text:
The role of duration of infectiousness in SIR models
I refer to J.H. Jones' Notes on R0.

The basic SIR model - as described in Jones' Notes - considers three factors that make up the reproduction number:

$\tau$ = the transmissibility (i.e., probability of infection given contact between a susceptible and infected individual)
$\overline{c}$ = the average rate of contact between susceptible and infected individuals
$d$ = the duration of infectiousness

The (basic) reproduction number then is
$$R_0 = \tau \cdot \overline{c} \cdot d$$
The duration of infectiousness enters the basic SIR model as the so-called removal rate $\nu$ which is nothing but the inverse of the duration of infectiousness: $\nu = 1/d$:
$\frac{ds}{dt} = -\beta s i$
$\frac{di}{dt} = \beta s i - \nu i$
$\frac{dr}{dt} = \nu i$
with

$s$ = the fraction of susceptible persons
$i$ = the fraction of infected persons
$r$ = the fraction of removed persons (recovered or died)
$\beta = \tau \cdot \overline{c} = R_0/d$ = effective contact rate or infection rate

My question concerns the way that $d$ enters the SIR model, because I
  find it not so plausible:

to consider all persons that are infected today and take a fraction $\nu$ of them that will have recovered tomorrow.

Wouldn't it be much more plausible

to consider all persons that became infected $d$ days ago and let these be recovered tomorrow?

The latter approach would be especially valid when the death rate can be neglected, i.e. when "removed $\approx$ recovered".
My impression is that most papers using a variant of the basic SIR model let enter the duration of infectiousness in the first way - leading to significantly different predictions than in the second case.
I implemented both and this is the difference (only due to the different ways that $d$ enters the progression formula, i.e. the values of $\beta$ and $d$ are fixed):

(In case that you wonder why the curves oscillate: I have modelled some sort of acquired immunity with finite duration of only some month - but in the very same way in both cases.)

This question reminds me of the equations for radioactive decay (see http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/halfli2.html). Over there, we assume that a constant fraction of particles decay per unit time. A particular particle can have a lifetime varying from zero to infinity, but the average lifetime of all the particles is simply the reciprocal of the decay constant. Perhaps something similar applies here? (Think of infected persons as particles, removal as radioactive decay, and $\nu$ as the decay constant.) If that is so, the first of the two approaches you mentioned is correct.

I guess the main difference is that radioactive decay follows a Poisson distribution, but recovering of a disease does not:  I assume it is somehow Gauss distributed around a characteristic maximum.

While the number of decays in a given time period for a sample follows a Poisson distribution, the particle lifetimes do not. In fact they have an exponential distribution. Also, how can recovery times for a disease have a normal distribution? A normal distribution stretches infinitely in both directions, whereas recovery time can never be negative.

Thank you, you are right in both cases. Nevertheless the distribution of recovering times might be "almost Gaussian" - because nobody recovers immediately after having been infected. So maybe THIS distribution is Poisson - as opposed to exponential?

My question concerns the way that $d$ enters the SIR model, because I
  find it not so plausible:

to consider all persons that are infected today and take a fraction $ν$ of them that will have recovered tomorrow.

Well, it is in fact not very 'realistic' as you point out, but in the assumptions of the model, we see that the population has no structure (it is well-mixed, constant) and there are no birth-death events. So, in this case, it is not so problematic to take $v$ as a constant across the entire simulation, because what you are trying to calculate is the rate at which the three sub-fractions of $N$ ($s$, $i$, and $r$) change, not really which individuals are moving from one class to another (which you cannot really know anyways, if you talk about fractions of $N$).

Wouldn't it be much more plausible

to consider all persons that became infected $d$ days ago and let    these be recovered tomorrow?

So, considering my previous comment, it would not make much sense really to take a time-delay form on $d$, because you cannot really know which individuals got infected at any given point, you can only talk about fractions of $N$ (there is no population structure, as they say in the model formulation). So, the fact that your formulation seems to have a slower dynamics might not be very informative, because what you did is simply applying $d$ to a fraction-of-the-fraction of the population classes, so it makes sense mathematically that it runs slower, but as per the model formulation it does not make much sense, unless you have population structure defined from the beginning (which in this case is not), and unless you can explicitely know individual-per individual class transitions. In fact, I believe that taking the fraction-of-the-fraction would lead to an artifactual 'undercounting' of these individuals that actually needed to be in the $i$ class (and overcounting of the other classes).

I don't see it problematic to take $\nu$ as a constant. I don't understand what you mean with "constant across the entire simulation". Furthermore, there is no single rate at which $s$, $i$, and $r$ change but two: $\beta$ and $\nu$. And I don't understand your which-individuals-argument. All I want to say: When "duration of infectiousness" does mean what is seems to be supposed to mean, it makes sense to remove all those newly infected $d$ days ago as recovered tomorrow, and not a fraction $\nu = 1/d$ of those that are infected today.

The persons infected today  consist of some newly infected yesterday, some newly infected the day before yesterday, ..., and some newly infected $d$ days ago. And only the latter will have recovered tomorrow (in the mean).

You want to treat the model as it had population structure, but it doesn't. That's the main problem as I see it.

So, it's not a problem with the model but how you use it.

Sorry, but I still don't understand your argument. And I still don't understand what's wrong with my argument. The only structure I am supposing is a "timely" structure: that it does matter when a person got infected.

I am not sure if I quite understand your question, but I think your problem is here: removal (and your d) is a rate (time/removal). It does not matter what time you choose; a day, a week, a year, as long as you adjust your c (which is /time) to same timescale. In other words, if you wish to use d over several days, you need to calculate your contacts over several days, and changing only one will erroneously lead to different results.

I'm afraid this misses the point.


text:
Cortico-cortical connections
I wonder what the principal ways of (direct) cortico-cortical connections are.
I came up with the following possibilities:

vertical: a cortical neuron connects to another one in roughly the same cortical column, but in another layer
horizontal: a cortical neuron connects to another nearby one, preferably in the same or neighboring layer
"intragyric": a cortical neuron connects to another one in the same gyrus (see here)
interhemispheric: a cortical neuron connects to another one in the same (or neighboring) area of the opposite hemisphere

Are all of these relevant? And/or are there relevant but completely different ways of cortico-cortical connections, e.g. "intergyric"?

Addendum: Maybe too late I found a concise summary in the Wikipedia articles on white matter and association fibers (the latter term I wasn't aware of when I asked my question), which doesn't contradict and complements Bryan's answer:

intracortical (Bryan: "intracolumnar" vs. "horizontal")
short association fibers ("also called arcuate or U-fibers [...]  connect together adjacent gyri")
long association fibers which "connect the more widely separated gyri and are grouped into bundles" (often called fasciculi, but probably not exclusively)
commissural fibers (Bryan: "callosal projections")

There definitely seems to be no reserved name for something like "intragyric" fibers (see second addendum here).

Your question "are all of these relevant" doesn't make much sense to me, but I am going to assume you are talking about it in terms of terminology and answer that way.
The "vertical" connections you describe are usually referred to in the context of cortical "columns" and are therefore referred to as "intracolumnar." Within a column, intralaminar connections by far dominate the total number of synapses, but connections between layers are also important (note that my answer Cortical projections from layers 2/3 back to 4? covers some of this as well, though that question is much more specific).
Horizontal connections refer to connections between cortical columns of the same cortical area (e.g., from V1 to V1 with a different orientation selectivity). These are often stronger between the same layers, but simply saying "horizontal" does not specify that you mean intralaminar horizontal connections.
"Intragyric" is not a word that is used - I think you made it up. Gyri aren't really specialized functional units, and although there may be some brain areas that are localized within a gyrus many span either several gyri or share a gyrus with other areas (for example, "Heschl's gyrus" isn't even just one gyrus). Therefore, you can't really generalize "gyric" connections as being in a particular class, you would have to refer to the specific areas that are connected to understand the nature of those projections.
Interhemispheric connections are fairly ubiquitous in neocortex, and they make up several white matter tracts that connect the hemispheres, most prominently the corpus callosum. As such, those connections are also often referred to as "callosal" projections.
Other terminologies that are used are "top-down" versus "bottom-up" according to the position of areas in the cortical hierarchy. "Lower" areas are considered to be those with primary sensory and motor functions, whereas higher areas are associative/executive areas. The canonical reference for these projections is Felleman, D. J., & Van Essen, D. C. (1991). Distributed hierarchical processing in the primate cerebral cortex. Cerebral cortex (New York, NY: 1991), 1(1), 1-47. The key feature of top-down versus bottom-up projections is a difference in the interlaminar pattern of connectivity between different cortical areas. It can be hard to really parse the precise hierarchical of some of the higher-order cortical areas, and the patterns of top-down and bottom-up are fairly mixed for areas at similar levels of the hierarchy, however.

I guess, it's easier to connect inside a gyrus than across gyri. But I may be wrong.

That's why I put "intragyric" into quotation marks.

How do we know that gyri aren't "really specialized functional units"? We even don't  know it unequivocally for cortical columns: see The cortical column: a structure without a function (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1569491/)

I specified "horizontal" by saying "in the same (or neighboring) layer", i.e. "intralaminar".

I wouldn't rely on that one paper: people still talk and think in terms of columns. I fully agree that they are not as discrete as people once thought, but it still makes sense to talk about intracolumnar units. I totally disagree that it isn't clear that gyri aren't really specialized functional units: there are several dissimilar functions that are held within gyri, and the boundaries of cortical areas often do not stick within a gyrus. This is very clear on any map of the human cortex. And for "horizontal" I was referring to use in the literature rather than how you used it.

I'd say it's also very unclear what you mean by "preferably": biology does what it does, regardless of what is preferable to you. :)

No matter if you say "vertical" or "intracolumnar" resp. "horizontal" or "intralaminar": this is only a trend, but there will be outliers.

I don't understand your latest comment.

Let us continue this discussion in chat.

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text:
Are there traits exhibiting avoidance of the mean?
Sometimes if two organisms with an unusually large value of a continuous trait mate their offspring on average will not have a value as large as one might naively expect. Regression toward the mean is the name for this phenomenon.
If I understand correctly for it to happen it is essential that the trait is controlled by recessive genes.
However if there was a continuous trait controlled by dominant genes or genes with heterozygote advantage we would instead observe avoidance of the mean right? Is there a real-world example of this?

