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What is the significance of the phospholipid bilayer being two-dimensional?
I'm wondering about the significance of the phospholipid bilayer being a two-dimensional fluid.
I found this powerpoint:
I also found that thetwo-dimensional fluids have limited degrees of freedom.
My question is the following: if you can please explain two-dimensional fluid, please explain the/a/any proximate cause for why the fluid is two-dimensional as opposed to 1 or 3 dimensional.
I'm guessing that based on the powerpoint I found that the limited freedom of movement is optimal for the purposes of the phospholipid bilayer in, let's say, a human brain cell, as having too much freedom in a 3-dimensional fluid would be bad in some way (break apart???), or a 1 dimensional fluid would be bad since fluidity is important for the addition or removal of membrane proteins.
Sincerely,
Carlton III
Edit:
I realized after reading The fluid-mosaic model (Singer and Nicholson, 1972) and Revisiting the fluid mosaic model of membrane structure, I realized that I did not have a basic understanding of the thermodynamic principles espoused in Singer’s article.
So, after combing the internet, I found an essay by Erwin Schrodinger titled “What is Life.” I’ve been reading, and this passage seemed relevant to my question about the significance of the phospholipid bilayer.
“PHYSICAL LAWS REST ON ATOMIC STATISTICS AND ARE THEREFORE ONLY APPROXIMATE
And why could all this not be fulfilled in the case of an organism composed of a moderate number of atoms only and sensitive already to the impact of one or a few atoms only? Because we know all atoms to perform all the time a completely disorderly heat motion, which, so to speak, opposes itself to their orderly behaviour and does not allow the events that happen between a small number of atoms to enrol themselves according to any recognizable laws. Only in the co- operation of an enormously large number of atoms do statistical laws begin to operate and control the behaviour of these assemblies with an accuracy increasing as the number of atoms involved increases.”
—Schrodinger
It was here that I realized that a higher number of atoms allowed not only for statistical laws to control the behavior of the assemblies, but that the higher amount of smaller parts created a recognizable pattern that conforms to the laws of statistics.
At first glance, It doesn’t matter how large or small the parts are, what matters is how they compose a larger whole due to their behavior, and the behavior is determined by their properties.
Maybe atoms are the “smallest” parts because less surface area allows for more powerful and simple properties. And in relation to biology, more complexity is added to the larger “wholes” that are made of smaller parts.
A single Atom is simpler than a single cell by virtue of cells being comprised of many atoms.
Another thing Schrodinger wrote is this:
“ An entire newcomer should not expect to obtain from the following few pages a full understanding and appreciation of the subject, which is associated with the illustrious names of Ludwig Boltzmann and Willard Gibbs and treated in textbooks under the name of 'statistical thermodynamics'. If you fill an oblong quartz tube with oxygen gas and put it into a magnetic field, you find that the gas is magnetized. The magnetization is due to the fact that the oxygen molecules are little magnets and tend to orientate themselves parallel to the field, like a compass needle. But you must not think that they actually all turn parallel. For if you double the field, you get double the magnetization in your oxygen body, and that proportionality goes on to extremely high field strengths, the magnetization increasing at the rate of the field you apply. This is a particularly clear example of a purely statistical law. The orientation the field tends to produce is continually counteracted by the heat motion, which works for random orientation. The effect of this striving is, actually, only a small preference for acute over obtuse angles between the dipole axes and the field. Though the single atoms change their orientation incessantly, they produce on the average (owing to their enormous number) a constant small preponderance of orientation in the direction of the field and proportional to it. This ingenious explanation is due to the French physicist P. Langevin. It can
be checked in the following way. If the observed weak magnetization is really the outcome of rival tendencies, namely, the magnetic field, which aims at combing all the molecules parallel, and the heat motion, which makes for random orientation, then it ought to be possible to increase the magnetization by weakening the heat motion, that is to say, by lowering the temperature, instead of reinforcing the field”
—Schrodinger
By lowering the temperature, you lower the environment’s resistance to the behavior of the assembly of oxygen. By doubling the environment, you double the behavior of the assembly of oxygen.
Likewise, maybe, through optimal conditions and or more and more atoms, you are able to increase the output of the behavior that is controlled by statistical laws.
Finally, maybe, the phospholipid bilayer is but one step towards a more complex system. From atoms to molecules, to a whole cell... and optimal conditions or more atoms increase the likelihood of life, from the simplest to the most complex.
Of course, I have no idea what kind of conditions would allow a transition from let’s say a fish to a reptile.
Edit2: So basically, the bilayer being a two dimensional fluid is a function of the distinct parts of the bilayer conforming to statistical laws to create a more complex system by necessity.

My reading of the slide is that the author is just repeating himself for emphasis. He explains how proteins are able to move about in a lipid bilayer. Then he uses a physico-chemico description of the lipid bilayer adding that this is "crucial". The reason the author regards it as crucial is because it allows proteins to move about. So there doesn't seem to be a question, unless you want to know why proteins have to be able to move about in membranes. If that is your question, do ask it. (Oh and please finish the [Tour]).

this may be what you are looking for https://www.youtube.com/watch?v=Ym3mTa5WEOY

The cell membrane is a two dimensional fluid because individual molecules can move freely in 2 dimensional plane but not in three dimensions. in this image phospholipids can move left and right and in and out of your screen but they are not free to move up or down.

This is true becasue each phospholipid has a polar and non polar end, the similar ends are attracted to each other but the dissimilar end repel each other, making the membrane sheet like layout one of the only chemically stable layout for significant numbers of them. if a phospholipid tries to move up or down (in or out of the cell) the other molecules around it repel it pushing it back into place, meaning it requires a great deal of energy to disrupt this layout.
It is a two dimensional fluid because, while in water it behaves in the following way.  To use the existing image, if a phospholipid moves in or out of the screen or to the left or right, the repelling parts of the molecules have not moved closer to their opposite part on other molecules so the can freely move in this way, that is 2 dimensions of movement. If however they try to move in the third dimension (up and down on the image) they cannot becasue the hydrophobic (nonpolar) ends of one phospholipid would have to approach the hydrophobic (polar) end of other phospholipids and move away from the hydrophobic (nonpolar) ends of other molecules both of which are energetically unfavorable (that require a lot of energy to do). likewise the hydrophilic ends are attracted to water (which is also polar) while the hydrophobic ends are repelled by water. So unless a tremendous amount of energy is put into the system they will stay in this arrangement, you can disrupt it with enough heat, which is one of many reasons enough heat will kill organisms.
All these behaviors are import for the many functions plasm membrane fulfill, most importantly as a barrier that can stop some molecules from passing through it and allow others, while still being flexible and self repairing.
This is actually difficult to explain with static images, if you are still a little fuzzy on the details try this video, it shows the full range of movements I am talking about. It is actually difficult to find material that goes into this part of the fluid mosaic model so I don't blame you for having problems.

Compartments
A two-dimensional fluid like structure, like a phospholipid bilayer, can generate closed surfaces that can envelop an entire region of space. This is what allows life to compartmentalize, to create separate pocket environments that are set apart from their surroundings. A single compartment generated by a single bilayer folding in on itself is what is called a liposome. A non-2D variant of a liposome would be a micelle.
A micelle is formed by surfactants (things that are like phospholipids, with a polar group and a non-polar tail) with a single fatty-acid chain such that they can't form bilayers. Instead, a sheet of micellar surfactants, when surrounded by water, close in on itself with the fatty acid towards the interior of the micelle, away from the water.

The two things might look the same, by they are not. Micelles have an inner chemical environment very different from their outer environment. Whereas micelles are surrounded by water, like liposomes, their inside is strongly hydrophobic. Only the polar heads of the surfactants in a micelle act as a surface, but the entire structure is solid and filled. When micelles assemble, they pack like a solid sphere.
Contrast that with the 2D character of the bilayer in the liposome. The bilayer acts as a boundary between an inner aqueous compartment and the outside, also aqueous. The two compartments can be kept separate even if their chemical nature is pretty similar.
The most important application of this property is that a cell can become insulated from its environment. But this is useful in all sorts of compartments inside the cell such as the maintenance of electrochemical gradients across the inner and transmembrane spaces in mitochondria, or the upkeep of specific control systems inside the nucleus.
Besides this property of working as a boundary without disturbing the interior, the fact that the membrane acts as a two-dimensional environment in an of itself means that stuff can diffuse laterally through the membrane without having to go through the interior of its inner compartment. This allows the cell to have specific arrays of proteins and glycoside-bound phospholipids freely diffuse through the membrane, controlling access and proving sensory perception of the outside without disturbing the ongoing chemical work inside the cell or any of its compartments.
I am not sure if this is the relevant information that the slide's author was referring to, but it striked me as a pretty big deal. So there you have it.
Also, welcome to Biology SE!

So, why wouldn’t it work if the proteins were fixed in position in the bilayer? The question was not about how the bilayer works as separating membrane, but about dimensional fluidity. (Also, answers are to questions, not people, so that personal remarks are not appropriate. Once a question has been posted, ownership is to the list, who can improve it or reject it. That is why We restrict personal remarks such as welcome to comments.)


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Predicting how proteins will be cleaved
Is it possible to predict how proteins coded from mRNA will be cleaved?
The reason I was interested in this is because I did some initial work to translate the raw Coronavirus RNA sequences, which you can see here: https://github.com/imranq/coronavirus. The background section below has more information on my approach.
With the "naive" approach to translate coronavirus RNA, using AUG as the start codon, I am able to identify 7 out of 24 proteins from Zhang lab sequences. However, I also did some string matching between my amino acid sequences and the Zhang lab final amino acid sequences. After doing that comparison, I see I have 21 out of 24 protein sequences coded in uncleaved protein sequences.
It would be nice to get to the final 24 proteins straight from the mRNA strand. Please help. Thanks!
Background
Here is the series of steps I used to convert coronavirus RNA into proteins.
1. The raw RNA sequences are here (sourced from the NIH):
https://github.com/imranq/coronavirus/blob/main/data/rawrna.json

2. The script to translate the RNA is here (assumes AUG is the start
codon):
https://github.com/imranq/coronavirus/blob/main/scripts/translate.js

The translated protein sequences are here:
https://github.com/imranq/coronavirus/blob/main/data/processed/translatedProteins.json

3. The script used to generate a comparison between the translated
proteins and the known protein sequences is here (using levenshtein
distance as our difference metric):
https://github.com/imranq/coronavirus/blob/main/scripts/compareTranslated.js

The data generated from that script is here
https://github.com/imranq/coronavirus/blob/main/data/processed/translatedComparison.json

4. Then we detect cleavage in proteins by running a sliding window
across RNA segments between the known and translated proteins. The
script to do so is here:
https://github.com/imranq/coronavirus/blob/main/scripts/detectCleavage.js

4. Finally we merge the datasets we generated from translation and
protein complexes into one dataset, translated proteins and protein
complexes matched to known proteins.

