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What were the challenges to sequencing the last 8% of the human genome that took 20 years to overcome and how was this done? (T2T Consortium)
CNN's March 31, 2022 article Scientists sequence the complete human genome for the first time says:

In 2003, the Human Genome Project made history when it sequenced 92% of the human genome. But for nearly two decades since, scientists have struggled to decipher the remaining 8%. Now, a team of nearly 100 scientists from the Telomere-to-Telomere (T2T) Consortium has unveiled the complete human genome -- the first time it's been sequenced in its entirety, the researchers say.

and

The research, published in the journal Science on Thursday, was previously in preprint, allowing other teams to use the sequence in their own studies.
Until now, it was unclear what these unknown genes coded.
"It turns out that these genes are incredibly important for adaptation," Eichler1 said. "They contain immune response genes that help us to adapt and survive infections and plagues and viruses. They contain genes that are ... very important in terms of predicting drug response."
Eichler also said that some of the recently uncovered genes are even responsible for making human brains larger than those of other primates, providing insight into what makes humans unique.
This remaining 8% of the human genome had stumped scientists for years because of its complexities. For one thing, it contained DNA regions with several repetitions, which made it challenging to string the DNA together in the correct order using previous sequencing methods.
The researchers relied on two DNA sequencing technologies that emerged over the past decade to bring this project to fruition: the Oxford Nanopore DNA sequencing method, which can sequence up to 1 million DNA letters at once but with some mistakes, and the PacBio HiFi DNA sequencing method, which can read 20,000 letters with 99.9% accuracy.

CNN's explanation is helpful as far as it goes, but with Nanopore's error rate of 1% to 3% (1, 2) and the difference between the repeats of some repeated sequences presumably a lot less than that, how was the error-prone Nanopore method combined with the HiFi method to nail the last 8% of the human genome accurately despite the repeated sequence challenges?
Question: What were the challenges to sequencing the last 8% of the human genome that took 20 years to overcome and how was this done? (T2T Consortium)
A premise of the question post is that it was the presence of repetitive sequences that posed the primary challenge, but the CNN article says "...because of its complexities. For one thing, it contained DNA regions with several repetitions..." which suggests there are other important factors as well.
Update: From the March 31, 2022 item in Science Most complete human genome yet reveals previously indecipherable DNA:

In six papers in Science, the Telomere-to-Telomere (T2T) Consortium—named for the chromosomes’ end caps—fills in all but five of the hundreds of remaining problem spots, leaving just 10 million bases and the Y chromosome only roughly known. And today, the T2T consortium announced in a tweet it had deposited a correct sequence assembly of the missing Y.

I think that of the six, the main paper is The complete sequence of a human genome

1Evan Eichler, a Howard Hughes Medical Institute investigator at the University of Washington and the research leader, said Thursday.

may need additional tagging, and the usage guidance for repeatitive-sequence may need some help as well :-)

The researchers did the easy bits first, and left the hard bits for later

@BryanKrause I think the question post as written is squarely on topic but it's those few words that seem to distract users here (but did not in Matter Modeling nor Politics). Each community's sensibilities are different and I'm not always as adept at shifting into the correct gear when moving from site to site. Does this look better?

Yes I think that is better. It may be a duplicate here but I don't have that post off hand.

@BryanKrause I'm having my morning coffee early today, I didn't see one when I did a quick check but I have time to look further now. If I find both the challenges and how they were overcome as described in the six new papers published in Science by the T2T Consortium already in answers here I'll vtc as duplicate myself! In the mean time I'll hunt them down and add links to the question. Thanks for your help!

The ~8% of the sequence that was missing was, as you say, complicated by high repeat content. Repeats make the problem of computational genome assembly hard at the best of times. Long repeat arrays make the same problem impossible unless you have sequencing technologies that have reads at least as long as the arrays in question.
A non-genomics example
Consider a sentence in human language where single words or phrases are heavily repeated. An example from German would be:

Wenn hinter Fliegen Fliegen fliegen, fliegen Fliegen Fliegen nach.

This is a grammatically correct and meaningful sentence that happens to have a "repeat array" of 6 copies of the word fliegen. But it can be confusing when the brain has trouble tracking that much information. Imagine that you only caught the beginning and the end, but otherwise you just know that the word "fliegen" was in there a bunch in that repeat array. How would you figure out what is going on? You just know:

Wenn hinter Fliegen Fliegen....

...Fliegen Fliegen nach.

Your understanding of the sentence is "anchored" in the unique words on either side of the fliegen array. But you have no idea what's going on in the middle there.
How you solve this problem is by paying close attention and remembering the sentence in its entirety. You may not be doing this habitually in casual conversation, but a highly motivated person who knows the language should not have any issues with this.
How this is related to genomics
Genomics technologies got very good at reading DNA a little bit at a time. At the time of the publication of the draft human genome originally in 2001, the predominant method of sequencing had an average read length of ~500 base pairs. A chromosome on the other hand is on the order of 100 million base pairs. This is ok from a genome assembly perspective without repeats. Even with repeats it is asymptotically ok for naive assembly as long as your repeat arrays are shorter than your longest reads. In other words, if your reads can pay attention through the whole repeat array, you can probably assemble the repeat array into the genome.
People got very clever with tools like BACs and YACs to get up to a million or so base pairs, though those tools still suffer from a lot of limitations and are quite labor intensive.
Now, consider that over half of the human genome is repeat. When we got lucky we were able to assemble human genome repeat arrays of around a million base pairs or so, but not in every case. Wherever we failed to assemble through such a repeat array, or where we simply were unlucky for some other reason, there exists a "gap" in the human genome.
In some cases we know what's on either side of the gap (e.g. it is in a chromosome), but not what's in the middle. In 2001 there were over 100,000 gaps with a total length of 80M bp in the human genome. That's a lot of missing stuff. In more recent genome builds it is actually higher (~5%), mostly because we simply ascertained more genome sequence since 2001.
In other cases we don't know what's on the other side of a gap, and these sequences are properly called "contigs"; these are little scraps of sequence that we weren't able to put into a chromosome at all, that we know exist somewhere but can't place properly. (There are some technical quirks here in that there anchored contigs and unanchored contigs, and a whole taxonomy of different flavors of not knowing stuff about sequence, but we don't need to get that down in the weeds!) The current standard build of the human genome, which improved dramatically on the 2001 publication, still has ~400 such contigs.
So there are lots of repeats in the human genome that were very hard to bridge. Up until now, the human genome has had a lot of Wenn hinter fliegen fliegen...??? without being able to read through the whole sentence.
Long read sequencing closes gaps
The T2T consortium is different in that it used "long read sequencing" of two kinds, nanopore ("ONT") and PacBio HiFi.
Nanopore reads are huge. They can get up to 1 million base pairs for very good runs. That's just enormously longer than methods like Sanger (~1000bp max) or current workhorse Illumina (~500bp max). You can read through tons of stuff with reads that long that was simply impossible.
The downside of nanopore is that you have somewhat low confidence in the accuracy of any given base, but on average it is still good enough to computationally take the average of a bunch of reads and get a good idea of what the genome looks like. Nanopore is great at stitching together problematic regions separated by repeat arrays, by just blowing through the whole array by brute force. HiFi is higher confidence but shorter (a mere ~20K bp per read!!) and much higher volume, so it is great for building the chunks to stitch together with nanopore.
Conclusion
The change of the T2T consortium was chiefly a technological change that allowed us to read through repeat arrays. People had previously used a lot of clever algorithms to bootstrap short reads, but they were still fundamentally limited by short reads failing on big repeat arrays. T2T removed that limitation, such that our long reads are now long enough to read through basically everything in the human genome.


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Intersexual competition regarding energy investiture of offspring
A while ago I remembered reading about a species that had evolved so that the male sperm cells promoted the energy investiture of the female in this offspring upon fertilisation. Since this was a r-selected species this hurt the females by reducing the likelihood that they would be able to give birth as many times due to the increased strain and so evolved some method that reduces the energy investiture in offspring.
Unfortunately I haven't been able to find references to this and was wondering if anyone here would be able to inform me which species I had likely heard about (or give examples of a similar behaviour), preferably with some references (I'm an academic, so probably able to access paywalled journal articles from the main journals).

Hi and welcome to the site. What is a "high" K species? (in what manner is it high?) Are you sure it wasn't seminal fluid? Try searching "effect of seminal fluid on female" (without quotes) and see if that helps. if it doesn't, edit to show what you found (showing research effort is expected on this site; "Nothing" is not accepted.) Try rephrasing the question to m.ake it clearer. Thanks

by high K I actually meant r-selected (don't work in biology so use the term very rarely and always get it mixed up). I have tried searching intersexual competition and only seemed to get results about macroscopic competition between animals rather then competition at a biochemical level. I did manage to come across t-Haplotype sperm in mice (see https://www.inverse.com/science/selfish-sperm-have-a-deadly-advantage). Most of my searches came up with results that were on a completely different track to what I was looking for, but I'll have to add "seminal fluid" to my searches and see

I think you'll find a lot more information on that different search.

source: Stack Exchange

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Why do larger neurons have less cytoplasmic resistance?
I'm studying neuron electrochemistry rn and my book basically says that the more the cytoplasm impedes the flow of ions, the slower conduction will be, therefore larger neurons will have lower cytoplasmic resistance. Can someone explain this to me?
I'm confused why a larger neuron would mean less cytoplasmic resistance...wouldn't it be more since there is more cytoplasm? And the ratio of cytoplasm : ion channels in membrane would increase with size as volume : surface area ratio increases, so it's not that. I thought maybe it has to do with the diameter of the axon since larger diameter tubes have less resistance, but the flow of an action potential down the axon isn't really like a liquid flowing down a tube...
Thanks for any help you can give.

Does this answer your question? Why do larger diameter myelinated axons have greater conduction velocities than small diameter myelinated axons?

