Do chromosomes change with time?

Do chromosomes change with time?

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An offspring is 23 chromosomes of mother and 23 of father, if one of the mate learns say music after the birth of their first child- will their second offspring have better music skills than former? about my knowledge of biology, so far I read about DNA, Genome, chromosomes and genetic engineering, I am an engineer by profession.

Short Answer: Probably, at least a little, much research still needs to be done. For a great paper on this see here.

Your question can be answered in two parts:

  1. Can Epigenetics be inherited - The answer to the simple question in your title, do chromosomes change with time, is yes. There are copying errors, and carcinogenic mutations that can permanently change cells' genomes. Less permanent is epigenetics, which are temporary chemical modifications to the DNA which changes how it is expressed. The epigenetics of the cell may change for various reasons from the cell undergoing mitosis to a wildly changing diet. However, when sperm and egg cells are formed these epigentic modifications are typically wiped from the genome in order to remove any possible damaging marks. However, there is a growing body of literature which states that some marks escape the purge and change the characteristics of the progeny. Studies include scare-treating mice, 1836 famine, fatty rats, human psychological changes. While the exact genes causing the change is unknown, there is clearly a strong correlation

  2. Can Music Skill be Captured in Epigenetics - Music skill is to difficult to measure biologically, but likely has some links in speech skills, which would be captured in the brain, and muscle skills. While there is some evidence for there being an muscle epi-memory, brain epigenetic inheritance is more tenuous (although see this exciting paper on RNA causing memory changes through epigenetics). I would say the general scientific consensus is that there is some relation between epigentics, and memory, and music skill - there is a great deal of work still to be done.

Until recently, the answer to your question would have been a definitive "no", because is smacks of the rejected Larmarckian ideas of the inheritance of acquired characteristics. And the example you provided, about musical skills, that would be "no" as well from a genetic perspective, although the hearing of music around the house may have cultural impacts on the second child. However the new field of epigenetics has revealed that DNA methylation, over the course of ones life can influence offspring of future generations. There was a community in Sweden that took very detailed health records over generations. The effects of a famine in 1836 showed up in the grandchildren of the survivors. It is further explained here:

Click here to order our latest book, A Handy Guide to Ancestry and Relationship DNA Tests

I'm doing research for a book and I have a question regarding sex and gender. One of the biggest issues facing the LGBTQ today is transgender discrimination. Many people of course are arguing there are only just two genders (i.e. sexes) male and female. But in doing research, there seem to be more combinations at least at the DNA level. Instead of just XX and XY, there can be XXX, XXY, and X and many others besides.

Does this have to do with being transgender? From a genetic perspective, are there more sexes than male and female, or is everything else just classified as a disorder?

-A graduate student from Wisconsin

What a great question! Yes, there are some genetic conditions that can make someone not clearly fit into the category of “male” or “female”.

There are people who have differences in their sex chromosomes, or the X’s and Y’s you are talking about. There are also people who are intersex, with bodies that don’t fit typical definitions of male and female.

However, being transgender does not mean someone has one of these differences. Being transgender has to do with how a person feels about their gender.

So what does all that mean exactly? Let’s dig deeper into what being transgender is, what sex chromosome conditions there are, and what being intersex is.

Being Transgender Is…

There are many things that make someone a “boy” and someone a “girl”. Before babies are born, many events happen to determine if they are a boy or a girl. One of these is brain development which is still not fully understood.

At birth, doctors look at the outside of our bodies to see if we are a boy or a girl, but determining our gender is much more complicated than that. A lot of the time, when someone physically looks like a boy, they also feel like they are a boy in their brains and hearts. Similarly, many people who have the body of a girl, feel like they are a girl in their brains and hearts. People whose feelings about their gender matches their bodies are cisgender.

However, sometimes our bodies do not match how we feel about our gender. Some people who physically look like boys may feel like they are girls. Some people who look physically like girls may feel that they are boys. These people are transgender, where they have feelings about their gender that do not match their body.

About 1 in 200 people identifies as transgender in the United States. That is 1.4 million people just here in America! There are no tests that can be done to know if someone is transgender - the only way to know is from the person telling you.

If someone does not feel like they are a boy or a girl, but something in between, they may identify as non-binary, gender non-conforming, or genderqueer. These are just some of the possibilities. Transgender people and non-binary people, just like anyone else, deserve respect, and for people to respect what gender they identify as.

Sex Chromosomes and Genetics

Chromosomes are the instruction manuals of our body, and help determine things like our hair color, eye color, and body parts. Some chromosomes are called sex chromosomes which help to determine whether someone has the reproductive body parts of a boy or a girl.

Usually, someone who has female body parts has two X chromosomes, and someone who has male body parts has an X and a Y chromosome. Sometimes, this is not the case.

There are some people who have differences in their sex chromosomes. For example, some people may have XXY, and some people may have one X or three X’s. These are genetic conditions, which means sometimes having these chromosome differences can result in medical complications.

Typically, if someone has a Y chromosome, no matter how many X’s or Y’s, they have the body parts of a boy. If someone doesn’t have a Y chromosome, they have the body parts of a girl. About 1 in 1,600 people may have one of these sex chromosome differences.

Now this is important: having differences in sex chromosomes doesn’t mean that someone is transgender. Because remember, being transgender has more to do with how someone feels.

Certainly there are people who have differences in their sex chromosomes who are transgender, just as there are people who do not have these differences and are transgender. Research does not suggest that people who have these differences are more likely to be transgender.

Being Intersex Is…

Now, there are other genetic conditions that have to do with people’s gender that don’t involve extra or missing X’s and Y’s. There are genetic conditions that cause people to be intersex.

Instead of having whole extra or missing chromosomes like with the sex chromosome conditions, many people who are intersex have specific changes in one of their genes.

As I said before, chromosomes are the instruction manuals of our body. Individual instructions are called genes. Each chromosome has hundreds and hundreds of genes.

Intersex conditions happen when a specific gene is different from what is typical. That difference changes how the gene works.

In some cases, when someone who is intersex is born, the doctors are unsure of if they physically look like a boy or a girl. In other cases, people who are intersex may have the body parts of a boy or a girl at birth, but may go through puberty differently, and find out they are intersex around puberty.

Often people who are intersex need medical treatments so that they can go through puberty or for other reasons. About 1 in 100 people is intersex. This is about 3.8 million people in the United States!

Again, this is important to note: being intersex is different from being transgender. People who are intersex have bodies that are physically different than we would usually expect with a girl or a boy.

Being transgender has to do with how someone feels about their gender. There are some studies that suggest that some people who are intersex may be more likely to be transgender. This depends a lot on the genetic condition.