The data generated from this algorithm is located here
https://github.com/imranq/coronavirus/blob/main/data/processed/mergedProteins.json

At the end of this pipeline, we get 21 out of the 24 proteins matched straight from RNA.
References:
Here are the papers / articles I researched to answer this question
Turning Genome Data into Proteins
Khan Academy Genetic Code: https://www.khanacademy.org/science/ap-biology/gene-expression-and-regulation/translation/a/the-genetic-code-discovery-and-properties
Zhan Lab - SARS CoV 2 - Nucleotide, Coding Region, and Protein sequences https://zhanglab.ccmb.med.umich.edu/COVID-19/
More in the readme here: https://github.com/imranq/coronavirus/blob/main/README.MD

Your question is very broad, and a bit unclear. Yes, the recognition sites of many proteases are known, so it is possible to predict where a particular one may cleave a protein substrate. Some searching in PubMed and Google Scholar should be informative in that regard. But I'm not sure what, if anything, you're expecting us to do from there.

Thank you Matt. I guess I was looking for any research ideas that could help understand rna to protein better. It seems like it’s a harder problem than I thought and warrants further research.

The cleavage site of the PLpro is obvious from https://www.ncbi.nlm.nih.gov/nuccore/NC_045512.2, it is L(N/K)GG.  For the 3CLpro it is more complicated and a paper says it is (small amino acid)-X-(L/F/M)-Q↓(G/A/S)-X. Also you need to implement the ribosomal frameshift and detect the correct start codon from the secondary structures. This is solely for ORF1ab.

Thank you that is helpful. I'm not sure what the notation " L(N/K)GG" means however. Also what is a ribosomal frameshift? I thought the start codon was largely the same across mRNA.

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text:
Help ID this plant with balloon-like feature containing seeds
I noticed this plant creeping over another Ipomoea quamoclit near my house in Kerala, South India. It has these balloon-like projections over them that break when popped. These projections do bear seeds. No visible flowers.
Leaves:

The balloons:

The seeds:

EDIT: This plant is a creeper, obviously.

I searched Google for Lantern plant and came across this article with the following image included:

Which is the same plant, but not the best of references, it doesn't give a scientific name and I am not sure Paper lantern plant is their right identification.
I think it is of the genus Physalis,
but as yet haven't been able to find the species that matches your leaf exactly.

Thanks! I suspect it belongs to the Physalis genus too.

I don't think the leaves match,this not the exact species but sure it belongs to physalis

The plant is definitely not a physalis! It appears to be a cardiospermum; the balloon like structures on physalis have an opening at the tip!

@AliceD why was my answer converted to comment?

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Help identifying winged, moth-like creature
I noticed this moth (?) on my sofa yesterday. It matched the color of the sofa, so it was pretty hard to see. It's about an inch long, with a yellow body and light brown wings. I think it's a T. bisselliella. I'm from Kerala, South India.

The wings:

This is not a Clothing moth, they are not so yellow and are much smaller, about 7-10 mm (1/3 inch). Please add a picture of the wings if possible, and rhe location it was found, that will make it easier to identify.

Try bugguide.net they are really good at this.

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Cough at 1000 km/h?
How fast does air move in the airways during a cough?
The following passage is from Talley and O'Connor's Clinical examination: a systematic guide to physical diagnosis (emphasis mine):

Cough is a common presenting respiratory symptom. It occurs when deep inspiration is followed by explosive expiration. Flow rates of air in the trachea approach the speed of sound during a forceful cough. Coughing enables the airways to be cleared of secretions and foreign bodies.

The speed of sound claim is unreferenced. I have found mention of coughs approaching the speed of sound in numerous popular sources (e.g. here, here, here (where it says 1000 km/h), and here), and innumerous books (e.g. here, here, here, here, here, and here); none of these references the claim. The same claim is also here. This book has a more exact (unreferenced!) claim:

Velocities as great as 28 000 cm/s (85% of the speed of sound) have been reported, but it is impossible to determine the gas velocity at points of airway constriction, where the greatest shearing forces will be developed. During this phase there is dynamic collapse in the bronchial tree, with large pressure gradients across the collapsed segment.

That speed is just over 1000 km/h. When I have searched for research literature behind this, I've only found much lower velocities at the mouth (rather than at a narrower location like the glottis), e.g. a peak cough velocity of 22m/s, also 11.2m/s, and 28.8m/s. The closest to a reference I found was this book with the following:

A cough comprises: ... sudden opening of the glottis, causing air to explode outwards at up to 500 mph or 85% of the speed of sound (Irwin et al, 1998), shearing secretions off the airway walls.

Irwin et al isn't primary literature either, and references Comroe JH, Jr. Special acts involving breathing. In: Physiology
of respiration: an introductory text. 2nd ed. Chicago:
Year Book Medical Publishers, 1974; 230-31. I don't have access to this book (does anyone here?), but I expect the references only continue from there.

My question is this: how fast is a cough in the airways (I am interested because such an explosive rush of air could explain the substantial damage seen in chronic cough), and does anyone know where the 1000 km/h claim comes from, or can point me to a legitimate reference?

If you are asking about whether a claim is correct/or not and where it comes from, you might receive more feedback on the skeptics stackexchange.

Perhaps. I'm not a skeptic though, I'm sure the claim is probably true; I would just be interested to find a reference for it so I can see how it was measured. I thought it would be more relevant on biology.SE.

This reference from CHEST lists 21 clinically measured peak flow rates during various modes of coughing. Of these patients, and for unassisted cough, the highest peak flow is about 4 liters/sec. The human trachea ranges from 13 to 27 mm diameter. The relationship between velocity, $V$ and flow $Q$ is
$$ V=\frac{Q}{A}$$
Assume the 4 liters/sec = 4000 cm^3/sec and minimum diameter, 13 mm = 1.3 cm, the cross section area being
$$A = \pi (D/2)^2 = 1.3 cm^2$$
Plugging in
$$ V=\frac{4000}{1.3} = 3077 cm/sec$$
which is a far cry from 28,000 cm/sec, so at this point I'm skeptical.
Things to consider is that the data taken in the paper was from sick humans so perhaps a healthy (and athletic) person may be able to exert much higher flow rates. But then healthy people generally are not stimulated to cough as much as a sick person with an airway compromised by sputum.
Although lower airways do have smaller diameters, the flow measured at the trachea is divided among them, so you wouldn't expect to see peak velocities in the lower airways, but rather the accumulation in the trachea.

Nice answer +1. I did a similar calculation to you, but I thought perhaps using that size for the trachea wasn't legitimate; a cough begins with a closed glottis, so in principle the airflow in the first moments is through a very narrow opening between the vocal folds and so in principle the flow rate could be higher. The flows in your paper are at the mouth which would potentially lead to a slower pickup in velocity at the beginning (if the actual speed were actually near the speed of sound which is the maximum speed that an impulse can be transmitted in air). I agree about smaller airways.


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What is the mechanism by which myelination reduces the capacitance of the axon membrane?
There are two mechanisms that have been proposed to me.
1) Layering of Schwann cell membrane with conducting fluid between the layers is analogous to several capacitors in series. Since capacitance in series add by the reciprocal rule (as resistors do in parallel), this reduces the total capacitance.
2) The myelin increases the distance between the 'plates' of the capacitor. For parallel plate capacitors $ C = \epsilon A/d$ where d = distance between the plates. Thus increasing the distance reduces the capacitance.
Which of these explanations best applies to myelin, or is it in fact a mixture of both?

Adding more capacitors in series does move the terminal plates on either side further away, but I wasn't sure this applied to the equation involving d because adding another capacitor means the charge stored on each plate is reduced also.

Circuit analogies don't 100% apply to myelin because membranes have complex electrical properties, but both of those explanations work and they are in fact essentially interchangeable: Take a membrane with distance d across the membrane and capacitance c. Then we add some myelin to get a new capacitance C at a new distance D.
If you 4X the distance between plates (D = d * 4), C=c/4 (from the formula you posted as (2) ); if you add 3 extra plates (so now you have a total of 4 plates), C=1/(1/c + 1/c + 1/c + 1/c)=c/4.
Importantly, myelin also increases the membrane resistance, and because myelin is typically very thick compared to a normal membrane (~10nm for one layer vs. 500-2500nm for myelin), you can almost consider myelination to increase resistance to infinity (compared to the axial resistance of cytoplasm) and the capacitance to zero.
See this page for some more info.
Note that the reason these explanations are interchangeable is that there is effectively no distance between the added plates in series and no difference in capacitance for each individual capacitor/piece of membrane (for example, see this page).


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Most accurate depiction of cortical homunculus?
I was looking at cortical homunculus and I realized there are several different pictures and they don't quite agree.  For instance:
http://wellbeing.media.mit.edu/2014/02/21/mindfulness-neuroimaging-and-neurofeedback/
http://nawrot.psych.ndsu.nodak.edu/Courses/465Projects11/PLS/4Thesomatosensoryandmotorcortices.htm
One area, for instance, are the feet, which I feel should have a fairly large (not as big as hands) area in the brain, mainly from the personal experience of having more sensations in feet, which like the hands has many nerve endings, though obviously much less fine motor ability.  But that's just my speculation, and I like an accurate depiction so I can start from there and make sense of this.  Thank you.

The reason they vary ever-so-slightly is down to a matter of opinion.

