't get otherwise.

I would like to add a small calculation to this question:
The membrane has a large capacitance (1 uF/cm^2). A 20 um diameter cell will have a capacitance of about 50pF.
The number of charges needed to change the membrane potential in 1 mV can be calculated by:
Q=C*dV
Acording to the fromula you`ll need 0.5 pC or about 3*10^-6 elementary charges to produce a 1 mV change.
A single ion channel such as the Shaker K+ channel can move 12-13 elementary charges during activation link. This would mean activation of 3*10^6 Shaker K+ ion channels.
You can see you`ll need to have a lot of channels to do the trick.
Even though the voltage changes due to these "gating" charges is small, the current generated by the movement of these charges can be measured. They are called "gating currents".

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text:
How do firing patterns arise from the activity of many ion channels?
In his answer to another question, Bryan Krause says:

Ion channels don't exhibit any firing patterns: neurons exhibit
  firing patterns that depend on all the channels present [...].

I understand it this way: The observable and measureable firing pattern1 of the neuron (created at the trigger zone) is the linear superposition of tiny "firing patterns2" of all the (voltage-gated) ion channels at the trigger zone, which in turn depend on the probabilities of opening and closing which are the same for all ion channels of the same type and obey some Hodgkin–Huxley-like law. These probabilities correspond directly to the shape of firing pattern1.
The rhythm with which each single sodium channel opens and closes ("firing pattern2") doesn't have to mimick firing pattern1 exactly, only roughly and probabilistically: the open-close-ticks must occur near to the spikes of  firing pattern1, but not exactly and not at every spike. And some complete outliers are allowed. The rest is superposition.
Seeing things this way, indiviudual ion channels do exhibit "firing patterns2", but these may look quite different than firing pattern1 (although not completely).

Is this kind of reasoning correct?

If so: Can the following conclusion be drawn: The time scale of a firing pattern1 depends on the number of ion channels at the trigger zone? This might be seen when looking at the rise time of a single action potential: If there is only one sodium channel, rise time will be larger, if there are many, it will be smaller. Is this correlation strictly linear?

Typically the activities of the ion channels are not called firing patterns as in neuroscience we refer to "firing" when we mean the elicitation of action potentials (spikes) but yes: Whenever an AP was fired a sufficient amount of sodium channels had to be open and therefore I thing your reasoning is correct. In other terms what you are saying is that the effective channel conductances change during an action potential.
On your conclusion: In the regime of natural parameters the time scale of firing pattern 1 mostly depends on the time constants of the voltage gated ion channels and not so much on the absolute number of channels (especially if all the conductances would scale equally).
In the world of Hodgin-Huxley like coupled- and nonlinear-dynamical systems the voltage does not scale strictly linear with increasing the participating max. conductances. The interplay of max. conductance and temporal gating dynamics resulting in the effective conductance itself depends on the voltage and there are nonlinearities. So the correlation between the number of channels and the AP rise time is not expected to be strictly linear.
See the figure for a little example: I tested my reasoning by increasing the max. conductance for the sodium channel of a simple HH model and checked the max. steepness of the voltage (normalized by peak voltage).
Hope that answers your question(s).

+1. Simulations are always appreciated! I've formatted your figure to remove the white space on the top but feel free to roll-back to the previous version if you don't like the result.

I like this answer, but I think it's a bit too forgiving of the misconceptions in the original question. The original question seems to presume that firing frequencies in neurons come from the open and closing times of ion channels, which is not accurate, or at least not accurate in the sense of how an ion channel physiologist/biophysicist would use those terms: channels flutter open and closed at much much higher rates.

Searching briefly, this page has a good depiction of the difference between single channel openings versus populations of channels: http://nerve.bsd.uchicago.edu/med98b.htm

Thanks for the edit, vkehayas. Yes, I fully agree Bryan! It took me some while to translate the question into a way I am used too discuss such issues. After reformulating my comments in that direction again and again I decided too just remove the paragraph completely and to give more like a minimal and "forgiving" answer but yes, you are right.

Thanks to all for your efforts (in trying to understand my question and giving helpful answers and comments). Especially thanks to you, @BryanKrause, for the link which gives me a better background.What I am still missing is a picture of single channel's "being open patterns". And why not relate these to firing patterns?

@HansStricker The link I shared has exactly that. See Figures 10, 11, 12 for example, or Figure 15. You'll see the channels more or less just flutter back and forth at a given depolarization. These flutters happen much much faster than action potentials. Action potentials arise from a whole bunch of channels randomly fluttering, and overall conductances through certain channel types are from an average of the number of channels open (i.e., their open probability), not all channels of one type are open at the same time.

@BryanKrause: Maybe you can understand how hard it can be to see the "forest (= the firing pattern) for the trees (= the open patterns)" - both conceptually and experimentally.What I still cannot see: Is there a refractory period of approx. 2 milliseconds for single ion channels or only for the neuron as a whole?

@BryanKrause: Just for the record: I did not suggest, that "all channels of one type are open at the same time". But they must be open somehow synchronized (= not too far away from the "beat"), otherwise no observable action potential would arise.

@HansStricker I don't see a reason why there should be a refractory period for an ion channel as conformational changes of proteins are purely stochastic processes driven by physical forces that act quasi-instantaneously and there are no saturation effects. It is just biased flickering between two or more favoured conformations (local minima in the proteins energy landscape).

Wikipedia explains refractory periods at the level of ion channels. What's wrong with that?

@HansStricker Voltage gated sodium channel inactivation is one of the contributing factors to refractory periods, but it is not the only contributing factor. Ion channels do not "fire" - it makes no sense to talk about "firing patterns" of an ion channel. The voltage gated sodium channels of cells with all sorts of firing patterns have the same inactivation kinetics, the differences in firing patterns are due to other differences. Also the 'synchronization' of voltage gated sodium channels opening is because of positive feedback from changes in membrane potential, not gating time.

@BryanKrause: I can not bring together the following: You say "channels flutter open and closed at much much higher rates" (than neurons fire). You say "channel inactivation is one of the contributing factors to refractory periods" (which is in the range of milliseconds). Wikipedia says; "Inactivation of ion channels occurs within milliseconds after opening." How does this fit together with "fluttering at much higher rates"?

You are mixing two different things: One is the probabilistic fluttering between open and closed states of the channels which you can imagine as a binary process (Bernoulli, short time scale) and the other on top is a slowly varying process dependent on the systems state (things like the voltage). The latter shapes the expectation value of the fast process over time. The quote from Wikipedia just states that the expectation value of the fast process goes down within miliseconds (which is slow in comparison). Hope that helps

Reading at Wikipedia: "This creates a current caused by the flow of ions through the channel. Shortly after opening, the channel is blocked by the peptide ball." This sounds (in my ears) as if it happened by an automatic and necessary inner mechanism of the channel. But you say "no, it happens by a contingent outer mechanism", right?

Yes! The ion concentration affects all the channels but the single channel has no memory about the duration of its own state. The net effect of ions flown through all channels (or wherever else, i.e. current clamp) in the proximity combined change the potential and give rise to an inactivation of single channels through  conformational switches.

So the flow of ions  through a single ion channel (and the resulting change in voltage) would not be enough to inactivate it - but it participates. Now I got it!

Let me summarize what I believe to have learned from Jojo's and Bryan's comments in form of a visualization: The red curve is the probability governing the open and closed state of an ion channel (as a function of time - we see two spikes) The dotted patterns below show 50 ion channels fluttering between open (black) and closed (white) states, according to the probability of being open. The thin black curve is a smeared out average of the first ion channel being open (showing two slight elevations, i.e. on a coarser time scale some kind of "firing pattern" – please forgive me, Bryan). The fat black curve is the smeared out average of all ion channels. The blue curve is the number of channels being open at a given point in time which is somehow proportional to the conductance, current, and/or voltage being measured. Noise is large due to the small number (25) of ion channels.

For 200 ion channels and overlaying the 200 patterns, it would look like this:

Find a higher resolution picture here.
See two related biological scenarios here and here.


text:
Number and function of voltage-independent ion channels
Googling for "voltage-independent" ion channels neurons doesn't give a good overview over the topic (and yields only approx. 50,000 hits, compared to 500,000 hits when searching for "voltage-dependent" ion channels neurons).
What I want to learn:

How many voltage-independent ion channels are there in the brain (or in specific parts of the brain, e.g. cortex) compared to voltage-dependent ion channels? (Rough estimate, order of magnitude: a tenth, a percent, ...?)
Which functional role do they play (compared to voltage-dependent channels which are mainly (?) concerned with the propagation of action potentials along the axon)?