Welcome to Biology.SE. What is a "recessive gene" (you almost certainly mean allele) and why do you think dominance/recessiveness is associated with regression to the mean? Please [edit] your post to address the above issues and include support (preferably including references to peer-reviewed sources) for the multiple assumptions you are making. You might also benefit from thinking about the genetics behind a "continuous" trait. Finally, please clarify why you think "dominant genes" would show "avoidance of the mean" — it may be that by working through the logic you will answer this yourself.

What is a “continuous trait”? What is a “mean right”? I’m afraid that if you come from a numerical discipline and ask questions on a biological site, they need to be expressed in a language we can understand.

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text:
Hodgkin huxley neuron not spiking consistently for currents greater than threshold?
Hi I am currently studying physics at the undergraduate level. As part of my final year project Ive got to implement the HH model and investigate certain types of behaviour.
My issue is the following.
I understand that for $I_{inj}>I_{thresh}$ we should expect action potentials that spike at a regular frequency.

Here I've got an input current that seems to generate 2 initial spikes however no further spikes are generated. Is this physical? The presence of the initial spikes must mean that the input current is greater than the threshold, but we do not see consistent spikes across the entire stimulatory current.
Increasing the current slightly gives the expected behavior:

Is this an error in the code or is this a real physical phenomena?
EDIT------------------------------
Following Bryan Krause's suggestions, here is the full picture with the gating variables.
Case 1:
Stimulus current with amplitude 35 mA with period 100ms

Case 2:
Stimulus current with amplitude 37 mA with period 100ms

Case 3:
Stimulus current with amplitude 500 mA with period 100ms

Welcome to Biology.SE. The Biology.SE community has agreed that questions that show little or no prior research effort are off-topic on this site as are "homework" questions unless you have shown your attempt at an answer. Please [edit] your question and tell us where you've looked for answers, what you do know about the topic, and where exactly you still have questions. Please take the [tour] and consult the [help] starting with [ask] for details.

@tyersome I believe I have shown my attempt at an answer  by providing the second example as going by the HH model, that is what I believe should have also been observed in case 1.

What are the equations this model is solving?  Your case 1 looks like a strongly damped oscillator in the voltage, whereas case 2 looks like an oscillating solution. If you have a nonlinear damping constant, that could explain the difference between case 1 and 2 qualitatively.

@AtmosphericPrisonEscape The HH model is quite a famous standard model in neuroscience.

This is happening due to sodium channel inactivation. Some relevant sources:
https://en.wikipedia.org/wiki/Ball_and_chain_inactivation
https://www.st-andrews.ac.uk/~wjh/hh_model_intro/ (I guess this link is broken for some people? works fine for me as-is; see the links before and after instead, then)
https://neuronaldynamics.epfl.ch/online/Ch2.S2.html
In the HH model, inactivation is sometimes referred to as the "h-gate" based on the parameter they use for this inactivation, assigned the variable "h".
Sodium channel inactivation changes the action potential threshold and can even prevent action potentials completely. The easy way to understand this is that inactivated channels aren't available to participate in the positive feedback loop of an action potential. Because of this, it's not quite correct to think of a constant threshold for action potentials for a given cell/model. Instead, there is a threshold for any given holding potential or recent history of the membrane potential. Most often, you'll be concerned with the threshold at the resting membrane potential, but if you apply a constant external stimulus (or if you trigger a lot of action potentials in sequence without enough time spent at hyperpolarized or resting potentials) then the number of available sodium channels is not the same as at rest.
I would suggest a couple things...first, try other steps, too! What happens if you use an even bigger stimulus? Second...plot out the HH gating parameters m, n, and h as a function of time, not just the voltage.

Ive added a few more cases to my original question. Based on your answer I can't understand why case 3 and case 1 look identical.

@Vishal Look at the h-gate! Compare h before the first stimulus to after the first action potential (or first couple, once the APs stop).

Your St. Andrews link is dead.

@AtmosphericPrisonEscape Works fine for me.

I cant access the St. Andrews link either…
With regards to the h gate behaviour, I can see that h is quite close to 1, which makes sense since the neuron is hyper polarised. I’m not sure what to take away other than h is high when the neuron is hyperpolarised and low when the neuron is depolarised.

@VishalJain h is only close to 1 at rest; later in the pulse, it is less than 1. In the first case, it's low enough that the threshold has shifted so the stimulus is no longer superthreshold after the first spike, and h continues to decrease (more inactivated).  In the second case, there is enough of a relaxation of the h gate during the hyperpolarization between spikes. In the third case, the stimulus is too strong and the h gate never has a change to reopen; h stays low and so there are not available sodium channels to open.

I don’t get why the neuron seems to come to a resting potential at V = 0 after the first spike in case 1, but got case 2 (with just a small increase in the injected current), the neuron properly hyperpolarises in between action potentials.
Looking at the gating variables values all make sense when you look at the corresponding membrane potential at that time step.
EDIT: reading the previous comment it seems as though that tiny increase in current was enough to give the h gate enough time to relax to properly reset?

@VishalJain It's not just the membrane potential that matters, but also the state of all the gating parameters. In both case 1 and case 2, there is never a time that the h gate makes it all the way back to 1; it looks like it recovers to around 0.9 in both case 1 and case 2. Case 2 has a strong enough stimulus to still trigger an AP with only 90% of the channels available; case 1 doesn't, but the subthreshold depolarization is sufficient to cause even more channel inactivation (h continues to decrease over time).

Ok it’s starting to make sense, last question on this and I think it’ll click.
I can accept that in case 1, we provided a stimulus that was super threshold when the cell was at rest, however once stimulated it was no longer large enough to generate further spikes.
However,  if you look at my original image where i provided an image where we had 2 such initial spikes, how can you explain this? Here we clearly simulated the cell once when it was at rest in a hyper polarised state and again once while the stimulatory current was being applied, however then we stopped generated spikes.

@VishalJain You can see in your "case 1" that there is kind of a mini-spike; it's enough for some voltage gated channels to open and depolarize the cell a second time, but not enough for a full positive-feedback spike. By the third such "event" it's even weaker. Same thing happened in your original case 0 except the stimulus was strong enough to make the second spike, but you do see that the second AP is a little weaker than the first, and the third fails. All of this is best understood by thinking about how many sodium channels are available, aka "not inactivated", aka "h".

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text:
Does DNA ligase have any role to play in replication on leading strand?
Actually I developed this doubt while solving some questions(they are poorly framed I suspect). According to my notes and my institute modules, 1 RNA primer is required on the leading strand as well to start DNAP activity, and at the end repairing enzyme will remove the primer and add the complementary nucleotides. Now, here's the problem i am facing, will the DNA ligase join the newly added nucleotides by the correction enzyme or it is not required? The questions that created this doubt say in the solutions that DNA ligase is not a requirement in replication on leading strand but i think it should be required to join the nucleotides added by the correction enzyme as is the case on lagging strand. Am i correct?

The work of DNA ligase is to form "phospho-ester bond" or  "phospho-diester bond"(bond joining phosphate of one nucleotide with OH of another nucleotide).
by forming this bond the DNA ligase seals gap b/w 2 nucleotide sequence.
Now in case of lagging strand okazaki fragments are formed and gap b/w two okazaki fragments are filled by DNA polymerase and then the final joint is done by DNA ligase by forming phospho-ester bond b/w a nucleotide(last nucleotide which was placed by DNA Polymerase)and another nucleotide (which is the first nucleotide in the nucleotide sequence of second okazaki fragment which is being joined together)
now there is no need of all this mechanism in case of leading strand because there is no okazaki fragment present in leading strand. So DNA ligase is NOT required in case of leading strand.
hope this helps!!
EDIT-->
as discussed in the comments below, the DNA ligase might be required in joining two leading strands of two replication fork of a replicon

Thanks bro, actually i talked to my teacher also about this and he admitted that actually DNA ligase IS required on leading strand when the nucleotides are finally added in the place of one Primer that is required at the starting of leading strand. However since its role is so small it is usually neglected and NCERT also has mentioned DNA ligase with only lagging strand so that's why...

@Vaibhav Agarwal yes bro i got your point , DNA ligase might be required in joining the leading strands of two replication fork
correct?

Actually the DNA ligase kinda works like this- we know everytime DNA polymerase has to start its activity, RNA primase is added . RNA primase consists of a few ribonucleotides added complementary to the DNA strand which serve as kind of a launch pad for the DNA polymerase . now when the DNA polymerase is done with its work after replicating the entire strand , the DNA polymerase 1 ( mainly, however other enzymes are involved as well) comes and removes the ribonucleotides and adds the complementary deoxyribonucleotides instead. Now the DNA ligase comes and seals the newly added deoxynucleotides

As a primer is added on the leading strand , some DNA ligase activity is required there. However it is generally ignored (as NCERT has done and we will follow for NEET) due to the very small role it plays there.

@Vaubhav ya bro you are correct in explaining that how DNA ligase and DNA polymerase work.

According to me too DNA ligase contribution is required for joining leading strand of two replication fork but this contribution is neglected in NCERT Textbook.
bro if you found my answer useful then pls upvote my answer. And thank you so much for accepting my answer as best the answer. : )


text:
Differences between neurotransmitters and neuromodulators
According to the Wikipedia article on neuromodulation

a neuromodulator can be conceptualized as a neurotransmitter that is
  not reabsorbed by the pre-synaptic neuron or broken down into a
  metabolite.

In another Biology SE answer I read that

neurotransmitters can be considered neuromodulators when their action
  is on channels outside of the synaptic cleft.

Trying to bring these two conceptualizations together I come up with the following more specific differences between neurotransmitters and neuromodulators:

Neurotransmitters have typical short delay times (until they reach a receptor). Neurohormones may have arbitrary long delay times (the time they need to diffuse through the extracellular fluid). As a slogan: "Neurotransmitters work at once, neurohormones with a distance-dependent delay."
Neurotransmitters have specific target neurons (via the receptors of the synapse where they are released). The number of target neurons of a neuron (affected by the neurotransmitters it releases at its synapses) is rather well-defined (and goes into the thousands). The number of target neurons affected by the neurohormones a neuron releases is not so well-defined (and I'm missing an idea of the order of magnitude).
Neurotransmitters are effective only once and for a short time (due to fast reabsorption or break down into metabolites). Neurohormones can be effective for a long period of time.
This is due to different biochemical mechanisms by which specific neurotransmitters and neuromodulators affect specific receptors.