Some people who are intersex have treatments because they would like their bodies to look more similar to a typical boy or girl, but some people do not and are happy with the bodies they were born with. That decision is up to them and their families. Some people who are transgender decide to have treatments to make their bodies look more like the gender they identify, but sometimes they choose not to.

Regardless of what people choose, it is important to respect these people and their decisions, and to use whatever names and pronouns (like he, she, or they) that they prefer.

So yes, there are people who have different sex chromosomes than just XX and XY. There are also people who have smaller genetic changes that make them intersex.

Both the sex chromosome differences and being intersex affects how someone’s body is working physically. However, neither of these things necessarily means these people are transgender, since being transgender has to do with how someone feels about their gender.

What Role Do Sex Chromosomes Play In Transgender People's Identities?

What role do sex chromosomes play in the identities of transgender people? originally appeared on Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world.

Answer by Sai Janani Ganesan, Postdoctoral Scholar at UCSF, on Quora:

Biological gender and gender identity are two very distinct concepts. Biological gender or sex refers to the anatomy and physiology of a human body, whereas gender identity is influenced by a multitude of factors, most of which we don’t fully understand.

Biological sex is purely determined by the choice of sexual differentiation pathway, which is guided by genes on the sex chromosomes (though not exclusively, for example: WNT4 on chromosome 1). Testis-determining factor (TDF) or sex determining gene Y (SRY) located on the Y chromosome is one such gene. SRY is largely responsible for testis formation. It is not the only gene, and a variety of pathways and proteins are involved in this process of sex differentiation, some even located in the autosomal regions, but SRY is… special.

The sex determining gene Y (SRY) was identified in the 1980s by Peter Goodfellow’s group [2]. Goodfellow’s group and others performed a series of experiments to demonstrate the role of the gene. In one such study, they looked at the genetic information of individuals who were anatomically female and had both XY chromosomes, and individuals who were anatomically male with XX chromosomes [3][4]. They found the SRY gene in an X chromosome in fifty cases of anatomically male with XX chromosomes. In one of the anatomically female case with XY chromosomes, they found a single nucleotide mutation in the SRY gene, that translated to a single amino acid change (from methionine to isoleucine), thus disrupting the testes development process. A single amino acid change from methionine to isoleucine in the SRY gene can cause an embryo with XY sex chromosomes to develop as a female. It is not difficult to imagine that such de novo mutations can also play a role in gender identity. In another study in 1991, they were able to transform female mice embryo to male (anatomically and behaviorally) by simply inserting one single SRY gene [5].

Gender identity is very poorly understood. But based on a number of studies from the popular case of David Reimer [who had gender reassignment surgery as a child and was brought up as a female after a botched circumcision and transitioned to a male at age 15], to multiple reports on genetically male (with XY chromosomes) and anatomically female who were brought up as female and later transitioned to male [6], it is safe to conclude that gender identity is less about behavioral, cultural, or social circumstances or upbringing and more biological.

While there are a number of genetic, biochemical studies [7][8][9][10] on gender identity, we don’t fully understand the involvement of specific genes. However, it is likely that genes [which in turn code for proteins, enzymes, hormones etc.], more than any other factor play a role in transgender identity. Can some of these genes reside on X or Y chromosome?—Perhaps. In my opinion, looking for biological variables as arbiters of gender identity is not a great idea for society.

This question originally appeared on Quora - the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google+. More questions:

Quora: the place to gain and share knowledge, empowering people to learn from others and better understand the world.

Basics: How can chromosome numbers change?

There in the foaming welter of email constantly flooding my in-box was an actual, real, good, sincere question from someone who didn't understand how chromosome numbers could change over time — and he also asked with enough detail that I could actually see where his thinking was going awry. This is great! How could I not take time to answer?

How did life evolve from one (I suspect) chromosome to. 64 in horses, or whatever organism you want to pick. How is it possible for a sexually reproducing population of organisms to change chromosome numbers over time?

Firstly: there would have to be some benefit to the replication probability of the organisms which carry the chromosomes. I don't see how this would work. How is having more chromosomes of any extra benefit to an organism's replicative success? Yes, perhaps if those chromosomes were full of useful information. but the chances of that happening are non existent and fly in the face of 'small adaptations over time'.

Secondly, the extra chromosomes need to come from somewhere. I'm not sure about this, but I believe chromosome number are not determined by genes, are they? There isn't a set of genes which determines the number of chromosomes an organism has. So the number is fixed, determined by the sexually reproducing parents. Which leads me to believe that if the number does change, and by chance the organism is still alive and capable of sexual reproduction, that the number will start swinging back and forward, by 1 or 2, every generation, and never stabilising. The chances of this happening are also very very slim.

Let's clear up a few irrelevant misconceptions first. Life probably started with no chromosomes — early replicators would have been grab bags of metabolites, proteins, and RNA that would have simply sloppily split in two, with no real sorting. DNA and chromosomes evolved as accounting and archiving tools: they were a way to guarantee that each daughter cell in a division reliably received a copy of every gene. Also, most living things now just have one 'chromosome', a loop of DNA, and perhaps a small cloud of DNA fragments. So to keep this simple we're going to ignore all that, and consider only us diploid eukaryotes, where the question of chromosome numbers becomes a real issue.

Normally, I'd be scribbling madly on a whiteboard, so we'll have to make do with some scribbles on the computer screen. Here, for instance, is a typical cartoon chromosome. It's a string of DNA, and scattered along it we have sequences for genes, that I've labeled "A", "B", "C", "D", and "E". I've also drawn a circular blob in the middle: that's important. It's not a gene, it's a structure called the centromere, which gets all wrapped up in proteins to form a kinetochore. It's a sort of anchor point when the cell needs to move chromosomes around, as it does during cell division, it hitches motor proteins to the kinetochore and using drag lines called spindle fibers, tows it to a new destination.

I mentioned that this was a diploid organism — that just means that every chromosome comes in pairs. This cell would have a similar chromosome to the one that has the ABCDE genes on it here I've draw it as containing the same genes, but in slightly different forms: abcde. This matters because during meiosis, when gametes (sperm and egg) are formed, the two chromosomes line up with one another and the cell machinery tows one chromosome to one daughter cell, and the other to the other daughter cell. It's accounting it makes sure each daughter gets a copy of all of the genes, one A or one a, one B or one b, etc., for instance.

For now, put the fact that there are two copies of each chromosome at the back of your mind and don't worry about it. Let's think about a single chromosome and ask what can happen to it.