Are there other (and possibly more concise) references than the one I found:
ROLES OF THE ION CHANNEL NALCN IN NEURONAL EXCITABILITY CONTROL (which states, that NALCN is "widely expressed in the nervous system")?
(I guess voltage-independent channels could support the mechanisms of Rall's model which doesn't pressume voltage-dependent ion channels but only modifiable membrane resistances, possibly realized by voltage-independent ion channels, right?)
Addendum: I made a bad mistake not pointing out, that I meant ion channels that are neither voltage- nor ligand-gated but just influence the membrane resistance passively. (Ligand-gated ion channels are of course examples of voltage-independent ion channels, but not the ones I wanted to ask for.) Are the voltage-independent ion channels I wanted to ask for possibly just what is called leak channels?

Yes those would be called leak channels; please don't change your question here though because that would be far to big a change. Note that like in my comment below, the prototypical leak channels (the two-pore-domain potassium channels) are not gated by voltage per se, but they still have some voltage sensitivity.

Those would be referred to simply as 'ion channels'. Voltage-dependent channels should get special mention.
This link from the Blue Brain Project should prove useful:

http://channelpedia.epfl.ch/ionchannels/

A query for 'voltage-dependent' gives me results from 58
channels. According to the original
reference
there should be at least 187 channels in this database (out of the
estimated ~500 ion channels expressed in the brain). That should
give you at least the order of magnitude.
An additional resource can be: https://icg.neurotheory.ox.ac.uk/.
'Non-voltage gated' channels are used to depolarize and
hyperpolarize the membrane. That is as much as specific the answer can be when talking about all of the ion channels. Their specific compartment localization makes a big difference, though. Those that are located in synapses have different functions compared to those that are non-synaptic, for example.
No, voltage-dependent channels are not
solely found in the axon. That is what makes dendrites active
compartments as well. See this very good
review
and my
answer
to
How does a neuron change as you learn?.
In brief, voltage-gated channels facilitate the integration of
inputs on the dendrites independently from the integration at the
level of the soma. This is thought to extent the information
processing capacity of the
neuron.

PS: A lot of your questions suggest that you would be interested in the NEURON simulation environment, as previously suggested to you by @bryan-krause. Using this tool could save you some trouble of trying to re-invent the wheel, as you can start off by using a pre-existing model from ModelDB.

Oops, I seem to have overseen something (what a shame): when did Bryan suggest NEURON to me?

Thanks anyway for your answer, I'll try to follow your advice(s).

First thing I stumbled upon at channelpedia: What does "distributed exponentially" mean? With respect to which variable (distance from soma?), and with positive or negative exponent? (I would guess negative, because channels decrease resistance, thus increase the time constant, thus decrease speed of propagation).

Marginal note: I said "mainly concerned", not "solely concerned".

Nice answer, I have two add-ons: 1) a lot of ion channels, regardless of gating, are made up of multiple subunits. In some cases they are not only heteromultimers, but each protein component can have multiple varieties that can each fit in with the other subunits. Because those subunits are somewhat exchangeable, the number of unique ion channels is quite high, although not all combinations are often observed for various reasons. 2) Lots of channels that are not thought of as voltage-gated still show some voltage dependancy. For example, IRK channels.

Without knowing to what exactly you are referring to, I'd venture to say that they are talking about inter-channel distances, i.e. distances from/to every ion channel's closest neighbour.

Might turn out to be the same.

@vkehayas: I found Bryan's suggestion of NEURON (in his last comment on his answer here: https://biology.stackexchange.com/a/65641/27928)

@Bryan: 1) goes too deeply into details, 2) is more concerned with what we know than how things are.


text:
Questions concerning synaptic input and dendritic processing
In the article How Spike Generation Mechanisms Determine the Neuronal
Response to Fluctuating Inputs, I read (p.11629)

I have four questions concerning some formulations:

What is "the membrane time constant" if this depends on the membrane resistance and capacitance which varies over the membrane? Maybe "local membrane time constant"? Or "mean membrane time constant"?
What do the authors probably mean with "instantaneous postsynaptic currents"? Occurring at the same time all over the dendritic tree?
What do they probably mean with "exponentially decaying synaptic currents"? The decaying of the PSPs while travelling down the dendritic tree?
What's the relation between "synaptic decay time constant" and "membrane time constant"?

(Having digested the paragraph a bit more, another - probably more accurate - reading of "instantaneous" came to my mind: "starting and ending abruptly with the abrupt opening and closing of the ion channel".)

I wouldn't suggest trying to understand this passage in terms of actual biology. This paragraph is the equivalent of the common physics trope "assume a uniform spherical cow" - they are simply describing some mathematical properties of a neuron given some assumptions. In many cases those assumptions may be very reasonable, but it doesn't make much sense to start from a uniform spherical cow and work backward into the actual shape of a cow.

I know what you mean. But the authors don't seem to be cowboys and they presumably know what they are talking about. And they obviously talk the language of actual biology (at least they use some of its vocabulary).

Started writing a comment and realized it was an answer...
These guys are basically saying "take a uniform spherical neuron" the same way you would say in physics "take a uniform spherical cow." There isn't a dendrite mentioned in the whole paper.
By "the membrane time constant" they mean exactly that: one membrane time constant, effectively the somatic time constant. They aren't talking about dendritic trees: they are essentially saying assume a uniform spherical neuron that gets inputs on its soma.
Membrane time constant is associated with the rate of change of the membrane voltage; synaptic time constant is associated with the rate of change of the synaptic current (this is what they refer to when they talk about exponentially decaying synaptic currents). Real biological synaptic currents have a time course governed my neurotransmitter concentrations and the gating properties of postsynaptic receptors. Real biological postsynaptic potentials (voltages) are governed by both the time course of the synaptic current and the capacitive properties of the membrane (i.e., the membrane time constant).
Instead of considering synaptic time constants, you could simplify a synaptic event as an instantaneous current impulse: essentially the entire current all in one instant rather than over time. The presence of the membrane time constant helps with making this assumption somewhat reasonable, because the membrane time constant ends up filtering input currents anyways, whether they are impulses or have a synaptic time constant.
In a simulated environment, you can make computations simpler by just adding a little time to the membrane time constant to roughly simulate the effect of the membrane time constant + synaptic time constant. Again, this is for computational efficiency, like when you assume a cow is spherical, not for perfect biological accuracy.

Can all of this really be true? Do these guys - who I really don't want to offend - really think of uniform spherical neurons? If so, they will have good reasons -  which in turn I would like to learn about.

I agree and I also am irritated, that they don't mention dendrites. But what does this mean/imply...?

Well they are testing a fairly specific parameter in their paper, and they want to know what effect it has on a soma-centric measure. It's much more tractable to start with simple assumptions. I'd also suggest the Magee 2000 paper that I suggested you read on another answer - as that one shows, by the time you get to the soma, synaptic properties and active dendritic processes somewhat normalize the EPSPs. If that's true, then it doesn't much matter where on the dendrites they initially came in, at least not for the integrative properties of the soma.


text:
Do non-functional (‘junk’) protein sequences exist?
For DNA one can distinguish between

protein-coding DNA sequences, i.e. nucleic acid sequences inside DNA (vs. non-coding sequences)
DNA sequences that do not code for proteins but are transcribed into functional RNA
non-transcribed DNA sequences that have other (e.g. regulatory or structural) functions
non-transcribed and non-functional DNA sequences (‘junk DNA’)

The relative proportions of these seem to depend heavily on the organism and are only roughly known.

What I wonder is whether there are protein sequences (i.e. amino acid sequences inside a protein) that have no functional purpose.

A non-functional protein sequence might be a sequence that is neither effective to the outside (e.g. as a site for post-translational modification) nor to the inside (e.g. in folding). But even those parts of the protein might contribute structurally by their sheer presence and mass which is important when considering proteins not only as chemical but also as somehow mechanical devices. This might be called its structural purpose.
Assuming that each part of a protein has either a functional or only a structural purpose the question arises what the relative proportions of functional vs. only structural parts are.

Could your title be : "Do non-functional protein sequences actually exist?" (possibly without the "actually")? It seems like you are saying that surely all sequences have some function.

