Calculation of Derivative Chromosomes

The Chromosome class handles derivative chromosomes. It describes the chromosome as an ordered series of Fragment objects. It allows for the introduction of further aberrations into the chromosome. Such aberrations need not be describable in the ISCN short notation. In fact, the parameters for the functions are generally Band and / or Chromosome objects instead of ISCN data.

Thus, more complex aberrations can be introduced in derivative chromosomes, e.g. an inversion in a chromosome derived from a translocation extending over the break point of the translocation.

If the StrictISCN option is set to true, many ways of introducing an aberration which cannot be described with the ISCN short notation will be prevented.

Introducing aberrations

Generally, the function used to find the break point in a chromosome, will return the last terminal fragment containing the break point, else the last occurence of that break point. Sometimes, a function is used to find a centromere and the break point on the same fragment of the chromosome.

Generally, a temporary collection is used for re-shuffling fragments from the input chromosomes and the replacement fragments for fragments containing the break points.

The functions used to introduce specific aberrations do normally not care if a centromere gets removed by the aberration, or if an extra centromere gets introduced though the type of aberration normally would not cause the transfer of centromeres (e.g. insertion of a centromere bearing fragment).

After each introduction of an aberration, the ISCN detailed notation of the chromosome is calculated. That function will raise an error if all centromeres were lost.

Addition

The break point and the centromere are searched for independently thus preferring for the outmost band for the addition. Orientation of the remaining fragments is calculated to maintain the last centromere.

If the centromere comes first, all fragments before the break point containing fragment are added to a temporary collection, then a replacement fragment starting with the first band of the break point containing fragment upto the break point, and then a new fragment of unknown origin which is marked centromere-free. Otherwise, we start with a new fragment of unknown origin which is marked centromere-free, add a replacement fragment starting with the break point and extending to the second band of the break point containing fragment, and then all fragments with higher number.

Deletion

There are two functions for deletions, one for a terminal deletion, and one for an interstitial deletion.

For a terminal deletion, the break point and the centromere are searched for independently thus preferring for the outmost band for the addition. Orientation of the remaining fragments is calculated to maintain the last centromere and the procedure of the introduction of a deletion follows the procedure for the introduction of an addition with the exception of the fragment of unknown origin which is not needed for deletions.

With interstitial deletions, both start and end band of the deletion are searched for on the same band. If not found together, they are searched for independently. The centromere is not searched for. Then we loop through the collection of fragments. If the number of the fragment is less than the number of the first band or greater than the number of the second band, the fragment is added to the temporary collection directly.

If the fragment containing the start band is encountered, both replacement fragments are added to the collection (hence, we must ignore the encounter of the end band containing fragment).
If the start band was encountered on a fragment not later than the end band, then the first replacement fragment starts with the first band of the fragment containing the start band and extends to the start band and the second replacement fragment starts with the end band and extends upto the second band of the fragment containing the end band;
if both start and end band reside on the same fragment and the end band comes first, the first replacement fragment starts with the first band of the fragment containing both start and end band and extends to the end band and the second replacement fragment starts with the start band and extends upto the second band of the fragment.
If the fragment of the start band has a higher number than the fragment of the end band, the first replacement fragment starts with the first band of the fragment containing the end band and extends to the end band, the second replacement fragment starts with the start band and extends to the second band of the fragment containing the start band.

With both terminal and non-terminal deletions, previously introduced aberrations can get lost. While with non-terminal deletions, at least one centromere will remain, the interstitial deletions may result with a loss of all centromeres and then raise an error.

Dicentric chromosomes

For the formation of a dicentric chromosome, a centromere containing fragment of the starting chomosome must be combined with a centromere containing fragment of the additional chromosomes. Both starting and additional chromosome may already be derivative chromosomes. The centromeric region may be of unknown origin ("?").

The user of this Chromosome.dicentric function should be aware of the fact that the formation of dicentric chromosomes is very often denoted as a translocation in the ISCN, e.g. in "der(5;7)t(5;7)(q22;p13)t(3;7)(q21;q21)" the "t(5;7)(q22;p13)" actually means "dic(5;7)(q22;p13)". Also the derivative chromosomes of whole arm translocations are dicentric chromosomes. Care must be taken to correctly distinguish between the Chromosome.translocate and the Chromosome.dicentric fucntions.