Here's something fairly common. An error in copying the DNA can lead to the loss of a piece of DNA. This happens with a low frequency, but it does happen — if we sequenced your DNA, we might well find a few bits missing here and there. We can get situations like this, where a whole gene gets lost.

Don't panic! Remember that we have two copies of every chromosome, so while this one is missing the "D" gene, there's that other chromosome floating around with a "d" gene. This is not necessarily bad for the individual, it just means he doesn't have a spare any more.

Another kind of error that can happen with a low frequency is a duplication, where the machinery of the cell accidentally repeats itself when copying, and you get an extra copy of a piece of a chromosome, like so:

This person has two copies of D on this chromosome now (and remember that other chromosome, with it's d gene — he actually has 3 copies in total now). This is not usually harmful: it gives the individual a little extra redundancy, and that's about it. It can change the total amount of the D gene product in the cell, and if it's a gene for which precise dosage is important, it can have visible effects…but in most cases, this is a neutral change.

You may have noticed that nothing has changed the chromosome numbers yet. Here's a situation that can lead to the formation of a new chromosome: what if there is a duplication of the centromere, rather than a gene?

Remember, I told you that the centromere/kinetochore is where the cell attaches lines and motors to haul the chromosome to the appropriate daughter cell. In this case, two lines are attached what if one tries to pull one centromere to the left, and the other tries to pull the other centromere to the right? Tug of war!

The end result is that the chromosome is broken into two chromosomes. I think this is a key concept that the questioner is missing: chromosome numbers really aren't significant at all! You don't need to add significant new information to create a new chromosome, and as I'll show you in a moment, a reduction in chromosome numbers does not represent a loss of genetic information. Chromosome are disorganized filing cabinets, nothing more we can shuffle genes around between them willy-nilly, and the cell mostly doesn't care. A fission event like the one described above basically does nothing but take one pile of genes and split them into two piles.

But there are some important effects. This may not be an entirely neutral situation. Let's bring back that abcde chromosome, and pair it up with our two new chromosomes, AB and CDE.

The accounting is accurate. This cell has two copies of the A gene, an "A" and an "a", just like normal, and the two new chromosomes can still pair up efficiently with the old chromosome in meiosis, just like before. This is a healthy, functioning, normal cell, except for one thing: if it goes through meiosis to make a sperm or egg, it's going to make a larger number of errors. There are three centromeres there, to be split into two daughter cells! Never mind what the Intelligent Design creationists tell you — the cell is really, really stupid, and it will more or less decide by eeny-meeny-miny-moe how to divvy up those chromosomes. If by chance the split is that one daughter gets AB + CDE, and the other gets abcde, both daughters have the full complement of genes and all is well. However, the split could also be that one daughter gets AB and nothing else, while the other gets CDE + abcde … and that's no good. One is missing a whole bunch of genes, and the other has an overdose of a bunch.

The net result is that although this individual is fine and healthy, a significant number of his or her gametes may carry serious chromosomal errors, which means they may have reduced fertility. They aren't sterile, though some of their gametes will have the full complement of genes, and can similarly produce new healthy individuals who will probably have fertility problems. (Note: the significance of those fertility problems will vary from species to species. Organisms that rely on producing massive numbers of progeny so that a few survive to adulthood would be hit hard by a change that cuts fecundity species that rely on producing a few progeny that we raise carefully to adulthood, like us, not so much. So you have to have sex 20 times to successfully produce a child instead of 5 times that won't usually be a handicap.)

So our two chromosome individual will have a reduced fertility as long as he or she is breeding with the normal one chromosome organisms, but those split chromosomes can continue to spread through the population. They are not certain to spread — they're more likely to eventually go extinct — but by chance alone there can be continued propagation of the two chromosome variant. Which leads to another misconception in the question: something doesn't have to provide a benefit to spread through a population! Chance alone can do it. We don't have to argue for a benefit of chromosome fission at all in order for it to happen.

So we can have a population with a low frequency of scattered chromosomal variants, some carrying the rare two chromosome variant and others the more common one chromosome form. What if two individuals carrying the two chromosome variant breed? They can produce offspring that look like this:

How many centromeres are there? Four, not three. This is a situation the cell machinery can handle reliably, and this individual will consistently produce good gametes that accurately carry AB + CDE, nothing more, nothing less, and will have no reduction in fertility. Now we have a potentially interesting situation: individuals with the one chromosome situation have full fertility when breeding with other individuals with one chromosome individuals with two chromosomes have full fertility when breeding with other individuals with two chromosomes it's when individuals with two different chromosome arrangements try to breed that fecundity is reduced. This is a situation where speciation is a possibility.

One last thing: what about reducing chromosome numbers? That's easy, too. Here's an organism with an AB chromosome, and a different chromosome with the genes MN on it. They can simply fuse in the region of the centromere.

This happens with a low frequency, too, and has been observed many times (hint: look up Robertsonian fusions on the web.) I think the key issue to understand here is that chromosome number changes are typically going to represent nothing but reorganizations of the genes — the same genes are just being moved around to different filing cabinets. This has some consequences, of course — you increase the chances of losing some important file folders in the process, and making it more difficult to sort out important information — but it's not as drastic as some seem to think, and chromosome numbers can change dramatically with no obvious effect on the phenotype of the organism. These really are "small adaptations over time", or more accurately, "small changes over time", since there is no necessary presumption that these are adaptive at all.

I've discussed fusion events and how they relate to evolution before, and there's an interesting difference in context there, too. My prior article was a response to Casey Luskin, an ignorant creationist who used his misunderstanding of genetics to foolishly assert the existence of a major problem, and that's where we have a conflict: ignorance is not a problem, but stupidly using your ignorance to push invalid ideas is. This question in my mailbox is also ignorant — the fellow really doesn't understand the basics of genetics — but it's self-recognized ignorance that, in a good way, prompts him to ask a sincere question.

If you want to dig a little deeper, there are many ways genetic information can be rearranged on chromosomes, and this has opened the doors to some interesting evolutionary research. I've described how we can map the reshuffling of chunks of genetic information over time, a process called synteny mapping, which allows us to reconstruct ancestral chromosomes. A fish might have 42 chromosomes, and we might have 46, but we can still trace how the ancestral arrangement was scrambled in many different ways to generate the modern arrangements.