I have removed the word sequence as a qualifier for protein wherever what you are talking about is the physical entity — the product of translation of a mRNA — a protein. Further, the terminology you use is unfortunate because the term ‘functional’ is often used in contrast to structural. I have therefore added “junk” as an alternative. Finally, your question is unanswerable. If a protein exists, it is impossible to prove that has no function. I have added this as an answer, but I think your question should be withdrawn on that basis.

I'm afraid you distorted the spirit of my question which was intended to be explicitely about amino-acid sequences inside a protein, not about the protein as a whole.

Oh dear, that's unfortunate. David's answer does still apply somewhat to your actual question, but could focus more on things like disordered or unstructured loops in protein structures, I guess. This paper might be interesting : https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2882790/

Sorry about that. And I only just picked up your comment as you hadn't put an @David in so that I would be notified. I would still avoid the word "sequence" like the plague when talking about actual entities. The reason is that it emphasises the conceptual pattern, rather than the physical entity. If I understand it you are talking about linear portions of the chain of amino acids in actual synthesized proteins. If this is the case, it is also a difficult question, but in a different way, and worth asking. I can help you construct another question if you wish.

@David: I would be pleased!

I suggest a question with the title: "Are there functionless stretches of amino acids in proteins?" And the question follows in the next comment. If it fits the bill (perhaps with changes) you could mount it and we could modify this question and cross reference them.

Suggestion for Question: The variation in amino acid sequence of the same protein in different species indicates that at certain positions different shapes or even polarity are possible. Nevertheless an amino acids at such positions may be necessary for the overall structure of the protein. In contrast I am interested to know about stretches of several (perhaps six or more) successive amino acids — tails or loops, perhaps — that evidence suggests to be unnecessary for the protein. Do these exist and, if so, what proportion of the proteome do they constitute?

This question is unanswerable as, if a protein exists as a physical entity in a cell it is possible to demonstrate it has a functional or structural role, but it is logically impossible to demonstrate it has no such role. The best one can say is that “it has no known function (role)”.
That said, in the course of evolution following gene duplication and divergence it is theoretically possible that on the way to acquiring a new functional role there is a stage at which a protein has no such role. One might be able to identify such proteins in a gene family like the globins by examining a range of species, as has been done for the globin genes. I am not aware of any such studies.


text:
Excitability of neurons
[The following includes a) two specific questions (at the end), b) an attempt to capture a dispositional concept (excitability) in geometric and physical terms.]
I assume that "excitability of a neuron" is a reasonable concept (and measure) to distinguish neurons: there are (as will be seen) neurons that are more or less excitable (in a quantifiable way).
What does "excitability" mean?
Excitability $E$ may be operationally defined as the sensitivity of a neuron to excitatory synaptical inputs. Mathematically stated: as the (decimal logarithm of the reciprocal of the) proportion of excitatory synapses that must be simultaneously active (i.e. generate an excitatory postsynaptic potential, EPSP) in order to collectively evoke an action potential.
Let $N$ be the number of all excitatory synapses of the neuron, $n$ be the the minimal number of simultaneously active synapses that is needed to evoke an action potential:
$$E = \log \frac{N}{n}$$
If the proportion is 100% (all excitatory synapses must be active), $E =  \log (1) = 0$, if it's only 10%, $E=1$ (higher excitability), if it's 1%, $E = 2$, and so on.
How to determine $E$ for a given neuron? With the operational definition given above:

Count the actual number $N$ of excitatory synapses.
Estimate the minimal number $n$ of simultaneously active synapses that is needed to evoke an action potential (by repeated experiments).

Especially the second number $n$ will be quite hard to achieve experimentally. But there is an alternative way to estimate this number, given a simplified model of the neuron:

All synapses have equal (mean) distance $r$ to the axon hillock
(where the action potential is generated).
The EPSP generated at a synapse is $u$.
The EPSPs travelling from
the synapse to the axon hillock have a constant decay constant
$\alpha$.
The threshold value for action potential generation is $\theta$.

When $m$ synapses simultaneously generate an EPSP of size $u$, these EPSPs will sum up at the axon hillock to
$$ U = m\times u\times 10^{-\alpha r}$$
Only if $U \geq \theta$ an action potential will be generated, that is, the minimal number of simultaneously active synapses to generate an action potential is
$$ n = 10^{\alpha r}\ \frac{\theta}{u}$$
With this we can estimate the excitability $E = \log\frac{N}{n} = \log 10^{-\alpha r}\frac{N\ u}{\theta}$ by
$$E = -\alpha r + \log(N) + \log \frac{u}{\theta} $$
$\alpha$, $u$ and $\theta$ are more physical constants (more or less the same for all types of neurons?), $r$ and $N$ depend heavily on the arbitrary geometry/morphology of the neuron (especially do longer and more strongly branched dendrites have more synapses).
My specific questions are (please feel free to answer only with "yes" or "no"):

Has the property of excitability (in the operational sense above) been investigated a) for single neurons, b) for morphological types of
  neurons?
Is there an observed significant correlation between morphological type and excitability? Note that larger dendritic trees have larger
  $r$ (decreasing $E$) but also larger $N$ (increasing $E$).

(Final remark: The relation between $r$ and $N$ of a neuron is partially reflected in the structure – especially the degree of branching – of its dendritic tree.)

Excitability has definitely been tested and measured, but I'm not sure about your exact definition (sort of hard to prove a negative).
For differences in "excitability" across neuron types, I can think of two general approaches.
1) You could simply consider the firing rate and define cells as more "excitable" simply if they fire more or have a lower current threshold (though one must be careful in interpreting the actual "mV" value of threshold, because resting potential and input resistance are crucial and thresholds are dynamic).
These parameters have nothing to do with the number of synapses on them or the number of synapses it takes to fire; if you focus too much on these parameters you risk making a comparison that isn't all that helpful (see the analogy below). This approach is most suited to comparisons across cell types.
2) The second type of excitability concerns the intrinsic properties of a cell: what is it's input resistance, spike threshold, how much current do you need to inject at the soma to evoke a spike, etc. These properties can indeed vary across cell types, but you really have to think about it in the context of (1) to avoid the same problems with the analogy below. A cell might be near threshold but receives very small inputs; should that cell be considered more excitable than another?
Instead, it makes more sense to think about changes of excitability: "how does Manipulation X affect the excitability of Cell K?" If it changes the amount of current you need to inject to the soma to evoke a spike by depolarizing the cell or increasing the input resistance, you would say it increases excitability. This is, in my experience, by far the primary way in which "excitability" is discussed in neuroscience, rather than as a factor that varies across neurons. I did a search on Google Scholar for "neuron excitability": every one of the first 20 results was using it in the context of a change in excitability from one condition or manipulation to another.
A tangential analogy (the problem with your proposed definition of excitability):
Your proposed definition of excitability is a bit like measuring income based on paycheck frequency or number of digits on the check. You could certainly do comparisons between jobs on those merits, and in some cases they might be valid for what you'd normally think of as "income", but as soon as you move between countries (i.e., brain regions or cell types) currency changes, and suddenly the number of digits doesn't help because you don't know if you are talking about British pounds, US dollars, or Brazilian real. And even within a population, if the paychecks come weekly rather than monthly, the same face value of a check means a totally different annual income (i.e., if a cell has synapses that are rarely active, they contribute less to depolarizing it than synapses that are active all the time).
Contributions to excitability
Your question proposes that morphology is a defining characteristic of excitability. In a previous question you asked, I directed you to a review by Magee, J. C. (2000). Dendritic integration of excitatory synaptic input. Nature reviews. Neuroscience, 1(3), 181. - this review is applicable here, too. Active conductances in the dendrites and variation of synaptic properties with distance from the soma (larger, faster EPSPs the further from the soma you go) act to regularize the influence of EPSPs with distance, so you cannot rely only on passive properties. That also means you can't simply assume that a cell with lots of synapses far from the soma is not excitable.
However, there are definitely differences in firing rates and firing thresholds across neuronal subtypes, and you can take these to mean differences in excitability. There are many papers that talk about the diversity of intrinsic properties or firing rates of cells. I'll list a couple here for further reading:
Llinás, R. R. (1988). The intrinsic electrophysiological properties of mammalian neurons: insights into central nervous system function. Science, 242(4886), 1654-1664.
Izhikevich, E. M., & Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the national academy of sciences, 105(9), 3593-3598.
It's also important to recognize that excitability is dynamic and cells that are highly excitable in one state may not be as excitable in another state, even though their morphology does not change.

I am glad you mention Llinas: I just started reading his I of a vortex.