Break point and centromere of the first chromosome are searched for independently.Depending on their relativ position, fragments are taken from the start of the chromosome or  after inversion from the end of the chromosome: If the centromere resides on a fragment with a lower number than the break point the straight version is taken, also if they reside on the same fragment and, if the break point is a centromere and it is on the same arm of the fragment as is the first band, or if the break point is not a centromere and the break point resides on the arm than the first band of the fragment. In all other cases, the inverted version is taken.

Fragments of the starting chromosome are then shuffled from the first or the last (then inverted) fragment to the break point containing fragment into the temporary collection. Then a replacement fragment is added which ends at the break point and starts at either the first band of the break point containing fragment (straight version) or at its second band (inverted version).

A similiar logic is applied for getting the fragments of the additional chromosome which will be added to the temporary collection starting with the replacement fragment, via a centromere, to the start / or end point of the additional chromosome.

If a break point is marked unknown ("?"), a replacement fragment of unknown band composition of the respective chromosome - which may also be unknown - is built and, if a centromere was found on the same fragment, marked centromere containing.

Duplication

Duplications may come as direct or as inverted duplications. If the second band is closer to the centromere than the first band the duplication is called inverted according to the ISCN (p. 59).

That definition of the ISCN is not useful for constructing derivative chromosomes, since there we must look at the series of fragments from one end of the chromosome to the next end instead of looking from the centromere in two directions. Hence, for the calculation an inversion means that the band named first will be the second band on the fragment to be inserted.

If the bands reside on the p-arm and that p-arm is inserted into the chromosome in plus orientation, or if the bands reside on the q-arm and that q-arm is inserted in minus orientation, we must use inversion.

Examples:

  • 46,XX,der(1)dup(1)(p11p21)

    • der(1)(1pter->1p11::1p21->1p11::1p11->1qter)
    inverted=true
  • 46,XX,der(1)dup(1)(p21p11)

    • der(1)(1pter->1p11::1p11->1p21::1p11->1qter)
    inverted=true
  • 46,XX,der(1)dup(1)(q11q21)

    • der(1)(1pter->1q21::1q11->1q21::1q21->1qter)
    inverted=false
  • 46,XX,der(1)dup(1)(q21q11)

    • der(1)(1pter->1q21::1q21->1q11::1q21->1qter)
    inverted=false
  • 46,XX,der(1;3)t(1;3)(q42;q29)dup(3)(p12p22)

    • der(1;3)(1pter->1q42::3q29->3p22::3p12->3p22::3p22->3pter)
    inverted=false
For fragment spanning aberrations (which are not defined in the ISCN), we use inversion if the first band named in the duplication resides on a fragment with higher number.

Basically, the chromosome is added from its start point upto the later break point, then the fragment(s) to be duplicated (which may need inversion), and finally the remaining fragments from the later break point.

There are two possible fragment compositions for inverted duplications. The function will automatically select one of them.

At first we shuffle all fragments before the fragment containg the later band into the temporary collection.

In inverted duplications, if both break points reside on the same fragment, three replacement fragments are needed. The first one starts at the first band of the break points containing fragment and extends to the later breakpoint. Next follows the duplicated region, i.e. the fragment starts with the later break point and extends to the earlier break point. Then the remaining part, i.e. a fragment from the later break point to the second band of the break poits containing fragment, is the third fragment. Fragments are ligated when possible.
If the first break point resides on a fragment with higher number than the second break point, a replacement fragment for the first break point is added; it starts at the first band of the fragement containing the break point and extends to the break point. Since it is invertedly duplicated, it is added again after inversion. Next, the fragments between the break points are added after inversion. The replacement fragment at the second break point starts with the second band of the fragment containing the second break point and extends to the second break point. Now a second replacement fragement at the first break point is added; it start with the first break point and extends to the second band of the fragment containing the first break point.
Finally, the remaining fragment(s) of the start chromosome are added.