I wonder if this list is somehow correct and complete. (This is my question.)
Next to this list a list of commonalities would be interesting:

The same molecules can be neurotransmitters and neuromodulators.
Both are stored in and released from vesicles by similar mechanisms.
Both get effective by interacting with receptors and affect if a ligand-gated ion channel opens or not.

Key points:

Neurotransmitters directly stimulate or inhibit ionotropic receptors (the receptors of ion channels) in the postsynaptic membrane within a single synapse.
Neuromodulators act on metabotropic receptors within or outside the synapses of many neurons at the same time; they modulate the release of neurotransmitters and excitability of ionotropic receptors; the signaling between metaboreceptors and ionoreceptors usually involves a cascade of secondary messengers.

Neurotransmitters
"Classical neurotransmitters" stimulate or inhibit the fast-acting ionotropic receptors of ion channels. Their actions last few milliseconds and are limited to a single synapse, which means they are released from a presynaptic membrane of one neuron and they target the postsynaptic membrane of one (or, sometimes two or maybe more) postsynaptic membranes of the neurons involved in the same synapse, or a single muscle cell or other target cell (Oxford Scholarship, The Revisionist).
Examples of neurotransmitters: noradrenaline, acetylcholine, dopamine.
Neuromodulators
Neuromodulators act on the slow-acting metabotropic receptors inside or outside the synapse of "thousands" of neurons at the same time. In long-term (minutes), they modulate the release of neurotransmitters and excitability of ionotropic receptors. They are usually (but not necessary) released from presynaptic membranes into the synapse by the same mechanisms as classical neurotransmitters but can then leave the synapse through "spillover" and act on the neurons other than those involved in the synapse. So, their action is diffuse, but usually still limited to to certain neural pathways. (International Encyclopedia of the Social & Behavioral Sciences, 2001, Encyclopaedia Britannica, Wikipedia, Current Opinion in Neurobiology)
Examples of neuromodulators: dopamine (D receptors), serotonin (5HT receptors), acetylcholine (M and nicotinic receptors), noradrenaline (alpha and beta receptors), histamine (H receptors), endorphins and neuropeptides (Wikipedia, Journal of Chemical Neuroanatomy, 2011.)
Neurohormones are released from neurons into the bloodstream and have a systemic effect, for example:

Oxytocin and vasopressin, which are produced in the hypothalamus travel to neurohypophysis from where they are secreted into the blood and act on the mammary glands and uterus.
Adrenaline, which is secreted from adrenal medulla acts, via sympathetic nervous system on various tissues, usually on the smooth muscles of the blood vessels, heart, gut, etc.

Can a certain molecule can be a neurotransmitter, neuoromodulator and neurohormone at the same time?
Yes, for example:
Noradrenaline acts as a classical neurotransmitter and neuromodulator in the postganglionic neurons of the sympathetic nervous system and as a neurohormone secreted from the adrenal medulla (International Encyclopedia of the Social & Behavioral Sciences, 2015)
Dopamine acts as a classical neurotransmitter and neuromodulator in the dopaminergic pathways in the deep areas of the brain, such as thalamus and pituitary gland (picture); as a hormone, it inhibits the secretion of prolactin from the pituitary gland.
Are both neurotransmitters and neuromodulators stored in and released from vesicles by similar mechanisms?
Yes or no. Neurotransmitters are always released into the synapse, while neuromodulators may or may not be released into the synapse (Oxford Scholarship).
Do both neurotransmitters and neuromodulators get effective by interacting with receptors and affect if a ligand-gated ion channel opens or not?
Neurotransmitters can be effective if the ligand-gated ion channel are open and neuromodulators can open or close the ion channels.

Since the same molecule can be both a neurotransmitter and neuromodulator, it may not be that important to define the differences between the both in detail:

It could, therefore, be concluded that the aspect of defining
  neurotransmitters has taken a back seat to the investigation of the
  actions of individual signaling molecules. (International Encyclopedia of the Social & Behavioral Sciences, 2015)

Your key points suggest: neurotransmitters and neuromodulators act on completely different receptors. If this is the case, my question becomes somehow obsolete, because this would be the main differentiating issue. But to be honest: my impression was another one: that they act in a significant manner on the same receptors (but possibly more or less directly?)

@Hans-PeterStricker  Yes, the whole point is in different receptors. Here's a PhD who strictly emphasizes this: https://www.quora.com/What-is-the-difference-between-neurotransmitters-and-neuromodulators. Neurotransmitters act directly and neuromodulators indirectly, but neuromodulators do not stimulate ionoreceptors; they just make them more or less excitable. But the same substance can act both as neurotransmitter and neuromodulator. Many substances have both roles, actually.

But the last point is essential: "they make them more or less excitable". This means: they act on them.

@Hans-PeterStricker neurotransmitters directly stimulate/inhibit ionoreceptors. Neuromodulators only change the "plasticity" of ionoreceptors, which makes them more or less excitable. It's like they make the door harder or easier to open. Or if you want, a neurotransmitter is like a bowling ball, and a neuromodulator can make the pins more or less hard to fall.

I know that, but it remains the same: they act on them, only differently (somehow more indirectly, less specifically and less strongly,  and somehow delayed or whatever - but they act on them). So what does it mean that they "only" change the plasticity: they change it.

@Hans-PeterStricker OK; I didn't mention in the answer but, neurotransmitters act on ionoreceptors directly, while neuromodulators first act on metaboreceptors, which usually trigger a cascade of secondary messengers, one of which will then act on ionoreceptors. So, a neuromodulator may not act directly on the ionoreceptors, but I can't exclude that.

To put it differently: they are enabling factors.

Now we get into the tedious details of secondary messengers (which I am aware of but only start to learn about).

For my excuse: I didn't know of metaboreceptors until now, but now I know. Thanks a lot.

@Hans-PeterStricker I added this: "The signaling between metaboreceptors and ionoreceptors usually involves a cascade of secondary messengers."

One last question: How do the metaboreceptors communicate with the presynaptic neuron (because you say "they modulate the release of neurotransmitters")?

@Hans-PeterStricker, via G-protein and, additionally via secondary messengers, such as ATP.

I ntentionally put a quote at the end of my answer, which suggests that, after understanding basic differences, it may be better to concentrate on individual messengers, like dopamine, etc.

There are so many details to be known! It's really complicated. What I only learned now: that metaboreceptors may be located in vesicles.


text:
Which proteins are part of the most different protein complexes?
Let n be the number of different protein complexes (as defined here) that a protein may be a stable part of for a considerable amount of time (and not only transiently). Which proteins have the largest n?
An answer should include the number of different protein complexes  the protein is part of.
Or where should I start doing my own research? I have no clue.

Can you better define "protein complex"?  Are you asking which proteins have the greatest number of distinct binding partners?  Are you asking which proteins are most promiscuous in their binding to other proteins?  While I appreciate your thought-provoking questions, Hans-Peter, I feel that you've made no attempt at research for this one.

@Dirigible, thanks for asking. But are your paraphrases more unambiguous than my "simple" question? I agree that "of the most different protein complexes" doesn't sound perfectly right. I'll try to do better.

@Hans-PeterStricker As an example of what Dirigible might mean: all proteins are translated by ribosomes, along with a bunch of accessory proteins and chaperones to assist in properly folding proteins. Therefore, the ribosomal proteins (and associates) may be said to be complexed with every other protein. I haven't checked but this almost certainly gives them the highest degree in a protein-protein interaction network. This is a trivially true answer to your question, but it's almost certainly not what you mean.

Also: I would suggest reading a little bit more about protein-protein interaction networks, which I'm pretty sure are what you are interested in: https://www.ebi.ac.uk/training/online/course/network-analysis-protein-interaction-data-introduction/protein-protein-interaction-networks

This answer does not address the number of complexes that a protein participates in, but rather a related question -- With how many proteins does a protein interact?  I acknowledge this  is a fundamentally different question, though I think it's a good starting point on which other people can build a better answer.

Since an organism isn't specified in the question or tags, this answer focuses on a simple and extensively studied model: E. coli. Taking the data from STRING v11 1 for all protein-protein interactions (PPIs) in Escherichia coli str. K-12 substr. MG1655, we can subset these PPIs to include only those of action type "binding".  This database provides PPI scores between 0 and 1 based upon experiments (co-purification, co-crystallization, Y2H), textmining, co-occurence, co-expression, and co-localization of coding genes across genomes.
If we set no cutoff for the confidence in these binding interactions, we see that 2585 proteins have ≥1 binding partner, and one protein has an astonishing 273 binding partners (pfo, a putative pyruvate-flavodoxin oxidoreductase).  Also, this database states this E. coli strain has 4127 distinct protein-coding genes, so approximately 63% (2585/4127) of genes encode a protein that interacts with at least one other distinct protein.
If we limit the interactions to those with a "high confidence" score (≥0.900), only 656 proteins (~16%) are seen to have ≥1 binding partner, with a maximum of 55 binding partners seen for 4 proteins.  Unsurprisingly, and consistent with the comment from Maximilian Press, these proteins are all associated with the ribosome (sra, rpsP, rpsI, and rpsR).  The spike in the graph below at 54 interacting partners for the high-confidence PPIs is a group of of ribosomal proteins, most of which are annotated as co-interactors.

Two important notes on interpretation of interactions in this database:

splice variants and post-transcriptionally modified proteins are collapsed into single nodes in the interaction network, so all gene product variants are represented by one coding sequence
self-interactions (e.g. dimerization) are not counted, which are a valid type of protein complex per the question

References

Szklarczyk D, Morris JH, Cook H, Kuhn M, Wyder S, Simonovic M, Santos A, Doncheva NT, Roth A, Bork P, Jensen LJ, von Mering C. The STRING database in 2017: quality-controlled protein-protein association networks, made broadly accessible. Nucleic Acids Res. 2017 Jan 4;45(D1):D362-D368.