Be sure to distinguish exactly what the diagram is showing. Your first reference is sensory cortex mapping. The second reference is motor cortex mapping. The text of the second reference is admittedly confusing about this, a search for "Wilder Penfield motor cortex" verifies.
It seems reasonable the feet would show sensory response similar to the hands. Stepping on a nail is just about as bad as bumping your hand into one. Motor control is different. Muscles are not all innervated the same. In some of the large muscles, say in the legs, one nerve can control hundreds of cells. In other cases, particularily in the face, one neuron might control only six muscle cells. Thus a greater number of neurons, and a larger portion of the brain, is needed for control in these delicately controlled areas. It would make sense a greater part of our brain would be needed for motor control in our hands versus our feet.


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Why protons flow back to the matrix through ATP synthase?
I am reading oxidative phosphorylation and I can't understand why the protons that are pumped out must go again into the matrix and finally produce ATP.
Suppose initially that the inside (Matrix-M) and outside of the membrane (Intermembrane space-IMS) are neutral (for sake of simplicity). The exergonicity of the redox reactions powers the proton pumping. As the pumping goes on an electrochemical gradient arises because of the concentration gradient the pumping produces and due to the electrical gradient which is produced due to the unequal distribution of protons.
After the equilibrium of the redox reaction an electrochemical gradient has established. I can't understand why the protons have to flow back into the matrix. The redox reaction equilibrium means that the ratio $\ce{H_{M}}/\ce{H_{IMS}}$ has a specific value. Do they flow back because of the electrochemical gradient? I was thinking that the flow back is coupled to the pumping, is that correct? I  mean we have the equilibrium: $$\ce{H_{M}} \rightleftharpoons \ce{H_{IMS}}$$
and by pumping we increase $\ce{H_{IMS}}$ so protons must flow back according to Le Chatelier principle. If that is the case then what is the purpose of ATP synthase? Why the protons must flow back through ATP synthase and not from any other region? Are respiratory chain and ATP synthase seperated and the only way for protons to flow back is throught ATP synthase?
I have read Biochemistry textbooks and still can't understand the importance of the so called proton motive force.

I will check it out.


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What favors the active transport in a membrane?
I was reading about active transport in membranes where ATP is used. ATP "reacts" with the protein pump and converts into ADP and also make a conformational change to the pump. Now this conformational change can transport molecules from low concentrations to high concentrations areas i.e. opposite in their concentration gradient. My problem is that for this to happen we must couple the hydrolysis of ATP with the "reaction" of transport along the membrane.
But I can't find it in textbooks and also I can't imagine if such coupling makes sense. In many textbooks it is stated that the energy that released due to the hydrolysis fo ATP is used to drive the pumping. I don't know if it is possible to couple two reactions with no common intermediates. Also in the pictures that show the active transport like the one in the left side the molecules can't go through the lipids.

So the molecules just move from low to high but the moving from high to low (diffusion) is blocked because the molecules can't move through the lipids. In other words it isn't like molecules make something that it would be otherwise violated because at first the motion from one side to the other is blocked. I mean even if we have no ATP the molecules won't flow from high to low concentration. Then what is the point of "active" transport? For a moment I thought to describe the above scheme for active transport as the following reaction: $$\ce{ATP + H2O + M_{in}} \rightleftharpoons \ce{ADP + P_i + M_{out}} $$
Which can be thought as the sum of:
$$\ce{ATP + H2O } \rightleftharpoons \ce{ADP + P_i}$$
and
$$\ce{M_{in}} \rightleftharpoons \ce{M_{out}}$$
But as I stated I haven't find a coupling reaction with no common intermediates and also it doesn't make sense to write the second equilibrium as the molecules can't go through the lipids. Also from the second reaction we should expect the concentrations on both sides to be equal (because the equilibrium constant must be equal to unity) no matter the concentration of ATP.
So can the first equilibrium alone describe the "active" transport? I mean if this reaction is exergonic then indeed by varying the amount of ATP we can alter the concentration of M outside of the membrane due to the Le Chatelier principle.
Edit ATP hydrolysis causes conformational changes to the protein channel which in turns "passes" molecules from one side to the other. Fine. But what if the lipids were permeable to the molecules? Then shouldn't the two concenctrations on the two sides (in and out) be equal or because the ATP hydrolysis is exergonic we will expect to have an imbalance in the concentrations?

Welcome to SE Biology and to Biochemistry. Biochemistry requires a different attitude than chemistry, but you still need to find a textbook that is written from a chemical standpoint and not a biological one. In this respect the best one available to consult online is Berg et al. on NCBI Bookshelf. The section you need is in chapter 13. You also need to stop thinking you know better ("I can't imagine if such coupling makes sense" indeed!) and read the sections of this book about this coupling, which is the energetic underpinning of life.

"But what if the lipids were permeable to the molecules?" - It will save you a lot of time to first discover whether this is true for the molecules being actively transported.

@BryanKrause Thanks for the comment. I think this is where I get it wrong because in thermodynamics we can treat diffusion as a "reaction". But here we have also the exergonic reaction of "pumping". So with no pumping allowed we will have passive diffusion. Whereas with pumping we will have a difference in the in and out concentrations because this reaction of "pumping" is favored.

But I can't find it in textbooks and also I can't imagine if such coupling makes sense. In many textbooks it is stated that the energy that released due to the hydrolysis fo ATP is used to drive the pumping

I've been reading Molecular Cell Biology of Lodish and it has used "coupling" of hydrolysis of ATP with other reactions a lot, ergo it is probably correct to phrase it that way.

I don't know if it is possible to couple two reactions with no common intermediates

It may be a little different for each transport but I consider active transport as a result of multiple equilibria each of which as important as the others. You may notice that by multiplying the Ks of different equilibria, the intermediate particles would be omitted.
For example
$\ce{H2SO4 + H2O } \rightleftharpoons \ce{HSO4- + H3O+}$   : $K_1$
$\ce{HSO4- + H2O } \rightleftharpoons \ce{SO4^{2-} + H3O+}$  : $K_2$
by multiplying these two we'll get:
$\ce{H2SO4 + 2H2O } \rightleftharpoons \ce{SO4^{2-} + 2H3O+}$ : $K_{overall}=K_1 \times K_2$
By doing so, a few problems arise, firstly you'll totally ignore the existence of $HSO_4^-$ as an intermediate by summarizing. Secondly, you may falsely consider the order of reaction as 3 instead of two related reactions with the order of 2. Thirdly, molar concentrations calculated with $K_{overall}$ tend to have deviations from reality, and so on...
Therefore

$\ce{ATP + H2O + M_{in}} \rightleftharpoons \ce{ADP + P_i + M_{out}}$

is too minimalized to be considered as a good representation of the reaction. As an example for better clarification, here is a paper about the active transport of $Ca^{2+}$ in the muscle cells and one of its pictures
The process involves 6 different species of the enzyme (E). Also, remember that the whole process should be displayed by these 6 equilibria. (Well, forming a complex between a molecule and a multi-charged ion requires several other equilibria which we may also be considered(stepwise production of $Ag(NH_3)_2^{+}$ for example).

because the equilibrium constant must be equal to unity

I didn't catch that pretty well, Anyway

What favors the active transport in a membrane?

The hydrolysis of ATP provides the energy for the next reaction(s). In our calcium transport example, an aspartate becomes phosphorylated which unstables the protein current conformation eventually leading to the consumption of the extra energy. The extra energy is consumed via the movement of the $Ca^{+2}$ against its entropy. The cycle can happen again and again.
For more readings on the conformation and stability of a single molecule read Force field (chemistry) and alkane conformation.

If you've just read about coupling in a Cell Biology text and from this deduce that "it is probably correct", you are perhaps not best placed to answer this question. I don't think the understanding of ATP and energy coupling lies in consideration of reactions of sulphuric acid, force fields or  alkane conformation.

@Sam So if the ATP hydrolysis doesn't take place at the protein, pumping won't happen? Because as you have written the reaction the protein is regenerated (like a catalyst).

@Anton Correct...


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Evolution of the Redundancy of the Genetic Code
In short
Looking at the genetic code, it appears that most redundancy is on the third letter rather than on the first or the second letter of the codon. Why has it evolved this way?

Longer version
In order to compare the relative redundancy accounted by each letter of the codon, let's assume that that every codon occurs at equal frequency. It is probably wrong but useful for the sake of the calculations. Using observed frequencies of codon usage in a given population would change the following probabilities but the question of why some positions in the codon has more redundancy than some others still hold.
A substitution of the first letter of the codon has a probability of $\frac{1}{2048}≈0.00005$ (Stop codon) to be synonymous. A substitution of the second letter of the codon has a probability $\frac{3}{256}≈0.012$ (nucleobases U and G) to be synonymous. A substitution of the third letter has a probability of exactly $\frac{2}{3}$ to be synonymous.
Probability of a substitution to be synonymous given that it occurred on the...

First letter: $\frac{1}{2048}≈0.00005$
Second letter: $\frac{3}{256}≈0.012$
Third letter: $\frac{2}{3}$

Why are there more redundancy on the third position than on the second (which has more redundancy than the first position) in the codon?

ever heard of wobble base pairs? i guess, the reason is that binding of anticodon to codon happens with directionality, 5'-3' (on codon side), that is why when first 2 bases are connected, third one in anticodon has not enough energy to break pairing even if it is very different.

To fully comprehend the concept of wobble base-pairing we need to consider the nucleotide sequences of the anti-codons in the tRNAs that have to "read" the genetic code when the mRNA is being translated on the ribosome.  The nucleotide in the anti-codon's wobble position is, for example, often inosine.  Under the rules for wobble base-pairing an Inosine can potentially base-pair with three other nucleotides.
In real terms that means a cell can use less than 63 unique tRNA genes to decode mRNAs carrying messages made of the 63 different "words" (codons).
In an active cell the Ribosome's A-site, where the charged tRNA binds, is occupied by the incorrect tRNA most of the time (based on the law of mass action where any charged tRNA can randomly diffuse into the binding site).  With tRNAs that can recognize multiple codons (which is what the wobble hypothesis gets us), any given protein can be translated faster (assuming  that correct charged tRNAs are limiting for the polypeptide polymerization reaction).
So those are the practical ramifications of the table that you presented, but the explanation, as for most why based questions about biological evolution, is a retrofit.  Natural selection can only work with the materials at hand, and so we can infer that during the period when this genetic code was finalized that the organisms who used it were more successful than the others.  And the current code is based on whatever the previous one looked like. "Descent by modification" is the original description.
[whoops, sorry about the pedantic voice on the "how selection works" bit, I just looked at your profile and realized you can likely teach me on this subject]


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Has any animal ever had a rotating part?
Outside of microscopic structures (I'm thinking of a flagellum, which I think is a true motor) has any animal evolved a part that continually rotates compared to the rest of its body?