Thanks for your demanding answer, anyway. I'll try to make the best out of it.

Careful with Llinas, I link to him with caution. He's a good scientist and easy to read, but in his reviews and books he is definitely writing from a persuasive angle. I don't mean that in some nefarious way, but he definitely has an opinion in mind that he's trying to convince you about; not everyone in the field would agree with everything he tries to convey.

I am careful, and know what you mean - but he is not the only one. Do you know of one prominent author to which your precautions don't apply?

Getting off topic here, but I think the distinction is more of writing style; some write like they are telling you the truth and don't really give away that there is another way. Such writing is often the most compelling. Others write intending to relate the state of the field, including the controversy, and make their opinions more obviously opinions. Of course caution is always warranted, but I mean to suggest that, at least in my experience and opinion, Llinas likes to start with the premise that his thinking is correct without much service to the possibility he is not.

(again I'm talking in terms of books, not necessarily his science)

I (believe to) understand what you mean, completely and in every respect.

And I totally agree with your (hidden) criticism.

Let us continue this discussion in chat.


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Functional role of voltage-gated potassium channels
Having better learned here how action potential creation works in some detail, I'd like to pin down the functional role of voltage-gated potassium channels: they mainly shorten the time it takes the neuron to get back to rest potential. Without potassium channels, the sodium ions that entered the neuron through a sodium channel would slowly diffuse away (electrotonically) and the sodium potassium pumps reset the potential. With potassium channels, this process is drastically accelerated (by quickly moving positively charged ions out of the neuron in situ). Without potassium channels, an action potential would be created nevertheless by the sodium channels alone, i.e. a peak of 40mV would be generated (equally fast!), but it would decay much slower, not yielding a pronounced peak.

Would you agree that this is a correct description of the main
  "purpose" of potassium channels involved in producing action
  potentials?

In any case, potassium channels seem to  work equally well when their "closing" potential would not be -80mV, but e.g. -70mV, i.e. the resting potential. But because it's -80mV the potassium channels produce an afterhyperpolarization. My second question is:

Does afterhyperpolarization play a ("positive") functional role,
  too, or is it just unavoidable? If so: Which "negative" and
  undesirable effects might it have? (In some respects it might
  have been better, if there was no afterhyperpolarization.)

The meaning of reversal potential
Ion channels do not themselves have reversal potentials except for via a weighted average of the ions that they conduct. The reversal potential for a given ion is given by the Nernst equation and besides physical constants is a function only of the relative concentrations of ions inside and outside the cell.
The equilibrium potential of the whole cell is given by the Goldman equation, which is similar to the Nernst equation but covers any number of ions. Note that you can also calculate a "reversal potential" for a channel using the Goldman equation by considering all the ions that a given channel will conduct.
The reason that a cell's equilibrium potential at rest is not equal to the potassium reversal potential is because cells are not permeable only to potassium at rest; although potassium dominates, there is some conductance to other ions, which depolarizes the cell slightly.
There is no way for a potassium-selective channel to have a reversal potential any different from the potassium reversal potential, unless it were to be permeable to other ions as well.
What would happen if there were no potassium channels?
If there were no potassium channels at all, cells would rest near 0 mV, give or take a few mV. The "leak" channels that allow cells to rest at a negative potential are primarily potassium channels. However, it seems like your question is mostly directed towards voltage-gated potassium channels.
What would happen if there were no voltage-gated potassium channels?
As you suggest, cells would repolarize much more slowly. However, your question still has inaccuracies.
1) This repolarization would not be from sodium diffusing away, it would be from potassium leaving the cell through leak channels.
2) The sodium-potassium ATPase is not directly responsible for the membrane potential or for repolarization in an action potential. Ion concentrations change very little during an action potential. The thing that changes is the permeability to different ions. The sodium-potassium ATPase is important, however, for maintaining the relative inside concentrations of sodium and potassium ions over the long term.
In addition, as you also suggest, there would be no afterhyperpolarization.
Is there a purpose to the afterhyperpolarization? Is it just unavoidable?
There is somewhat of a purpose. Although the afterhyperpolarization isn't strictly necessary to get action potentials to fire, there are some hyperpolarization-activated channels in some cells, and in all cells the hyperpolarization facilitates the removal of the inactivation block of sodium channels. In general words, it serves as a bit of a 'reset signal' beyond mere repolarization.
However, the afterhyperpolarization is also pretty much unavoidable without a very fine-tuned engineering of the repolarization process (you would need to rapidly close potassium channels as they approached rest, which would also slow down the return to rest).

Overall, this material would be well-covered in an introductory neuroscience textbook. My personal recommendation is Purves:
Purves, D., Augustine, G. J., Fitzpatrick, D., Hall, W. C., LaMantia, A. S., McNamara, J. O., & White, L. E. (2014). Neuroscience, 2008. De Boeck, Sinauer, Sunderland, Mass.
(any other edition is fine, too, and there a lot of other good alternatives as well)

Thanks a lot for this - once again - great answer! You say: "repolarization would not be from sodium diffusing away". Not at all? Or only to a (much?) lesser extent than potassium leaking?

(Yes, you are right, I was mainly interested in voltage-gated potassium channels, I should have made this explicit. On the other side: I wouldn't have learnt about the important functional role of potassium leak channels!)

@HansStricker The net diffusion of sodium across the membrane will (almost) always be sodium coming in, because the reversal potential of sodium is greater than the membrane potential of the cell. The Nernst equation is your friend. Only if the membrane potential is raised higher than the reversal potential for sodium could sodium net flow out. This is plausible if calcium currents push the membrane potential to a high voltage, but this would be a very minor amount and would reverse as soon as the cell was back to the sodium reversal potential.

Ah, once again, I've not been clear enough! I meant diffusion not across but parallel to the membrane.

@HansStricker Since you'd like to emphasize your question on voltage gated potassium channels, you are mainly talking about action potentials; in the context of an action potential, you have sodium coming in all throughout the cell. There could be some flow into the dendrites, but the flow of sodium into the dendrites is going to depolarize them (and many dendrites also have active sodium conductances) unless there is leak of potassium out of the dendrites: you have to cross the membrane eventually. :)

No, I believe not to talk only about action potentials, but also about electrotonic potentials as described at minute 2:00 in the video I linked to. Wandering electrotonic potentials seem to be responsible for the propagation of action potentials (at least in the video). They wander passively, by diffusion and electrostatic repulsion. And they might be enough to degrade the initial peak slowly.

@HansStricker Your question stated: "Would you agree that this is a correct description of the main "purpose" of potassium channels involved in producing action potentials?" and also "Does afterhyperpolarization play a ("positive") functional role, too, or is it just unavoidable?" - both are referring to action potentials, and yet now you say you don't mean just action potentials. I think you might have some confusion here and it would be helpful if you made more clear what you are actually asking and make sure you are making your questions specific.

I find your critique a little bit unfair. Electrotonic transport of sodium ions occurs already during action potential creation and cannot be completetly separated from it. I ask - among other things - how electrotonic (horizontal, parallel) and potassium-channel based (vertical, across membrane) transport of positively charged ions compare and compete. And I cannot see any severe confusion in my mind - and to be honest, not even in my question.

Please do some more reading: if you cannot tell that you are asking about 8 different things at once, you are not sufficiently understanding what you are studying. Note how many different things I had to address in my answer to cover your original question, and now you are bringing in addition concepts in the comments. You seem to be trying to learn by coming up with hypotheses for how things work and then proposing them here rather than learning the basic concepts first. Please get an actual textbook and don't rely only on Khan academy.

Sorry for insisting, but you still said nothing explicit about the effect of sodium ions which just came in through a sodium channel wandering/diffusing away from the site, in both directions (to soma/dendrites and down the axon). This effect does exist inarguably, but it might be much smaller than others (i.e. compared to potassium ions diffusing away through leak channels). Could you please confirm?

Yet another point: Meanwhile I am quite sure that if there were (hypothetically) only sodium ions and channels (and no potassium ions and channels at all), the action potential - once created - would never go away, not even slowly, because why should the probability of sodium channels being open ever decrease again significantly once it reached a maximum (giving rise to maximal voltage) - given that ion channels "have no memory about the duration of their own state" (@Jojo)?

I have to correct myself: the sodium channels would remain maximally open only when there were (hypothetically) no inactivation gates (described by variable $h$). In the presence of inactivation gates - closing at maximal voltage - $m$ would oscillate slightly around its maximal value.