In anaphase, the paired chromosomes (sister chromatids) separate and begin moving to opposite ends (poles) of the cell. Spindle fibers not connected to chromatids lengthen and elongate the cell. At the end of anaphase, each pole contains a complete compilation of chromosomes. During anaphase, the following key changes occur:

  • The paired centromeres in each distinct chromosome begin to move apart.​
  • Once the paired sister chromatids separate from one another, each is considered a "full" chromosome. They are referred to as daughter chromosomes.​
  • Through the spindle apparatus, the daughter chromosomes move to the poles at opposite ends of the cell.​
  • The daughter chromosomes migrate centromere first and the kinetochore fibers become shorter as the chromosomes near a pole.​
  • In preparation for telophase, the two cell poles also move further apart during the course of anaphase. At the end of anaphase, each pole contains a complete compilation of chromosomes.

Quick Notes on Chromosomal Aberration | Cell Biology

Alteration in the structure of individual chro­mosome or chromosomal aberration may occur spontaneously or by induction. Such changes may result in quantitative alteration of genes or rearrangement of genes. The breakage and reunion of chromatid segments result in a number of abnormalities in the chromosome structure. Thus origin of structural changes is caused by breaks in the chromosome.

Any bro­ken end may unite with any other broken end, thus potentially resulting in new linkage arrange­ments. Depending upon the number of breaks, their locations, and the pattern in which broken ends join together, a wide variety of structural changes are possible (Fig. 12.1). The first cytological demonstration of chromosomal re­arrangement in plants was made in maize by B. McClintock.

2. Types of Chromosomal Aberration:

Four different kinds of structural changes of chromosome have been demonstrated (Fig. 12.2, Table-12.1):

(i) Deficiency (parts of chromosome lost or deleted),

(ii) Duplication (parts of chromo­some added or duplicated),

(iii) Inversion (sec­tions of chromosome detached and reunited in reverse order), and

(iv) Translocation (parts of chromosome detached and joined to non-homo­logous chromosome).

Of the various chromosomal aberrations, inversions and translocations only represent changes in position of chromosome segments of different sizes, the total chromosome mass remaining unchanged. All segments are present in the original dosage, but distributed in a new way, i.e. qualitative alterations.

In cases of dele­tions or deficiencies and duplications, quanti­tative alterations occur in the chromosome complement, with certain chromosome segments being lost or doubled.

Structural homozygotes are those in which alterations such as translocation or duplication occur in both the homologous chromosomes and as such termed as translocation homozygote or duplication homozygote. In cases, where only one chromosome of the pair is structurally altered, the term structural hybrid or hetero- zygote is used (Fig. 12.3).

3. Deficiency of Chromosomal Aberration:

Deficiency or deletion represents a loss in chromosomal material and was the first chromo­somal aberration indicated by genetic evidence. This evidence, presented by Bridges in 1971 in Drosophila melanogaster, showed a deletion of the X-chromosome that included the Bar locus.

Deficiency or deletion are of two types:

A single break near the end of a chromosome would be expected to result in a terminal deficiency

(ii) Intercalary deletion:

If two breaks occur, a section may be deleted and an intercalary deficiency is created.

Origin of intercalary deficiency is represented in Fig. 12.4. Terminal deficiency might seem less complicated and more likely to occur than those involving two breaks.

Heterozygous deficiencies during meiosis form a loop in a bivalent and it can be observed in the pachytene stage (Fig. 12.5).

Effect of Chromosomal Aberration:

Deficiencies have an effect on inheri­tance also. In presence of a deficiency, a reces­sive allele will behave like a dominant allele and this phenomenon is called pseudo dominance. This principle of pseudo dominance exhibited by deficiency heterozygotes has been utilized for location of genes on specific chromosomes in Drosophila.

Thus chromosome deficiencies have greatly facilitated the checking of linkage maps.

A somatic cell that has lost a small chromosome segment may live and produce other cells heterozygous like itself, each with deleted section of a chromosome. Phenotypic effects sometimes indicate which cells or portions of the body have descended from the originally deficient cell.

If the deficient cell is a gamete that is subsequently fertilized by a gamete carrying a non-deficient homologue, all cells of the resulting organism will carry the deficiency in the heterozygous condi­tion.

Recessive genes on the non-deficient chro­mosome in the region of deficiency may express themselves. Heterozygous deficiencies thus usu­ally decrease the general viability.

4. Duplication of Chromosomal Aberration:

Duplication represents additions of chromo­some parts. A chromosome segment is present in more than two copies.

Origin of Duplication of Chromosomal Aberration:

Duplication originates out of unequal crossing over (Fig. 12.6).

If duplication is present only on one of the two homologous chromosomes, at meiosis (i.e., pachytene) a characteristic loop is obtained (Fig. 12.7).

Effect of Duplication of Chromosomal Aberration:

The duplication was-critically exa­mined in the B (bar) locus of the X-chromosome of Drosophila. Barred eye is a character where eyes are narrower as compared to normal eye shape. This phenotypic character is due to duplication for a part of a chromosome. The Bar character is due to duplication in region 16A of X-chromo- some (Fig. 12.8).

Barred eye individuals (16A 16A) give rise to ultra-bar (16A 16A 16A) and normal wild type (16A) due to unequal crossing over (Fig. 12.9). Barred eyes have different phenotypes in homozygous bar and hetero­zygous ultra-bar individuals although in each case, number of 16A segments remains the same (Fig. 12.10). This was called position effect.

Types of Duplication of Chromosomal Aberration:

Duplication are of different types on the basis of position of duplicated segment (Fig. 12.11):

(i) Tandem duplication – adjacent region

(ii) Displaced homo-brachial duplication – at a displaced position of the same arm

(iii) Displaced heterobrachial duplication – on the different arm of the same chromo­some

(iv)Transposed duplication – on a different chromosome

(v) Reverse tandem duplication – duplicated segment found as a reverse repeat at adja­cent region.

5. Inversion of Chromosomal Aberration:

Inversion represents reverse gene order in the chromosome.

Inversions originate when parts of chromosome become detached, turn through 180°, and are reinserted in such a way that the genes are in reversed order (Fig. 12.12). Some inversions presumably result from entanglements of the threads during the meiotic prophase and from the chromosome breaks that occur at that time.

For example, a certain segment may be broken in two places, and the two breaks may be in close proximity because of a chance loop in the chromosome.

When they rejoin, the wrong ends may become connected. The part on one side of the loop connects with a broken end different from the one with which it was origi­nally connected. This leaves the other two bro­ken ends to become attached. The part within the loop thus becomes turned around and inverted.

Inversions may survive the meiotic process and segregate into viable gametes. Chromosome pairing is essential in the produc­tion of fertile gametes. The mechanism by which homologous chromosomes heterozygous for inversions accomplish such pairing in the meio­tic sequence is depicted in Figs. 12.13 and 12.15.

The products of crossing over and sub­sequent stages of meiosis are different for the two types of inversions.