Also in direct duplications, if both break points reside on the same fragment, three replacement fragments are needed. The first one starts at the first band of the break points containing fragment and extends to the later breakpoint. Next follows the duplicated region, i.e. the fragment starts with the first break point and extends to the second break point. Then the remaining part, i.e. a fragment from the later break point to the second band of the break points containing fragment, is the third fragment. Fragments are ligated when possible.
If the first break point resides on a fragment with lower number than the second break point, a replacement fragment for the second break point is added first; it starts at the fisrt band of the fragment containing the second break point and extends to it. Next comes the replacement fragment for the first break point; it starts at the first break point and extends to the second band of the fragment containing the first break point. Finally, all fragments after the fragment with the first break point are added, including the fragments of the duplicated region and the fragment containing the second break point.

The function will also accept centromere containing fragments; then it will give raise to a derivative chromosome with additional centromeres. The ISCN manual does not describe such duplications, maybe they must not be described with the "dup" symbol.
An example of such a case is "der(1;1)dup(1)(p21q12)", its transliteration into detailed ISCN is "der(1;1)(1pter->1q12::1p21->1qter)".

Homogeneously staining regions

There are three positions for homogeneously staining regions: somewhere inside a fragment, at the end point of a fragment, or at the junction of two fragments from distinct chromosomes.

If one band only was given, the hsr is somewhere on a fragment or on an end point of a fragment. Hence, a special function tries to locate the band as an end point of a fragment. If it is found as the first band of a fragment, the index returned is one less than the index of the fragement. The fragments of the starting chromosome are added upto the fragment at index (including it). Then the hsr is added. There after follow the remaining fragments.
If it could not be found, the "normal" search for the band is undertaken. The fragments of the starting chromosome are added upto the fragment containing the insertion point (but not including it). Then a replacment fragemtn is added which starts at the first band of the fragment containing the insertion point and ends at the insertion point. Then the hsr is added. There after follows another replacement fragment which starts at the insertion site and extends to the second band of the fragment containing the insertion site. Then, all remaining fragments are added.

This function also allows terminal hsr, which may be not correct in the ISCN.

For hsr at the junction of two fragments from distinct chromosomes, a special search procedure is used which requires both bands to be break points of adjacent fragments. Then all fragments upto that point are added to the collection, a new fragment of the hsr, and then all remaining fragments.

The function for hsr at the junction of two fragments from distinct chromosomes does not complain, if fragments from the same chromosome are given, e.g. at the junction of an interstitial deletion "der(1)del(1)(p21p33)hsr(1;1)(p21;p33)". This feature may not be acceptable in the ISCN.

Interchromosomal Insertion

Interchromosomal insertions come as direct or as inverted insertions. If the second band is closer to the centromere than the first band the insertion is called inverted according to the ISCN (pp. 61f).

As with duplications, that definition of the ISCN is not useful for constructing derivative chromosomes, since there we must look at the series of fragments from one end of the chromosome to the next end instead of looking from the centromere in two directions. Hence, for the calculation an inversion means that the band named first will be the second band on the fragment to be inserted.

As we can see from the examples below, it does not at all matter how the bands are ordered with respect to the centromere. Only the arm the fragments originate from, the arm into which it will be inserted and the orientation of the arm relative to the derivative chromosome are relevant. Luckily, the fragment to be inserted cannot be derived from a derivative chromosome according to ISCN, hence we can assign arbitrary values for such cases.

Examples:

  • 46,XX,der(5)ins(5;2)(p14;q22q32)

    • der(5)(5pter->5p14::2q32->2q22::5p14->5qter) (p. 62)
    invert=true
  • 46,XX,der(5)ins(5;2)(p14;q32q22)

    • der(5)(5pter->5p14::2q22->2q32::5p14->5qter) (p. 62)
    invert=true
  • 46,XX,der(5)ins(5;2)(q14;q22q32)

    • der(5)(5pter->5q14::2q22->2q32::5q14->5qter)
    invert=false
  • 46,XX,der(5)ins(5;2)(q14;q32q22)

    • der(5)(5pter->5q14::2q32->2q22::5q14->5qter)
    invert=false
  • 46,XX,der(5)ins(5;2)(p14;p13p23)