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From stem cells to fully differentiated cells
I'd like to understand better how stem cells produce fully differentiated cells via progenitor cells. I assume the following:

Only cells that are not fully differentiated do divide at all.
When a stem cell divides (at least) one copy remains a stem cell (and remains at its place), the other one starts to differentiate and to travel away.
Between the stem cell and the fully differentiated cell there may be one or a few progenitor cells.

My questions are:

How many cell generations are there between the stem cell and the fully differentiated cell? Any answer from "zero" or "one" (with one progenitor cell inbetween) to "quite a few" seems possible, but  maybe "zero generations" do never occur, i.e. no copy of a stem cell fully differentiates at once, i.e. without an intermediate progenitor cell.
How many cell generations are there between the stem cell and the last progenitor cell in the lineage from stem cell to fully differentiated cell?
How many cell generations are there between the last progenitor cell and the fully differentiated cell? By definition there should be zero, because when there is another not fully differentiated cell between them, then this would be another progenitor cell.

The questions are for somehow typical numbers (of generations), but the answers may depend on the tissue (resp. the type of the stem cell), so it would be interesting to know how strongly (this depends).

The answer may depend quite a bit on the boundary between stem cells and progenitor cells, which is a bit artificial and not entirely settled upon. Also "There are essentially three or four types of adult stem cells, one for each of the three germ layers, plus one for the neural crest, possibly" is false - even a source like Wikipedia would show you that with a very cursory attempt.

@BryanKrause: Thanks for the hint on adult stem cell types. I deleted the remark, since it is not crucial for the question.

I don't think it will be possible to give a general answer to this question, because the number(s) you are looking for will be different for almost every cell type. Also note that some fully differentiated cells (i.e. B-cells) can & will divide under special circumstances.

From this answer to a similar question one can derive that between a hematopoeitic stem cell and a mature blood cell there may be up to 16 generations (with 216 ≈ 70,000).

To the downvoter: What's wrong with this argument? (I changed it a bit.)

I didn't downvote, but it may be because you answered your own question on the same day you asked it by quoting an archived answer. And as you can probably agree, the answer itself is incomplete and doesn't really answer your own question adequately and contextually. That'd be my guess. On that rather reasonable basis I'd hazard to say both you and others would consider down-voting such answers.


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Exoskeleton Bug Identification
I found these bug shells / exoskeletons / casings in the corner of my room and I am wondering what they could be. They are about 1-2 cm long. The light colored spots on the floor are likely related. I was thinking they might be from pill bugs, but this is a second-floor room so I am unsure. Located in NW Washington, USA.
Thank you!

They are all wrapped in spider web, so you have a nice spider keeping your bugs down. If you could unwrap a few, then you might be able to get an ID. I suspect several different types of insects. The bottom middle (darker one) is likely a cranefly or something similarly leggy.

Welcome to Biology.SE. Looks to me like a spider has been feeding on a mixture of things including something pill bug like — I suspect the spots are spider droppings. Can you try opening up some of the little sacks and getting clearer pictures of the contents? Also, you might want to  check above where you found the bodies for webbing or a spider.


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Is this some kind of trashline orb weaver?
Is this some kind of trashline orb weaver or some other type of spider? Location is southwestern Virginia and the photo was taken in late July, in the morning.

The first two photos show the markings on the spider’s body. The color wasn’t quite preserved intact—-the spider’s body is a rust colored shade of orange, similar to the color of red clay dirt when it’s dry. The spider’s body is probably between the size of a green pea and an small garbanzo bean and is bulbous with relatively short black shiny legs. Total spider size including legs looks to be roughly nickel sized.
The web is highly complex with three key features numbered 1-3 in the last two photos. The first of these photos is front-on. The second is slightly to the side and shows that the orb web is slightly conical and how it connects to the trashline. Apologies for the photo quality, this was the best I could do with my phone’s camera. Fortunately the web was dew-laden which made the threads stand out more than normal:

The trash line (?) which is a short fat string of trash whose color and texture exactly matches that of the spider and is composed of bug shells and from what I could tell bits of clay dirt! The spider hides at the end of this structure and is perfectly camouflaged except for its front legs which it sticks out.

There’s an orb web that looks standard except for one difference that doesn’t translate well in photos: the web has a slightly conical shape, with the center of the web pulled toward the trash line and a small hole in the orb web apparently forming the opening of a tunnel to the trash line.

There’s what looks like a tunnel formed by a handful to half a dozen threads going between the orb web and the trash line. These go directly to where the spider is sitting. I’ve never seen it use the “tunnel” as a tunnel so not 100% certain that’s what it is, but that’s what it looks like structurally.

The rest of the web is a collection of chaotic random threads densely filling 3D space behind the orb web, and a few sparsely filling the space a couple of inches in front of the orb web. I’ve only ever seen these webs in the corners of fences.
The spider enlarges the web over time with the orb web gradually moving forward out from the corner, presumably being torn down and reconstructed farther and farther forward over time, so these webs can become quite large, measuring a good foot and a half or more on the side.
This is the first time I got a good view of the spider FWIW. I generally don’t view the web in the morning, and all other times of day the spider is steadfastly hiding in its trash line; this time it happened to come out and expose its body clearly. It was doing something but not sure what, maybe building on the trash line?
Any idea what type of spider this is, and what function each part of the complex web serves?


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How are cells that have died replaced by new ones?
I'd like to have a clearer picture how cells that have died are replaced by new ones.
I assume the following:

Normally, when a cell dies it will be replaced by a new one of the same type.
It will be replaced by the division of another cell (of the same or another type). One copy remains where it is and keeps its type (for later use) and the other one possibly travels to its target location (where the died one has lived) and possibly changes its type (during travel or after arrival).

My questions are:

Are these assumptions essentially correct? Or are they overly simplified?
What are possible distances between the regenerating dividing cell and the target location? I assume some static cells will be replaced in situ, possibly skin cells. Others may be regenerated far away, especially floating cells, like blood cells.
If the distance is large: How does the regenerating cell know it has to divide? And how does the regenerated copy know where to travel to?
When one of the copies of the regenerating cell starts to travel,why doesn't the other?
Are there cases where the regenerating cell is already of the same type as the cell that has died – and so are its two copies?
What about the (programmed) lifetimes of the regenerating cells?

I hope these questions - which would give me one consistent picture - can be answered in one comprehensive answer.


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Long-term potentiations that last for a lifetime
One reads more often than not that

long-term potentiation has been reported to last for as long as several weeks
LTP is persistent, lasting from several minutes to many months

and most sources seem to explain mechanisms of LTP that just last as long - from hours to days to weeks to months. Only rarely it is explicitly mentioned that such-and-such LTP lasts for years or a lifetime, and most authors seem to hesitate to make such claims.
But there are memories (and learned skills) that can be retrieved many years and even decades later, even though not (consciously) used in the meantime.
I have no idea how this kind of "really long-term potentiation" is explained. Three options come to my mind:

The long-term potentiated synapses and the "memories" related to them have actually been used in the meantime (just "unconsciously" or in completely different contexts) and thus been re-newed and re-strenghtened every now and then.
They degraded but have been re-newed without having been used, but by some other mechanisms than "normal" LTP.
They actually did last for such a long time (i.e. didn't degrade) - and the authors just hesitated to claim it (because they could not prove directly).

Is one of these three explanations the correct one, or is there another one?

No time for an answer but some dendritic spines live long enough to sustain memories that can last for as long as the animal lives (Yang et al 2009). Each time a memory is recalled, it is also reshaped --potentially strengthened, attenuated, or otherwise altered.

@vkehayas. Hi, Vassilis, great  to hear from you again! The explanatory problem is that a memory or skill (as a holistic entity) may be un-recalled for decades and thus not reshaped. It's only the synapses involved in the memory that are re-strengthened, attenuated, or otherwise altered - just by being part of many other memories that were recalled. Does this picture make sense? (Alternatively one might consider that the memory itself actually was recalled, but unconsciously, maybe in dreams?)


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Are there nuclei with "real" interneurons?
In Kandel's "Principles of Neural Sciences" in the chapter about the anatomical organization of the brain one reads (p. 323, 4th ed.):

»Although a variety of [relay] neurons are involved at each stage in information processing, these neurons generally fall into two functional classes: principal (or projection) neurons and local interneurons. The axons of principal neurons convey information to the next stage in the system. Interneurons may receive inputs from the same sources as the principal cells, but they contact only local cells involved in the same processing stage [(relay)].«

This means: All neurons of a "relay" (= functional unit) receive external input, but only some give external output. I wonder if there are examples of functional units (nuclei, cortical areas, etc.) with significant numbers of

interneurons receiving input only from local cells
principal neurons receiving input only from local cells

If there were, there would also be distinguished input neurons, receiving external input but not giving external output.

I don't think assigning those classes the adjective "real" makes any sense. Additionally, in an ANN, there aren't any interneurons if we think about it like the brain. Otherwise almost the entire CNS is interneurons, except for the motoneurons and sensory neurons themselves.

@BryanKrause: Of course, the entire CNS is interneurons (except motor, endocrine, and sensory neurons), but I asked for smaller populations of neurons like nuclei and cortical areas. And why shouldn't a layered ANN have interneurons?

I think I wasn't very clear. What I meant is that the definition of what an "interneuron" is varies with systems, and ANNs and the brain are not organized very similarly. One could just as much consider a hidden layer of an ANN to be a collection of neurons that project to another layer. It's fine to call them interneurons in an ANN context, I'd just be hesitant to carry that definition over to analogies.

@BryanKrause: I dropped the ominous adjective "real" because it adds nothing to my question and was responsible for some confusion, as I am afraid. Now the question should be rather clear-cut - or isn't it still? Also, mentioning ANNs didn't add anything essential to my question, so I dropped it, too.

I think that's better. I feel like it's missing some motivation as-is, but maybe someone will come along with an answer. You're likely to find cases like this in the periphery/sensory organs, but I'm kind of missing the "why" of why this matters.

@BryanKrause: I could imagine that functional units with "real" interneurons and "proper" input and output neurons might do different kinds of "computations" or have different "modes" of computation than those without them. But this would have to be shown, e.g. by corresponding ANNs.