Neurons are like leaky cables. If you make them longer, the resistance increase (along the long axis); if you make them thicker (larger cross-sectional area), the resistance decrease. The word "larger" is quite ambiguous here. However if we assume the neuron grows evenly along all axis by a factor of k, the theory goes that
$R_{k} = \rho  \frac{kl}{k^2A} = \rho  \frac{l}{kA} = \frac{1}{k} * \rho \frac{l}{A}$
where l is the original length and A is the original cross-sectional area, so the resistance is 1/k of the original value. If k is greater than 1, the resistence is reduced.

Hi @X, can I changed your equation to latex format - can you double check I've preserved the original meaning?

@user438383 thanks, it looks very pretty. Today I learned latex in comments on cell biology ;-)

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How widespread among mammals is the glymphatic system's metabolite clearance in the brain during sleep currently known to be?
The glymphatic system and "brain washing" (metabolite clearance) during mammalian sleep:
Xie et al. (2013) Sleep Drives Metabolite Clearance from the Adult Brain (also here) has been cited over 3,000 times. It describes in-vivo brain imaging and radio-labeled β-amyloid techniques to document sleep-correlated modulation of interstitial space and β-amyloid clearance rate. If I understand correctly the Glymphatic system was first named in this work by corresponding author Maiken Nedergaard.

Abstract:
The conservation of sleep across all animal species suggests that sleep serves a vital function. We here report that sleep has a critical function in ensuring metabolic homeostasis. Using real-time assessments of tetramethylammonium diffusion and two-photon imaging in live mice, we show that natural sleep or anesthesia are associated with a 60% increase in the interstitial space, resulting in a striking increase in convective exchange of cerebrospinal fluid with interstitial fluid. In turn, convective fluxes of interstitial fluid increased the rate of β-amyloid clearance during sleep. Thus, the restorative function of sleep may be a consequence of the enhanced removal of potentially neurotoxic waste products that accumulate in the awake central nervous system.

From Wikipedia's Glymphatic system:

The glymphatic system (or glymphatic clearance pathway, or paravascular system) was described and named in 2013 as a system for waste clearance in the central nervous system (CNS) of vertebrates. According to this model, cerebrospinal fluid (CSF) flows into the paravascular space around cerebral arteries, combining with interstitial fluid (ISF) and parenchymal solutes, and exiting down venous paravascular spaces.1 The pathway consists of a para-arterial influx route for CSF to enter the brain parenchyma, coupled to a clearance mechanism for the removal of interstitial fluid (ISF) and extracellular solutes from the interstitial compartments of the brain and spinal cord. Exchange of solutes between CSF and ISF is driven primarily by arterial pulsation2 and regulated during sleep by the expansion and contraction of brain extracellular space. Clearance of soluble proteins, waste products, and excess extracellular fluid is accomplished through convective bulk flow of ISF, facilitated by astrocytic aquaporin 4 (AQP4) water channels.
The name "glymphatic system" was coined by the Danish neuroscientist Maiken Nedergaard in recognition of its dependence upon glial cells and the similarity of its functions to those of the peripheral lymphatic system.
1Bacyinski A, Xu M, Wang W, Hu J (2017). "The Paravascular Pathway for Brain Waste Clearance: Current Understanding, Significance and Controversy". Frontiers in Neuroanatomy. 11: 101.
2Kiviniemi V, Wang X, Korhonen V, Keinänen T, Tuovinen T, Autio J, et al. (June 2016). "Ultra-fast magnetic resonance encephalography of physiological brain activity - Glymphatic pulsation mechanisms?". Journal of Cerebral Blood Flow and Metabolism. 36 (6): 1033–45.
3Konnikova M (11 January 2014). "Goodnight. Sleep Clean". The New York Times. Retrieved 18 February 2014. She called it the glymphatic system, a nod to its dependence on glial cells"

Cetacean sleep and conscious breathing:
Wikipedia's Dolpin; Sleeping and Whales; Sleep indicate many species of each type of mammal are conscious breathers i.e. many are not thought to be able to go somewhere safe and undisturbed and enter extended periods of unconscious sleep.
Question:
How widespread among mammals is the glymphatic system's metabolite clearance in the brain during sleep currently known to be?
I've mentioned conscious breathing in cetacean sleep as an example of both how challenging it may be to investigate some mammals and of where it might be less likely to be found. Since Xie et al. (2013) there must have been a substantial investigation in humans not only to address the "Why we absolutely must sleep?" question but due to the significant place that Amyloid beta holds in the investigations of human disease, including Alzheimer's disease.
Potentially helpful:

This extensive answer to What is happening physically when I get sleepy and when I wake up?
This answer to Do all mammals have a Ventricular system? says "The ventricular system is common to vertebrates." and links to Lowery and Sive (2009) Totally Tubular: The Mystery behind Function and Origin of the Brain Ventricular System
Jessen et al. (2015) The Glymphatic System: A Beginner’s Guide (also here)

in meta: Should the glymphatic system be covered by extending the lymphatic system tag? Does it warrant a separate tag? . The different way that dolphins sleep was brought to my attention in the NPR podcast The Extraordinary Lives Of Migratory Birds some of which may fly continuously for 7 to eleven days without stopping!

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What is an intuitive explanation of linkage disequilibrium?
Is it possible to give a simple and intuitive explanation of the concept of linkage disequilibrium? You know, so I can sort of sound like I know what I'm talking about. Everything I read about it has me lost.
I am a writer and specifically I write lyrics and raps and I love this phrase "Linkage Disequilibrium". I would love to put it in a rap I'm writing about a friend of mine.

What have you read so far and what is your current understanding? Where specifically are you needing help with understanding?

non-random assortment, torment / the haters who wanna split us, we don't even see 'em / wouldn't want to be 'em / me 'n my homie tight like alleles in linkage disequilibrium / we're correlated, ya see / you n' me, tied up in LD

love to see spontaneous collaboration @acvill

I'd recommend looking at some learning resources (links). If you don't understand what you read, you are welcome to bring your thoughts here and ask for help with what doesn't make sense. https://biology.stackexchange.com/questions/31618/what-is-linkage-disequilibrium-supposed-to-measure, https://www.discovermagazine.com/the-sciences/basic-concepts-linkage-disequilibrium, https://faculty.washington.edu/tathornt/sisg2013/Kerr/3LD_Kerr.pdf

Just channeling my inner Aesop Rock, @MaximilianPress

Intuitively, Linkage Disequilibrium, suggests a problematic sexual relationship. Biology, yes, explanation of the term, no.

Thanks so much everyone. It's just a couple lines in a song to make people have to think a little bit in order to understand what I'm saying, and I believe I already have enough to make that happen. In other words I'm totally gonna use a little bit of that from @acvill. With your permission of course

Be my guest, @JasonScaff

I’m voting to close this question because if it were intuitive, the poster wouldn’t have needed an explanation. This leaves the question of whether the purpose of this site is to explain concepts for which good accounts can be found elsewhere. The answer is no.

During sexual reproduction, the process of crossing-over means that parts of the maternal and paternal chromosomes become shuffled up with one another into chromosome 'chunks', as shown by the red and blue colours here:

We can tell by looking at this that if you had two genetic markers right next to each other on a chromosome that they very likely to be inherited together on the same chromosomal chunk. Similarly, if they are on opposite ends of the chromosome, they are much less likely to be inherited on the same chunk.
All other things being equal, we say that the markers close to each other are in high linkage disequilibrium (LD) with one another and markers further apart with be in lower LD with one another. In other words, the probability of recombination occurring between two markers, driven by physical distance and variable recombination rates is what causes differences in LD.
If we want to get a bit more in depth, then the recombination rate (i.e. the probability of a recombination event occurring between any two markers) varies across the genome. Something like a gene fusion event may totally impede recombination, meaning that region is always inherited as a single 'LD block'. This can result in things like supergenes in eusocial insects. Conversely, there are regions of very high recombination which reduce the amount of LD between markers.

This is not an intuitive answer or indeed a simple answer for a non-specialist. I am not a geneticist and was not familiar with this term, but I am an educator, so I would expect a good answer to start with a single sentence summary and then go on to explain any technical terms. For example if I do a web search I find statements like "Linkage disequilibrium is the non-random association of alleles of different loci." Now to explain it I would have to find a replacement for the word "allele" and clarify "loci" as the positions of genes, and then explain what is meant by association.

@David feel free to write your own answer then if you think you have a better way of explaining it

No. I am not the student, not the teacher, but am explaining what is lacking in your explanation and suggesting how you might improve it. But it is not easy.


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How are cotyledons able to affect the structure of plants?
How are cotyledons able to affect the structure of plants? I am asking in the context of leaf venation, root and stem structures.

Did you Google this? It's a basic in botany. If you have an intro Biology textbook, it will be there. See what you can find, and if you have a specific question, edit your question to include the information that confuses you. Thanks.

@anongoodnurse Yes, I did. The question is not only about what are they-- which I can find out but more about how they can affect the structure of plants: this is something I wasn't able to figure out. I have edited the question to make it clearer. I hope this helps. Thank you : )

This is still basic plant biology, one of the first things one learns about plants: are they monocots or dicots? As I said, if you have an intro Biology text, it's there. And it's everywhere on the internet. This is an answer you can find for yourself if you look and read. Getting answers fed to you cuts down on your work but doesn't help you in the long run, which is why we require evidence of an attempt to answer a question on this site.