    • der(5)(5pter->5p14::2p23->2p13::5p14->5qter)
    invert=true
  • 46,XX,der(5)ins(5;2)(p14;p23p13)

    • der(5)(5pter->5p14::2p13->2p23::5p14->5qter)
    invert=true
  • 46,XX,der(5)ins(5;2)(q14;p13p23)

    • der(5)(5pter->5q14::2p13->2p23::5q14->5qter)
    invert=false
  • 46,XX,der(5)ins(5;2)(q14;p23p13)

    • der(5)(5pter->5q14::2p23->2p13::5q14->5qter)
    invert=false
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(p14;q22q32)

    • der(1;5)(1pter->1q43::5q34->5p14::2q22->2q32::5p14->5pter)
    invert=false
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(p14;q32q22)

    • der(1;5)(1pter->1q43::5q34->5p14::2q32->2q22::5p14->5pter)
    invert=false
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(q14;q22q32)

    • der(1;5)(1pter->1q43::5q34->5q14::2q32->2q22::5q14->5pter)
    invert=true
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(q14;q32q22)

    • der(1;5)(1pter->1q43::5q34->5q14::2q22->2q32::5q14->5pter)
    invert=true
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(p14;p13p23)

    • der(1;5)(1pter->1q43::5q34->5p14::2p13->2p23::5p14->5pter)
    invert=false
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(p14;p23p13)

    • der(1;5)(1pter->1q43::5q34->5p14::2p23->2p13::5p14->5pter)
    invert=false
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(q14;p13p23)

    • der(1;5)(1pter->1q43::5q34->5q14::2p23->2p13::5q14->5pter)
    invert=true
  • 46,XX,der(1;5)t(1;5)(q43;q34)ins(5;2)(q14;p23p13)

    • der(1;5)(1pter->1q43::5q34->5q14::2p13->2p23::5q14->5pter)
    invert=true
Fragments before the acceptor band are shuffled into the temporary collection. Then a replacement fragment starting at the first band of the acceptor containing fragment upto the acceptor band is added.
If both donor start band and donor end band reside on the same fragment, a new fragment is set up from donor start to donor end. This fragment may need inversion, as discussed above.
If the donor start orginates from a fragment with lower number than the donor end band, a replacement fragment for the donor start band starting with it and extending to the second band of its fragment, is added. Then follow the fragments of the donor chromosome between start and end band. Finally, a replacement fragment for the donor end band starting at the first band of its fragment and extending to the end band, is added.
If the donor start orginates from a fragment with higher number than the donor end band, a replacement fragment for the donor start band starting with it and extending to the first band of its fragment, is added. Then follow the fragments of the donor chromosome between start band and end band after inverting each. Finally, a replacement fragment for the donor end band starting at the second band of its fragment and extending to it, is added.
In all cases, the rest of the acceptor chromosome follows: a replacement fragment at the acceptor band from it to the second band of its fragment, and all the remaining fragments.

Some problems may arise when one chromosome is unknown or the bands of a chromosome could not be determined exactly. Then some fragments must contain a centromere while others don't though their notation is the same.

Examples:

  • 47,XY,der(?)ins(?;1)(?;p13p32)

    • der(?)(?::1p13->1p32::?)
  • 47,XY,der(2;?)t(2;?)(q21;?)ins(?;1)(?;p13p32)

    • der(2;?)(2pter->2q21::?::1p13->1p32::?)
  • 47,XY,der(2;3)t(2;3)(q21;?)ins(3;?)(?;?)

    • der(2;3)(2pter->2q21::3?->3?::?::3?->3?)
  • 47,XY,der(1)ins(1;3)(p22;?)

    • der(1)(1pter->1p22::3?->3?::1p22->1qter)
  • 47,XY,der(1)ins(1;3)(?;q11q21)

    • der(1)(1?->1?::3q11->3q21::1?->1?)
In contrast to the ISCN, this function allows the insertion of centromeric fragments which gives raise to multricentromeric chromosomes. E.g."ins(1;3)(q41;p22q22)" yields "der(1;3)(1pter->1q41::3p22->3q22::1q41->1qter)".