Inversions can be of two types:

(i) Paracentric inversion and

Paracentric inversions are those inversions where inverted segments do not include centro­meres. On the other hand, in a pericentric inver­sion, inverted segment includes centromere.

Paracentric Inversion:

In paracentric inver­sion, a single crossover or an odd number of crossovers in inverted region results in the for­mation of a dicentric chromosome (having two centromeres) and an acentric .chromosome (with no centromere). Of the remaining two chromatids, one remains normal and the other carries the inversion.

The dicentric chromatid and the acentric chromatid are observed at anaphase I in the form of a bridge and a fragment (Fig. 12.14). Crossing over within and outside inversion lead to various kinds of deficiencies and duplications.

Pericentric Inversion:

In pericentric inver­sion, the pachytene configuration observed is similar to that of paracentric inversion. But the products of crossing over and configurations at subsequent stages of meiosis differ. Two of the four chromatids will have deficiencies and dupli­cations. No dicentric bridge or acentric fragment are formed (Fig. 12.15).

As the two chromatids resulting from cross­ing over have deficiencies and duplications, the gametes having these chromosomes do not function and lead to considerable gametic or zygotic lethality. The plants show pollen steri­lity. The only crossovers which can be recov­ered are double crossovers, and the observed frequency of recombination between any two genes is considerably reduced.

Thus inversions are called crossover suppressors. This property of inversion has been utilized in the production of CIB stock, used by Muller for detection of sex linked lethal mutations. Three different kinds of non-crossover progenies (1 : 2 : 1) are obtained by selfing of an inversion heterozygote (Fig. 12.16).

6. Translocation of Chromosomal Aberration:

Sometimes a part of a chromosome becomes detached and joins to a part of a non-homologous chromosome, thus producing translocation. Translocations have been described in a number of plants and are important factors in the evolu­tion of certain plant groups such as Datura and Oenothera.

Types of Translocation:

Three types of translocations are observed:

(i) Simple translocation:

The broken part gets attached to one end of non-homo­logous chromosome.

(ii) Shift translocation:

Broken part gets inserted interstitially in a non-homologous chromosome.

(iii) Reciprocal translocation:

When parts of chromosomes belonging to members of two different pairs become exchanged (Fig. 12.17).

If a translocation is present in one of the two sets of chromosomes, that will be a translocation heterozygote. In such a plant, nor­mal pairing into bivalents will not be possible among chromosomes involved in translocation.

Due to pairing between homologous segments of chromosomes, a cross shaped (+) figure invol­ving four chromosomes (quadrivalent) will be observed at pachytene. This ring of four chromo­somes at metaphase I can have one of the following three orientations (Fig. 12.18):

In this orientation, alternate chro­mosomes will be oriented towards the same pole.

This is possible by attaining an “eight” (8) like configuration.

In this orientation, adjacent chrotromeres will orient towards opposite poles. A mosomes having non-homologous centromeres ring of four chromosomes will be observed.

In this orientation, adjacent chromosomes having homologous centromeres will orient towards the same pole. A ring of four chromosomes is obtained.

Alternate disjunction gives functional gametes. Adjacent I and Adjacent II will form gametes, which would carry duplications or defi­ciencies and as a result would be nonfunctional or sterile. Therefore, in a plant having a trans­location in heterozygous condition, there will be considerable pollen sterility.

The different kinds of progenies in the ratio 1:2:1 are obtained due to self-fertilization in a translocation heterozygote through alternate disjunction (Fig. 12.19). The first case of translocation was found in Oenothera. Tradescantia and Rhoeo also have translocations In heterozygous conditions.

Balanced Lethals and Balanced Hetero­zygosity:

When translocation involves more than two non-homologous pairs of chromosomes, meiotic rings containing six, eight or more chromosomes can be obtained. These events are not rare and are extensively seen in Oenothera.

Oenothera has the following characteristics:

(i) Some of its races produce new hereditary types at a frequency that is much higher than that commonly expected for muta­tion.

(ii) Many Oenothera races, such as O. lamarckiana, produce seeds that are about 50 percent lethal when ordinarily self- pollinated but fully viable when outbred to other races.

iii) All Oenothera races have seven pairs of chromosomes. The first meiotic meta- phase configuration ranges from seven individual bivalents through various com­bination of rings and bivalents to a single ring of 14 chromosomes.

In O. lamarckiana a ring of 12 chromo­somes instead of a ring of 14 chromosomes is observed. Since alternate segregation is almost exclusively observed for these rings, duplica­tions and deficiencies are generally absent and entire translocation complexes segregate as a unit in each gamete.

In O. lamarckiana alternate segregation in the ring of 12 gave two comple­xes: 3.4, 12.11, 7.6, 5.8, 14.13, 10.9 and 4.12, 11.7, 6.5, 8.14, 13.10, 9.3 (symbolizing each of the seven arms of each of the seven pairs of metacentric chromosomes as 1.2, 1.2, 3.4, 3.4, 5.6, 5.6 13.14, 13.14).

Each is also bear­ing the 1.2 chromosome of the segregating biva­lent. Any other type of segregation in the heterozygote would produce unbalanced gametes. Thus each complex of six chromosomes is con­sidered as a linkage group. These two were named as gaudens and velans by Renner (Fig. 12.20).

O. lamarckiana does not produce either velans / velans or gaudens / gaudens, although both homozygotes are chromosomally balan­ced. Apparently, recessive lethals are main­tained in both the velans and gaudens com­plexes, so that homozygous combinations are lethal. This lethality affects the zygotes, so that half the seeds do not germinate. The gametic or zygotic lethality leads to survival of only heterozygotes.

In gametic lethality, only one of the two types of gametes function on the male side, the other type being functional on the female side, thus giving rise to only one type of progeny, which is heterozygous. In zygotic lethality on the other hand, both types of gametes will function on male as well as on female side, but the homozygote progeny due to recessive lethal genes does not survive (Fig. 12.21).

Similar to Oenothera, Rhoeo discolor is a structural heterozygote where there is a ring of 12 chromosomes in meiosis (Fig. 12.22).

7. Other Forms of Chromosomal Aberrations:

Centric Fusion and Fission:

Centric fusion is a process that leads to a decrease in chromosome number. Two acrocentric chromosomes join together to produce a metacentric chromosome. This phenomenon is also called Robertsonian translocation.

Dissociation or fission is process that leads to an increase in chromosome number. In dissociation, a metacentric (commonly large) and a small supernumerary metacentric fragment become trans-located, so that two acrocentric or sub-metacentric chromosomes are produced.