A more universal microscopic example is the ATP synthase in mitochondria. The flagellum example only applies to bacterial flagella. Can't help on macroscopic examples.

Have a look at this: there's a reasonably well-written popular discussion of why the evolution of such a body part is very difficult to imagine. However the page does mention this as the single known macroscopic example (a rod rotated by cilia).

Not a 360 degree rotation but Owls can rotate their heads by 270 degrees without any serous damage.

Duplicate http://biology.stackexchange.com/questions/7932/why-are-there-no-wheeled-animals

@HuguesFontenelle Not really a dupe, admitedly, if there were animals with wheels then that would answer this question but the lact of animals with wheels doesn't mean the lack of any rotational body part.

@SanjuktaGhosh Thanks, I had considered that though.  The thing is it can rotate, it is a wind then unwind mechanism where the rotation creates increasing torque.


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What is the rest state for eyelids - Open or Closed?
If one were to not apply any efforts on the eyelid muscles, will they remain open or closed?
In movies when we see a person die, either case could happen - their eyelids could be open or closed when they pass away. (Not sure if that's the case in real life, as I have been fortunate enough to not witness any deaths).
I started thinking about this when I got into meditation. During meditation one is supposed to relax all their body muscles. I wonder, if I were to reach that perfect stage of relaxing what will happen to my eyelids. Will they automatically open? I feel like I've to make tiny yet finite deliberate effort to keep them closed. Not sure if that's the case with everyone.

This depends to some extent on how you define "resting state" (it matters).
Innervation of the eye occurs in the brainstem and upper spinal column, so is, like most brainstem functions, on autopilot (like breathing.)
If you define resting state as that which the lids would assume without any innervation, then the resting state of the eyelids is semi-open. This is the state of the eyelids of most people who die.
However, that position is not beneficial to the living eye, as it would lead to corneal breakdown. When people lose eyelid innervation, for example, following a stroke, the lids don't close completely. Ointment must be applied several times daily and the eye is often taped in the shut position to protect the cornea.
If you define resting state as that which occurs in sleep and in most comatose states, the eyes close completely, because innervation of eye muscles is intact and a main function is to protect the cornea, i.e. vision. This is done with a completely closed eye.
Comprehensive Review in Clinical Neurology, Cheng-Ching et al.


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Can prawns be classified as fish, or is their position ambiguous?
Today a zoologist told me that prawns and fish are very similar, but zoologists/taxonomists have put them in different categories because their distinction is unclear (like hydrogen in the periodic table). This completely bewildered me, as I know prawn and fish are in different classes because there is no similarity between them. I have no connection with biology now but studied it in high school — but even then, I could not believe it. Can someone please elaborate on this?

Introduction to phylogeny
What makes that two species being closely related or not has nothing to do with whether they look a like or whether they live in similar environment. It has to do with their evolutionary history. Evolutionary history used to be inferred from phenotypic traits ('phenotype'≈'how an individual looks like') but today it is most often inferred from genetic data.
First you should have a look at this recent answer to get a short introduction to phylogeny.
Phylogeny of animals
Here is a basic tree of all animals

From wikipedia

A fish is any member of a group of organisms that consist of all gill-bearing aquatic craniate animals.

Craniates are Chordates, therefore fishes are chordates. You can have a look at the position of chordates on the above graph. Note that all mammals, birds, reptiles and others are also chordates. Note that fishes do not represent a monophyletic group (if you don't understand the term 'monophyletic', then you need to read the linked post above).
A prawn is a crustacean. Crustacean (incl. prawns, shrimp, crabs, ...) and Hexapoda together form a monophyletic group. Crustaceans are arthropods and are therefore much more closely related to insects, molluscs and spiders than to any lineage that we would call fish. Here is a tree of arthropods (and related clades). See the position of arthropods in the above tree. You can also have a look at the position of crustaceans within arthropods below. Please note that the tree is a bit outdated a present crustaceans as being monophyletic which is wrong (according @har-wradim, see comment below).

Your discussion with your friend
There is no doubt about the phylogenetic position of crustaceans as being part of arthropods and therefore not being very closely related to fishes. I think you misunderstood what your friend tried to tell you.
A note on developmental biology
All multicellular animals, undergo a grastrulation during development during whihc a hole is formed called the blastopore. In all deuterostomia (incl. fishes) the blastopore becomes the anus, while in prostomia (sister clade to deuterosomia which includes arthropods), the blastopore becomes the mouth. This a very major difference in how these different clades develop from a single cell (after fertilization) to a multicellular adult.
Online ressources
If you want to have a look at the tree of life, you can find great ressources on this post.


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How do neurons find each other?
Neurons form complicated networks in brains, but their connections can't be random (at least not entirely). Brains function similarly among all members of individual species, and that functionality is largely dependent on neuron organization. Furthermore, various brain regions have predictable functions, and there are even parts of the brain where specific cells carry out specialized functions (place cells are an interesting example).
Great! We know neurons can organize into very complex networks, but how? They need to find each other, somehow.
The best I can guess is that either:

Neurons find other target neurons with specific chemical signals.
Neurons don't "find" each other, exactly, but grow in predetermined shapes from from set locations. In this case, the connections would simply be due to neurons bumping into each other as they grow in their predetermined paths.
Or both.

In the first case, there would be a mechanism for searching each other out. In the second, there would be a mechanism for staying in one spot (and growing from there). What are the names of said mechanisms? How do I find out more about them?

I would add another mechanism: Neurons grow more or less randomly, and there is a mechanism eliminating those that formed "wrong" synapses.

Q: We know neurons can organize into very complex networks, but how?
The answer is your first guess: Neurons find other target neurons with specific chemical signals.
Q: What are the names of said mechanisms?
This process is called axon guidance, by which the growth cones of developing axons are directed to reach their targets. This process depends upon a slew of cellular and molecular cues. The first axons to grow in any particular brain region are called pioneer axons and are the most dependent upon these cues. Later axons are able to follow (and diverge from) previous axons by the interaction of cell adhesion molecules on their surfaces. Dendritic development is also important for your question, but dendrites tend not to travel as far.
Here are some of the molecules that we know to participate in axon guidance:

Cell adhesion molecules and substrate adhesion molecules, including IgSF CAMs and cadherins
Some chemokines, e.g. CXCL12
Netrins, ephrins, and semaphorins
Slits, via the Slit-Robo cell signaling pathway
Developmental morphogens, e.g. Wnts and Hedgehog

The list goes on, and this is an area of active research. Each of these cues is recognized by one or more specific receptors on the developing neuron, which upon recognition of the ligand molecule either attracts or repels the axon from (or both, depending on the context). Recognition can function either short-range (by direct contact with a ligand) or long-range (e.g. by detection of a concentration gradient), depending on the molecular cue.
For more information, you may want to read Sanes et al., Development of the Nervous System.

This is a very good question.
There are specific chemical signals, for instance:
1.) LRR proteins, which help signal neurons to each other. These are transmembrane proteins which are characterised by their leucine-rich repeat. They serve as some kind of protein labels for other neurons. These proteins are also known in pathogen recognition in our immune system.
2.) We also have Neurexins. This is a presynaptic protein that helps connect neurons in the synapse. They are known binding a family of proteins, the Neuroligins. Neurexins have actually also previously been implicated in autism/shizophrenia. The failure of the right connections likely lead to an incorrect balance of excitatory and inhibitory connections, which result in dysfunctions in neural circuits and consequently to such maladies.
https://en.wikipedia.org/wiki/Neurexin (wikipedia)
http://www.ncbi.nlm.nih.gov/pubmed/23931994 (research)
(http://) books.google.nl/books?id=qMe5BgAAQBAJ&pg=PA152&lpg=PA152&dq=neurons+predetermined+paths&source=bl&ots=LsYBkr431V&sig=ewc2geKBL1QUYogPXPh21tGC5Ww&hl=nl&sa=X&ved=0ahUKEwiTqJ3Z-YHOAhWLVxQKHcN2DI84ChDoAQgrMAI#v=onepage&q=neurons%20predetermined%20paths&f=false (book)
(http://) www.ncbi.nlm.nih.gov/pubmed/17868438 (research)
These sites could help out in further research (apparently I cant post more than 2).
There are probably many more proteins involved, but these are the main ones I know of, and the ones I have studied in my education. Scientists also often state that there is no predetermined path, but rather a rearrangement of neural pathways (I´d suggest visiting the third website link, philosophy of psychology page 152).
I hope this helped you out with your question, and if you've got more questions on how these molecules work with signaling in depth, I´d be glad to answer them.


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What is the identity of this fruit/tree found near Berkeley, California, USA?
Please help identify this fruit/tree found near Berkeley, California.
The tree had no leaves. The fruit looked like a pear from far. It has no flesh. When the outer skin is peeled, the seed looks like a large avocado seed. Very little smell from the fruit/seed not a bad smell and not an appetizing smell as well.
Could this be a Yellow Buckeye?

Ask any Ohioan. Looks like a Buckeye.

Given that it's in central California, it's almost certainly California buckeye (Aesculus californica).  The tree is common in the Coast range and Sierra foothills of California.  It has adapted to the Mediterranean climate of the region by growing during the wet winter and spring and then dropping its leaves during the hot, dry summer.  The large seed is toxic if consumed.


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Can beavers control the direction a tree falls?
We humans can easily control the direction a tree falls by making a number of strategic cuts, essentially creating a hinge:

This prevents trees from falling on equipment and people and sets them up in a good location for the subsequent processing steps. I'm curious if beavers also perform directional felling and, if they do, how do they choose the direction (eg to fell the tree towards the damn, in a river, away from thick brush, etc)?

In this picture (and others), it appears as though the beaver has created a hinge. Is their any method to their technique or do they just start chewing and hope for the best?

As far as I know, beavers do not control this process.

It is difficult to find a scientific answer to this question, but let me insert this citation from a specialist site:

Contrary to popular belief, beaver cannot plan the direction in which trees will fall. Many trees become hung up in the branches of surrounding trees and are lost to the colony. In heavily forested areas, this loss may amount to one-half of the trees felled.