As theorized about here, there might be another "purpose" of voltage-gated potassium channels: They give spreading action potentials - especially in myelinated axons - the form of wandering decaying pulses (compared to a stationary peak at the site of creation, that simply decays, nevertheless giving rise to a rise of the potential at distant sites).
What this shaping is good for – per se – is another question. Why is it per se better that the potential arrives at the next trigger zone as a pulse: the ion channels there won't see a difference, will they? They are unaware of whether potassium channels were present or not at the first trigger zone, they will experience roughly the same (rise of) potential after roughly the same time.
Well, as a pulse (which fades out as it faded it) the signal is shorter, otherwise it lasts longer, making temporal fine tuning harder.

I don't understand what you are suggesting here, and your link in reference is simply to another answer by yourself.

Sorry for that, I'll try to explain - and visualize - it in more detail.I guess it's not nonsense - and maybe even common knowledge - but hard to explain in a few words.

Sorry, I could also be more explicit in my criticism. What is a "wandering decaying pulse"? That doesn't sound at all like what an action potential is, so I don't understand how voltage gated potassium channels could be conveying a property that action potentials don't have.


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Abrupt movements of birds and reptiles vs. smooth movements of mammals
How can it be explained (in evolutionary and/or neuronal terms), that the  spontaneous movements of birds and reptiles are seemingly "abrupt" and not so "smooth": Their spontaneous movements seem to start abruptly and end abruptly (while the spontaneous movements of mammals tend to be smoother: starting more slowly, ending more slowly)?

One line of (speculative) reasoning might go like this: Making smooth (= not abrupt) movements is "evolutionary better" (for the muscles and tendons - they don't wear out so fast). But it takes more computational power (= neurons) to perform smooth movements.

My experience with birds and mammals doesn't agree with the dichotomy you present. Can you provide objective data showing the movement patterns you suggest?

No, it's just a subjective impression (which might be backed by data of relative velocities and acceleration).

Exactly. My subjective impression doesn't match yours, so we each have n = 1. How can this question be answered?

Why do you say n = 1? We both have observed hundreds of birds, reptiles and mammals during our life time. (Only the level of exactness (= time resolution) could have been better.)

Rats make rather abrupt movements too. I would expect the difference you observe in movement speed is caused by size more than it is caused by being a bird vs a mammal. But why size would matter?
An increase in the linear dimension $x$ lead to an increase in the cross-section of muscles $x^2$ and an increase in the volume (and hence mass) of $x^3$. The strength of muscles is affected by their cross section $x^2$. Hence as animal grow bigger, the ratio $\frac{x^2}{x^3} = \frac{1}{x}$ becomes smaller and so does their ability to create large acceleration of their body parts. Their movement become smoother and less abrupt.
You might want to have a look at this highly related post too.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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What does the thalamus consist of?
There is a long list of thalamic nuclei which are somehow embedded in the thalamus, a "large mass of gray matter located in the dorsal part of the diencephalon", according to Wikipedia.
I wonder what the nuclei are embedded in:

In a pool of glia cells or of other more or less unspecific "thalamic
neurons"?
Does the thalamus consist mainly of nucleic or of non-nucleic
neurons?
How are the non-nucleic neurons of the thalamus classified?

Edit: In the Scholarpedia article on the thalamus one learns, that thalamic nuclei essentially are relays, and that there are relay neurons and interneurons in the thalamus. Might it be the case, that relay neurons can but interneurons can not be assigned to a specific nucleus (= relay), that means: interneurons build a somehow separate neuronal structure that is somehow interwoven with the nuclei?

Comments are not for extended discussion; this conversation has been moved to chat.

@BryanKrause: Thank you!


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Speed of passive transport of ions in the dendrite
I tried hard to get them, but I didn't get any numbers. My (subjectively) best Google search was for "speed propagation post-synaptic potential".
My question is:

How fast are ions transported passively inside the dendritic tree (and soma),
  probably depending on their atomic mass, charge, and of the local geometry?

Especially I want to know when a post-synaptic potential generated x μm away from the axon hillock "arrives" there, i.e. can be detected/summed up with other PSPs. Disregarding all of the eventualities (see above):

What is the order of magnitude of the speed of passively transported
  ions in the dendritic tree?

"I assume that ..." - why do you assume this?

Your edits do improve the question, but you are still asking two very different questions.
We don't really need to answer these questions:

How fast are ions transported passively inside the dendritic tree (and soma), probably depending on their atomic mass, charge, and of the local geometry?
What is the order of magnitude of the speed of passively transported ions in the dendritic tree?

to answer this part:

Especially I want to know when a post-synaptic potential generated x μm away from the axon hillock "arrives" there, i.e. can be detected/summed up with other PSPs

The speed of propagation of electrical signals in neurons don't depend on particular masses of particular ions or diffusion per se. Instead, passive electrical conduction is best understood using the cable equations which treats conductance within neurons as electrical RC circuit. The electric field propagates at the speed of light.
Therefore, EPSPs actually propagate almost instantaneously (given how short the distances involved are relative to speed of light) in that they produce an electric field. However, the peak decays with distance, and the rise time of an EPSP depends on the compartment because of capacitive filtering along the length of the dendrite. The decay peak is described by the length constant:
$$\lambda = \sqrt{\frac{r_m}{r_i+r_o}}$$
In this equation, rm is the resistance of the membrane, ri is the resistance of the intracellular space, and ro is the resistance of the extracellular space and is effectively negligible.
The length constant is the distance at which the peak amplitude will have decayed 63% from the peak at the signal origin.
The temporal filtering comes from the capacitive properties of the membrane along the length of the dendrite. The authoritative works describing these properties are several papers in the 1960s from Rall, Rall, W. (1962). Theory of physiological properties of dendrites. Annals of the New York Academy of Sciences, 96(1), 1071-1092. and Rall, W. (1969). Time constants and electrotonic length of membrane cylinders and neurons. Biophysical Journal, 9(12), 1483-1508. are good references.
The effective time constant for signals originating closer to the soma is much faster because there is less membrane to charge along the way. Exactly "how far" you have to travel to make a certain amount of difference depends on the properties of the membrane, which vary across neurons, vary in different parts of the dendritic tree, and vary dynamically within a neuron due to synaptic transmission.
Magee, J. C. (2000). Dendritic integration of excitatory synaptic input. Nature reviews. Neuroscience, 1(3), 181. is a fairly accessible review that covers a lot of these issues and more. It's important to recognize that although passive propagation of signals is important in dendrites, it's never purely passive and active conductances have important roles as well; in many cells, these active conductances plus differences in the initial shape of EPSPs throughout the dendritic tree act to mitigate the effects of distance.
See also Koch, C., Rapp, M., & Segev, I. (1996). A brief history of time (constants). Cerebral cortex, 6(2), 93-101. for more on the time constant and some evolution of the ideas about neuronal time constants since Rall.

Thanks. But alas, you destroyed my hope that the propagation of potentials (PSPs and action potentials) might be understandable by the flow of charged ions.

Oh but the mathematics of electricity are much more tractable than Monte Carlo simulations of ion flow in a complex environment, so it isn't a hope at all but a dread. :)

I'm having a horrid back spasm at the moment or I'd finish my answer but I'll just add in a comment that the things you actually care about for temporal integration are the durations of EPSPs, rather than their rise times.

Will I find the number I was asking for (the order of magnitude of the speed by which EPSP signals are transported) in one of the papers you mention? Or do I have to calculate it solving complicated equations with some typical parameters?
Alternatively, the effective speed can simply be defined as "(measured) distance of synapse and axon hillock" divided by "(measured) time until EPSP becomes effective at the axon hillock". Finally, this is what I am looking for.

(The question arises, how this time can be measured. Maybe by stimulating simultaneously some synapses that have the same distance to the axon hillock and which are sufficient to evoke an action potential?

What you are really looking for (I think) is the rise time of EPSPs and how that varies with distance from the soma; you will definitely find at least an order of magnitude approximation for that in the papers I linked. I'd suggest starting from Magee. If you had a particular cellular morphology you wanted to test (even a toy one), then probably the best way to do these measurements is in a simulation environment like NEURON from Yale. "time until EPSP becomes effective": again, the parameters you should be interested are 1) time to peak, 2) width. These will describe an 'effective window.'