Cotyledon is a structure of embryos of seed-bearing plants. During seed germination, cotyledon is raised up above the soil and turns green temporarily. They temporarily carry out photosynthesis for net food production for a few days during which the plant's leaves are still underdeveloped, unable to carry out photosynthesis at sufficient rate.
After the leaves become maturely developed and start carrying out photosynthesis, producing food at sufficient rate, cotyledons fall off onto the soil. They are decomposed by putrefying bacteria in soil and converted into nutrients, which dissolve in soil water and can be absorbed into plant.
Edited to add: To answer the question "how are cotyledons able to affect the structure of plants?", we have to clear up some ambiguities within the question itself.
Your question is, "How are cotyledons able to affect the structure of plants?". Instead, you may want to ask, "What is the effect of cotyledons on plant structure?" and "how do cotyledons affect plant structure?" The former ask what the effect is, and the latter ask to explain the process of "affecting". These two questions might be what you want to actually ask.
In Biology, when you are relating two concepts to each other, you have to know what they mean. Visually, you are trying to fill out the gap between the two:
$$\text{cotyledons}\rightarrow\dots\rightarrow\text{plant structure}$$
However, the ambiguity lies in each of the two concepts. What attribute of "cotyledons" are you referring to? What "plant structure" are you referring to? By "cotyledons", are you referring to "the development of cotyledons during seed germination"? This was what my previous effort was trying to answer. By "plant structure", do you mean "dry mass"?
Another way to think about it, when you ask "how does $X$ affect $Y$?" very often $X$ is an explanatory variable (or independent variable), while $Y$ is a response variable (or dependent variable). "cotyledons" and "plant structure" are not variables themselves. Variables are attributes which varies. For example, when you simply say "eye" is the variable, it is not clear how it varies because it is simply a body part. However, "eye color" is a variable because it varies - brown, blue and green. To apply the same logic, how does "cotyledon" vary? How does "plant structure" vary?
I really wish to know what your motivation for the question is. If it is a homework, it is implicit and please ask your teacher to clarify. If it is out of curiosity, target what you are truly asking. The question is simply too ambiguous to answer.

I have edited this. I hope you can understand what I am trying to ask :)

Do you mean "how does removal of cotyledons affect structure of vascular bundle development"? The most ambiguous part of your question is still "cotyledon". Do you mean the size of it, or simply the presence of it?

I assume I correctly imply your question. After removal of cotyledons, the young seedlings cannot carry out photosynthesis for food production at sufficient rate for a period of time as the leaves are still underdeveloped. In this period, food is continuously mobilized for growth and development of seedlings without replacement. This leads to net food consumption. With limited availability of food in seedling, it will soon enter food shortage and eventually deplete its food.

Without enough food (to provide energy and building materials), growth and development is stunted to conserve food for survival. With stunted growth and development of vascular bundles, they appear shorter and thinner than those in seedlings with intact cotyledons.

I think - perhaps - you're reading too much into this question; it's not sophisticated enough to be probing the depths of energy production/genetic expression/other. i think it's asking the difference between monocots and dicots, but the wording is poor. That's just my opinion. It's great that you're teaching, and trying hard to understand the OP, but we tend not to answer such basic questions, especially when no research effort is shown.

I just wish I could help. The question is simply too ambiguous to answer. I recall the OP said they are a high school student and usually high school curriculum emphasizes energy usage in seed germination. That's why I chose to answer the question like so.

"I just wish I could help." That's perfectly understandable, and laudable. I didn't mean to minimize cotyledon's ability to supply energy. Just thinking out loud. Botany was one of my favorite Biology courses, and I have a ginkgo tree because it's a monocotyledonous tree (which is cool!), but I couldn't elucidate the precise mechanisms responsible for vascular tissue patterning.


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What's the definition of 'natural prey' and 'natural predator'?
I am sure we all see both of these phrases used commonly, but is there a reason as to why the terms 'natural predator' and 'natural prey' are used as opposed to just 'predator' and 'prey'?
Below are two examples of each amongst numerous others from Wikipedia.
The Wikipedia article on Wolverine says

Wolves are thought to be the wolverine's most important natural predator, with the arrival of wolves to a wolverine's territory presumably leading the latter to abandon the area.

The Wikipedia article on Leopard seal says

The only natural predator of leopard seals is the killer whale.

The Wikipedia article on Leopard says

The leopard is primarily threatened by habitat fragmentation and conversion of forest to agriculturally used land, which lead to a declining natural prey base, human–wildlife conflict with livestock herders and high leopard mortality rates.

The Wikipedia article on Reptile says

Snake farming has been troubling for conservation in the past as it can lead to overexploitation of wild snakes and their natural prey to supply the farms.

Are there preys that wouldn't be natural preys to their predatory animal? Are there predators that wouldn't be natural predators to their prey?

Can you cite an example?

@BryanKrause, I have managed to attach a few to the body of the question itself.

whenever you have a question about definition in biology the answer is "it depends." Which is why we need context for the question.

Natural world be used in situations like these for 1 of 2 possible reasons (and potentially both simultaneously):

to indicate ecologies that exist due to the organisms evolving together in that area (vs interactions with non-native species)

to indicate non-human interactions.

Humans have strongly altered the ecologies of many organisms, including through the impacts of introducing non-natives. As our species grew and spread across the globe in the last couple hundred years, we ourselves have acted as the non-native species -- entering ecological communities in which we did not evolve with the local species.
The above context has traditionally been viewed as "non-natural" because it was mediated by human decision-making and technology vs. "nature" undergoing evolution.


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Effective population size formula in haploid populations undergoing serial bottlenecks
This classic Lenski paper computes the effective population size of an evolving E. coli population subjected to daily population bottlenecks as $N_e = N_0 * g$, where $N_e$ is the effective population size, $N_0$ is the population size directly after the bottleneck and $g$ is the number of generations between bottlenecks.
Unfortunately, the formula was not derived in the referenced paper and the referenced articles appear to not describe the formula directly, but only provide the fundamentals for deriving it.
Can someone explain how this formula comes about?

The effective population size is the harmonic mean (time average of $1/N$) of the time dependent population size:
$\frac{1}{N_e} = \frac{1}{t_f - t_0} \sum_{t = t_0}^{t_{f}} \frac{1}{N(t)}$
where $t_0$ is the foundation of the E. coli line, $t_f$ is some time much later when Lenski's poor grad students are sequencing them (with the understanding that $t_f - t_0 \ll N_e$, $t_0$ may be before the experiment began), and $N(t)$ is a deterministic function produced by removing individuals from the population with a pipette (throwing the rest in the freezer for the living fossil record) and letting them expand to cover a newly inhabited plate.
Since the population size is cyclical in Lenski's experiments (this procedure is done at regular time intervals, so at approximately consistent generation time), the average over one cycle should be the same effective population size as integrating over all time.  In other words:
$\frac{1}{N_e} = \frac{1}{t_{nextBN} - t_{BN}}\sum_{t=t_{BN}}^{t_{nextBN}} \frac{1}{N(t)} $
where $t_{BN}$ is the start of the bottleneck and $t_{nextBN}$ is the generation before the following bottleneck (once a day I think? so, $\sim$6 generations per cycle if I remember correctly). In the Lenski lines, the population grows rapidly from inhabiting a new environment on the fresh plate, so we can assume the growth rate is exponential with some rate $\gamma$ (e-folds per generation).  Now we have:
$\frac{1}{N_e} = \frac{1}{t_{nextBN}-t_{BN}} \sum_{t=t_{BN}}^{t_{nextBN}} \frac{1}{N_0 e^{\gamma t}} = \frac{1}{\Delta t N_0} \sum_{0}^{\Delta t} \frac{1}{e^{\gamma t}}$
In the second expression I have defined $\Delta t = (t_{nextBN} - t_{BN})$ as the time between bottlenecks, and the sums are equal because we are free to start counting generations at $t_{BN} = 0$.  I also pulled the constant $N_0$ out of the sum.
Computing the sum of the series over a finite number of generations $\Delta t$, we find the following:
$\frac{1}{N_e} = \frac{1}{\Delta t N_0} \frac{ \left(e^{\gamma} - e^{-\Delta t \gamma}\right)}{\left(e^{\gamma }-1\right) }$
Now, I looked up Lenski's 1991 paper (here: https://www.jstor.org/stable/2462549?casa_token=dNMGpr9sBFcAAAAA:BrRjPHxwmxAuegCuN8eHFXr2w4slkPLJwTOrpD6nQRIHsx6ukS4kWaIYHtPuwgxWQ9j7G_6ICPpCTKZA7XW0izImSN_-7wwXpS_lnGWhJSN3PbWRiSU) and he states (in the same section) that $N_0 \sim 5\times 10^6$, $N_f \sim 5 \times 10^{8}$; if $ N_f = N_0 e^{\gamma \Delta t}$ and $\Delta t \sim 6$ (assuming the cycle is once per day), we find that the growth rate for each bottleneck is roughly $\gamma \sim 0.75$ (in that ballpark).  This is extremely quick growth, so the $e^{\gamma}$ terms in the numerator of the above expression dominate over $e^{-\gamma \Delta t}$.  This means we can approximate the inverse effective population size as follows.
$\frac{1}{N_e} \approx \frac{1}{\Delta t N_0} \frac{e^{\gamma} }{e^{\gamma}-1} \sim \frac{2}{\Delta t N_0}$
Note, there is a factor of roughly 2 here that I suppose Lenski is ignoring? Using Lenski's variable $g = \Delta t$, this reproduces the relationship he quoted, up to a factor of $\frac{e^{\gamma}-1}{e^{\gamma}} \approx \frac{1}{2}$:
$N_e \approx \frac{1}{2} g N_0$
As a little tip, if you ever have a population genetics question you're not sure about, just scour Kimura's papers.  Everything you can ever think of is sitting in one of them, including this question:  https://www.jstor.org/stable/2406157?casa_token=cWTvTL8k29QAAAAA:GVDLvS2SL7FJioYREhU0qjAIU5ynBpcncl7Z8r7xZh6S_PQWIVh2Di0bKt9BbVgfJIo-O-CMiFudnSnDMjmwzth1YDTA_EoPoQ7jATWxuzzR2gzcke4
EDIT: I initially introduced a sign error in the penultimate expression, which was originally $\frac{1}{N_e} \approx \frac{1}{\Delta t N_0} \frac{e^{\gamma} }{e^{\gamma}+1} \sim \frac{1}{\Delta t N_0}$, where there was a negligible factor of roughly 2/3 from $\gamma=0.75$ that can be treated as approximately 1.  The above text is now corrected, and has an apparent factor of 2 that would need to be dropped to match Lenski's expression.

Thank you for this comprehensive answer. I guess we can drop the factor of ~2/3 because in this context the error it introduces is irrelevant due to the large uncertainty in all other parameters?

Additionally, I found this paper (https://onlinelibrary.wiley.com/doi/10.1111/j.0014-3820.2001.tb00772.x, also from Lenski) that derives $N_e = N_0\Delta t\gamma$. Again, I guess $\gamma$ can be neglected?