Another source says the same.

But scientists think beavers may actually plan the direction of falling:

By measuring the falling angle of 888 trees of a variety of sizes cut
  near 8 different dams in southwestern Saskatchewan, we tested the
  hypothesis that beavers (Castor canadensis) fell trees in a non-random
  direction. We predicted that trees would be preferentially felled
  towards the dam to minimize the costs of transporting materials to the
  dam and to minimize the amount of time beavers spend on land. We
  established a 150 m wide × 250 m long transect at each dam and
  determined the felling angle of at least 100 aspen trees cut in each
  transect. We found that trees were felled by beavers with a mean
  felling angle of 357.9°, a direction not significantly different from
  that of the dam. In all, 62% of trees were felled within 45° of the
  direction of the dam. While our data are consistent with the
  hypothesis, an experimental test is required to establish the
  reason(s) for the pattern we found.

Their picture is better than thousands of words:

And another paper:

We studied patterns in the orientation of cutting when beavers (Castor canadensis) cut trees around Alum Creek Lake in central Ohio. For 462 trees, we measured the slope at the base of the tree, the orientation of the cut relative to this slope, the distance of the tree from the water, the radius of the tree, and the symmetry of the cut. The land around Alum Creek Lake generally slopes toward the water, so to direct the fall of a tree towards the water a beaver should cut a symmetrical tree from the downhill side. Cutting from the downhill side occurred for trees >9.0 m from the water. Near the shore, trees tended to lean toward the water and would fall toward the water regardless of the side from which the beaver cut. At distances <9-0 m from shore, beavers cut predominantly from the uphill side where it should be easy to sit and there is little danger of the tree falling on them. At all distances, beavers showed random orientation when cutting trees on shallow slopes (<20°), whereas on steep slopes (especially slopes >30°) they cut predominantly from the uphill side. Beavers cut small trees (<5.0 cm diameter) mostly from the downhill side, but tended to cut trees >5.0 cm in diameter from the uphill side. Overall, enough factors interacted that no single pattern of cutting existed for all trees.

@Remi.b I've mentioned the study that actually tried to check the theory. They found some correlation :)

@Remi.b this sentence relates to your point - that the actual studies are scarce. Of course, if we have some budget and grants we can check any theory we want $)

Thanks for the answer. Actually, that study did not conclude that the beavers planned the direction of fall, only that there was a correlation between the direction of fall and the direction of the damn. I'll wait and see if anyone else can dig up some more recent/conclusive study, but I have been unable to and will likely accept your answer later.

There's this paper, which finds that the direction a beaver cuts from is related to the terrain slope, tree lean and distance from the shore, which implies that they are felling directionally.

@llan Oh ok. Intuitively, in my head it sounded a bit like "testing is too complicated" rather than "probably nobody cared about testing this". All good then.

@canadianer yep, I mentioned it :)

Sorry, I meant to link to this paper: https://kb.osu.edu/dspace/bitstream/handle/1811/23987/V103N5_143.pdf?sequence=1

@canadianer Believe me, poor beavers do their best to fell the trees in a right direction. They just don't have sufficiently long arms to handle the appropriate axes as humans do. Thus, they have no choice - they use their teeth and lost directions because of dizziness caused by their circular movement.... $%))

This is exactly what would be expected: beavers would be expected to try to fell directionally (towards the dam or, if necessary, avoiding obstacles) as there is an advantage to the individual and therefore an evolutionary advantage. On the other hand (especially regarding obstacles) they would not be expected to show the same degree of judgement as an experienced human lumberjack.


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COVID-19 infection data when partitioning to communities
Suppose we think of the disease in a certain country as follows.
We have a set of "communities" $C_1,\dots,C_k$ in the country where $k$ is some small constant, say $10$. Each individual is a member of exactly one of the communities.
The communities can be simply a partition of the entire population into groups of ages, races, cities, economical situations etc.
In each point in time there are $R_{i,j}$ for each $i,j\in[k]$ (which seems to be closely related to the infamous $R_0$). $R_{i,j}$ is the excepted amount of individuals in community $j$ that a sick individual from community $i$ is going to infect. Note that, not necessarily, $R_{i,j}=R_{j,i}$.
So, $R_{i,i}$ measures the infection inside the community, while $R_{i,j}$ for $i\neq j$ measures infections between different communities.
I don't know if this is relevant for here, but do you know of some data or estimates of such parameters $R_{i,j}$ from somewhere in the world using any partition?

While this is highly relevant, there are 2 problems: (1) Identifying transmission events is extremely hard (especially where the pandemic is out of control and track & trace is overwhelmed). (2) Demographic characteristics differ widely between countries and communities, so your estimates would only be valid locally. The closest thing to this I have seen is estimates for intra-household transmission (secondary attack rate) by demographic (e.g. Bernal et al.).


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Incomplete dominance with gain-of-function allele
Can someone cite an example of incomplete dominance with gain-of-function mutation?

As a trivial example, one could use the epigenetic silencing of transformed reporter genes.
Briefly: Genetic constructs are transformed into some organism (in this case, plants). These constructs usually include a "reporter" gene that is expressed at high levels, which allows workers to artificially select successful transformants. Examples might be GFP genes, metabolic genes complementing auxotrophies, or antibiotic resistance genes, all of which would be clear examples of a "gain of function" mutation when integrated into the genome.
After one or more generations, these reporter genes often get "turned off", in that their expression decreases dramatically or ceases entirely (this tends to happen most when the reporter is expressed very highly or is present at high copy number). I'd suggest looking into the linked paper for more information.


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Does a critical mass of infected individuals exist after which mutations will overtake vaccination attempts?
As we know, all organisms have a probability to undergo mutations when they replicate. For every infected individual with the Covid-19 their bodies are environments in which the SARS-CoV-2 may mutate beyond existing vaccines.
Therefore, as the number of infected individuals increases, there will come a point where mutations in the SARS-CoV-2 would occur faster, perhaps even concurrently in different countries, than vaccines may be developed and deployed to stamp out the virus once and for all.
So my questions are as follows: is there a critical mass* of infected people, beyond which our existing vaccine development & deployment time frames will not be able to cope with? Do we have an estimate of this number?
*I understand this is not a single, fixed number but a fuzzy, probabilistic range.

Whoever downvoted it, it would be nice if you explained to a new poster here why instead of being a silent and unhelpful critic.

I didn't downvote - but I think your question could be a bit more focused. It might be better off sticking to a specific scientific question at the beginning and removing any reference to 'What should we do next..?' - since that part is more opinionated and unrelated to biology.

OK will edit accordingly, thank you for your feedback.

I agree with @user438383 - the question actually gave me an idea for a more pointed question.

@MeEngineerTrustMe you seem to be conflating many different concepts in one place. Viruses are rather different in terms of what may happen to them, you may want to take a look at my post here: https://biology.stackexchange.com/a/97324/59521

Also note that not all mutations will be able to circumvent the effects of vaccination. Some mutations may not cause changes in the protein at all, others may keep the protein structurally similar to an extent such that they are still recognizable by antibodies etc. To answer your question one needs to know the mutation rates of sars cov2 and I wasn't able to find any specific study on it.

Epidemiological modeling
If a virus is able to change so that it renders previous vaccination inefficient, reinfecting those who were previously vaccinated, one could describe this process using epidemiological SIS model (Susceptible-Infected-Susceptible) or its modification that includes a vaccinated group (like SISV model), and indeed estimate how quick should be vaccination in order to eradicate dthe virus before everyone gets infected. One could even add a D (deaths) compartement and study whether the virus may lead to extinction of the huiman species (unlikely, since the survival rate is very high).
Real viruses
In reality we are not dealing with such a situation, since there is no reason to think that mutations make SARS-CoV-2 able to overcome the immune defenses (although they do make it more contagious and more dangerous to non-vaccinated individuals).
To clarify the issue let me outline the scenarios where viruses do escape vaccine resistance.
Influenza
Flu is known to be susceptible to vaccination, and this is a lasting vaccination. What makes this virus to come back every year is gene reshuffling, where it exchanges some of its several genes with similar viruses living in animals (the roles of some of these animals in flu outbreaks gave rise to such names as swine flu, * birs flu*, etc.). This means that every few years we are dealing with an essentially new virus (rather than a virus that has accumulated many mutations), which is not visible to the antibodies created by previously administered vaccines. In this sense, one cannot exclude a possibility of a new coronavirus causing a pandemic in a decade or so, just like the current outbreak follows similar ones due to SARS in 2002 and MERS in 2012.
HIV
HIV is know to adapt very quickly to the new antibodies, evading the immune defenses. This makes it impossible (or at least very difficult) to develop a vaccine against this virus. However, HIV is much less contagious than flu or coronavirus, since it needs to infect specific cells/tissues. In orther words, it is stopped by the barriers of the immune system other than those boosted by vaccination. Coronavirus is a much simpler virus than HIV and will never reach the same degree of sophistication via mutations.
Bacterial pathogens
Bacteria are known for routinely developing resistance to antibiotics, which has been somewhat of a hot issue in terms of antibiotic development. They however share the same weakness as HIV - being less contagious (and far more complex).
To summarize, the devil is in the details: the scenario outlined in the question is good for science fiction, but it has very low probability to be realized in real life.

Thank you for your explanation!

@user1136 Thanks, I corrected it.

We also have the example of several highly contagious viruses which were widespread prior to the development of vaccines, yet which are now eradicated, or nearly so.  E.g. smallpox (eradicated), polio (eradicated except in a few countries), and measles (which would probably be eradicated if it weren't for the anti-vaxers :-().  So while it's possible for a virus to evolve to evade vaccines, that's the exception rather than the norm.

@jamesqf excellent point ! Thanks.