Insertions inside a derivative chromosome between fragments originating from different chromosomes must not be calculated with this function but with the function for intrachromosomal insertions (e.g. "der(1)t(1;3)(q31;q13)ins(1;3)(p22;q22q24)" is an intrachromosomal insertion if the inserted fragment originates from the translocated fragment, giving raise to "der(1)(1pter->1p22::3q22->3q24::1p22->1q31::3q13->3q22::3q24->3qter)"; if it originates from a different chromosome, it is an interchromosomal insertion giving raise to "der(1)(1pter->1p22::3q22->3q24::1p22->1q31::3q13->3qter)"). By default, all insertions naming two chromosomes in their "ins()" clause are treated as interchromosomal insertion by the CyDAS application.

Intrachromosomal Insertions

Like interchromosomal insertions, intrachromosomal insertions come as direct or as inverted insertions. If the second band is closer to the centromere than the first band the insertion is called inverted according to the ISCN (p. 61).

As with duplications and interchromosomal insertions, that definition of the ISCN is not useful for constructing derivative chromosomes, since there we must look at the series of fragments from one end of the chromosome to the next end instead of looking from the centromere in two directions. Hence, for the calculation an inversion means that the band named first will be the second band on the fragment to be inserted.

As we can see from the examples below, it does not at all matter how the bands are ordered with respect to the centromere. Only the arm into which it will be inserted is relevant: an acceptor on the p arm requires inversion, on the q arm does not.

Examples:

  • 46,XX,der(2)ins(2)(p13q21q31)

    • der(2)(2pter->2p13::2q31->2q21::2p13->2q21::2q31->2qter) (p. 61)
    invert=true
  • 46,XX,der(2)ins(2)(p13q31q21)

    • der(2)(2pter->2p13::2q21->2q31::2p13->2q21::2q31->2qter) (p. 61)
    invert=true
  • 46,XX,der(1)ins(1)(p35p12p22)

    • der(1)(1pter->1p35::1p22->1p12::1p35->1p22::1p12->1qter)
    invert=true
  • 46,XX,der(1)ins(1)(p35p22p12)

    • der(1)(1pter->1p35::1p12->1p22::1p35->1p22::1p12->1qter)
    invert=true
  • 46,XX,der(2)ins(2)(q13p21p23)

    • der(2)(2pter->2p23::2p21->2q13::2p21->2p23::2q13->2qter)
    invert=false
  • 46,XX,der(2)ins(2)(q13p23p21)

    • der(2)(2pter->2p23::2p21->2q13::2p23->2p21::2q13->2qter)
    invert=false
  • 46,XX,der(1)ins(1)(q31q12q22)

    • der(1)(1pter->1q12::1q22->1q31::1q12->1q22::1q31->1qter)
    invert=false
  • 46,XX,der(1)ins(1)(q31q22q12)

    • der(1)(1pter->1q12::1q22->1q31::1q22->1q12::1q31->1qter)
    invert=false
  • 46,XX,der(1)inv(1)(p21p33)ins(1)(p31q12q22)

    • der(1)(1pter->1p33::1p21->1p31::1q12->1q22::1p31->1p33::1p21->1q12::1q22->1qter)
    invert=false OR
    der(1)(1pter->1p33::1p21->1p31::1q22->1q12::1p31->1p33::1p21->1q12::1q22->1qter)
    invert=true ?
The calculation of such chromosomes consists of two major steps: the fragment must be deleted at the original site and then inserted into the acceptor band.

First, the fragment to be moved is added into a special temporary collection.
If both start and end band reside on the same fragment, a new fragemtn is instantiated which may need inversion as discussed above.
If the start band originates from a fragment with lower number than the end band, a replacement fragment starting with the start band and extending to the second band of the chromosomal fragment containing it is added first. Then follow the fragments between start band and end band. Thereafter, a replacement fragment from the first band of the fragment containing the end band upto the end band is added.
If the start band originates from a fragment with higher number than the end band, a replacement fragment starting with the start band and extending to the first band of the chromosomal fragment containing it is added first. Then follow the fragments between start band and end band after inverting each. Thereafter, a replacement fragment from the second band of the fragment containing the end band upto the end band is added.