First, no problem!  Second, thank you for citing that paper.  I had not seen it and it's obviously relevant. There is also this paper, by the same authors: https://academic.oup.com/genetics/article/162/2/961/6049989?login=true. Regarding the difference between the two solutions, there is also a strange difference that comes up if you integrate rather than sum to compute the harmonic mean of the population size.  I will post the result (only) in another comment in a few mins.  Also, I made a dumb mistake and flipped the sign in the denominator of the second to last equation (oops!).

The solution if you assume continuous generation time is the following: $\frac{1}{N_e} = \frac{1}{\Delta t} \int_0^{\Delta t} \frac{1}{N_0 e^{\gamma t}} dt = \frac{1-e^{-\gamma \Delta t}}{N_0 \gamma \Delta t}$.  Since $\gamma \Delta t \approx 6 \times 0.75 = 4.5$, the exponential decay is negligible.  This gives $N_e \approx N_0 \gamma \Delta t$, matching Wahl and Gerrish.   I am not quite sure where the difference comes from, but it's entirely possible I made a mistake above.  Wahl and Gerrish also claim that their results match Lenski (1991) (the original paper we are discussing).  ctd below

I'll try to look at the discrete case in my answer again and see if I can find some issue that alters the result (other than the sign error).  I think difference has something to do with changing the discrete sum with the element having no units to the differential dt.  I am going to edit the sign error in my original answer, but I will make it clear where the mistake was so you can track it.


text:
Are individual auto-reactive 'lymphocytes' or auto-reactive 'clones' generated in the central lymphoid organs?
Clonal deletion is a well-known mechanism of immune central tolerance. But individual lymphocytes or lymphocyte clones are subjected to apoptosis? If clones, then what is the reason to allow mitosis in auto-reactive cells? If lymphocytes, then why do we use the adjective? I mean are there several rounds of mitosis in a (potentially) harmful say B lymphocyte prior to negative selection step?

I think you misunderstood the definition of clone at this level. As clonal deletion is a central tolerance mechanism, of all the possible clones of B cells (a clone is a B cell with a particular arrangement of the BCR), those clones (not identical clones, but different clones each) that are self-reactive will undergo apoptosis. That means that self-reactive clones are deleted and they won't divide anymore.

so, 1 clone = 1 B cell, any reference?

Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.


text:
How does a neuron recover from after hyperpolarization?
My question is, how does a neuron recover from AHP? It’s been puzzling me for a long time, and I really can’t find a single source that explains it in detail. Apparently the sodium potassium pump restores it following hyperpolarization, but I really can’t imagine how it would do that!
My only hypothesis as to how that would work would be that the sodium potassium pump increases the hyperpolarization beyond Ek, so as to reverse the direction of K current back into the cell, but that for me doesn’t make much sense, because that effect for one would be very temporary; once K flows in to the cell, it would depolarize the membrane, decreasing the potential back to something lower than Ek, and we will be back where we came from.
Also I read somewhere in a neurophysiology book that ENa is the ceiling of the action potential, and Ek is the floor of the action potential, so wouldn’t the hyperpolarization caused by the sodium potassium pump push it beyond Ek, contradicting the book?
Anyways I hope that wasn’t too long, and please someone help me out, I’m supposed to be studying anatomy but this whole thing is time consuming.

Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.

The Goldman equation is your friend when understanding voltage changes in neurons. Forget about ion concentration changes unless you're focusing on them specifically, they are ordinarily too small to matter in the cycle of an action potential. What matters instead is permeability, and changes in permeability to different ions underlies all of the voltage changes you see in a neuron: responses to excitatory and inhibitory neurotransmitters, triggering and propagation of action potentials, repolarization, hyperpolarization, everything.
It's also helpful to think about the Nernst equation, which is very similar to the Goldman equation except it involves only one ion. The Nernst equation will give you the "reversal potential" (or "Nernst potential" or "equilibrium potential"; your "EK" is for "Equilibrium potential for K") for each ion. When you increase permeability of the membrane to some ion, the result will always move the cell's potential in the direction of that ion's reversal potential.
During an action potential, there is a positive feedback loop involving voltage-gated sodium channels; as more sodium permeability opens up in the membrane, the voltage moves towards the reversal potential for sodium, which is typically around +20 mV, far more positive than rest. In mammalian neurons, repolarization is aided by opening voltage-gated potassium channels, at the same that the sodium channels close. The reversal potential for potassium is typically around -90 mV, slightly more negative than rest.
Because there is more permeability to potassium while these channels are open compared to rest, the membrane potential will be closer to the reversal potential for potassium than at rest.
As the voltage-gated potassium channels close, that additional permeability to potassium is gone and the cell is back to having only resting "leak" channels open, so it returns to the resting voltage. Yes, these are also most permeable to potassium, but the resting cell also has some small permeabilities to other ions, hence why the resting potential (typically around -70 mV, -65 mV) is slightly more positive than just potassium's reversal.
Some textbooks and internet resources say stupid things about the role of the sodium/potassium pump, and say it's necessary for "returning the cell to rest" or something like that, which misleads students like you into thinking that the pumps are important for this recovery from afterhyperpolarization.  You know how I mentioned that ion concentration changes are too small to matter? Well, if the Na/K pump wasn't working, those small changes would accumulate over time (think minutes to hours; not a fraction of a second) and would matter. Thanks to the pump, your life can be simpler as you understand neurophysiology, because the pump is always keeping the concentrations of sodium and potassium different inside the cell compared to outside. If you're just thinking about one action potential cycle, though, forget the pump!

Thank you for your answer! However, I have another small question, if you don’t mind. Let’s forget that I said the Na-K pump returns the membrane potential back to the resting one. Then, what actually does? I have an idea about that, which I tried to confirm by calculating the ratio between the Na and K currents as soon as the voltage gated K channels close, assuming the membrane returns to the resting conductances, and the Na current is larger due to the increased electrochemical driving force. So does that mean that Na influx is responsible for depolarizing the membrane back to the RMP?

@NeuroIsHard Ions of all types are moving all the time. The net flow for a given ion is always in the direction suggested by the Nernst equation for that ion, so sodium is always flowing in to the cell as long as the cell is more negative than E(Na), and potassium is always flowing out of the cell as long as the cell is more positive than E(K). You can calculate the potential at which the sum of all ions according to their charge is zero with the Goldman equation.

If you think just in terms of sodium and potassium, at E(rest) you can say that the net flow of Na+ in to the cell equals the net flow of K+ out of the cell. If you are more negative than E(rest), then there is a little less K+ flowing out (because you're closer than rest to the reversal potential for K+) and a little more Na+ flowing in (because you're further from the reversal potential for Na+ than at rest). It's not fair to say it's "sodium flowing in" because "less potassium flowing out" is equally (or more) important; it's the overall balance that matters, given by the Goldman equation.


text:
Temporal space-use modeling - How can I quantify temporal variation into a single value without losing magnitude?
For my ecological research on the impacts of intensity of space-use on vegetation structure I need to quantify temporal variation in the intensity of space-use across years (resulting in a single value for each pixel of my research area).
So for example if I have the following space-use data:

Pixel
2017
2018
2019
2020

1.
5
5
4
5

2.
3
5
1
4

3.
1
0
1
1

I'm looking for a summary value for each column that quantifies the variation but also the magnitude of the space-use. I originally was looking into using a coefficient of variation but ran into the problem that high constant space-use and low constant space-use generates the same CV value. So is there a statistic out there similar to the CV that can still account for the total intensity of space-use as well?

If I understand correctly, you want a single number that represents both magnitude and variation. This sounds to me to be impossible for informational reasons; if you want to represent two values with one value, you have to lose information unless the two are strictly related in which case there is no information to lose. What isn't clear to me, though, is why you want/need to do this. Why can't you use the data in the form you have? What is the specific research question you are testing?

Yes correct - and fair point, something I'll take into consideration. Because I'm looking at responses in vegetation it is important for me to capture both the magnitude and variation. My research relates to elephants and their impact on vegetation. So for example if in 2018 they utilize a certain pixel heavily but leave it alone until 2021 that patch can recover. However, if they keep coming back to that patch the continuous utilization in theory leads to more vegetation damage. If I use a standard utilization distribution value this won't take into account that annual variation.

So I'm looking for a way - if possible- to quantify that annual variation whilst also taking into account the total impact

That sounds like quite a complex nonlinear relationship, where you would need some way to model patch recovery. You are not going to be able to use some standard summary statistic to capture that, it will need to be something very specific to your domain, and which may not even exist. What are the other variables in your study? Is it actually necessary to do this to test your hypothesis/es? Alternatives may be to use a simpler measure, or separate "use" from "rest".

I will be able to use metrics such as NDVI, EVI and percentage canopy cover to monitor the vegetation response, it is just quantifying the temporal variation of elephant space-use that is the last piece of the puzzle I am trying to solve. In the modelling I have already done I can see that there is a lot of annual variation in their space-use so I'd like to try and accomodate that, but have no idea if that is possible because I have not been able to find any other research on it. The values I am using are about as simple as I can make them without losing too much information.

But what is your hypothesis?

That high and consistent elephant utilization will lead to higher vegetation damage

I do not think you will find a general answer outside your research domain.
There is no general way to express both magnitude and variation as one number without losing information; unless you have a strict relationship between the two, such that the two numbers do not provide separate information (an example would be data with a Poisson distribution, where mean and variance are equal), this is simply not possible.
I'm answering from just a general statistics perspective, as I have little to no domain-knowledge in your area, but if you haven't encountered a measure already in the papers you generally read in your field, then I think it probably doesn't exist.
If you want to test whether "high and consistent elephant utilization will lead to higher vegetation damage", some options I can see are:

Test "high" and "consistent" separately; "high" could be from averaging/summing usage and regressing on your measure of damage, "consistent" could be from measuring the standard deviation, or using a measure like "years of high usage" with some threshold.

Fit a model with both your separate measures of "high" and "consistent", and look for a significant interaction. That is, a model of the form Damage ~ High * Consistency. There are certainly theoretical issues with this type of model, especially given the expected covariance between the two predictors, but I think it could still be practically useful, and in particular could be used to motivate not using measures of magnitude or consistency alone.