I'm going to answer this one with a No.  Outside of a simple simulation with very unrealistic constraints, we can't know the basic parameters to generate such a number.  From an omniscient point of view there would be some number where this becomes inevitable, but from that point of view we could say it is inevitable or impossible right now.  Some aspects to consider:

The viral mutation rate can vary, depending on the sequence (and mutations) of the RNA-dependent RNA polymerase.  That rate is presently considered slow.  There is a limit (mutational load - most mutations are undesirable) to how much that rate could increase, but the limit depends on how people react to the virus, how they are treated, and so on.  If one virus is in a position to infect many cells and people, it can tolerate a higher rate of errors.
The virus can invade animal reservoirs, such as minks and cats.  We do not know all the animal reservoirs, and given the scarcity of human testing, our understanding of these other reservoirs must be quite limited.  We can't predict what adaptive mutation the virus might undergo to adapt to known, let alone unknown, hosts.
RNA viruses can undergo template switching in which the 'front' of one virus is appended to the 'back' of the other.  (This can be called 'recombination', though it is different from recombination in normal human cells - see this paper)  The odds of this happening may depend more on where, how, and in what species the viruses interact, than on the number of people infected.
On the plus side, there are conserved amino acid positions at which mutations will be poorly tolerated, which may be recognized by a sufficient fraction of the vaccine-induced antibodies.  We can't necessarily predict whether neutral mutations presently arising will permit further mutations at residues we think are well conserved.

We really have no way of knowing whether such a point of no return has been passed already, except by an empirical approach - waiting to see whether very different Covid strains emerge from hidden animal reservoirs or rare recombination events in humans.


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The Perfect Predator?
I’m not a biology major or even studying it in any way so I apologize if this makes no sense.
I’m curious, if say the Jurassic Park team came up to you and asked you to genetically engineer the perfect predator, what characteristics would you give it?
And I guess by "perfect predator" I mean a predator that could consider any living thing prey? Sorry again if this doesn't make sense.
Besides the obvious “Super strength” or “Super speed” or things that make no sense at all like “laser eyes” of course.
I’m thinking things like a flexible spine that expands and contracts to increase its bound when it runs, like a cheetah or etc.
Feel free to include any features from extinct or even made up animals as long as its actually theoretically possible (again no laser eyes!!)
Like I said this is not for any research or anything, purely for my own curiosity so any thoughts are welcome. Thanks!

Biologically, the notion of a "perfect predator" isn't well-defined, because it isn't clear what is being perfected.
Predators are just organisms that eat other organisms. What would it mean to be "perfect" at being a predator?  Would it mean:

Fastest possible at chasing its prey? But it just needs to be faster than the prey, if it even bothers to chase its prey. Sea anemones are predators.
Most exactly adapted to hunting a specific prey? Are anteaters a near-perfect predator?
Deadliest possible poison? But many effective predators don't bother with poison.
Using the minimum possible energy to catch its prey? Are passive predators like pitcher plants nearly perfect?
Impossibly smarter than its prey? But it doesn't need to be smart. See again the pitcher plant.

Perhaps humans are the "perfect predators" because we've so dominated our prey that most of them live and die entirely at our whim, to the degree that many of us are barely even aware of them until their flesh is delivered to our dinner plate.
I hope I've made my point here, that the notion of a perfect predator doesn't really make sense biologically. Mostly, I think it's just a narrative idea of "thing that people would find really scary if it was hunting them."


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How to convert system of equations with explicit substrate consumption into an implicit one?
I have a description of competition between two bacteria that is described by the system of equations:

S = substrate, μ = bacterial division rate, K = half saturation constant, y = yield (cells per unit of nutrient), N = concentration of bacteria.
Is it possible to convert it to a system of implicit substrate consumption such as the logistic system? For instance into this:

where μ = maximum growth rate and K = carrying capacity.
Essentially, the term Ṡ should disappear, μⱼS become μ, and Kₛ+S become K. I tried such conversion but I got the figure on the right panel instead of the original on the left:

On the left,
μ = μ₁ = 0.81
ν = μ₂ = 0.91
y₁ = 2.5*10^10
y₂ = 3.8*10^10
K₁ = 3.0*10^-6
K₂ = 3.1*10^-4
S₀ = 1*10^-4 (g/L)
N¹₀ = 1.0*10^2
N²₀ = N¹₀*200
D = 6*10^-2 (/h)
Vol = 200 mL

Obviously, the conversion I did has not included the terms y₁, y₂, K₁, and K₂. Thus, the red species never took over. How am I to bind all these variables in fewer terms into a logistic system?
Thank you

Could you explain the goal of the modification? As I see, if you model two independent logistic equation there will always look as the panel on the right. The interaction between the populations in the first set of equations is given by dS/dt which depends of both populations, while each populations only depends on S and it self.

The point is: the implicit form is present in more examples than the explicit, thus it would be the preferred way to analyze the interactions. By converting the first set into the more common way of representation, I will have a consistent data set instead of having some described in one way and other in another...

I would show an example of a numerical solution, but you don't give values for D and S0 ...

Thanks, I have updated the question to incorporate these values. The example is taken from SCIENCE 1980;207:1491 (E. coli C-8 = N₁; P. aeruginosa PA0283 = N₂).

in DOI: 10.1126/science.192.4238.463 I have found the relation μ = μmax[S/(S + K)]. This allows to convert d/dt N₁ = (μ₁SN₁)/(K₁+S) to d/dt N₁ = μN₁. Only the logistic term is missing, which I can guess estimating the carrying capacity.

There may be some way to do this, but I don't see how. My best attempt is in my answer.

By combining the parameters as shown in the science paper (actually a Monod term), I get a much larger μ for E. coli than P. aeruginosa, as expected. I estimated carrying capacity by the sum of bacteria in the original model. Yet, E. coli does not overgrow P. aeruginosa (https://u.cubeupload.com/gigux/CASE13.png).

In the previous post, I mixed up the growth rates. I actually did obtain a crossover using μ = μmax[S/(S + K)]: https://u.cubeupload.com/gigux/3cfCASE13.png

In general, no. You're trying to reduce the a three-dimensional dynamical system ({S, N1, N2}) to a two-dimensional system ({N1, N2}), which can't be done in general.
One way to approximate a two-dimensional system is to assume that the nutrient dynamics are on a fast time scale, so that for a given N1, N2 you can write down the quasi-equilibrium S*(N1,N2) and plug it back into the N1 and N2 equations.  If I've done the math right, the value of S* as a function of N1, N2, and the other model parameters is the solution to the cubic equation dS/dt = 0, or:

for S. Unfortunately, this probably means the answer (although it will have a closed-form solution) will be too complex to do anything with analytically, although you could solve it computationally.
I tried this (code below): the dynamics actually track the full system very well for a while, but then the equations seem to blow up (the lines are the full 3-d dynamics, the points are the quasi-equilibrium approximation).  It would take a lot more thought and analysis to figure out what's going on here — most likely, the equations just aren't biologically well-posed. (In the full system, S crashes down from about 1e-4 to 2e-7 very suddenly around t=12, then declines extremely slowly after that ...)
@RogerVadim suggested that one could also try the limit of slow resource dynamics, but in this case (assuming we mean dS/dt << 1) the dynamics are simple and unrealistic; slow resource dynamics means we would hold S constant at its starting value and see what happened. In this case, because the per-capita growth rates of N1 and N2 are constant at constant S, we would just get exponential growth or decay for each species (depending on whether the birth rate was greater or less than the death rate).  There are plenty of other things you could try to simplify the system - what if D=0? What if D is non-zero but << 1 ? Is there a way fix the 2-D (fast resource dynamics) system so that it works, either by changing something computational or reformulating the system? - but nothing easy is immediately obvious to me.

p0 <- c(mu1 = 0.81, mu2 = 0.91, y1 = 2.5e10,
        y2 = 3.8e10, K1 = 3.0e-6, K2 = 3.1e-4,
        S0 = 1e-4, D=6e-2)

y0 <- c(S = 1e-4, N1 = 1e2, N2 = 2e4)

library(deSolve)
g1 <- function(t,y,parms) {
  g <- with(as.list(c(y,parms)),
  {
    m1 <- mu1/y1*(S*N1)/(K1 + S)
    m2 <- mu2/y2*(S*N2)/(K2 + S)g
    c(S = (S0-S)*D-m1-m2,
      N1 = m1*y1-D*N1,
      N2 = m2*y2-D*N2)
  }
  )
  list(g)
}

Seqfun <- function(S, y, parms) {
  Seq <- with(as.list(c(y, parms)),
  (S0-S)*D - mu1/y1*N1*S/(K1+S) - mu2/y2*N2*S/(K2+S))
  return(Seq)
}

g2 <- function(t,y,parms) {
  Seq <- uniroot(Seqfun, interval = c(0, 1e3), y = y, parms = parms)$root
  cat(y[["N1"]], y[["N2"]], Seq, "\n")
  g <- with(as.list(c(y, parms)),
            c(N1 = mu1*(Seq*N1)/(K1 + Seq) - D*N1,
              N2 = mu2*(Seq*N2)/(K2 + Seq) - D*N2)
            )
  list(g, S = Seq)
}

tvec <- seq(0, 60)
r1 <- ode(y = y0, times = tvec, func = g1, parms = p0)
r2 <- ode(y = y0[-1], times = tvec, func = g2, parms = p0)

png("bact.png")
par(las=1, bty="l")
matplot(r1[,-(1:2)], type="l", log="y", lty =1, xlab="time", ylab="density")
matpoints(r2[,2:3], pch=1)
dev.off()

Probably, one could also consider the limit where the neutrient dynamics is very slow?

Thanks, I'll need some time to digest this answer...


text:
Could bacteria and phages be found in tissues?
in the literature, there are several studies of the gut virome and microbiome, for instance Reyes et al. on Nature (https://www.nature.com/articles/nature09199?error=cookies_not_supported&code=f5201dbe-3cda-4e09-ba17-688d0352ef81).
Now, it makes sense to find bacteria (hence phages) in stools. However, there are other studies reporting bacteria from tissue, for instance Kostic et al. on Genome res (
Article Genomic analysis identifies association of Fusobacterium wit...
). In this specific case, the identified bacterium (Fusobacterium nucleatum) is an endocellular parasite and has virulence factors that allows it to penetrate tissues. But my question is more general:
Would be normal to identify bacteria and bacteriophages INSIDE human tissues?
In particular, would whole genome sequencing metagenomic experiments be likely to identify bacteria genome from human tissues? And if yes, how can we explain the presence of bacteria inside loci that are supposed to be sterile?
Thank you

Do you mean in healthy or diseased tissues? There are some bacteria, viruses or parasites in healthy tissues.

in both cases, there are differences in abundances and species between diseased and healthy tissues but in general, in the absence of an obvious infection, tissues should be sterile. Or not?