Direct fission of centromere of metacentric chro­mosome leads to two telocentric chromosomes (misdivision). Fusion and fission are the main mecha­nisms by which the chromosome number can be decreased and increased during evolution of the majority of animals and in some groups of plants (Fig. 12.23).

A new type of chromo­some may arise from a break (i.e., a misdivision) at the centromere. As shown in Fig. 12.24, the two resultant telocentric chromosomes may open up to produce chromosomes with two identical arms (i.e., iso-chromosomes). This type of chromosome is produced in irradiated mate­rial. At meiosis they may pair with themselves or with a normal homologue.

Sister Chromatid Exchange:

A sister chro­matid exchange is an interchange of DNA between sister chromatids in a chromosome, presumably involving DNA breakage followed by fusion. Sister chromatid exchanges are diffi­cult to find using common cytological methods because the chromatids are morphologically identical.

Such chromatid exchanges were first described in studies in which 3 H-thymidine was added during a replicating cycle which was followed by another cycle in a non-radioactive medium. Analysis of this phenomenon has been greatly facilitated by the use of bromodeoxyuridine (BrdU), a thymidine analogue that can be incorporated into the DNA of replicating cells instead of the original base.

If BrdU is followed by a fluorescent dye (Hoechst 33528), the fluo­rescence of the segments that contain BrdU is greatly diminished in comparison with those of the original base. Furthermore, there is also a similarly decreased staining with the Giemsa stain.

The use of this technique, however, has been unable to discover whether the chromatid exchange could occur spontaneously or whether it is induced by the BrdU.

It has, though, been of great help in differentiating the various inherited diseases characterized by chromosome fragility, which have an increased frequency of sister chromotid exchanges and a tendency to have associated neoplasia. Some of the diseases (e.g. Bloom’s syndrome, Fanconi’s anemia, and ataxia- telangiectasia) are presumably related to defects in DNA repair.

Sister chromatid exchange has also been important in studying the effect of mutagens on the chromosomes. Various mutagenic drugs that are alkylating agents, such as mitomycin C and nitrogen mustard, produce a great number of breaks and chromatid exchanges (Fig. 12.25). The intimate association of sister chromatid exchange with mutagenesis and carcinogenesis may have important medical implications.

Effects of Chromosomal Aberra­tion:

In most cases, homozygosity for deficiencies or deletions has a deleterious effect and leads to death. Duplications may have more desirable effects than the loss of chromosome substances. Even in this category, there is a disturbance of chromosome balance and in instances of large duplications, a reduction in fertility as well as in vigour may occur.

Translocation in Oenothera lamarckiana produces 50% non-viable seeds. The viable seeds are all translocation heterozygotes (bal­anced lethal system). In Rhoeo discolor, the only translocation heterozygotes are survivors. In Clarkia, Paeonia, translocation and normal homozygotes are also common.

Sometimes in Oenothera, Rhoeo, chromosomes disjoin in an irregular manner, new translocations are produced and crossing over between different complexes may take place. All these changes produce recognisable phenotypic effects.

The occurrence of inversions is less recor­ded than translocations. In flowering plants with vegetative reproduction, for instance, in Tulipa, heterozygosity for inversions has, however, turned out to be frequent and in Paris quadrifolia, every plant seems to be heterozygous for one or several inversions (Muntzing).

That, inversions are common in plants with vegetative reproduc­tion is due to the fact that structural alterations arise and accumulate in them without particular disadvantages. Reproduction is not affected on account of structural aberrations. Since these plants in question reproduce exclusively or pre­dominantly in vegetative way, the aberrations affecting sexuality and seed setting are of no prime importance.

8. Detection of Chromosomal Aberrations:

The alterations of chromosome structure can however be detected through comparative analysis of karyotypes. The gross chromosomal changes and their location can conveniently be studied through clarification of chromosomal details and their comparison with unaltered genotypes.

The study of meiosis too provides with a powerful method of detection, provided the changes are adequate to bring out the detectable changes in meiotic behaviour.

The study of detection includes formation of loops for the deficiency, inversion bridges for inverted segments as well as ring formation for structural heterozygotes. The formation of multivalent also clearly indicates the duplication of chromosomes. As such, meiotic analysis can provide clear indication of the changes the chromosomes have undergone affecting their structure.

However, gradually a number of modified methods have come up through which finer segments of chromosome can be micro­scopically differentiated. These methods permit identification of minute chromosome segments which otherwise become difficult to resolve through karyotype or pachytene analysis or study of meiotic details.

The two methods which are now widely applied for detection of chromosomal and genomic alterations are (1) chromosome banding and (2) In situ hybridization (ISH).


During metaphase, the “change phase,” all the chromosomes are aligned in a plane called the metaphase plate, or the equatorial plane, midway between the two poles of the cell. The sister chromatids are still tightly attached to each other by cohesin proteins. At this time, the chromosomes are maximally condensed.

Figure 9 Metaphase. Photo credit Kelvin13 Wikimedia.

Homology Effects

Sean M. Burgess , in Advances in Genetics , 2002

B. Overview of meiotic chromosome dynamics

The S phase preceding the meiotic divisions in yeast takes approximately three times longer than S phase in nonmeiotic cells ( Cha et al., 2000) . It has been proposed that this additional time is required to establish the foundation on which meiotic chromosome dynamics will be played out. This foundation may include the binding of factors required for homolog pairing, recombination, bouquet arrangement, or SC formation ( Zickler and Kleckner, 1999 ). Immediately prior to meiotic S phase (i.e., in premeiotic G1), homologs are paired along their lengths by multiple, interstitial interactions as detected using FISH ( Section V.A Weiner and Kleckner, 1994 Burgess et al., 1999) . During the period of S phase, pairing interactions between homologs are lost and restored ( Weiner and Kleckner, 1994 Cha et al., 2000) . Cohesion between sister chromatids is likely established during meiotic S phase, as it is established during S phase in nonmeiotic cells ( Uhlmann and Nasmyth, 1998 ).

Following DNA replication, meiotic recombination is initiated by the formation of DSBs catalyzed by the Spo11 protein ( Sun et al., 1989 Cao et al., 1990 Padmore et al., 1991 Bergerat et al., 1997 Keeney et al., 1997 Borde et al., 2000) . At least 10 genes other than SPO11 are required for the initiation of DNA double-strand breaks, including RAD50, MRE11, XRS2, REC102, REC103/SK18, REC104, REC114, MEI4, MER1, MER2, and MRE2, while mutations in a second class of at least four genes give a 5–10-fold reduction in DSB formation (reviewed by Keeney, 2001 Table 3.2 Figure 3.3A1 Section IV.C ). Some members of this second class, including RED1, MEK1/MRE4, and HOP1, are likely involved in forming higher-order chromosome structure rather than in participating directly in DSB formation (reviewed in Roeder, 1997 Zickler and Kleckner, 1999 Dresser, 2000 and below). Another member of this class includes the motor protein KAR3, which may be involved in chromosome movement during meiotic prophase ( Bascom-Slack and Dawson, 1997 ).