Use or modify an ecological model. I don't know much about this area, and it would probably take you quite a bit of reading to find something applicable, but cumulative damage seems to be a recurring issue in ecology, and though you may not find a model used in your specific domain you might find similar ones with parameters you can adjust and fit to your data. I'd expect a differential equation where the current year's vegetation quality predicts the next year's growth with some saturating characteristic (i.e., logistic growth), with elephant presence having a separate additive or multiplicative impact on vegetation quality, growth, or both. One paper I found quickly is this one:

Owen-Smith, N. (2002). Credible models for herbivore-vegetation systems: towards an ecology of equations: Starfield Festschrift. South African Journal of Science, 98(9), 445-449.
which seems like it could be useful, and it cites an older book chapter:
Caughley, G. (1976). Plant-herbivore systems. Theoretical ecology: principles and applications, 94-113.
The approach would be to fit the parameters of a model like this one to predict your observations of the vegetation based on elephant presence.


text:
Would viral diversity result in a change in the effectiveness of CRISPR systems in a population of bacteria, within a closed system?
I have here my hypothesis, does this make scientific sense? Assume this situation is occurring in a closed environment with only bacteria and bacteriophages.
The effectiveness of CRISPR/Cas9, being an adaptive defence system, is heavily reliant on the phages that it, or its ancestor has previously hosted. This is because Cas proteins require the virus’s physical presence in order to extract spacers from the virus’s genome and implement them into the CRISPR locus. Therefore, an environment bearing a smaller number of different virus types should theoretically lead to a higher degree of effectiveness for CRISPR systems. Low quantitative viral diversity should lead an influx in CRISPR’s effectiveness as, over time, a population of bacteria and its offspring should gain possession of spacers that provide them with a competitive advantage within their given environment. Hypothetically, this should lead to an increased bacterial population size as bacteria are now more easily able to ward-off viral infections. Consequently, this would most likely lead to a relative decrease in the viral population as the abundance of relevant spacers in the bacterial population will lead to a lower successful infection rate, causing an increased number of viruses to die upon the unsuccessful infection of a host bacterium, preventing induced viral lysis of the host, a process consisting of the disruption of the cellular membrane, resulting in the death of the host cell and the release of cytoplasmic compounds, including a large quantity of additional viral particles into the given medium, leading to a steep rise of the viral population. In contrast, CRISPR’s effectiveness should be diminished in an environment containing high levels of viral diversity as it would be far more difficult for bacteria to obtain the necessary spacers for CRISPR to be effective against the vast variety of bacteriophages in the given environment. Due to the decreased effectiveness of CRISPR systems, it would be more strenuous for bacteria to fight of viral infections, leading to a decrease in the bacterial population or a more moderate reproductive rate. Inversely, it is likely that viral population will flourish due to the scarcity of relevant spacers. This shortage in relevant spacers would result in an increased rate of infection of host cells, causing an increase in lysis and a rapidly multiplying viral population. Fluctuations in the bacterial population can be a strong indicator of the current effectiveness and efficiency of CRISPR systems as its main purpose is to aid bacteria in their survival. Quantitively, a good representation of the fluctuations in bacterial population size is percentage (%) rate of change. Percentage rate of change of a population provides a concise value that indicates whether the population in question is stagnant, increasing, or decreasing.
To me, it makes perfect sense, but I am not an expert in this field, just a high school student.
When I plugged this relationship into an online simulation, found here, I obtained a trend that suggested there is no correlation between viral diversity and the size of a bacteria or virus populations. I'll attach below a graph that shows the relationship I obtained.
Figure 4: Scatter plot graph showing the relationship between viral diversity (maximum virus types | 20, 40, 60, 80, 100) and the percentage (%) rate of change for both the bacterial and viral populations over a period of 500 ticks, within a closed environment. Graph includes two trendlines for each dependent variable, along with an equation for each line, a R2 value, and a R value.

Just looking for some insight, have I got this all wrong?
(This is a repost as I deleted the other variation of this question due to improper formatting)

Bear in mind that CRISPR is just one of many defenses bacteria use against phage. There is a diverse range of Restriction-Modification systems that also identify and disable foreign DNA, cell surface receptors can be mutated so the phage can't bind, etc. So I wouldn't expect a very tight relationship between CRISPR and phage pressure.


text:
What is the phenomenon when animals mimic other animals in order to survive?
The caterpillar Hemeroplanes triptolemus adopts the appearance of a snake when it detects danger. What is this phenomenon called in which animals mimic other animals in order to survive? Is it morphological adaptation, if not why not?

Deimatic display:

Deimatic behaviour or startle display means any pattern of bluffing
behaviour in an animal that lacks strong defences, such as suddenly
displaying conspicuous eyespots, to scare off or momentarily distract
a predator, thus giving the prey animal an opportunity to escape.

This could also be referred to in more general terms as Batesian mimicry.

In Batesian mimicry the mimic shares signals similar to the model, but
does not have the attribute that makes it unprofitable to predators
(e.g., unpalatability). In other words, a Batesian mimic is a sheep in
wolf's clothing. It is named after Henry Walter Bates, an English
naturalist whose work on butterflies in the Amazon rainforest
(described in The Naturalist on the River Amazons) was pioneering in
this field of study.

This is distinct from aposematism, in which a positive defence mechanism is present and advertised:

Aposematism is the advertising by an animal to potential predators
that it is not worth attacking or eating. This unprofitability may
consist of any defences which make the prey difficult to kill and eat,
such as toxicity, venom, foul taste or smell, sharp spines, or
aggressive nature. These advertising signals may take the form of
conspicuous coloration, sounds, odours, or other perceivable
characteristics.

The phenomenon whereby one animal mimics another is called mimicry by zoologists as opposed to camouflage, although plants can be mimcs as well.
There are this many varieties of mimicry, so it's best to refer to the wiki reference:
2.1 Defensive
    Batesian
    Müllerian
    Emsleyan/Mertensian
    Wasmannian
    Vavilovian
    Gilbertian
    Browerian
2.2 Aggressive
    Predators
    Parasites
2.3 Reproductive
    Bakerian and Dodsonian
    Pseudocopulation
    Inter-sexual mimicry
2.4 Automimicry

https://en.wikipedia.org/wiki/Mimicry
Is it a morphological adaptation? It effects pigmentaiton and morphology and it is encouraged by random mutations which confer to the mimic a resemblance which has an evolutionary advantage, i.e. a resemblance to an animal which is avoided by predators.


text:
What is meant by ‘local structure’ of proteins?
The EBI/EMBL training course includes the following definition of Secondary structure of proteins:

Secondary structure refers to the regular, local structure of the protein backbone, stabilized by intramolecular and sometimes intermolecular hydrogen bonding of amide groups.

What does the word ”local” mean in this case?
Is there anything that is not local in the case of protein structures?

‘Local’ appears to be a term that is used in relation to the structure of proteins to distinguish specific small parts of it from the overall structure, which in this context appears to be termed the ‘global’ structure.
I write ‘appears’, because I had not met it before, but I draw this conclusion from a section of a review in the journal, Computers, entitled Local Structure Comparison of Proteins:

Starting from the 3D coordinates of the atoms in a protein…
global structure comparison can determine the similarity of two complete protein structures.… However, a protein’s global
structure does not always determine its function.…   For this
reason there has been increased interest in local structure
comparison to identify structural similarity between parts of
proteins.

One does not, in my experience, encounter this term in definitions of secondary structure in general biochemistry texts, which might use something more generally comprehensible like “sections of the overall structure”. Although EBI/EMBL is an authoritative institution, its staff tend to have expertise in research and computational work rather than education.


text:
Walking or running makes me consume 200 to 550 kcal/h, that's true, but always 68 to 72 kcal per kilometer whatever the effort done. Why?
My connected watch tells me that when :

I'm walking I'm consuming 200 - 250 kcal per hour,
running: from 500 to 550.

and this is ok.
But it also tells me, that how many kilometers are my trips, I'm consuming 70 kcal (68 to 72) for each kilometer, whatever I am going cool slowly (at 4.5 km/h) or running 10 kilometers (at 9 km/h).
It's not what I would have guessed.
In my mind, my body should spend more calories during a distance where it is doing more exercise than when it doesn't.
It's possible that I'm doing a logic mistake, but I'm missing something here, and I'm intrigued.

Connected devices aren't perfect, no matter how "smart" they're advertised to be. To actually determine the amount of energy you're using requires an awful lot of specialized equipment.

In addition to Matt's comment, are you considering resting metabolism? All the "background" stuff: keeping your brain on, your digestive system going, running your kidneys, synthesizing replacement proteins in all your tissues. If you include that in your calories per distance, there's going to be more background per distance when you move slower. If you sit still, your calories per distance are going to become infinite.


text:
Species identification: plant with pitfall trap-like structures
I found this plant in Tuscany (Italy, mediterranean climate, about 60 m above mean sea level). Photos were taken at roughly the beginning of spring after a period of drought followed by a couple days of rain. Average temperature oscillates between 7-10°C, relative humidity is around 75-80%.
Unfortunately I didn't have a ruler at hand but the plant was not very tall, I'd say about 12-15 cm (5-6 inches) at most.

Family is likely Araceae. Not familiar enough with Italian flora to know possible candidates. I may have time to dig in later, but I suppose some European users more familiar with possible candidates will be able to respond before I have time.

I think that is probably a plant in the genus Arisarum based on the almost complete covered inflorescence ("trap-like" structure). In particular, it looks most like Arisarum vulgare (common name: Friar's cowl). This plant is found throughout the Mediterranean region including Italy.
The striped structure with a "lid" isn't a trap, but instead an inflorescence (branch bearing multiple flowers — in this case a spadix with its bract being the "trap"). The inflorescences are from the plant with the rounded-arrowhead shaped leaves.
That leaf shape is characteristic of several genera in the Arum family (Araceae), but the size and very rounded tip looks most like specimens of Arisarum vulgare.
The size and early spring flowering time also fit what is described for this species.