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How is "firing together" detected in Hebbian learning?
I assume, that the signal that forces a synaptic receptor/ion channel complex to change its behaviour (i.e. strengthening in the course of upregulation) must be the combination of the state of the complex ("occupied" or "open" or any other state except the ground or rest state) and an extraordinarily high membrane potential at the complex (caused by a retrograded action potential).
The not-ground state indicates that the presynaptic neuron recently has fired, the potential indicates that the postsynaptic neuron recently has fired. According to the rule "fire together, wire together", both conditions must be fulfilled for Hebb-like strengthening to occur.
I assume further that the membrane potential that triggers the upregulation of the complex must be significantly higher than the typical post-synaptic potential generated by the synapse, otherwise activation of the synapse alone would suffice for strengthening to occur, which violates Hebb's rule.
Is this way of thinking essentially correct? Or is strengthening triggered by other signals than the ones mentioned above?

Are you looking for an explanation of the biology, or something else? It sort of seems like you are trying to derive biology from logic rather than logically understanding biology; that's a good way to generate hypotheses but might not be the best approach for understanding what is already known about biology.

Not from logic, but from what I can imagine: How can a receptor be upregulated but only shortly after (or while it is "active") and shortly after its neuron has created an action potential? (The first it "knows" by its own state, the latter it "knows" from the membrane voltage at its location. So my imagination goes. Both together result in the physical process of upregulation.) But of course, I am looking for an explanation of the biology.

The dynamics of Hebbian or associative synaptic plasticity are thought to be governed primarily through the function of the NMDA glutamate receptor. The short answer is that you are basically right on all counts.

Figure of the NMDA receptor present the nervous system.
By Blanca Piedrafita [CC BY-SA 1.0 or CC BY-SA 2.5], via Wikimedia Commons
The NMDA receptor is a non-selective cation ionotropic receptor. The reversal potential of the NMDA receptor is around 0 mV, in contrast to the resting membrane potential of a 'typical' excitatory neuron which is around -70 mV. This means that a pretty strong stimulus is required in order for the NMDA receptor to be activated. Whereas some current can pass through the channel upon binding of its preferred ligands (glutamate or glycine), the pore is normally blocked by a magnesium ion. This mechanism confers some degree of voltage-dependent regulation of ion flow through the channel. When a strong stimulus raises the membrane potential at sufficient levels the magnesium block is lifted, allowing more current to pass through. The slow kinetics of the NMDA receptor allow the temporal integration of incoming signals. This makes the NMDA receptor function as a coincidence detector or AND gate. There are many more known details about the mechanisms involved but the above should suffice to answer your specific question.
Further reading: https://en.wikipedia.org/wiki/NMDA_receptor

At first glance I am not quite sure, if your answer covers (subjectively) the details of my question, but I am confident and will have a closer look. Thanks anyway!

If you feel that you need more info, let me know and I will update my answer.

Thanks for the offer, but it will take some time to formulate my concerns. Let me first digest your answer.


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How do viral envelopes contain molecules coded for by viral genes when they are derived from the host cell's plasma membrane?
I have been studying viruses from " Biology: A Global Approach " by Campbell, Urry, et al. Regarding viral envelopes in animal viruses, the textbook writes, " ..the viral envelope is usually derived from the host cell's plasma membrane, although all or most of the molecules of this membrane are specified by viral genes."
I understand that the capsid proteins and glycoproteins on the surface of the viral envelope and coded for by viral genes, but the envelope formation happens in a process similar to exocytosis, where the new viral capsids are wrapped in the membrane as they bud from the cell. How can the viral envelope contain molecules coded by the viral genes (apart from the surface glycoproteins)?

I think by "all or most of the molecules" they are excluding lipid molecules. Is that what you are concerned about? Or are you asking how virus-encoded proteins can embed themselves in the plasma membrane?

@timeskull It wasn't clear to me which molecules the textbook was referring to me as viral-gene-encoded. I did consider the possibility that they were simply excluding the lipid molecules, and was seeking some solid clarification regarding the same. I guess that means that the viral encoded particles are the glycoproteins that embed themselves in the membrane?

I don't have access to the book, so I can't be sure how they meant that statement, but most likely "all or most of the molecules" in the lipid membrane excludes the lipid molecules themselves. One of the defining characteristics of viruses is that they don't do their own metabolism. Even if they did, viral genes could only specify the enzymes for lipid synthesis, and these wouldn't be included in the membrane.
However, viruses often DO manipulate the host cell's lipid metabolism. From this review of Lipid Interactions During Virus Entry and Infection:

Large enveloped viruses are not the only viruses that manipulate cellular lipid metabolism. Microarray analysis of HCV infected cells show significant changes in the expression of genes involved in lipid metabolism (Woodhouse et al., 2010). Recent transcriptomic and proteomic analyses indicate that the expression of host genes involved in lipid biosynthesis, degradation, and transport is profoundly altered by HCV; in particular cholesterol biosynthesis genes were found to be upregulated (Woodhouse et al., 2010). Parallel lipidomics analysis also showed changes in selected lipid species, particularly phospholipids and sphingomyelin (Diamond et al., 2010). This suggests that HCV reprogramming of host lipid metabolism attempts to maintain host homeostasis in spite of the elevated demand of metabolic precursors by the virus.

So, membranes in the cell are composed of different types of lipids, and they aren't equally good for making virus membranes. Some viruses have been shown to upregulate production of the lipids they need, so in that sense those lipids are products of virus genes. That's a bit of a stretch, though, imo.
For proteins in the viral membrane, they aren't necessarily all glycoproteins, though it looks like most are. M1 and M2 membrane proteins in influenza aren't glycosylated, for example.
Here's an image from another review showing virus budding through the plasma membrane:

One kind of virus budding. Viral glycoproteins, inserted into the cellular membrane at the endoplasmic reticulum and processed through the Golgi to the plasma membrane (see Figure 3), associate with the assembled viral nucleocapsid. The direct association pictured here is characteristic of togaviruses. For other viruses, possessing helical nucleocapsids, the association is mediated by a peripheral membrane protein. Cellular membrane proteins are excluded from the envelope of the mature virion. This may occur during assembly, as pictures, or by prior formation of a viral membrane patch (or raft), before the nucleocapsid arrives at the membrane.

In this image, you can see the host membrane proteins (the white ovals) being excluded from the patch where the viral proteins (black shapes) accumulate and which later envelops the nucleocapsid. This process is likely what your textbook is referring to.


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Why did Rivers replace Koch's postulates?
In 1937, Rivers introduced a new set of postulates that were meant to replace those formulated by Koch.
However, I couldn't find an article (or other scientific literature) that describes why Koch's postulates weren't valid anymore.
Is there literature that explains why the old postulates were not valid anymore?

What's wrong with the reasons Rivers gives?

If you read his 1937 article, Rivers himself makes a case for why Koch's postulates are too restrictive and that all the postulates need not be satisfied to confidently associate a pathogen with a disease. Here, I've highlighted excerpts and added my own emphasis.

[Koch's] dictum has had a profound influence on workers investigating infectious maladies and for many years an infectious agent was not accepted as the cause of
a disease unless the postulates had been satisfied. With the development of the science of immunology, however, immunological reactions added much to the knowledge of the specific relation of microbes to disease, and now it is possible to bring excellent evidence that an organism is the cause of a malady without the complete satisfaction of the postulates.
...
At the time when they were formulated Koch's postulates were essential for the progress of knowledge of infectious diseases; but progress having left behind old rules requires new ones which some day without doubt will also be declared obsolete. Thus, in regard to certain diseases, particularly those caused by viruses, the blind adherence to Koch's postulates may act as a hindrance instead of an aid.

Koch's postulates were published in 1890, but the first virus wasn't isolated until 1892 (at the earliest), so the postulates cannot be readily applied to diseases resulting from viral infections. That is not to say Koch's postulates were wrong, just that their blind application to all diseases may prevent the identification of novel etiological agents due to the requirement for isolation in pure culture. Rivers addresses this, and supplies less restrictive postulates for the characterization of viral infections.

It is obvious that Koch's postulates have not been satisfied in viral diseases. Moreover, it is equally evident that proof of the etiological significance of viruses has been obtained without their satisfaction. Such a statement, however, does not imply that certain conditons do not have to be met before the specific
relation of a virus to a disease is established. The conditions are: (a) A specific virus must be found associated with a disease with a degree of regularity. (b) The virus must be shown to occur in the sick individual not as an incidental or accidental finding but as the cause of the disease under investigation.