Table 3.2 . Meiotic Mutant Phenotypes

AllelePairing levels aRecombination initiation (DSB formation/resection) bSC morphology [axial elements (AE), synaptonemal complex (SC), interaxis connectors (IC)]References c (pairing levels, recombination initiation, SC morphology)
spo11 Δ+/+ND/NAAE − , SC − [1–3], [4], [3]
spo11-Y135F+ + ++ND/NAND[5], [6], [NA]
rad50Δ++/+ND/NAAE +/− , SC − [1], [3], [4], [7]
rec102Δ++ND/NAAE + , SC − [8], [9], [10]
mei4Δ++ND/NAAE + , SC − [8], [11], [12], [13]
mer 2Δ++ND/NAAE + , SC − [2], [2], [2]
hoplΔ+ + ++/+++ND to &lt 10% of WT/yesAE + , SC − [1], [3], [8], [14], [3], [15]
mer1 Δ+ + +/++∼10% of WT/yesAE + , SC − [1], [8], [16], [17]
red1Δ++ND to 20% of WT/yesAE + , SC − [8], [18], [19]
mekl Δ/mre4 Δ++++10–20% of WT/yesAE + , SC +/− [8], [18], [19]
sae2Δ/coml Δ+100%/no [20], [20], [21], [20]
rad50S++/++100%/noAE + , SC +/− [1], [3], [7], [7]
mre1 1S+100%/noAE + , SC + (nonhomologous)[22], [22], [22]
hop2Δ+ to +++100%/hyperAE + , SC + (nonhomologous)[23], [23], [23]
dmc1Δ+ + +/+++100%/hyperAE + , SC + (delayed)[1], [24], [18], [25], [26], [24], [25]
rad51Δ+++100%/hyperAE + , SC + (delayed)[24], [18], [26], [25], [24]
rad51 Δdmc1 Δ+ + +100%/hyperND[1], [24], [26], [24]
ndj1 Δ/taml Δ++++ (delayed)NDAE + , SC + (delayed)[27], [ND], [28], [29]
zip1 Δ++++100%/yesAE + , SC − , IC + [8], [18], [24], [30]
zip1 Δdmc1 Δ++NDAE + , SC − , IC − [24], [ND], [24]
zip2++++NDAE + , SC − , IC + [31], [ND], [31]

Meiotic DSBs, recombination intermediates and products can be detected physically (in real time) during meiosis using gel electrophoresis and Southern blotting techniques. These intermediates include (in temporal order of appearance): 3′ ssDNA tails produced by exonucleolytic digest of the 5′ ends of breaks, single-end invasions (SEI), double Holliday junctions (dHJ), and mature recombinant DNA products ( Cao et al., 1990 Sun et al., 1991 Bishop et al., 1992 Collins and Newlon, 1994 Schwacha and Kleckner, 1994 , 1995 Nag et al., 1995 Allers and Lichten, 2000 Hunter and Kleckner, 2001 ). Mature recombinants arise at the end of pachytene, when full levels of SC are present ( Table 3.1B Roeder, 1997 Zickler and Kleckner, 1999 ). Many of the genes involved in meiotic recombination and SC formation are listed in Figure 3.3A . The recombined DNA products, in conjunction with cohesion between sister chromatids, hold the homologs on the meiotic spindle and ensure a proper reductional division at anaphase I of meiosis (reviewed in Moore and Orr-Weaver, 1998 ). These connections presumably provide the tension necessary to align chromosomes between the spindle poles ( Nicklas 1977 ).

The conversion of DSBs into recombinant products involves many of the same genes that are required for homologous recombination in mitotically dividing cells ( Section III.A Smith and Nicolas, 1998 Paques and Haber, 1999 ). The yeast RecA homologs, RAD51, and the meiosis-specific DMC1 gene, are likely involved in homology sensing. Both rad51 Δ and dmc1 Δ mutants form meiotic DSBs, yet the breaks become hyperressected and fail to form dHJs with the homologous chromosome ( Table 3.2 Bishop et al., 1992 Shinohara et al., 1992 Schwacha and Kleckner, 1995 Xu et al., 1997) . While RAD54 is likely involved in the homology-sensing mechanism for homologous recombination in mitotically dividing cells (see Section V.A ), the related gene TID1/RDH54 likely takes over this function during meiosis. The tid1Δ/rdh4Δ mutant is severely defective for meiotic recombination, while RAD54 appears to be dispensable ( Shinohara et al., 1997b Schmuckli-Maurer and Heyer, 2000 ). The severe recombination defect exhibited by the rad54Δ tid1 Δ/rdh4Δ double mutant, however, is suggestive of some overlapping roles for these genes in meiotic cells ( Shinohara et al., 1997b) . Other genes involved in meiotic recombination include RAD52, RAD55, RAD57, and RPA1 ( Gasior et al., 1998) , which are also involved in homologous DSB repair in nonmeiotic cells (see Section III.A ).

During meiosis, homologous chromosomes are used as the substrate for recombinational repair of the DSB ( Kleckner, 1996 Roeder, 1997 Schwacha and Kleckner, 1997 ). In contrast, in mitotically dividing cells, DSBs introduced during G2 are repaired using the sister chromatid as a template for repair ( Fabre et al., 1984 Kadyk and Hartwell, 1992 ). DMC1 and RED1 likely play important roles in homolog/sister discrimination in meiosis. RED1 is important for the formation of DSBs that are channeled into an interhomolog-only pathway, and DMC1 is important for directing such breaks into dHJ formed between homologs ( Schwacha and Kleckner, 1997 ). Defects in homolog/sister bias have also been inferred by observing increased levels of unequal sister chromatid exchange in certain mutant strains. One such mutant includes mek1 Δ/mre4Δ ( Thompson and Stahl, 1999 ). MEK1/MRE4 has been shown to encode a kinase that phosphorylates Red1 protein ( de los Santos and Hollingsworth, 1999 Bailis et al., 2000) . Since mek1 Δ/mre4Δ and red1 Δ mutants exhibit nearly identical meiotic phenotypes, presumably MEK1/MRE4 is also required for DSB formation along the interhomolog-only pathway ( Xu et al., 1997) . Another class of factors implied to be involved in interhomolog bias by this genetic criterion includes genes involved in meiotic cell-cycle checkpoint functions, encoded by RAD17, RAD24, MEC1, and MEC3 ( Grushcow et al., 1999 Thompson and Stahl, 1999 ).