I see. I think that in most cases brains are simply much more complicated than that; there are too many good reasons to keep, for example, an efferent copy of an output signal (making the output neurons...improper). Probably the retina is a relatively complex structure that fits at least some of your requirements, but computationally it is quite boring compared to other brain areas.

Let us continue this discussion in chat.


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Does positive electricity run through neurons in the exact same way as it runs through copper?
Does positive electricity moves in the exact same way as electric current moves through copper,silver and gold? From what I understand, electricity propagation in neurons is not linear as it is in a wire but rather in a cross-sectional way, moving forward little by little depolarizing the adjacent part ot the axon untill it gets to its destination.This is because the neuron cell membrane is made mainly by fat, and fat is consider an insulator. Besides, this is not an electric current but rather an ionic current, so atoms cannot move the way electrons do.
https://www.youtube.com/watch?v=RNdvrkolW0M

Does this answer your question? Please search the site before asking a question. There's tons of information already here

@AliceD In other words, it is a polarization wave that propagates with a speed of sound in water (since it involves actual liquid flow). Whereas in copper we have a plasma wave, which propagates with the speed close to the speed of light.

@AliceD, I am not asking about the action potential in general, I am asking about the way charges move in the nerve fiber, and if they move just like they move in copper. I thought it was a specific question. Thank you for your reply.

@Roger Vadim Thank you very much!, I have done some research on this topic but I cannot understand the exact difference between a plasma wave and a polarization wave. Would you mind to clarify please?


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How does hypokalemia antagonize lidocaine's effect?
I was reading the lidocaine user's manual for dentistry use and according to it and I quote "Lidocaine in concomitant use with acetazolamide, thiazides and loop acting diuretics. The hypokalemia ("a low level of potassium (K+) in the blood serum") induced by these drugs, antagonizes the lidocaine effects" which seems a bit weird as a potassium deficit would hyper-polarize the membrane increasing membrane potential making it to hard to get to the threshold potential right?

Thanks for adding the quote; I agree it's odd. I could see systemic concerns with lidocaine reducing heart rate which would be a bad combo with hypokalemia, but antagonism is not the concern there. Is this possibly a bad translation? Is there other context beyond what you quoted?

As a matter of fact, I couldn't find the exact same info in the English version, but I can guarantee you there is no translation error. I could provide you with a copy of it if you wanted to.

Here is the link where you can download the Spanish version of the manual https://zeyco.com/producto/fd/ is the part about drug interactions

Thanks; it's clearly in both English and Spanish inserts. Inserts for similar formulations like https://www.accessdata.fda.gov/drugsatfda_docs/label/2018/021381s006lbl.pdf or https://www.accessdata.fda.gov/drugsatfda_docs/label/2018/006488s097lbl.pdf don't mention any such antagonism. Certainly it makes sense as a possible contraindication for other reasons, but I agree with you that the mechanism and concern they mention isn't making much sense to me.

The following is a suggested answer only -- and is NOT intended to be authoritative; since it is not clear from the literature on Lidocaine why its efficacy is reduced in hypokalemia.
While it is true that hypokalemia will tend to induce hyperpolarisation of cell membranes, which in the case of neurons inhibits the elaboration of the action potential (by increasing membrane potential), other effects should also be considered, in the first instance that the concomitant tendency for K+ to flow out of cells generally also implies the countervailing tendency for Na+ channels to promote the transport of Na+ into cells -- more channels operating with greater facility.
Since Lidocaine is a sodium channel blocker -- which prolongs the inactivation of voltage-gated Na+ channels -- then prima facie, a generalised condition of hypokalemia suggests that the associated operation of more sodium channels will tend to antagonise its action.
At the same time, since the Na+/K+ ATPase would be operating to maintain homeostasis of intracellular cations (K+ in particular) in the face of any such efflux of K+ from cells, this effect would likely be accentuated by virtue of the corresponding efflux of Na+ from the same cells; notwithstanding the findings cited in the study below [1] concentrating on myocardial activity, that ''hypokalemia significantly inhibits Na+/K+-ATPase pump activity causing intracellular Na+ and Ca2+ accumulation''.  In that case, it is presumably the implication of the Na+/Ca2+ pump which complicates any effect on Na+ channels.
Additionally, the finding that hypokalemia inhibits the Na+/K+ pump would imply a tendency to recalcitrance in the opening and function of sodium channels which, since that would favour the action of Lidocaine (as a sodium channel blocker), contradicts the premise of the question.
[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5399982/
https://en.wikipedia.org/wiki/Sodium%E2%80%93potassium_pump

@Bryan Krause (or whoever down-voted the answer) Please indicate what is wrong with the reasoning. I think any objection deserves explanation. While I don't KNOW that this answer is correct, whatever the answer is, presuming the premise of the question is valid, almost certainly involves some effect of hypokalemia on Na+ channels presumably as a consequence of changes in IC K+. If it is true that the Na+/K+ pump is inhibited in hypokalemia, it would suggest recalcitrance in the opening of Na+ channels favouring the action of Lidocaine which contradicts the premise of the question.

Thank you very much! Although I wonder why hipokalemia improves sodium channels activity.

@Quique I'm not sure that it does -- it was merely a suggestion based on the idea that since K+ will flow out of cells in order to redress a condition of hypokalemia, then it is likely that Na+ will flow into the same cells via the most efficient mechanism, which would be sodium channels. However, my answer was not well-received so there is probably some more obvious effect which I'm overlooking. There still doesn't seem to be any explanation for the effect you cite on Lidocaine activity. The consensus among the erudite here seems to be, ''We dunno and it's not really important''. Fair enough.


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How to model social structure in SIR models
I refer to J.H. Jones' Notes on R0.
More details in this question at Mathematics SE: How does the reproduction number depend on characteristics of the physical contact graph of a population?

The basic SIR model - as described in Jones' Notes - considers three factors that make up the reproduction number:

$\tau$ = the transmissibility (i.e., probability of infection given contact between a susceptible and infected individual)
$\overline{c}$ = the average rate of contact between susceptible and infected individuals
$d$ = the duration of infectiousness

The (basic) reproduction number then is
$$R_0 = \tau \cdot \overline{c} \cdot d$$
I wonder how to model social structure in a SIR model, which might influence both transmissibilty $\tau$ and average rate of contact $\overline{c}$ and thus the reproduction number $R_0$, resp. the infection rate $\beta = \tau \cdot \overline{c} = R_0 / d$.
Specifically I wonder which "control parameters" appropriately describe the social structure of a population and may influence transmissibilty $\tau$ and average rate of contact $\overline{c}$ in a specific and comprehensible way.
Among these parameters may be:

typical (mean) numbers of household members and acquainted persons
typical ratio of shared acquaintances
typical numbers of strangers one meets (e.g. per month)
typical times of contact to household members, acquainted persons, and strangers
the amount of persons with outstanding many social contacts, better: the standard deviation of the contact rate
the accepted physical distance to family members, acquainted persons and strangers
(source)

I am looking for approaches that let go such parameters into the infection rate $\beta = \tau \cdot \overline{c}$ in a quantitative way.


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Hopfield-like neuron assemblies
There seems to be general agreement that theoretical Hopfield networks (consisting of artifical neurons, namely McCulloch-Pitts neurons) are biologically rather implausible, among other reasons because of their (rather strictly) symmetric synaptic weights. On the other side, some authors claim that there are neural assemblies in the brain that qualitatively behave like Hopfield networks, i.e.

they are strongly interconnected
they synaptically store a limited number of (activity) patterns
which they reach as attractors when fed with noisy or incomplete input patterns
they "learn" (mainly) by the Hebb rule

The system of hippocampal CA3 neurons is suggested to be one such assembly.
My questions:

Is there an agreement among experts that hippocampal CA3 neurons really behave similar to a Hopfield network?
Which other assemblies (possibly nuclei?) are believed to behave similar to a Hopfield network, too? (Some examples would be welcome.)

For the benefit of others coming across the question, could you include a brief explanation of what a Hopfield neural net is?

"Is there an agreement among experts that hippocampal CA3 neurons really behave similar to a Hopfield network?" - The difficulty with such agreement is that behave similar is very non-specific. Probably no expert will say either CA3 behaves nothing like a Hopfield network, nor CA3 behaves totally like a Hopfield network; rather, in some (perhaps many) circumstances or for some functions, Hopfield networks are sufficient to replicate CA3-like behavior.

I think it really depends on the level of detail and accuracy needed.
Giving a quick look on Google Scholar, it appears that indeed there is (or at least was) a belief that hippocampal networks could be reasonably modelled by Hopfield networks (e.g. see Neuromodulatory control of hippocampal
function: towards a model of Alzheimer’s disease by Menschik and Finkel, and its references). However, many of these papers are somewhat old (though this certainly does not invalidate them!) and computational neuroscience moves fairly fast.
So yes, to a certain extent, after reading some papers that corroborate it, it might appear that some macroscopic behaviour of CA3 neurons can be reproduced by Hopfield networks.
That being said, in more recent works, I have personally never seen anyone model biological neurons with such simple neurons, when cellular level accuracy is required (often it isn't). At least stochastic Hodgkin-Huxley or integrate-and-fire, for instance, are used, even if as point processes (so that it is a system of ODEs/SDEs, not PDEs/SPDEs). Even the neurons used in today's deep neural networks (which make no effort towards biophysical plausibility) are (or at least can be) more complex than sigmoiding a linear combination of inputs!
Also, for slightly larger scales, as you note, the connectivity structure is extremely unrealistic. (Just look at the histology!)
So anyway, it depends on the goal. For simple macroscopic, qualitative similarities it may suffice. But if the goal is biophysical accuracy of simulation then I would look at newer papers and see what they do.
Check out Synaptic mechanisms of pattern completion in the hippocampal CA3 network by Guzman et al.
As for your second question, just searching for papers on Hopfield networks finds a number of them. However, they appear to be largely computational or mathematical, rather than neuroscientific modelling papers.
Maybe others can find better ones though!
Disclaimer:
I am not in the field of hippocampal modelling nor have I worked much with Hopfield networks, so take my thoughts with a grain of salt.
My suggestion is to do an extensive literature search, and post what you find as an answer here :)

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


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Anyone Know What This Is?
So I don't know much about plant structure or biology in general but I found this little guy while on  X10 and x40 lenses on our school microscope while looking at a leaf. I'm not sure if it's part of the leaf or if it's something that attached to it (I did find bits of filamentous algae on the leaf so it could be something aquatic?). I will provide both pictures and if I can, the videos I took of it. It has a spring shaped tail that seems to connect it to the edge of the leaf that's causing it to spring back rapidly after it moves out from the leaf.link to the pics shown as well as the videos taken at the same lens strengths as well as other stuff I found
EDIT: I am from Michigan, and based off of a lab that I'm doing today in the same class the plant is an Elodea, a freshwater aquatic plant. Don't know if that info helps any but hopefully it does!