Source: user Hectonichus on Wikimedia Commons —
License: Creative Commons Attribution-Share Alike 3.0 Unported


text:
Giant inflatable laboratory in the jungle. How to find it?
When I was a child (circa year 2000), I watched a documentary (in English) about some biologists doing research about jungle (perhaps Amazon). The biologists lived in a base which was a huge inflatable structure, that was resting on top of the trees. The base had some labs in it and living quarters.
I can't find anything related on Google. It's just spam about inflatable castles.
Can someone tell me what was the name of the research project from the documentary I watched?

Can you remember what language it was in, what year it was made, anything specific about what was being studied, who was in it?

It's not the BBC "Life in the Canopy"?

I’m voting to close this question because it is not about biology as defined in the [help] — specifically it isn't about a biological mechanism, process, or research technique. In addition, you are asking multiple questions, which would be reason to close even if this were on topic. Please consider reviewing the [help] starting with [ask], what is on-topic and what is not.

@tyersome it is about history of biology, because giant inflatable research base is a historical achievement. Also, it is a research technique of establishing a lab in a difficult environment. Also I removed the extra questions.

@user46147 if this question were to remain open, it would be helpful to know when you watched this documentary, and which country and language you watched it in.

@bob I added the info you requested.

Thank you for removing the extra questions, but I still think this is not appropriate here. There is a site for history questions — [HSM.SE] — I don't know if your question fits their criteria, so please check their help section for suitability. If you do decide to try there, please delete your question from this site before reposting because cross-posting is impolite. Alternatively, you can request migration of this question by flagging your post for moderator intervention and explaining what you want and why. –

After more intense search, I found the following research article ( https://doi.org/10.1002/ppp3.10125) by Margaret Lowman.
She discusses canopy research, stressing that forest canopy is poorly researched topic. She outlines the history of previous research on that topic, and points to the spectacular research of Frances Halle from Institut de Botanique in Montpelier.
His team managed to launch a huge effort involving inflatable rafts, slides and dirigibles, that has been named "Radeau des Cimes" (Raft of the Peaks in English).
The structure facilitated canopy sampling and hosted 50 researchers.  Over time, the inflatables have surveyed the rain forests of Cameroon, Panama, Brazil, Gabon, and Australia [copy from the article linked].
Here's a picture from radeau-des-cimes.org :

The colors of inflatables match my memories, so I consider the search a success.


text:
What are protein iBAQ abundance values in SWATH mass spectrometry?
I am reading a journal paper where they used SWATH mass spectrometry to quantify the abundance of proteins in synaptosomes isolated from different species. I am trying to determine whether some proteins of interest are present in synaptosomes.
I have looked at the supplementary material of this paper, and they have a table called "Protein iBAQ abundance values for discovery proteomics (DDA) measurements of mouse, rat, marmoset and human synaptosomes used for the spectral library."
I am not very familiar with SWATH mass spectrometry. In the context of SWATH mass spectrometry, what are protein iBAQ abundance values and what do they represent? Would it be correct of me to say that they represent the abundance of a protein present in the synaptosome?
Any insights are appreciated.


text:
How many photons does a GFP molecule absorb per second?
I'm trying to calculate how many photons will a GFP emit per second. The calculation seem easy just multiply the number of absorbed photons by the quantum yield. But how can I obtain the number of absorbed photons?
I know this would be directly related to the absorbance of the protein and the light intensity.
Is there an equation that relates both parameters to obtain the number of photons absorbed?
GFP absorbance at 488 nm:
$A_{488}=5.6\times10^4M^{-1}cm^{-1}$.

This paper is behind a paywall, but the supplementary material is available for free. In the last paragraph of page S-3 they seem to be calculating what you're after, referring to three different papers as their sources. Goes beyond my (bio-)physics knowledge to comment on the accuracy though.

Since the quantum yield isn't the main focus here, I'll just take the Wikipedia figure of 0.79 photons emitted / photons absorbed
The rest can be worked out from first principles.  The absorbance represents the number of log10 units by which light is reduced, but its units are designed to confuse:  5.6E4 (L/mol) / cm = 5.6E7 cm^3/mol / cm = 5.6E7 cm^2/mol GFP.*  This represents the area you can paint with 1 mol of GFP to reduce light passing through by 90%.  But let's substitute the value of a mole, to get 9.3E-17 cm^2 = 0.93 A^2 per GFP.  That chromophore casts a nice little shadow.
But our units aren't giving us photons - why not?  Well, the absorbance and fluorescence is proportional to the illumination.  So we need some notion of the amount of light, preferably something like irradiance (W/m^2).  The first figure I saw on a search was about 300 kW/m^2; you'll need to decide on your own.  So take 9.3E-21 m^2 * 300 kW/m^2 = 2.8E-15 W absorbed per GFP assuming this 90% absorption level.**
Now we still have to figure out the joules per photon.  The frequency of this light is (3.0E8 m/s)/488 nm = 6.1E14 / s = 610 THz (hmm, maybe a little more cyan than green).  We take that times Planck's constant = 6.63E-34 Js and get 4E-19 J/photon.  Divide 2.8E-15 (J/s)/GFP by that and we have 7000 photons per second passing through GFP, of which we're supposing 90% are absorbed.   And then I have to also multiply by 0.79  quantum efficiency.  Taking those together it is approximately 5000 photons
I encourage you to rework this since there's some chance of foul-ups here, and remember to get your own numbers for the microscope irradiance.
*Remember absorbance is -log10(transmittance), so an absorption of 1 means 90% of the light is blocked.  So the 56,000 there indicates that 1 mole of GFP can cut the light by 90% ... 56,000 times over again.  Or we can divvy it up into 56,000 different square centimeters and reduce light in all of them by 90%.
** 90% of this will be absorbed at a painted surface, such as a slide.  In a cuvette the energy absorbed would be much less because most of the GFP is in shadow, while spreading the GFP out further would increase the photons absorbed a bit because the rear part of the 90% is still in shadow.  I think 90% absorption isn't tremendously unreasonable to use since people will try to arrange for as bright a signal as they reasonably can, which may be localized to small features on a slide; but for example absorbing 68% of photons (reducing transmittance by the square root of 10 with an absorbance of 0.5) would cover twice the area, collecting 36% more photons total.  The limit at 0% would be ln(10) = 2.3 times higher than the figure at 90% absorption, but you can't see GFP if it's spread out to 0% absorption.

Hi @Mike_Serfas I think you nailed it. Just as a favor to people that will read this in the future could you please explain in more detail the way you get the per molecule absorption (specially how you go from absorbance to area). Also could you change the format so the equations are displayed in a diferent row?

@BPinto - thanks for making me look at this again.  Spreading out the GFP more varies the amount of light absorbed by more than I was thinking, though I should have known, because at 90% much of it is in shadow.  I'm not sure it's wrong to assume 90%, but there's no two sigfigs to be had here.  As for the equations ... well, I don't enjoy trying to code those formats when the text-based version seems so practical.


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How can you diagnose albinism in a naturally light-colored person?
Not all albinos have white hair. There is a type of albinism where the affected person has light yellow hair and the skin color can be the same as a normal North European person.
How can you diagnose this type of albinism in a person who would naturally have very light blonde hair and pale skin, even if they didn't have albinism?
I mean, Boris Johnson isn't an albino, but there are albinos who have exactly the same hair and skin color as him.

Welcome to the site. What research have you done on your own to answer this question? The Biology.SE community has agreed that questions that show little or no prior research effort are off-topic on this site unless you have shown your attempt at an answer. Please [edit] your question and tell us where you've looked for answers, what you do know about the topic, and where exactly you still have questions. Our goal is not simply to be an answer site, but rather a site that promotes self-learning with some expert help along the way.

Short answer
Due to the considerable phenotypic overlap of different types of Oculocutaneous Albinism (OCA), molecular testing using a multigene panel or comprehensive genome sequencing is generally preferred for a precise diagnosis and is available for most types of OCA.
Using family tree combined with a clinical assessment can get you close. But a targeted sequencing panel looking for mutations in known genes that cause albinism would be the best way to do this.
More Info
Melanin, a black or brown pigment formed from tyrosine, is responsible for the color of skin and hair. Melanin is synthesized in melanocytes, which are specialized, dendritic secretory cells derived from the neural crest. These cells migrate to the basal layer of the epidermis during embryogenesis. The presence of melanin in the epidermis helps provide protection from ultraviolet radiation.
Disorders include decreased and excessive pigmentation.
Oculocutaneous albinism is a group of rare disorders caused by various gene mutations, but the most well known is the gene encoding tyrosinase, which catalyzes several steps in the production of melanin. Obviously in OCA, you'll have less melanin and this gives people with the disease the characteristic depigmented appearance. The disease is inherited in an autosomal recessive pattern (so both parents must have at least one of the mutated alleles).
Source: "UpToDate.com"

Typically the eyes are affected.
"Oculocutaneous" albinism affects both eyes and skin.  On this page the effects on iris and retina/choroid are illustrated.  While I could find a type of albinism in OMIM for which "Nystagmus, photophobia, and marked visual defect were not features", that entry still describes depigmented irides.  I have a hard time picturing a variation in which the eyes would have full pigmentation throughout, which would not be described as a skin color variation.  (That doesn't mean there isn't one!)

You could either look at the family history and see if there were any individuals with albinism or contact a gene counsellor. Here is an extract from the healthline website: "The most accurate way to diagnose albinism is through genetic testing to detect defective genes related to albinism." (https://www.healthline.com/health/albinism#symptoms)
I hope this helps!


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Why do the phosphatidylserine and Phosphatidylethanolamine favor one side of the cell membrane?
Thie picture below shows that the phospholipids phosphatidylserine (PS) and Phosphatidylethanolamine (PE) are more likely to be found on the inside of cell membranes than on their exterior.

Why is this so? What prevents them from creating a shape that is wave-like (illustrated) or some other shape?

Welcome to SE Biology. I have edited your question slightly, especially to define abbreviations. Please finish reading the [Tour] as it will help you understand how this site operates.

I’m not sure if this would help answer your question, but in living organisms the lipid composition of each membrane leaflet is highly regulated. A flippase translocates PS and PE to the cytoplasmic side of the membrane.