Chromosome organization in the meiotic nucleus also influences the efficiency of recombination, perhaps even more strongly than in nonmeiotic cells. Short homologous DNA segments were found to undergo recombination at an 8- to 17-fold decrease in efficiency when present at ectopic positions on nonhomologous chromosomes compared with segments located at allelic positions ( Goldman and Lichten, 1996 ). Furthermore, the efficiency of ectopic recombination was greater for pairs of loci located near the telomeres than for pairs of interstitial loci. One interpretation of these data is that homologous chromosomes are already co-localized before ectopic recombination takes place, with contributions from both pairing interactions and from the bouquet ( Goldman and Lichten, 1996 ). These authors then went on to explore whether homolog associations may limit interactions between homologous DNA segments present at ectopic positions. They found that when interactions between homologous chromosomes were somewhat compromised (e.g., in a ndj1 Δ/tam1Δ mutant or in the presence of a competing homeologous chromosome from a related species), the levels of ectopic interactions increased ( Goldman and Lichten, 2000 ).

DSB-independent contacts between homologous chromosomes are also likely to be relevant to DSB formation. For example, the presence of nonhomology on one homolog has been shown to affect the levels of DSB formation at an allelic region on the other homolog in trans ( Xu and Kleckner, 1995 Bullard et al., 1996 Rocco and Nicolas, 1996 ). This effect may be similar in nature to the alteration of chromatin structure at an allelic position in trans in the presence of heterology, which has been shown to occur in premeiotic cells at a known meiotic DSB hot spot (see Section V.A Keeney and Kleckner, 1996 ). Homolog pairing is not absolutely required for DSB formation, since high levels of DSBs were observed when no homolog was present in haploid yeast programmed to enter meiosis ( De Massy et al., 1994 Gilbertson and Stahl, 1994 ). Such DSBs, however, were delayed somewhat in this situation, suggestive of some effect of homolog association. Pairing could thus act to influence the timing of DSB formation or to influence where DSBs occur along the length of a chromosome.

In summary, meiotic recombination appears to be mechanistically similar to the DSBR pathway that functions in mitotically dividing cells. Meiotic recombination has specialized features which provide programmed formation of DSBs, promote interhomolog-specific interactions, and also promote other features of meiotic chromosome metabolism not discussed here (including crossover control and formation of the SC see Figure 3.3A ). In addition, homolog pairing interactions occurring independent of DSB formation may influence meiotic recombination.


Model potentials

As briefly described in the main text, we employed coarse-grained molecular dynamics (MD) simulations with the Langevin thermostat. Specifically, we employed a velocity-Verlet MD integrator with a fixed time step of 0.01. In our MD simulations, we modeled chromosomes as chains consisting of spherical monomers and linearly connecting springs, and modeled condensins as point particles.

Each chromosome consists of N monomers with diameter σ = 1, mass m = 1, and friction γ = 1. The potential for chromosomes is described as (2) where Uexcl and Uspr represent the volume exclusion among monomers and spring interactions between neighboring monomers in the chain, respectively.

The excluded volume interaction Uexcl is described by a Weeks-Chandler-Andersen (WCA) potential, which corresponds to the repulsive part of the Lennard-Jones potential: (3) for and 0 elsewhere, where ri, j denotes the distance between the centers of the i-th and j-th monomers. At ri, j = σ, the interaction energy is ϵ = 1kBT, where kB and T are the Boltzmann constant and the temperature, respectively. To avoid numerical instability, we introduce a cut-off at a maximum energy of the potential ϵcut = 1000kBT.

The spring interaction Uspr between neighboring monomers in a chain is described by the harmonic potential: (4) where ri, i+1 is the distance between the i-th and (i + 1)-th monomer centers, dB is the natural length of the springs, and ϵspr is the spring coefficient. We chose the parameters dB = σ and ϵspr = ϵcut. The spring has no excluded volume (phantom spring). Thus, spring-spring and spring-monomer can pass through each other, which is mediated by the strand-passage activity of topoisomerase II. Note that actual frequency of the strand passage was low due to the excluded volume of the monomers connected by springs (see S1 Appendix).

The potential for condensins is described as (5) where Uloop and Uattr represent two functions of the condensins, chromatin loop-holding and inter-condensin attractions, respectively.

With the loop-holding potential Uloop, a condensin interacts with two defined chromatin monomers to make a chromatin loop. The potential is described by the harmonic potential: (6) where is the distance between the i-th condensin and its two interacting monomers, and M is the number of condensins that interact with one chromosome by the loop-holding potential in other words, the chromosome has M loops. Since we consider the consecutive loop structures in a chromosome by condensins, the length of the chromatin loop is L = N/M, and the i-th condensin bonds to the (i − 1)L-th and the (iL − 1)-th chromatin monomers to make a loop with length L, where the order of condensins is aligned with the order of chromatin monomers. Floop is the strength of the interaction.

The inter-condensin attraction potential Uattr is described by the harmonic potential: (7) for and 0 elsewhere, where denotes the distance between the centers of the i-th and j-th condensins. Δ, M′, and Fcond are the threshold distance, total number of condensins (M′ = M for one-chromosome simulations and M′ = 2M for two-chromosome simulations), and the strength of attractions, respectively.

Initial loop formation process

We established an initial configuration of chromosomes with crossed loops as follows. Consecutive loop structures were made using a loop extrusion mechanism deterministically. The polymer length N, loop length L, and condensin number M have a relation N = LM. The number of crossing Cr determines the structure within a loop.

Fig 7 shows a schematic picture of the deterministic loop extrusion process with crossings. Each condensin has two bonds. Each bond connects condensin with a chromatin monomer by the harmonic potential. First, the two bonds connect similarly between the i-th condensin and the (i − 0.5)L-th monomer (Fig 7a). The condensins are arranged at regular intervals of L. As time passes, the two bonds proceed in a step-by-step manner in the opposite direction along the chromosome chain (Fig 7b). Then, a loop is extruded by each condensin (Fig 7c). After a certain time step, the length of the extruded loop becomes L/Cr, and then the condensin makes a crossing structure in the loop by changing the spring connection to monomers (Fig 7d). The process of making the crossing structure is shown in the inset of Fig 7. After the length of the extruded loop becomes L/Cr, the two chromatin springs cross at the same time as the condensin bonds proceed (Fig 7B). Then, the condensin bonds continue to proceed. This loop extrusion process finally results in a loop structure with crossings (Fig 7e).

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