Tissues within the organs are usually sterile, but not necessary 100%. Theoretically, sterile means zero microbes, but in practice, sterile means no microbes detected by usual medical tests. So, yes, there can be few microbes in healthy tissues. And there are a lot of microbes in the gut, saliva, on the skin as part of normal flora. But you are probably asking if there are microbes "in the tissues" not only "on" the skin or in the body cavities.

correct, I am talking deep solid tissues such as muscles

@Gigiux If there is not enough specificity in your question such that you need to clarify your intents in the comments, your question is not specific enough and you should edit it.

It seems this question was also asked on ResearchGate.  There are already some answers there.

Per my comment to the question, here is an answer to the same question asked on ResearchGate:

Whole genome sequencing of human tissue samples often results in reads aligning to bacterial references, and this is actually a method used in the diagnoses of infectious diseases.
Understanding the Promises and Hurdles of Metagenomic Next-Generation Sequencing as a Diagnostic Tool for Infectious Diseases
Identification of low abundance microbiome in clinical samples using whole genome sequencing
However, because pathogen DNA may be present at a much lower abundance than host DNA, it may be difficult to distinguish true infections from contamination and false positives. Steven Salzberg addresses these concerns and offers a computational solution in a recent publication:
KrakenUniq: confident and fast metagenomics classification using unique k-mer counts
"Usually, the vast majority of the reads match (typically 95–99%) the host, and sometimes fewer than 100 reads out of many millions of reads are matched to the target species. Common skin bacteria from the patient or lab personnel and other contamination from sample collection or preparation can easily generate a similar number of reads, and thus mask the signal from the pathogen."

To expand on this answer, it is important to realize that accurate identification of low-abundance organisms in metagenomic reads requires very good reference genomes.  A separate paper from the Salzberg group discusses a startling discovery:  many high-copy repeats in the human genome have been incorrectly annotated as bacterial proteins in the NCBI RefSeq database.
Human contamination in bacterial genomes has created thousands of spurious proteins
This suggests that researchers should be careful when attempting to infer the presence of low-abundance bacteria or phage in human tissue sequencing data, particularly when the presence of those organisms is not corroborated by other analyses.

NERVES and BRAIN
After chickenpox infection, some Herpes viruses travel along the nerves and may remain dormant in the dorsal root ganglia of the spinal nerves...they can be activated later and cause shingles.
According to (jvi.asm.org):

Herpes simplex virus 1 (HSV-1) establishes latency in neurons of the
  brains and sensory ganglia of humans and experimentally infected mice.

INTERVERTEBRAL DISCS
PubMed:

Our findings further validated the presence of low-virulence anaerobic
  bacteria in degenerated IVDs, and P. acnes was the most frequent
  bacterium.

sorry, I should have specified that I was referring to tissues not directly in contact with the environment, such as brain and muscles - blood is out because there is compelling evidence for viruses in the bloodstream such as Anelloviridae.

OK, what about Herpes simplex virus in the nerve ganglia after chickenpox infection? I updated my answer.

sure, those I know about. My data from WGS from tissues indicates the presence of non-human viruses and plenty of bacteriophages. Would it be normal to find them inside tissues?

Most people probably have Herpes simplex viruses latent in their nerves and, some, even in the brain, as I wrote in my answer. Other possible candidates are Mycobacterium tuberculosis (in latent tuberculosis), Epstein-Barr virus (in chronic infectious mononucleosis), Borrelia burgdorferi (Lyme disease). I mean, these bacteria can persist inside the brain, bone or other tissues after healing. It's called latent asymptomatic infection.


text:
How to calculate phage infection rate from decreased PFU counts?
Some experiments measured the effect of particular chemicals on the infectivity of lytic phages in terms of influence on the PFU/mL counts.
For example, the reduction of PFU/mL of exposed phages over controls might be 2 logs (let's say from 1000 PFU/mL in controls to 10 PFU/mL in exposed). If I knew the infection rate of the control phage (let's say 1), how can I calculate the infection rate of the exposed phages?
Thank you

I think you have a few problems here - first off would be that it should be PFU (plaque forming units); as CFU is for bacterial colony forming units. Second, assuming a standard concentration of bacteria, what do you think is measured by the PFU/ml?

Thank you, yes I have mistaken CFU with PFU, I have corrected the post.


text:
Luciferase promoter vector over p-AcGFP1-C1 vector
AcGFP1 vector can emit light by itself, whereas in case of Luc vector a substrate is needed for the reaction. Nevertheless, Luc is said to be more specific or better than AcGFP1. Why is this so called? What are the advantages of Luc vectors over AcGFP1?

You are confusing luminescence and fluorescence. GFP does not emit light. The abbreviation stands for Green Fluorescent Protein. You need to shine a blue light source at it and it will fluoresce green. The problem is that many organisms have background fluorescence, a cell without any GFP can often have a little bit of fluorescence by itself or contain pigments that mask the signal.
Luciferase assays depend on a chemical reaction which oxidises a molecule (luciferin in the case of firefly luciferase) and photons are emitted.  This is much more sensitive than fluorescence but is also a lot more expensive and usually (but not always) requires cell lysis. It is very rare for a cell to emit light by itself so the background will be a lot lower allowing you to see smaller difference.
There are many reasons to choose one over the other in an assay, if you share a bit more on how you intend to use the reporter you can get a more detailed answer.

The vector to use will depend on what you want to do.
The possible problems with GFP are :

The lost of function of the fusion protein (you add 238 amino acids to your protein, that's a rather big change !). There are vectors allowing fusion in C- or N- ter of your protein to try to avoid that.
The GFP may separate from its fusion protein, making observations or immunoprecipitations useless.
With a high expression vector, you may have a saturation of fluorescence in your cells so quantification would be difficult.

With luciferase assay, you add the substrate so your quantifications can be made as soon as the reaction start and luminometers are sensitive enought to detect very low Luc activity or use very few cells.
BUT
GFP vectors allows you to do in vivo assays (quantification, intracellular localisation, cell sorting...) while Luc assays needs the lysis of your cells.
So, depending of your goal it will be better to use one system or the other.


text:
How to prevent HL-60 cell contamination?
I have thawed Hl-60 cells from liquid nitrogen chamber two times in RPMI 1640 media (containing 10% FBS, L glutamin, penicillin/streptomycin). In the first day the cells remain okay. But when subcultured from the first flask to new flasks (cell solution : media= 1:3) all the flasks became contaminated on the 2nd day of culture. Cloud was found in both time. It can be mentioned that I used sterile one-time usable pipettes and uncoated flask for growth. All the transfers to other flasks and media addition were done very carefully and done inside clean bench. Before using clean bench, it was sprayed by 70% EtOH.
Has anyone experienced like this problem?  Please share and if have, please give some valuable suggestions or references.
Thanks

The single most likely reason for the contamination is that your frozen stock is contaminated. Assuming you've been properly trained in cell culture, you're working in a correctly-maintained biosafety cabinet, your reagents are all sterile (has your media been sterile-filtered after adding FBS, etc.?), and the incubator is clean (water bath pan has been autoclaved, sterile water with biocide/fungicide added to it, entire incubator wiped down and all removable parts autoclaved periodically, etc.), then stock contamination is the most reasonable answer. Try thawing earlier passages than you have been working with, or order a new vial or two from ATCC or whoever your cell vendor is. Make sure your pipetors are clean, and you're using sterile filtered pipet tips.

There is a simple reason for this "cloudy" cultures. HL-60 is a suspension cell line (see ATCC on this), so most of the cells stay in the liquid phase and do not adhere to the plastic surface of the culture flask. Some may, but usually they don't adhere very good and come off when moving the flask or gently tapping it.
Suspension cultures look different from bacterial contamination, they are less dense and you can see the cells (which are much bigger than bacteria) in the microscope when you look at the culture. Bacterial cultures often of build up deposits of bacteria at the border of the medium. And the media of bacterial contaminated cultures are almost always yellow, as the metabolism products make the media acidic. An image would be helpful here.

Under inverted microscope cluster of very tiny colony were observed along with the cells. It was clearly distinguished between the unwelcoming materials and cells. The color of the media was not so changed, it was the same like normal media.  @Chris

Ok, then please post some images of the culture. And if possible microscopic as well.

Sorry to say, they were discarded, and thinking to thaw new vial of HL-60 again. That is why searching for suggestion or advice.


text:
Detailed working of the voltage-gated sodium channel
Hodgkin and Huxley formulated the ion currents through the three voltage-gated ion channels Na, K, and L as
$$\sum_{k}I_{k}=g_{\rm Na}\,m^{3}h\,(u-E_{\rm Na})+g_{\rm K}\,n^{4}\,(u-E_{\rm K%
})+g_{L}\,(u-E_{L}).$$
From Gerstner et al, Neuronal Dynamics, 2.2 Hodgkin-Huxley Model
What they probably didn't know - but is known today - is, that the sodium channel possesses four voltage-sensors (S4), opposed to one ball (IFM) which may close the channel and is described by $h$:

From Wikipedia, Ball and chain inactivation
Do I interpret Hodgkin and Huxley correctly, in that they found experimentally that three of the four voltage sensors must be in the up (= open) state for the pore to be open? Does this hold "exactly", or should the exponent in $m^3$ not be taken too "literally"? For example, the four voltage-sensors might be slightly different and have different deviations (when in their resp. up states), and only their "average" deviation counts, which is somehow reflected in the exponent $3$? The question then arises, why the exponent is an integer number. Couldn't it be any real number then?


text:
Causes of the stochastic behaviour of voltage-gated ion channels
I came up with the following electro-mechanical model of a voltage-gated ion channel, resp. of its voltage sensor as described here and here. The voltage sensor is a bistable system with two local energy minima $E_1(V)$, $E_2(V)$, the first one indicating "closed", the second one "open":

From Bezanilla, The Voltage Sensor in Voltage-Dependent Ion Channels, p. 567. You can interactively explore a voltage-dependent energy surface here (schematically).
I created a spring model with Algodoo which looks like this (green: the voltage sensor (= a peptide subunit), white springs: keep it in place, blue: favours the closed state, red: simulates voltage, opens the gate):

(You can download the model here and explore it interactively with Algodoo.)
To behave stochastically - i.e. the probability of being open $p(V) \sim e^{-\Delta Q(V)/kT}$ which presupposes a thermal equilibrium - there must be fluctuations that can lift the system above the energy barrier between the two energy minima.
My question concerns the source of these fluctuations in the real ion channel: are these thermal (mechanical) fluctuations (e.g. other molecules hitting or tearing the sensor) or are these fluctuations of the membrane potential?