There seem to be two questions here.
The poster seem to know the answer to the first question — that in the title — that their shape fits into one or other side of a curved membrane. So I would recommend the title be edited to address what appears to be the main concern.
Instead of “Why do these phospholipids insert into one side of an already spheroidal cell membrane?” the concern appears to be the effect of the insertion on the shape of the membrane: “Why doesn’t the insertion of these phospholipids cause a wave (ruffled rug) shape, rather than a spheroid?”
If this is, indeed, the question then the answer would be that the ‘empty spheroidal’ shape of cell membranes is determined by other forces, principally thermodynamics. The main one is that which causes a lipid bilayer in the first place — the polar head being oriented to the aqueous environment, whereas the hydrophobic tails are in contact with one another. This still leaves hydrophobic “edges” to any membrane sheet, which therefore fuse into a hollow spheroid to remove them from contact with water.
So, although I am not a cell biologist, I would hazard that the wedge-shaped phospholipids help relieve bending stresses in a membrane that has already adopted a spheroidal shape for thermodynamic reasons.


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Zayed et al. (2022) "Cryptic and abundant marine viruses at the evolutionary origins of Earth’s RNA virome"; expressed sequences or transcribed?
Phys.org's Ocean water samples yield treasure trove of RNA virus data summarizes Zayed et al. (April 7, 2022) in Science Cryptic and abundant marine viruses at the evolutionary origins of Earth’s RNA virome.
The Phys.org summary includes the following paragraph:

In these current efforts to detect RNA viruses, there were no viral particles to study. Instead, researchers extracted sequences from genes expressed in organisms floating in the sea, and narrowed the analysis to RNA sequences that contained a signature gene, called RdRp, which has evolved for billions of years in RNA viruses, and is absent from other viruses or cells.

When I hear expression I think of a polypeptide final product, although it is certainly a multistep process. My understanding is that the data analyzed by Zayed et al. were RNA sequences extracted from the seawater, and not protein.
I'm thinking that "transcribed" or perhaps just "present" should have been used (depending on the details of the methodology) instead of "expressed" but I'm not sure of that at all. Wikipedia's Orthornavirae describes the transcription so I know that one does not have to start with DNA to invoke the term transcription:

The RdRp is used to transcribe the viral RNA genome into messenger RNA (mRNA) and to replicate the genome

This is the extent of my understanding here, so I'd like to ask:
Question: In Zayed et al. (2022) "Cryptic and abundant marine viruses at the evolutionary origins of Earth’s RNA virome" did the study look at "expressed" sequences, or "transcribed", or both, or neither?

Related:

In marine DNA viral diversity studies, what would "paradigm of rampant mosaicism" refer to? (2019)

Pardon me for not specifically answering with regard to marine viruses; I think the crux of an answer depends on addressing your misconception!

expressed sequences or transcribed?

This is semantics, and important semantics to be familiarized with in biology research.
The word expression is not the most strictly defined word, and is used differently and in a context-dependent fashion. For example, in such research as you point to, one often studies gene expression by looking at the transcriptome independently, to "gauge which genes are expressed", without assurance of translation of said RNA into protein, nor assurance of localization, or function, or even maintenance of said protein. The life history of every protein certainly goes beyond the central dogma of molecular biology, and many simplify the picture into only gene transcription and translation, but these are just proxies (or rather stages) of gene expression. Translation itself is no guarantee of final function (i.e. points or stages at which it may be easy to quantitatively measure expression, which can only be indicative).
Expression is most often associated with the process of active use of a gene, of it being 'put into play'. This is unfortunately complicated by the fact that being 'put into play' requires passage through a lot of hoops. It is NOT synonymous with transcription, or a gene that crosses the transcription + translation hurdle.
Real life use
Colloquially, you can say a gene will be expressed when a signal reaches the nucleus that will put a cascade of transcription factors into motion that will eventually assemble transcriptional machinery to transcribe a gene. Hormones can 'cause' gene expression. Alternatively, you can say expression can occur when ribosomes are unblocked or assembled, or post-transcriptional silencing machinery is lifted to re-allow translation of specific mRNA strands. Yet further, a gene is clearly not 'expressed' if the protein is non-existent, and this can come about through improper folding or swift removal or mislocalization, and so on. There are many contexts in which you can use this flexible word, and it always has a connotation of gene information flow, rather than a mechanism which is responsible for gene information flow. Today, the word expression is often used more frequently on the transcriptional side of things, where we have an easier time using robust and longer-established techniques (e.g. RNA-seq) and talking about results than on the protein translational side of things, which require further insights into post-translational modifications, trafficking, integration into membranes, protein folding chemistry, export, all that jazz. However, do not forget that proper insulin gene expression really ultimately means that the resultant protein-hormone insulin is in active circulation in the body... and NOT that insulin-coding mRNAs are present abundantly in the cytoplasm of beta cells of the pancreas.
Take-home lesson: remember, the central dogma (DNA->RNA->protein) is an organizing concept, and many words refer to it, but these same words may not be comprehensive or technical or stringent enough to describe particular events, only our conceptualization of them.
tl;dr
Transcription is a specific term (copy-reading of DNA into mRNA strands) while expression is a conceptual term (which points to but does not completely encompass information flow from DNA into protein, eventually)

"Transcription is a specific term (copy-reading of DNA into mRNA strands)..." and yet in my question I cite Wikipedia's Orthornavirae: "The RdRp is used to transcribe the viral RNA genome into messenger RNA (mRNA)" so does the misconception belong to the Wikipedia article's authors? It looks like you're contradicting that by invoking "copy-reading of DNA" as a necessary part of transcription and saying that without DNA the word "transcription" should not be used.

@uhoh Transcription of DNA is not defined in terms of the functionality of the product of the process — only that it is RNA.  Whether or not your quotation from the anonymous author of the unedited Wikipedia article correctly reflects its intent, it is plain wrong as a general definition. Transcription of DNA is the production of the RNA complement of a section of DNA. Note that I avoid the word “copy” in my definition as it does not correspond to normal English use. I avoid mRNA because tRNA rRNA, etc. are also transcription products, as well as pre-mRNA.

@David Thanks. The purpose of my first comment is only as follows: the answer begins by addressing me personally; "I think the crux of an answer depends on addressing your misconception!" I am simply pointing out that it's not my conception, it's what I found reading as part of adding some research to a question. So the answer should start by finding fault in the sources I've cited rather than going after me personally.

@David Also, answers should address "expression" in the context of the linked paper in Science (and as far as I can tell, this answer doesn't address this conclusively). I hope to have my hands on it later this morning, but like the Cell paper cited in my earlier question that you so aptly answered, I am not sure I will be able to understand the present paper to the extent necessary to say for sure if "expression" in this context applies or not.


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Nature of firefly Luciferase reaction mechanism?
The bioluminescence of the firefly luceferin (FL) is a two step process, with the first step requiring the enzymatic/catalytic ability of the luciferase to convert the FL into  luciferyl adenylate.
Are there any descriptions for the mechanism in which the Luciferase facilitates the reaction of ATP with the firefly luciferin?

I answered a similar question of yours about aequorin, initially explaining how to go about finding the information and subsequently explaining in some detail aspects of the enzyme mechanism. Perhaps you didn't see my expanded answer, but until you respond to that (accepting it if it answers your question) I have no way of knowing whether that type of answer is what is required.  I described how to go about finding literature on enzyme mechanisms. What are the results of your efforts to do that in this case?


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Is raw meat or raw vegetables easier for humans to digest?
Which one is easier for a human digestive system to digest, raw meat or raw vegetables?
I have heard some of my friends who say that raw (or uncooked) meat is easier to digest than raw (or uncooked) vegetables.
It initially sounds absurd to me but then they back their argument with something more logical like, "raw vegetables have cells surrounded by rigid cell walls made primarily out of cellulose which are hard to break by the digestive enzymes".
Are they correct?
Anyway, for simplicity, let's assume on a fine day, a healthy adult eats 50g of raw beef and on another fine day she eats 50g of raw broccoli. Which of the two will she digest faster, provided she didn't eat anything else apart from these foods on those particular days.
My Own Investigation  I tried googling a lot but couldn't find anything that explicitly or even implicitly address my question. Most of the sites (like this one) address "raw food vs cooked food" type questions. However, all of a sudden, I remembered something that I studied almost two years back in my secondary school, class 10th science textbook. I quote the paragraph here,

Access the full chapter here (NCERT Class 10th Science Textbook) and check out 7th line (from top) of the 8th page.
This source further support their (my friends') claim in some manner.

Please clarify what you mean by "easier." Easier as in more mass breakdown, greater absorbing of nutrients, less indigestion,...?

also which vegetable,  all meat is more or less the the same but vegetable covers a huge range of tissue compositions. also almost all herbivores can digest meat, they have to be able to to reabsorb their own dead cells.

it will be wrong to compare human digestion with animals that eat grass(cellulose)and it is not very helpful to compare human digestion with other animals that eat the same diet as us.

@theforestecologist by easier I mean, which one (of equal mass) of the two undergo faster breakdown. And as far as vegetables are concerned, considered a typical mixture of green vegetables that we eat, e.g. cauliflower, cabbage, lettuce, broccoli, etc.

@GauravKumar You should focus on one vegetable. Knowing how well a mix of random vegetables will digest is basically impossible. Maybe stick to comparing broccoli and beef, for example.

@user438383 fine, let's stick to beef and broccoli!


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Mass spectrometry: What is meant by the 'most intense peptide ions' in data dependent acquisition (DDA) mode?
I am learning about data dependent acquisition (DDA) mode in mass spectrometry from this online resource. I have come across the following statement:
In DDA mode, the mass spectrometer selects the most intense peptide ions in a first stage of tandem mass spectrometry, and then they are fragmented and analyzed in a second stage of tandem mass spectrometry.
I am not sure what is meant by the "most intense peptide ions". Does most intense refer to the most abundant peptide ions? Any insights are appreciated.