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What are these little brown insects
We have these little insects in our house, they look brown and round to the naked eye, they seem to be somewhat attracted to light since we found a cluster of ~6 on the wall next to a light, otherwise we find them one here and one there.
They are very very small, can barely tell what shape they are without magnification, they look almost like a dot.
Images below are taken with a loupe with 30x and 60x magnification but they are of squashed bugs so not the greatest photos, sorry. Will post pictures of live ones if I find more.
Location: San Jose, California, USA
Full quality images: https://drive.google.com/drive/u/0/folders/15FU-KEzqmXy7s69VfmA1UJoM_o0elWWz

EDIT: added some images of live insect on the wall, no magnification, 30x and 60x to the drive folder.

Great pictures! Can you update your question with your location?

Mist with alcohol for better unsmashed photos.

Woops, this is in San Jose, California, updated question as well.
Also took some pictures of a live insect on the wall with and without magnification and added to the drive folder.

if you can please sit some on graph paper or a ruler to photograph, then their size can be known.

The beetles are about 3mm (1/10 inch) long - so not any wood eating beetle. That's good.
The elytra (wingcase=main body) has parallel lines.
The antennae have the terminal 3 segments enlarged, so not cigarette beetle.
Looks like the drugstore beetle, Stegobium paniceum.
http://en.wikipedia.org/wiki/Drugstore_beetle
If you can easily get a pheromone trap, that will help confirm by catching the male beetles.

Photo from wikipedia.

i looked for pheromone traps for drugstore beetle but can't find them, closest I found was this trap that says cigarette beetle and someone in the comments mentions that it also worked for drugstore beetles, which sounds odd, any thoughts?
https://www.amazon.com/JF-oakes-Pantry-Beetle-Pre-Baited/dp/B006J9IK08

I only found the idea of pheromone traps online - I've never lived in an area that has this beetle as a problem. Anyway, those photos are quite good, see if you can get one of the antennae.

there should be a half decent picture of the antennae in the drive folder, I am hoping to remember to take another one with a ruler next to the beetle, once I have that I will try to repost the drive folder images here as well.
As for the trap, I found one on amazon for $20, will first comb through my kitchen to see if I have an infestation, otherwise they just look lost, a few here and there, some even in the bathroom, not a lot in the kitchen.


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Cell Theory- does the first cell not contradict cell theory
In cell theory, we have cells arise from other existing cell.
But the first cell did not arise from existing cell, and that means there are some other condition which allows cell to be formed.
I understand the chance of forming the cell without other cells has a low probability, but given it is still possible, does that not contradict the statement itself that you must have other cells to form new cells even ignoring the first cell as a special case?

Can you please clarify what it is about the standard models of abiogenesis that you do not understand?

@jakebeal Thanks - I understand we can create cells from non-living material, but I do not see why we can leave that out in cell theory, and say cells are only created from other existing cells. We can say this is the only way cells are created by living material (ignoring cases which cells arise from non-living material), is from other cells, but then all living materials have cells (from the definition of cell), and so that makes that statement trivial?

I think this is mostly a confusion of the meaning of "laws" that govern fields like physics and the "laws" that govern biology. Biology tends to stubbornly break any sort of "law" you try to constrain it with (besides those of physics), but that doesn't necessarily make biological "laws" less useful, it's just that we tend to take for granted how things need not be as they are in biology.

Sometimes the probabilities of events are so low, that we can neglect them for all practical purposes. A classical example in thermodynamics: if we have a gas in a container, there is a non-zero probability that all the molecules assemble in one half of this container, while in the other part we have vacuum. It never happens in practice - the probability of such an event is $\propto 2^{-N_A}$, and if one observes a container, one would have to wait for longer than the age of the universe (which is much longer than our lifespan, the existence of the humankind, and the existence of life). Thus, we can confidently treat it as a law, and claim that the sea had never opened in front of Moses.
Same about the acquisition of the cellular membrane: the event might have happened only once in a few billion years, and in very special conditions, which are not at all common nowadays. It is negligible for all practical reasons, to the precision that makes it possible to consider it a law.

It's also worth noting that existing life will inhibit the emergence of new life, as existing life will tend to quickly eat anything with the potential to become new life.


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Rectangle-like structures and their folding in biology
I've heard that mathematics helps to explain some biological problem. For example gömböc, which was a well hidden body from mathematicians, explains the body structure of some tortoises in relation to their ability to return to an equilibrium position after being placed upside down.
My question is an attempt to find an analogous application for a very special rectangle in biology: There exists a unique rectangle with sides $a$ and $b$, where $a$ less $b$, with two ways of being folded along a line through its center such that the area of overlap is minimized and each area yields a different shape – a triangle and a pentagon. The unique ratio of side lengths is $\frac {a} {b}=0.8150237$.
The special rectangle is like a bistable structure with some minimum of overlapping and folding angles: $45^\circ$ and $\approx 24.66^\circ$ (for over ratio of sides there is just one folding angle: for eg. long rectangle is always folded at $45^\circ$).

(more details about folding rectangle and pictures in OEIS: A366185 )
Any ideas where the property may appear in biology (including molecular biology) are highly welcomed.

An image showing the two ways of folding might be helpful in this case. I for one can't visualize getting a pentagon out of a single fold on a rectangle. Also is the a/b ratio correct? Not meant to be "0.8" rather than "08"?

@bob1 yes, correct "0.8", I also added a picture & OEIS link to an article (Folded rectangle) on how the special rectangle was found.


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More informative phylogenetic trees
In the presentation of phylogenetic trees, the geometric shape of the trees often seems somehow arbitrary and is more driven by aesthetics than by informative reasons.
But wouldn't it make sense to give the geometry (distances and angles) specific meanings? Or is this already done (when it's done right)?
Some basic principles:

The vertical axis represents time (on a linear, logarithmic, or "anti-logarithmic" scale).
The horizontal axis represents the amount of genetic change (measured in appropriate units).
The line of one species (= population with virtually identical DNA) goes vertically from bottom to top.
The line ends when the species becomes extinct.
A new species branches off of an existing species by a horizontal line perpendicular to the line of the latter.
The length of the new (horizontal) line reflects the amount of genetic change.
At its end the line continues vertically.
There are no other branchings along the horizontal line.

By these principles and with perfect knowledge (and a good measure of genetic change) we would have a perfect rectangular tree like this:

But our knowledge isn't perfect: we know little to nothing about lots of intermediate species which didn't leave traces. Hypotheses about these unknown species can be reflected by inclined lines whose slopes can tell for example:

a) Their have been many pronounced genetic changes in a short period of time after the new species branched off. (grey: hypothesized intermediate species)

b) Their have been few small genetic changes in a long period of time after branching off.

I'm looking for discussions/considerations of this kind of drawing
  phylogenetic trees (papers, web pages, or simply good search terms).

An interesting - and new to me - point of view is given in Joseph Ahrens' answer to this Quora question:
How do you interpret ancestry in phylogenetic trees?
What slowly becomes clear to me: It's about the interpretation of straight line segments, maximal straight lines, of horizontal vs. vertical lines, and nodes (= branching points) in phylogenetic trees, especially: which of them is to interpreted as a species?

One interesting search term would be "phylogenetic network"

Thanks, but I am not sure if this helps.

Phylogenetic trees don't tell you anything at all about species (which is a vague term anyway). I suggest you do more reading on both topics. I'm voting to close this as unclear what you're asking.

I am asking for more informative ways to draw phylogenetic trees.

Here's the issues with your well considered project:
1/ Temporal datasets to proportion trees: That's probably the most absent thing in species measurement. You'd need data sets of time for beetle species, for mammals, plants in millenia and million years. 90+% of that information is absent.
2/ Genetic proximity to arrange trees. Scientists publish their genome studies into the ToL project. There is lots of distance data to compare all animals.... Genetic distance doesn't graph easily because on the same tree, some distances can be 500 times longer than others. On a tree of 20 extant species, you will have branches 5mm long and 5 meters long, half the the species are on your screen and the other half are higher than the ceiling. It's best to represent them with another symbol, else interactive 3D trees where you can switch compact/large views and the tree zooms out crazily, it's illustrative and cool, else use a weighted proximity length which is 1+ similarity/50, that doesn't really work either. either way, I couldnt find a way of clearly displaying that info on the tree.
Phylogeny trees don't lend themselves well to being informatively measured. You start by thinking "Oh I could find a pretty way of doing that" then when you apply the datasets, your trees become uncontrollable and jumbled up because of exponential branch lengths.
I programmed phylogenetic trees based on the 81MB ToL tree of life project to represent many millions of species, to do 3D physics trees and HTTP lookups to provide wiki texts and images for all species. There is www.biostars.org a very kind and helpful bioinformatics forum for postgrads that do trees all day.
There are many (dozens) of informative tree graphics programs coded by academics, to visualizw and analyzw species data, arranged into different trees and sorting through them.