Welcome lilgyz. Could you give us a bit more to go on such as what country/area you're living in, what type of plant was the leaf from, perhaps a picture of the whole leaf?

I'm from michigan. Unfortuantely I don't know what kind of plant it is nor did I get a picture of the plant but I can if I can figure out what plant it was


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Didehydro cysteine as a modification in unreduced/unalkylated proteomics
I am analysing proteomic data, some of which was digested with the Thermo SMART Digest Kit and some by in-gel digest. I am not a laboratory scientist, and have noted that the samples processed with SMART Digest Kit have very low proportion containing cysteine residues (~0.5% compared to 30% with in-gel digestion). We now have a belated realisation that the SMART Digest Kit does not reduce or alkylate proteins, and that thus disulfide bonds will largely remain.
In an aim to recover as much data as possible, I tried removing the fixed carbamidomethyl mod, however only a few unmodified Cysteines are found. I performed an open search on a small subset of data obtained with high fragment ion resolution, and identified a number of peptides determined to containing cysteine with a -2.0157 Da modification, labelled as "2-amino-3-oxo-butanoic acid" or "didehydro [cysteine]" (shown is -2H on https://www.unimod.org/modifications_view.php?editid1=401). [ed - I appreciate this is not a recognised modification of cysteine!].
If I undertake a fixed search with this as a variable modification I find many more cysteine containing peptides (up to 5%) with a majority with this -2H modification.
However, this modification doesn't seem to be a recognised one for cysteine, and I am no chemist. I wonder if anyone has come across this modification before and can explain it? Ed - I presume it's more likely to represent a different amino acid with a modification which gives a near-identical mass to cysteine -2H.
Incidentally, despite the claims that the SMART Digest kit has immobilised trypsin which should not auto-digest, we have very strong signal from trypsin auto-digestion products!

Welcome to Biology.SE. The link you give doesn't list that modification as being associated with cysteine (or with cystine for that matter) — can you clarify why you think 2-amino-3-oxo-butanoic acid is associated with cysteine? Also, didehydro should be followed by what is being modified — what is it? Please [edit] your post to clarify. Also please note that 'thanks' and 'signatures' are not used on SE sites, so I will edit your post to remove them.

Never mind about my previous didehydro question I reread your title. However, didehydro cysteine is not the same thing as 2-amino-3-oxo-butanoic acid ...

Thanks @tyersome - I am also unclear why the -2H modification is described as both didehydro and 2-amino-3-oxo-butanoic acid. Perhaps this is the residue that results when a specific amino acid is "didehydrated."  I don't know enough chemistry to to know if cysteine can be "didehydrated," and I wonder if it's more likely if I'm finding amino acid variants where cysteine has been replaced. No amino acids are constituted by C3H3ONS. The modified monoisotopic mass corresponds to 100.99354 which is closest to the mass of threonine (101.04768), but this is orders of magnitude above a 20ppm error.


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Synaptic connectivity in the newborn's brain
In my understanding, learning is related to the strengthening and weakening of synaptic connections. Very roughly said: Synaptic connections that are used often are strengthened, those that are used rarely are weakened. This is basically the Hebb rule.
Assumed that the Hebb rule holds at least partially (of course, there are other factors at work during learning), I wonder if in a newborn's brain the areas where learning will take place are equally weakly connected by synapses (so the pathways will be "built up") or are equally strongly (maximally) connected (so the pathways will be "carved out") or something inbetween. Or are there areas of both/all kinds?
(I assume that there is a maximal connection strength beyond which no further strengthening takes place.)

This is a really interesting question, but I honestly don't think anyone can answer it yet. I might be wrong, but the problem is our models (rats, primates etc.) are born at different developmental periods to us, neurologically speaking. So it's a difficult question to answer using available techniques. If you think about a specific brain region of interest, then you might be able to find some developmental papers that will give you a bit more insight.

Thanks for the comment. But don't you - or any of your colleagues - have a feeling how it might be?

A feeling with respect to species and developmental period and brain area.

My gut says that when a synapse forms it will probably be in a middle ground, then can be affected by either "Long-Term Potentiation" (strengthening), or "Long-Term Depression" (weakening). But there's so many changes going on in a developing brain, that it might be different in different regions. Edit, this feeling is based on when individual synapses form, which happens in different regions at different times (but is likely to be similar cross-species).

If it's a feeling you want, this becomes a primarily opinion based question. I have a feeling that there are strong and weak and as yet non-existant pathways at birth.

All synapses start infinitely weak (I.e, there has to be no synapse before there is a synapse). The degree of development of different brain areas at a given stage of life varies dramatically. I don't think this question is answerable in any general sense but to say something vague like that, without more specificity up front. Voting to close in agreement with @anongoodnurse


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The human brain in numbers I: neurons
Even though knowing the number of neurons in a functional unit or with the same function is not of main importance, it may be interesting to know their orders of magnitude, especially in the human brain. For example:
|------------------|------------------|
| cerebellum       | 100,000,000,000  |
| cortex           |  20,000,000,000  |
| telencephalon    |  10,000,000,000  |
| brainstem        |   1,000,000,000  |
| sensory neurons  |                  |
|          haptic  |     500,000,000  |
|          visual  |     100,000,000  |
|        auditory  |           2,000  |
| limbic system    |                  |
|         amygdala |      10,000,000  |
|------------------|------------------|

Surely, for many parts of brain you will find a reference where the number of its neurons is estimated (e.g. for the amygdala) - when you search hard enough. I also found The Human Brain in Numbers where some numbers are given. But I am looking for a reference where many of these numbers are given in a systematic way, ideally in a table like the one above. Is there any?

For which parts do you want such numbers? The more detail you go into, the more likely you are to get nothing. It would be, say, easier to get info on the 4 lobes than on hundreds of areas. So, do you want info on simply the 4 lobes?

As many as possible;-) My interest is not specific but general. And please do not ask, why I want these numbers: I just want to know which ones exist or are known (approximately).

A related question - yielding a partial answer - can be found here: What are the estimates in total neurons and average connections per neuron for each of the processing areas of the visual cortex?

First of all, let me clear out that these numbers are calculated, not observed (obviously, nobody has counted the number of neurons in any part of brain). So, take these with a grain of salt.
I was unable to find any report that collects and displays all numbers together (Bio Numbers too didn't yield significant information). So I will compile here all the numbers I have found so far (and keep adding as I find more):
|----------------------|------------------|------------------------|
|PART OF BRAIN         |NUMBER OF NEURONS |               REFERENCE|
|----------------------|------------------|------------------------|
|The human brain       | over 120 billion |  Herculano-Houzel, 2009|
|Telencephalon         |  12-15 billion   |           Shariff, 1953|
|Cerebellum            |   101 billion    |    Anderson et al, 1992|
|Cerebral cortex       |  21-26 billion   |      Pelvig et al, 2008|
|Amygdaloid complex    |    12 million    |    Schumann et al, 2005|
|Hippocampus (CA1)     |  11-24 million   |        West et al, 1990|
|Brainstem             |   < 1 billion    |  Herculano-Houzel, 2009|
|Visual cortex         |   140 million    |       Leuba et al, 1994|
|Auditory cortex       |    1 billion     |University of Washington|
|Corpus callosum       |   200 million    |          Healthline.com|
|Spinal cord           |    1 billion     |University of Washington|
|Cortical minicolumn   |      80-120      |               Wikipedia|
|Cortical hypercolumn  |   5,000-10,000   |               Wikipedia|
|----------------------|------------------|------------------------|

I will continue adding more numbers as I find them. Again, nobody will claim these numbers to be exact, these are just estimates from calculations. Even different sources show different numbers. For example, the Washington University page puts the number of neurons in visual cortex to 528 million. Thus, don't expect these numbers to be anywhere near exact.

References:

Herculano-Houzel, 2009
Shariff, 1953
Anderson et al, 1992
Pelvig et al, 2008
Schumann et al, 2005
West et al, 1990
Leuba et al 1994
University of Washington
Healthline.com
Wikipedia Cortical minicolumn
Wikipedia Cortical hypercolumn

Just great! More than I did expect.

It would be great if the table was hierarchically organised (where possible): top level: the human brain. Way down: the amygdala,...

@hansstricker again, I don't get you. How are you categorizing them to get a hierarchy? From front to back? Number of neurons?

I mean hierarchized by being-part-of. Doesn't this make sense, at least sometimes? I mean, some parts of the brain are immediate parts of the brain (cerebrum, brainstem, cerebellum), others are parts of parts, and so on.

May I add the numbers for cortical minicolumns (ca. 100) and cortical hypercolumns (ca. 100 x 100) in your table?

@hansstricker with proper citations, why not? Every answer, including mine, on Biology.SE is open for improvement! Right now I am quite busy, so will not be able to help anyone out much :)

@HomoSapien: This is a hierarchy which I have in mind: https://en.wikipedia.org/wiki/List_of_regions_in_the_human_brain . It would be great to have this with the acoording number of neurons.

120 billion? I always thought it was closer to 90 billion.

@forest however surprising it is, its just a scientific claim. You never know until you count them all :P


text:
Ion-gated ion channels
Today I've heard for the first time of calcium-gated ion channels but find it hard to get an idea how they work, where they are located, and which role they play.
I assume calcium-gated ion channels are just a special form of ion-gated ion channels, which would be a fourth group of ion channels next to voltage-, lipid-, and ligand-gated ion channels (with ligands being some larger molecules). But on ion-gated ion channels even less is to be found on the internet.
One specific paper that mentions ion-gated ion channels is this (Experimental Neurology, 2001)
One paper that mentions calcium-gated ion channels is this (New England Journal of Medicine, 2015)
Where do I find a general introduction into ion-gated ion channels - if they exist?