And I'll note that this isn't something special with ion channels, it's true of many other types of proteins as well as non-biological molecules.

My model definitely does have (two distinct) energy minima, as can be seen by just watching it (above) or trying it out  (at Algodoo) or by checking the Geogebra link which reflects the Algodoo model. It's not about one spring, but about a system of springs that definitely may have different and distinct energy minima.

I don't understand your second comment.

Ah I'm sorry I missed the structure of your model entirely. You can disregard. My second comment was just to state that this isn't unique to ion channels; lots and lots of other molecules or proteins have the same sort of behavior where they switch between distinct states.

@BryanKrause: Do you have any idea concerning my original question: Do the random fluctuations stem more from the immediate molecular (mechanical) environment of the voltage sensor or from the membrane potential (which in turn stems from dendritic input/PSPs).

I believe it's from the molecular environment of the voltage sensor. I also think you have to consider spatial scale here; membrane potential is best thought of at a scale of an electrotonic stretch of membrane. Molecular interactions, on the other hand, are much smaller, and at that level the precise spatial presence of individual ions could have some influence, but I wouldn't consider that "membrane potential." I personally have no idea whether that presence matters on the scale of molecular vibrations/temperature. From the perspective of neuroscience it doesn't matter at all.

Let us continue this discussion in chat.

The fluctuations arise form thermal energy and can be described by the Eyring equation


text:
Tips for longer fragment size and higher purity of insect DNA
Aim
In a pilot experiment I tested three different genomic DNA extraction methods on the non-model organism Pieris mannii (southern small white; Insecta, Lepidoptera, Pieridae). The goal was to generate DNA fragments of ≥30 kbp average length for library preparation for PacBio SMRT long read sequencing  (HiFi)).
Methods
The three methods/kits used were: Qiagen blood & tissue kit (column assay), Beckman & Coulter DNadvance  (magnetic beads kit) and standard Phenol-Chloroform extraction.
Laboratory raised organisms in the prepupal stage (termination of larval growth phase, after last excretion of intestinal content, no chitinous exoskeleton) were harvested and frozen at -20°C. For the DNA extractions the head and the first two leg pairs (ca. 20mg) were cut and processed according to the kit/standard protocols with some modifications for high molecular weight DNA:

avoidance of freeze-thaw cycles
pestles were used for grinding the tissue (no liquid nitrogen)
inverting instead of vortexing
cell lysis and proteinase K digestion at 56°C and 300rpm overnight
planned: use of wide-bore pipette tips (impossible because of very long delivery waiting time)

Results summary

Method
Avg. DNA fragment length (bp) range
A260/280 range**
A260/230 range**
Nanodrop avg. conc. (ng/µl)
Qubit avg. conc. (ng/µl)

Qiagen
1038 - 18366
2.07 - 2.12
1.77 - 2.15
1151.8
104.9

Magnetic  beads
7350 - 12586
1.98 - 2.11
1.60 - 1.76
1048.7
155.8

Phenol-Chloroform
19552 - 27359
2.03 - 2.14
1.94 - 2.10
1389.2
215.4

*assessed with Agilent Femto Pulse
**Nanodrop results
The DNA fragments seem to be strongly sheared, the samples contaminated with organic compounds (especially the Magnetic bead ones) and the huge difference in concentration between Nanodrop and Qubit measurements may indicate RNA contamination.
Questions
How can DNA fragment length and purity be increased? Which are the most important measures? What life stage do you recommend using?
Ideas:

use of wide-bore pipette tips
shorten incubation time (cell lysis & proteinase K digestion)
use freshly eclosed imagines with soft exoskeleton to avoid slimy samples after cell lysis & proteinase K digestion (reason for contaminations?)
RNase A treatment

this is a fantastic question. very clear and comprehensive, informative, and using formatting effectively to drive home the point. I don't know enough to answer it though!

Welcome to Biology.SE! Strongly agree with MaximilianPress — I hope you will become a regular contributor.  ——— I don't know how easily you can obtain samples, but you may need to try all of your suggestions (e.g. do a time course for the lysis/protK step) and see what works best. In addition, my understanding is that the Nanodrop is infamously prone to inaccuracy, so I would tend to trust the other results more. You might also want to think about doing something like contour-clamped homogeneous electric field (CHEF) electrophoresis to get a idea of the size distribution of your fragments.

In absence of wide bore tips you can try cutting of some portion of the tip's front. Just ensure that the volumes you draw does not spill out. Obviously you won't be able to draw the maximum volume anymore.

Insect samples are difficult to work with primarily because they contain a bunch of polysaccharides, like chitins, that are similar enough to nucleic acids that they can co-precipitate. Standard extraction procedures (e.g. Qiagen blood/tissue kits) do not handle this well without some modifications to get rid of these contaminants. The slimy aspect of your extractions is the result of these contaminants.
Back in my day (>20 years ago) handling plant specimens, which run into similar problems with poly-phenolics, extractions were performed using modified phenol-chloroform  extractions. The specific form was a called a PCI (phenol-chloroform-isoamyl alcohol) extraction, with added B-mercaptoethanol and poly-vinylpyrrolidone in CTAB (cetyltrimethyammonium bromide) buffer.
I've had a quick search for Insect DNA extractions and found that similar protocols are in place for insects for long read-sequencing (see ref 4 in link). It looks like SDS with CTAB buffer is the way to go, followed by PC or PCI extraction.
In addition, measuring DNA and RNA concentrations by spectrometry (nano-drop etc) is unreliable - that method is great for telling you about DNA/RNA in protein solutions (the original purpose of the method), but is not really reliable enough for DNA/RNA quantitation for Gen 3 sequencing (or Gen 2 for that matter).
Instead, do as you have done, use a Qubit or other fluorescence method to quantitate and run your samples through a Bio-analyzer (Agilent) (high speed electrophoresis, with metrics on the sample added during analysis).

Thank you very much for your input!

I think @bob1's answer is good, and covers a lot of the bases.
One thing that I think is missing however is the use of a nuclear preparation as an initial step- my understanding is that this can help with a lot of the issues of phenolic/chitinous contaminants in difficult organisms like plants/fungi/insects. Here is one suggested protocol.
I would also recommend checking what's on protocols.io. Here is a protocol for insect HMW DNA prep, and here is a possibly relevant discussion.

Those might be difficult on a whole organism - generally work well from cultured cells though, and I suspect that larvae will do quite nicely, as the OP is using.


text:
Functional role of the myelin sheath
One usually reads that the functional role of the myelin sheath is being a good insulator, accelerating the speed of action potential propagation along the myelinated axon.
I tried to understand this and came up with these possibilities:

The immediate reason why action potential propagation along myelinated axons is "faster than normal" is a relative lack of leak channels in the membrane. I.e. it is the membrane of the neuron (not the myelin sheath itself) that is a "better insulator than normal". Why there are no leak channels underneath the myelin sheath would be another question. But the myelin sheath would probably be one of the reasons. Thus, it would be an insulator only "indirectly".
Or there are leak channels, but there's no place to go for the ions out of the neuron (no extracellular fluid to diffuse to)?In this case, it would be the myelin sheath that is the "immediate" insulator. But the leak channels would be useless. (So why to maintain them?)

So my question is:

Are there significantly less leak channels underneath the myelin sheath than normal,
  or not?

The myelin itself is an insulator. It wouldn't matter if there are leak channels under the myelin sheath or not: they are covered by a thick, fatty, non-conductive layer of folded membranes. Your title "Functional role of the myelin sheath" is not really related to the question you ask "Are there significantly less leak channels underneath the myelin sheath than normal, or not?" The answer to the second question has nothing to do with the function of the myelin sheath, the question would be whether cells have trafficking mechanisms to keep leak channels out of places where they are useless.

I disagree with your last sentence, starting with "the answer to the second question": The myelin sheath itself might be a cause and part of a trafficking mechanism to keep leak channels out of place... and so has possibly to do with it.

@BryanKrause:  You say "it wouldn't matter if there are leak channels under the myelin sheath or not". I claim: it does, because it is expensive. (It would be cheaper not to have them, without loss of functionality.)

"I claim: it does, because it is expensive" - exactly, but then we aren't talking about the function of the myelin sheath anymore, which was the title of your question. Do you want to ask about function of myelin? If so, the presence of leak channels under the myelin is irrelevant. Do you want to talk about efficiency? If so, then the function of myelin is irrelevant.

This is already answered here

@BryanKrause: Why not just accept that these two questions are tightly and obviously related?


text:
How are neuromodulator receptors distributed?
Irrespective of where, when and how neuromodulators are released, eventually they are detected by some receptors in the membrane of a target neuron (typically G protein–coupled receptors)
Neurotransmitter receptors are typically distributed on the dendrite and the soma of a neuron (and only occasionally on the axon):

at excitatory synapses (more distal)
at inhibibitory synapses (more proximal)

Does this rule of thumb also hold for neuromodulator receptors:

excitatory → more distal
inhibitory → more proximal

And are they clustered (like ligand-gated ion channels at synapses)?

Thanks for the hint, I'll rephrase the question accordingly.

Do you have evidence that excitatory synapses/receptors are overall more distally distributed than inhibitory synapses? What is certainly true is that there are very few excitatory synapses on the soma. But at least when considering input densities, further out from the soma excitatory and inhibitory input densities are of roughly the same magnitude in the cortex: doi.org/10.3389/fnana.2016.00124. What you suggest, although unlikely, may still be right, but I can't think of any evidence from the top of my head. As for neuromodulator synapses/receptors, they are probably even less well studied.

Now that you ask me: no, I have no evidence, it's just a vague impression I gained: that inhibition - for regulatory (damping) purposes - occurs preferrably near the soma. For "calculatory" (finer tuned) purposes (concurring with excitatory synapses on an equal footing) it may occur also more distally.

Now think of neuromodulators performing more regulatory tasks (slow, unpronounced), even though not necessarily damping. Nearer to the soma they might perform these tasks more efficiently.