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Understanding Hodgkin-Huxley's model and activation variables
This question is about the Hodgkin-Huxley model as introduced in Eugene M. Izhikevich, Dynamical Systems in Neuroscience, p.33 ff.

I'm having trouble to understand and interpret the differential equation for the activation variable $m$:
$$\dot{m} = (m_\infty(V) - m)/\tau(V)$$
which enters via
$$p = m^a h^b$$
into the equation
$$I = \bar{g} p (V − E)$$
for the net current $I$ generated by a large population of identical
channels where $p$ is the average proportion of channels in the open state, $\bar{g}$ is the maximal
conductance of the population, and $E$ is the reverse potential of the current.
$m$ is the probability of one of $a$ activation gates to be open. Interchangeably: $m^a$ is the proportion of open activation channels (assuming all of its activation gates must be open simultaneously).
The differential equation might give us $m$ as an explicit function of time but it – explicitly – involves $V$ which is – implicitly – another function of time, which in turn depends on the number of open gates. Things are horribly complicated!
On the other hand — since it's about voltage-gated channels and there are "immediate" voltage-sensitive regions in the channel protein which presumably don't have memory ("the single channel has no memory about the duration of its own state"), but possibly a time lag — I expected the being-open-probability of an activation gate to be a "pure" (possibly time-lagged) function of $V$.
My question comes in two disguises
(1) Given two explicit functions $m_\infty(V)$ and $\tau(V)$ like these:

together with $m(0)$ and $V(0)$, how could we ever arrive at an explicit solution for $m(t)$, assuming that $V(t)$ depends somehow on $m(t')$ for $t'\leq t$, but possibly also on some injected currents.
(2) How can an intuitive and sensible interpretation of the terms in
$$\dot{m} = (m_\infty(V) - m)/\tau(V)$$
be given? What does the time constant $\tau(V)$ and its dependence on $V$ mean? In which respect and by which hypothesised mechanism is the gate "faster", when $\tau$ is smaller? How can the voltage-sensitive steady-state activation function $m_\infty(V)$ be intuitively explained other than by "giving the asymptotic value of $m$ when the potential $V$ is fixed (voltage-clamp)" or by some complicated description of experiments to determine it? What does $m_\infty(V) - m$ mean, i.e. "the deviation of the current activation from the steady-state activation"?

1) In practice, no one attempts to obtain explicit solutions for m(t), especially considering the presence of many other ion channel species, nor is there any need to. The standard of art is to use numerical simulations with a sampling interval dT that is sufficiently smaller than any relevant time constants.
2) I'm not sure what intuitive and sensible interpretation you are looking for; it may not make sense to come up with an intuitive explanation for each and every subset of terms. The use of time constants implies that the system is modeled as a linear time invariant system at a given voltage.

What does the time constant τ(V) and its dependence on V mean? In which respect and by which hypothesised mechanism is the gate "faster", when τ is smaller?

The time constant is a scalar that describes the rate at which the system approaches some equilibrium. You could think of the changes in channel state as chemical reactions of the form:
Open <=> Closed
which has some equilibrium and some rate constant - both the rate constant and equilibrium conditions can be a function of voltage, as depicted in the figure you provide. The physical meaning of a rate constant being voltage dependent would be that the activation energy for the transition between states is a function of voltage; when the activation energy is lower, the reaction can progress more quickly (in either direction).

How can the voltage-sensitive steady-state activation function m∞(V) be intuitively explained other than by "giving the asymptotic value of mm when the potential V is fixed (voltage-clamp)" or by some complicated description of experiments to determine it?

That's exactly what it means, and the descriptions are not complicated: the steady state value for a reversible reaction is the point at which the number of units moving from open to closed would be the same as the number moving from closed to open, so on average you see no more change: that's what steady-state means.

What does m∞(V)−m mean, i.e. "the deviation of the current activation from the steady-state activation"?

Yes, "the deviation of the current activation from the steady-state activation" is accurate. The equation is an equation for the change of m, and the change of m is proportional to the "distance from equilibrium" - this is a characteristic of any process that follows linear time invariant dynamics. Note that there are other ways to write this equation that involve a "forward rate", a "backward rate", and the concentration of units in each state (the Wikipedia Hodgkin-Huxley page you linked has these equations), but you can simplify these to the equation you show here because some proportion of the "forward rate" process is cancelled by the "backward rate": your equation is sufficient to describe the net change.

Thanks for your answer (which I edited slightly)! Please let me announce a reply to your answer which will show that it is definitely worth the effort to obtain explicit solutions for $m(t)$ (and to play around with them). Among other things: to see how action potentials happen to be created (beyond a not so well-defined threshold), or how being open (of a channel) cannot follow fast changing voltages.Please stay tuned!

With regard to $\tau(V)$: It's all about the inertia of gates, let it be activation, inactivation, or deactivation gates. I never found time constants being called "inertia coefficients" or the like, but in the case of ion channels, this would hit the nail on the head. (Note, how inertia has to do with delay.)

If you are interested in a preview: send an email to stricker@syspedia.de.

Thanks explicitly and especially for your link to Linear time-invariant theory, which was new to me.

"to see how action potentials happen to be created (beyond a not so well-defined threshold), or how being open (of a channel) cannot follow fast changing voltages" - all of these things can be answered with simulations.

That's what I am after, doing my own.  Or do you know some impressive and instructive simulations in the public?

I believe I've suggested the NEURON simulation environment to you several times.

Yes, you did, and yes, I had a look at NEURON, but unfortunately it's not a tool I could use out of the box: it needs a good understanding of terminology, theory and models (naturally!) but also of sensible variables and of the tool itself. Not so easy for someone like me (with not so much time). Thanks anyway.

https://senselab.med.yale.edu/modeldb/showModel.cshtml?model=5426 there are many premade models for NEURON like this one; frankly if you aren't willing to take the time then I feel a bit like I'm wasting my own time trying to answer your questions - it would take less time than I have spent answering questions to go through the tutorials and try out tweaking an existing simulation.

Since you seem particularly interested in ion channels lately, here is a whole list of models people have implemented in NEURON to demonstrate the effects of dozens of channels: https://senselab.med.yale.edu/ModelDB/ModelList.cshtml?id=3540

Let us continue this discussion in chat.


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Species extinction attribution
In climate sciences there is the new field of extreme weather event attribution (EWEA). It investigates quite successfully on the one side how climate change (i.e. rise of global and regional mean temperatures) leads to an increase of the frequency and intensity of extreme weather events (of different types: droughts, floods, hurricanes, at different places). On the other side EWEA investigates for a given extreme weather event (a specific drought, flood, hurricane) how climate change contributed to its causes (making it more probable in a sense).
I wonder if there is a corresponding field of species extinction attribution (SEA) which investigates how climate change and extreme weather events contribute to the causes of the extinction of a species. Both on the statistical (frequentists') and on the anecdotal level. Anecdotal means: considering a specific species that's gone extinct recently (so we know the circumstances quite well) and investigating how the rise of mean temperatures and/or extreme weather events have caused it.
On the one side SEA might be "easier" than EWEA because the extinction of a species is a better defined event than extreme weather events. On the other side there may be more and more complex additional causes (next to climate and extreme weather events), mainly the destruction of habitats and interruption of migration routes.
So my question is: Is there something like extinction attribution science with a focus on climate change as a main driver of species extinction?

Maybe species extinction is too much, and (severe) decline of species population (species decline for short) would be more appropriate?

I am afraid this is not a question about a problem in biology, but about the catagorization or directions of development of biological research. Although not without interest, I do not feel it is appropriate to this list. Please re-read the [Tour] and Help pages.

There used to be a whole journal devoted to this question: Climate change responses

https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.2001104

I’m voting to close this question because it is not about biology in the terms of SE Biology (as I wrote at the time).

Even though without focus on climate change, this paper is about extinction attribution in the sense that the relation between traits and extinction risk is investigated:
A review of the relation between species traits and extinction risk (2019)
And of course the impact of climate change on species populations is investigated carefully (only under another umbrella term: "climate attribution science", not meaning "what contributes to climate change" (as in weather event attribution science) but "to what does climate change contribute"), for example
Climate attribution science and the Endangered Species Act (2021)