KIR could be considered as a ion gated ion channel. In this case Mg+2 blocks the channel from the inside preventing the "outward" conduction of ions.

The main families of calcium-gated channels I am aware of are the calcium-gated potassium channels and the internal ryanodine receptors involved in calcium-induced calcium release - you could start from those linked Wikipedia articles.
I wouldn't really make these a fourth category, they should either be thought of as voltage-gated channels that are modulated by intracellular calcium, or as ligand-gated channels - the ligand just happens to be a calcium ion.
Some channels in this category are not influenced by calcium directly but via calmodulin, which is a common mediator of calcium-driven intracellular influences.

Ryanodine receptor is also a good example.

@WYSIWYG Thanks - added.


text:
What is the modern experiment in which a frog was heated at the slowest rate?
I did a bit of research on the boiling frog phenomenon. It turned out that:

In the 19th century, there have been done three experiments in which a frog in water was heated very slowly. It didn't jump out and then it died.
Modern experiments did also heat frogs, and they did jump out.
Actually, a frog dies in water of $40^{\circ}$ C. Therefore, to properly conduct the experiment the water should be heated from a normal temperature to 40 degrees.

In order to prove that the 19th century experiments were wrong, there should be a modern experiment where the frog is heated just as slowly as in the 19th century. According to Edward Wheeler Scripture (see Wikipedia), he performed the experiment with a rate of 0.002 degrees per second.
Are there modern experiments which also have such a slow rate? What is the slowest rate of a modern experiment?
EDIT
The following article claims that the modern experiment with the slowest rate is still 9 times as fast as that of Scripture. Is this really true?

If the current climate science stats are accurate, all frogs on earth are being heated at a rate of 0.2° C per decade, on average. Sure, there may be a few covariates to account for, but the sample size is huge.

As noted in one of your links: "they don't sit still for you" seems to be the problem. If you put a frog in a pot, it doesn't matter if you heat it at all, if you allow them to escape they will escape. I kind of doubt anyone has actually published on that, though; people don't usually publish such trivialities.

@acvill, unfortunately frogs won't be able to jump out of the earth when it becomes too hot

@Bryan Krause, if the frog did escape, then it would indeed be too trivial to publish. Exactly the fact that the frog didn't escape, made it memorable.

@Riemann It seems the modern commentators are saying that the frog doesn't need any temperature increase to escape. If you put a frog in a pot it will jump out if it can, heat or no heat, so they don't see the point to do the experiment with a gradual temperature change. Presumably in the original experiment (which I haven't read) the frog was not actually able to escape, otherwise it would have (again, not because of heat, but because of frogs doing frog things, like moving around freely when they can).

@Bryan Krause, wouldn't it be possible to wait until the frog is sleeping or something like that?

@Riemann It seems like that would be a separate experiment, but not necessarily; how do you plan to put a sleeping frog in a pot without waking it up? Behavior under sleep is also different from waking behavior - reduced response to stimulus is a hallmark of sleep. Also, your question implies Scripture did this experiment; I can't see any source that suggests that he did. Wikipedia says he "recounted" aka told a story about; in the cited source he refers to experiments by Heinzmann and Fratscher.

OP: The most amazing of all your statements is that a dead frog jumped out of hot water! No wonder the experiment could not be reproduced! ("...a frog in water was heated very slowly. It didn't jump out until it died.") Like I said, that is one for the books. Or if one prefers journals, The Journal of Irreproducible Results.

I don't really read enough German to read Heinzmann, but it seems that most, if not all, of his experiments were done in decerebrate frogs. It's a study of the reflex arc of the frog's leg and spine, rather than the behavior of the frog, from what I can tell.

"a frog dies at 40 C" - citation needed I think.

@Anongoodnurse: very good point! I corrected it

@bob1 I added citation

@Riemann - thanks, but that isn't a citation for fact it literally says "The facts go roughly like this: ...   ...The fatal temperature for a frog is below boiling point, more like up to 40 °C." without citation. The link for a supposed citation (provided at the end of the article, not referenced) is to zeit.de and is paywalled, so unverifiable.

To clear up some things, I have made a partial answer here.
While it is old, you shouldn't discount the observations made by scientists from the 1800's. Many great scientists from this period laid the foundations for science as we know it now. These include names such as Charles Darwin, Alfred Wallace, Robert Koch, Gregor Mendel, and Louis Pasteur, to name a few well known biologists, whom no-one would think to doubt. Scientists in the 1800s were certainly exact in their measurements, observations and records, and I don't doubt that the observations that they made were exactly what they claimed they were.
To this end, I had a look at Goltz's 1869 book1 (PDF here) in the original German, and put it through Google translate ('cause I don't read German well enough to follow at this level) at the relevant point. Fortunately the PDF linked is text-selectable, so I was able to copy this directly and edit some minor misinterpretations from the paste. Google translate is pretty good for German and German has not changed significantly since the 1800's I believe.
Here's the bits I copied from pages 127 and 128 (you can see the errors at line-ends and in special characters, and where some bits can't be recognized as they are in the spine end of the text):

Von drei gleichzeitig gefangenen, gleich grossen und reiz-
:en Fröschen schneide ich zweien mit der glühenden Platin-
linge des galvanokaustischen Apparats die Köpfe ab. Dem
tten sonst unversehrten blende ich die Augen, um unnütze will-
1 liehe Bewegungen desselben möglichst auszuschliessen. Darauf
ce ich den zuletzt geköpften Frosch in ein weites blechernes
iäss, dessen Boden mit mehreren Schichten Leinwand bekleidet
und bringe ihn sogleich in die hockende Stellung, welche
hirnte Frösche immer annehmen und dann nicht wieder von
')St verlassen. Das Gefäss fülle ich jetzt so weit mit Wasser,
'S nur ein kleiner Theil des Thieres daraus hervorragt. Zu
1 Enthaupteten setze ich dann den geblendeten Frosch, wel-
r sich alsbald ebenfalls in hockender Stellung niederlässt und
iangslos verharrt. Den zweiten Geköpften behalte ich in der
le des Gefässes unter Augen. Jetzt fange ich an das Gefäss 128 Ueber den Sitz der Seele dea Frosches und
zu erhitzen, die steigende Temperatur des Wassers an einem :
dasselbe eingesenkten Thermometer ablesend. Die Zimmertempi
ratur beträgt 17i”C.
Hat das Wasser aber erst die Temperatur von 25“ erlangt, li
verändert sich die Scene. Dem behirnten Frosch beginnt es uj
behaglich zu werden. Er verändert den Ort, steckt den Kot
weit zum Wasser hinaus, und fängt an, schneller zu athmen. j
höher die Temperatur steigt, desto ängstlicher werden seine B<
wegungen. Verzweiflungsvoll schwimmt das gequälte Thier ij
Behälter umher, bald den Kopf weit hinausstreckend und imm<
geschwinder nach Kühlung jappend, bald auf den Grund d<
Gefässes tauchend, um dort der Pein zu entrinnen. Die Hita
nähert sich gegen 38“. Das Thier macht verzweifelte Sprüng«
um aus dem Behälter zu entkommen. Es klimmt an den glatte
Wänden empor und muss in das heisse Wasser zurück gestosse
werden. Die immer geschwinder auf- und niederfliegenden Atb
mungsmuskeln erlahmen, die Athmung setzt aus. Immer wild^
werden die Schmerzensäusserungen, und endlich bei einer Teib
peratur von etwa 42“ verendet das gequälte Thier unter tetan^
sehen Krämpfen.

And the translation:

I cut off the heads of two of three frogs of the same size and attractiveness that were caught at the same time with the glowing platinum pieces of the galvanocaustic apparatus. To the
I blind the eyes of those who are otherwise undamaged in order to exclude useless voluntary movements as far as possible. Then I put the last decapitated frog in a wide tin vase, the floor of which was covered with several layers of canvas
and immediately bring him into the squatting position, which
brain frogs always accept and then not from again
')St leave. I fill the vessel with water now,
'S only a small part of the animal protrudes from it. to
I then place the blinded frog on the decapitated one, which soon also settles down in a crouching position and
fearless. I'll keep the second decapitated man in the
le of the vessel under the eyes. Now I start the container, the water has reached a temperature of about 25", both frogs sit still in the warm bath. On the decapitated one sees the movements of the thighs, so common in decapitated people: he might pull one thigh up a little more or straighten a zoe, movements such as those used outside of the bath
Lingering second decapitated also shows, which are therefore not dependent on the increasing temperature, and which incidentally will soon stopBut once the water has reached the temperature of 25", the scene changes. The brained frog begins to get uncomfortable. He changes the place, sticks the feces
far out to the water, and begins to breathe faster. j
the higher the temperature rises, the more anxious his movements become. The tormented animal ij swims in despair
container around, soon stretching out the head far and imm
Quickly yapping for coolness, soon to the bottom d
vessel to escape from the torment there. the hita
approaching around 38". The animal makes desperate leaps
to escape from the container. It climbs to the smooth
walls and has to be thrown back into the hot water
will. The respiratory muscles, which fly up and down faster and faster, become slack and breathing stops. Always wild
the expressions of pain become manifest, and finally at a body temperature of about 42" the tormented animal dies with tetanic convulsions.