I don't have a source at the moment (and hence a comment instead of an answer), but I would imagine the authors of that resource are referring to the most intense peptide ion m/z (mass/charge ratio) signal as measured by area under the curve (AUC). The software picks the largest peak(s) and targets them for further analysis during the second mass spec run. This can also be done manually.


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What is the function of dihydrofolate reductase in humans?
According to StatPearls, synthetic folic acid — as an artificial dietary supplement — needs to be converted into the active form tetrahydrofolate (THF) by dihydrofolate reductase.

In the cells, folic acid is reduced to THF, a biologically active
form, in a two-step process that requires two molecules of NADPH and
the enzyme dihydrofolate reductase (DHFR).

But naturally occurring folates — as natural constituents of the diet or derived from intestinal flora — are derivatives of tetrahydrofolate, (the active form), so the human body doesn’t need to convert them using dihydrofolate reductase.
If this is the case, why do humans have the enzyme dihydrofolate reductase?

Welcome to SE Biology. We find it useful if posters can support their suppositions (in this case "from what I understand") by sources, either text books or online articles. Then we can check if they have perhaps misinterpreted them. Second, we expect posters to show a little research. Have you checked what readily available web sources such as Wikipedia say about DHFR? Also notice that @user438383 has kindly corrected your spelling. However you can do that yourself by writing out your question in a word processor and switching the language preference to English.

I have now cited a source and clarified your question, which initially I had difficulty in understanding. Let me know if I have changed your meaning in any way.

Thank you @David, that's exactly what I meant. English is not my native language.

The poster’s assumption that the sole role of dihydrofolate reductase (DHFR) is to convert folic acid to tetrahydrofolate is incorrect. The enzyme is important in at least two metabolic pathways in mammals — the degradation of phenylalanine and the synthesis of thymidine.
Phenylalanine degradation
The degradation of phenylalanine to tyrosine requires tetrahydrobiopterin:

Tetrahydrobiopterin is synthesized de novo in mammals, the last stage being the reduction of dihydrobiopterin catalysed by dihydrofolate reductase:

[Sources: Berg et al. Biochemistry 5e (2002) Ch.28]
Thymidylate synthesis
Thymidine triphosphate (dTPP) is an essential DNA precursor, and is derived from thymidylate (dTMP). This latter is formed by the methylation of dUMP using N5,N10-methylenetetrahydrofolate, which itself is converted to dihydrofolate. This must be reduced to tetrahydrofolate in a reaction catalysed by dihydrofolate reductase in order to regenerate the methylenetetrahydrofolate:

[Source: Berg et al. Biochemistry 5e (2002) Ch.25]

IMO, the accepted literature position is that DHFR plays no role in the de novo synthesis of tetrahydrobiopterin (BH4), which is synthesized from GTP, where the final step (reduction of side-chain carbonyl groups) or steps is catalysed by sepiapterin reductase.  De Novo synthesis of BH4 is insensitive to methotrexate, for example. DHFR does participate in a 'salvage' pathway for BH4 biosynthesis, which allows pteridines such as sepiapterin to be converted to BH4 (sepiapterin is not thought to be an intermediate in BH4 biosyn)

Biosynthesis and metabolism of tetrahydrobiopterin and molybdopterin

Biosynthesis of tetrahydrobiopterin in the presence of dihydrofolate reductase inhibitors

*** Biosynthesis of tetrahydrobiopterin by de novo and salvage pathways in adrenal medulla extracts, mammalian cell cultures, and rat brain in vivo


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Reptile identification - Is this a green iguana?
At first instance it looks like an iguana and since this photo was taken near the coast of Pernambuco, Brazil it could only be the green iguana, but as you can see from the photo the reptile is black. Perhaps green iguanas can be black under strict circumstances, but I could not find any instances concerning that from a reputable source, only from some dubious pet blogs and it was due to the lighting, temperature and overall cage conditions. It's worth noting that there were multiple animals and they were all black. In response to tyersome comment, the picture was taken in summer so I'm gonna assume it was hot at the time, regarding the size it seems to have almost 2 meters. This has to definitely be from the Iguanidae family and it appears to share similarities with the green iguana but the color is off.

Welcome to Biology.SE. You've done a good job of providing information, but it would be helpful if you could add: 1) an estimate of the iguana's size; and 2) as much environmental, habitat and behavioral information you can. In particular, was it cool/cold when the picture was taken?

Okay thanks for the heads up. I've updated the post. Also added another photo that I've found.

Could be a hybrid or simply a melanistic green iguana.

Never heard of this melanistic phenomenon before, very interesting. That might be it, many thanks.


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Insect Identification please
Location Kothrud, Pune
This was found on Sonchafa plant.

About a centimetre wide in the middle?

It could be a Yellow-spotted stink bug Erthesina fullo
https://www.padil.gov.au/pests-and-diseases/pest/main/136074/772

EDIT:
more frequently found in India is Erthesina acuminata
http://insecta.pro/taxonomy/1037721
For more information, read the excellent answer on this question:
Can anyone identify this grey spotted insect -- is it a tree bug species?


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What's the best way to purify my His tagged protein? Supernatant super viscous after first sonication?
I am trying to purify my his-tagged protein of interest, disulfide isomerase. It is about 40kDa and is cloned in pET28a vector, at XholI and NdelI, and expressed in BL21.
I'm having issues with my protein purification.
My current protocol:

1L culture incubated at 37°C for 6 hours until OD600 reaches 1.5-2.0.
IPTG is added to a final concentration of 1mM and is then further incubated for another 3-4 hours until OD600 reaches 2.2-2.7.
I then lyse the cells using 1X binding buffer with 1X Protease inhibitor, no urea, 0.1mg/ml lysozyme, and DNase1.
solubilize/sonicate with 1X binding buffer WITH 8M urea and 1X protease inhibitor.
purify my protein by doing affinity chromatography using a nickel column with 1mL of Ni-Nta resin.
I washed twice with 1XBB with 8M urea, 15-20mM imidazole, and 1X protease inhibitor.
elute with 1XBB with 8M urea, 250mM imidazole, and 1X protease inhibitor.

During the solubilization step, I sonicate twice. After my first sonication and spinning down in the centrifuge for about 30min, my supernatant comes out super viscous and when I run it through my ni-nta column, it ends up clogging it and causing it to run super slow (1 drip = 5min). What can I do to fix this issue?
Should I try using 6M urea instead of 8M? Would that help with the viscosity?
Also, my elutions come out really dirty still with a lot of contaminant protein. How can I clean up my elutions?
My protocol for my wash calls for protease inhibitor, but I feel like that's a bit wasteful. Can I wash without using protease inhibitor first and then do another wash with the protease inhibitor? Or should I be using protease inhibitors in every wash?

Do you have DNAse in your buffers? This is most likely the chromosomal DNA which is causing problems here. Depending on how harsh you sonicate it should break down, but if you sonicate short and with low energy this must not happen.

It sounds like your protein is expressed in inclusion bodies. If that is the case, you shouldn’t need to worry about chromosomal DNA since it is rather trivial to wash away before solubilization. Be sure to centrifuge and filter your sample before applying it to the column to remove any insoluble debris.

As Chris said in the comments, make sure you have sufficient DNase in your lysis buffer. That combined with good sonication will definitely shear nucleic acids and make your solution less viscous. If you don't feel the lysate starting to warm up when you're sonicating, you might want to increase the power. To that end, keep the lysate on ice while sonicating so the heat doesn't denature your protein of interest irreversibly.
You may also want to increase the amount of lysis buffer you're using to dilute everything a little bit, as you'll be concentrating and eluting it later. Sometimes lysates can be so thick that even harsh sonication won't completely eliminate it, and you run the risk of damaging your protein.
As far as the dirty eluate is concerned, a couple tips. First, after binding, make sure you wash the column extensively before eluting. You may find with experience that washing with a little bit of imidazole helps clean up non-specific binding as well. If you have one available, use an automated fraction collector (or even collect small fractions by hand) instead of doing a bulk elution. This way you can test each fraction separately and get rid of the ones with the most contamination and least specific product. Keep in mind that very concentrated samples, even if they are quite pure, will look dirty if you load too much protein on the gel, so keep a protein quantitation kit that's compatible with your buffers handy.
Another option to doing a bulk, single-concentration imidazole elution (say, at 250 mM like you're doing currently) is to do what's called a gradient elution. Say you're using a 10 ml column. After washing with 10-20 column-volumes (CV), start eluting with 10 ml of perhaps 50 mM imidazole, let it run out (but not totally dry), then add 10 ml of 100 mM, and so on. This is obviously much easier if you have an FPLC or similar setup, but it can be done reproducibly by hand if you're careful. Collect 5 ml fractions, and test them individually before pooling the good ones.
Protease inhibitors aren't strictly necessary in the wash, but I'd include them at least in the first wash, as that's when proteases are most likely to be non-specifically associated with your column beads and acting on any available substrates. Keeping everything cold is helpful, as well.

I've done an awful lot of protein purification both in academic and industrial labs, with a lot of different types of equipment, so if you need more info just let me know.

I was told to try to use 6M Urea instead of 8M urea to help with the viscosity, but I'm not too sure about that. Should I change the urea to 6M? would it make a big difference? I don't want to do anything to ruin my chances of getting a lot of protein. Should I just stick with the 8M and use more DNase in my lysis buffer to see if it works before changing to 6M urea?

@Yoshokie I don't know if dropping the urea from 8M to 6M will make a huge difference. Sonicating more would be my first troubleshooting step - as long as you keep the lysate cool (i.e., not too hot to touch), you can't really denature it any more than you're already doing with the detergent (I'm assuming) in your lysis buffer and the urea, which is a chaotropic agent. Urea won't cleave DNA, no matter how much or little you have, so sonication and good quality DNase are your best bets.

Agree with all of the above. I have found benzonase a very good alternative to DNase. It is robust but it will lose activity in Urea above 7M. The added benefit of it removing DNA and RNA is improved solubility of most proteins. It is very stable so a small contamination in your final preparation may cause problems if you're wanting the protein to bind DNA or RNA.

@Michael_A that's actually one thing I didn't think of - the urea could be interfering with the DNase's activity. Another reason to reduce it...