You can see the bits, which the translator can't cope with - these are bits which didn't transcribe well, due to being in the spine of the book and not scanned properly. I also can't read these or even make a guess at what the proper word would be in many cases, though I have fixed those that I could. However, I think that the general text is largely fine to read and easy to interpret.
Basically, what Goltz did was attempt to study the nervous system and physiology of frogs. He did this by comparing decapitated or decerebrated frogs with intact ones (apart from blinded eyes, to exclude visual stimuli). He placed both of these in room temperature water and then heated it. When heated, the decapitated frogs did not show any reflex action and would sit still until dead unless stimulated by a different stimulus, which was some mild acetic acid applied to the back of the frog (bottom of page 128, not translated here). On the other hand, intact frogs would violently try to escape and would have to be placed back into the heated container, up to about 42 C, at which point they died.
Edited to add:
On page 130, there is a passage:

Behälter einen solchen, welchem ich das Gehirn mit einem qu
Schnitt dicht vor den Sehhügeln abgetrennt hatte. Zu ihm s*
ich einen geköpften Frosch, welchem ich die Hinterbeine i
oben geschilderten Weise verschränkt hatte. Beide Frösche bli!
ganz regungslos sitzen, bis die Temperatur des Wassers 32|'*
reicht hatte. Da machte der hirnbesitzende Frosch mit dem
eine Bewegung nach oben und fing an schneller zu athmen.
35“ machte er mit dem Körper eine kleine Wendung und sp
dann plötzlich mit einem kräftigen Satz aus dem Behälter hii
In’s Wasser zurückgebracht, machte er alsbald einen zweiten Sp>
aus dem Geföss. Ausserhalb desselben wiederholte er die Hi
bewegungen nie, sondern verharrte nach dem einen Satz, mit
ehern er das Bad verlassen hatte, in Ruhe. Nachdem er, i:
wieder in’s Bad zurückgebracht, im Ganzen sechs Sprünge g'
hatte, und das Wasser inzwischen allmälig eine Hitze von
erlangt hatte, starb er unter tetanischen Krämpfen. Während
ser Scenen hatte der Geköpfte mit verschränkten Füssen ruhi
gesessen. Bei 37?“ machte er die zuckenden Bewegungen, dij
aussahen, als wenn er die verschränkten Füsse auseinander bri
wollte. Bald wieder beruhigt, blieb er regungslos sitzen. Ui
Zeit, als der Behirnte in Krämpfe verfiel, begann bei dem ^
köpften die Wärmestarre der Muskeln. Ohne dass die v
schränkten Füsse sich lösten, wurden die Schenkel |
allmälig etwas nach hinten gestreckt, und das ganze Thier
hart und steif.

Translated:

Lately I have completed this experiment in the following way-
changes; Instead of the blinded frog, I put one in the container, which I pierced the brain with a qu
cut just before the brow mounds. To him a decapitated frog, whose hind legs i
entangled in the manner described above. Both frogs bli!
sit completely motionless until the temperature of the water is 32
had enough. Then the brain-possessing frog did that
a movement upwards and began to breathe faster.
35” he made a small turn with his body and sp
then suddenly with a powerful leap out of the container
Brought back into the water, he immediately made a second spat from the vessel. Outside of this he never repeated the hi movements, but after one set he stayed with
as soon as he had left the bath, in peace. After he had had six jumps in all when he was brought back into the bath, and the water was gradually getting hotter
he died from tetanic convulsions. While
The decapitated man had these scenes with crossed feet
sat. At 37?” he made the twitching movements that looked like he was breaking his crossed feet apart
wanted to. Soon calmed down, he sat motionless. wow
Time when the crippled went into convulsions began at the
beheaded the thermal rigidity of the muscles. Without the v
when feet broke loose, the thighs were gradually stretched back a little, and the whole animal
hard and stiff.

This is using frogs with their hind limbs crossed (and pinned?; see image page 103), so that they can no-longer swim properly and jump.  The frog still gets out and is returned to water that is gradually getting hotter. Eventually it does not attempt to escape again. Note that the intact frog still tries to make movements and escape, just can't in the long run. I can only speculate on why it doesn't continue to try to escape, perhaps the water is too hot for proper function at this point, or perhaps it has learned that it can't escape, so gives up, which is a pretty sad conclusion to come to.
So, TL:DR - frogs try to escape when the water is too hot for them!

Goltz F. 1869. Beitrāge zur lehre von de function der nervencentrum des frosches. Berlin.

Thanks for the elaborate answer! This corresponds to what Wikipedia says about Friedrich Goltz's experiment. See https://en.wikipedia.org/wiki/Boiling_frog#Experiments_and_analysis

However, according to Wikipedia, Heinzmann and Fratscher got results in which a normal frog did not jump out

@Riemann - you can track those publications down and have a look at them yourself. The author of the Wikipedia page obviously only looked at Sedgewick 1888, as they don't provide a reference for Fratscher. Heinzmann is in German, but translatable. Numerous experiments performed, but my German isn't good enough to read it, and I don't have the time to put in to translate it all.

I also haven't been able to track down Fratscher. All references come back to Sedgewick.


text:
What is evolutionary advantage of Spirogyra to be multicell?
Spirogyra is just a set of cells connected to each other; it has no leaves, roots, etc... It even doesn't have multiple layers of cells like Hydra. So what is evolutionary advantage for Spirogyra cells to connect to each other? Why not to live separately like Chlorella?
P.S. I think this question is different from this one: Why do some bad traits evolve, and good ones don't? The reason is that I don't see that connecting cells to each other is "bad trait". If anyone can argument that such connecting is obviously "bad trait", they are welcome to write it in comments or in answer.
I think it is obvious that been multicell is advantage, but the advantage primarily is ability for organism to combine cells of different types that perform some specific tasks better that 'universal' cell of single cell organism. So, there are no question what is advantage to be multicell for apple tree. But spirogyra looks like something unusual for me. It has multicellularity (in my understanding it is actually very ancient organism), but what is advantage of this trait?
We can of course imagine that multicellularity is "bad trait" here, and that organisms similar to spirogyra became just "evolution raw material" like dinosaurs became ancestors of birds. But this idea doesn't look correct for me, I think we have to dig deeper here. We see that colonies of similar cells are widespread and spirogyra is not the only such organism. We have also Volvox, and Cladophora is more complex but shares the same idea. So, such organisms are too widespread to be "evolutionary error" in my opinion.
From comments I can see 2 ideas:

It is more complex to eat such organism.
Such organisms can attach to the substrate.

These ideas may be correct. BTW what is advantage to attach to the substrate? Many even single-sell species can do that (for example, Vorticella).

Well, the hairs catch onto objects well, might be harder for predators to eat.

well to start it is harder to eat a long strand of cell than a singe cell.

Does this answer your question? Why do some bad traits evolve, and good ones don't?

@tyersome I have no idea whether it is good or bad to be multicellular, so the link may or may not be the correct answer. I thought about that last days when I shew Spirogyra in microscope to my children, so I asked may be there is obvious answer that biologists know; I am computer programmer myself.

If you have "no idea whether it is good or bad", then why did you ask what the "advantage" is? If there some subtle distinction you are trying to make can you please clarify. ——— One of the problems with this type of question is that they assume that there must currently be an advantage and ignore the huge influence of contingency of evolution. You may find this, introduction to evolutionary theory from UC Berkeley to be of interest.

@tyersome I ask because I want to investigate ;) I added more thoughts to question body to explain the details.


text:
How many end segments does the axon of a typical cortical pyramidal cell have?
I tried to do some research - starting with a Google search for "typical axonal trees" - and found the following pictures:

source

source (axons are red)
but didn't find a concise answer to this and some related questions:

How many end segments (which don't branch anymore) does the axon of a typical cortical pyramidal
  cell typically have. I guess it's a much smaller number than the
  number of end segments of a typical dendrite, but how large is it
  roughly: some tens, sometimes less than ten?

I'd like to exclude from this question the typical axonal "end trees" which branch into the axon terminals.

@vkehayas: I followed your advice.

Some things to consider: What do you think that this is measure is relevant for? Are you making the implicit assumption that these terminal branches make more synapses? Please edit your question to help us understand what is the underlying question you are trying to answer.

In my original question - where I asked it all together - I made a distinction: number of synapses = number of end segments times number of synapses (= axon terminals) per end segment. But I am quite sure that not every kind of "end segment" has the same number of synapses (= axon terminals) (not even roughly). This number most probably depends on other things.


text:
Evolutionary advantages of gyri
Sulci and gyri are complementary views on the very same brain-anatomical phenomenon

(Note that there is the named concept of gyrification, but not of sulcification, but it's the very same process.)
As the main evolutionary advantage of sulci/gyri stands the enlargement of the surface of the brain, i.e. the neocortex.
As another evolutionary advantage of gyri (not sulci) Wikipedia mentions "increased speed of brain cell communication".
But there seems to be another (as usual: unintended) evolutionary advantage of gyri (not sulci) which I could not find discussed/investigated/analysed in detail: being prerequisite of internal long-range connections of the neocortex in a somehow systematic way (which goes beyond mere "increased speed"):

I am looking for references where this - possible - evolutionary advantage is discussed.

Addendum: In the above mentioned Wikipedia article on gyrification one reads

that axonal tension forces between highly interconnected
  cortical areas pull local cortical areas towards each other, inducing
  folds.

If this was true (it's only stated as a hypothesis), it would suggest that folds are a consequence of such connections, not their prerequisite.

Addendum: In Gray's Anatomy I read:

I wonder why fibers passing the walls of a sulcus and fibers connecting adjacent gyri are explicitely mentioned (BTW: Isn't a fiber passing the wall of a sulcus connecting two adjacent gyri? Don't both of them must have U-shape? Is being intracortical vs. subcortical their only difference?) but not the ones connecting the walls of a gyrus (which would be straight, see above)? Aren't there such fibers?

I think your addendum is a bit misleading; you quote from a source suggesting that it is a known fact, when the source material clearly presents it as one of several hypotheses. The source does not suggest that folds are a consequence, it proposes that they could be. As to the rest of your question, can you not follow the sources linked from wikipedia as a starting point?

I corrected the addendum.


text:
What does synapses hold together?
From three answers to the same question at Quora I've learned of three forces that keep synapses together:

They are held together by cell adhesion molecules (e.g. neurexin and neuroligin).
They are surrounded by support cells (glia?) that hold them together.
They are packed densely together (and just couldn't move, even without specialized support cells).

I'm sure all of these ways of holding synapses together play a role.

But are there others?

In any case it may make sense to ask

which of these "forces" is the strongest, and how strong is it?

For example: If axonal tension is supposed to be a driving force of gyrification, the "weakest link in the chain" is probably the synapse. So the forces holding the synapse together must be strong enough to counteract the forces that drives the neurons in different areas of the cortex apart (whatever these may be). For "axonal tension" or "axonal tethering", see also here.