Afterwards, the fragment is deleted using the function for non-terminal deletions.

Now all fragments before the acceptor band (which may now be found on a fragment with a different number than before) are shuffled into the "normal" temporary collection, then a replacement fragment from the first band of the fragment containing the acceptor band upto the acceptor band. The fragments of the special collection for the region to be moved are added without further consideration (adjustments and inversions were done previously). The second replacement fragment for the acceptor starts at it and extends to the second band of the acceptor fragment. The remaining fragments are added last.

Because of the deletion step in this function, the fragment moved must not contain the only centromere of the chromosome.

Inversion

In inversions, we have to differentiate between three cases.

If both start and end band reside on the same fragment (only this version follows strict ISCN standards), the fragments before the start band are shuffled into a temporary collection. After a replacement fragment from the  first band of the fragment containing the start band to the earlier band of start and end band, a new fragment starting with the later band and extending to the earlier band is instantiated and added. There after follows a second replacement fragment from the later of start and end band to the second band of thier original fragment. Finally, the remaining fragments are added.
If the start band originates from a fragment with lower number than the end band, fragments before the start band are shuffled into a temporary collection. Then comes a replacement fragment from the first band of the fragment containing the start band to the start band. The inverted region starts with a replacement fragment starting at the end band and extending to the first band of the fragment conatining the end band; next follow the fragments between end band and start band which are inverted; last a replacement from the second band of the fragment containing the start band to the start band. Here after, the rest of the original chromosome is added, starting with a replacement fragment from the end band to the second band of the fragment containing the end band, and all the remaining fragments.
If the start band originates from a fragment with lower number than the end band, fragments before the end band are shuffled into a temporary collection. Then comes a replacement fragment from the first band of the fragment containing the end band to the end band. The inverted region starts with a replacement fragment starting at the start band and extending to the first band of the fragment conatining the end band; next follow the fragments between start band and end band which are inverted; last a replacement from the second band of the fragment containing the end band to the end band. Here after, the rest of the original chromosome is added, starting with a replacement fragment from the start band to the second band of the fragment containing the start band, and all the remaining fragments.

The function does not require the bands to be named in the order shown in the ISCN manual (in paracentric inversions, the proximal band comes before the terminal band; in pericentric inversion the band of the p arm comes before the band of the q arm). Highly complex inversions can be calculated:

der(1)i(1)(q10)del(1)(q12q25)del(1)(q23q32)inv(1)(q21q31) = der(1)(1qter->1q32::1q23->1q21::1q31->1q25::1q12->1q10::1q10->1q21::1q31->1qter)

Isomerization

The function for isomerization is used for formation of (simple) isochromosomes and iso-derivative chromosomes as well as iso-dicentric chromosomes.

If the band used for isomerization is a centromere, the fragment that centromere resides on is looked at.
If its first band is on the same arm as the arm designated in the centromere, the fragments before that fragment are shuffled into the temporary collection. Then a replacement fragment starting with the first band of the centromere containing fragment upto that centromere is added both direct and inverted. Finally, the fragments before are added again in reversed order after inverting each.
If the other arm is named, the fragments from the end of the original chromosome downto the centromere are added first after inverting each. Then a replacement fragment starting with the second band of the centromere containing fragment downto that centromere is added both direct and inverted. Finally, the fragments after the centromere are added again, without inversion.

If the band used for isomerization is not a centromere, an isodicentric chromosome has to be set up. First, a centromere for the chromosome specified with the break point is search for. If none was found and strict ISCN compliance is not required, any other centromere is searched for.
If the centromere comes before the break point, the fragments before the break point containing fragment are shuffled into the temporary collection. Then a replacement fragment starting with the first band of the break point containing fragment upto that break point is added both direct and inverted. Finally, the fragments before are added again in reversed order after inverting each.
If the centromere comes behind the break point, the fragments from the end of the original chromosome downto the break point are added first after inverting each. Then a replacement fragment starting with the second band of the break point containing fragment downto that break point is added both direct and inverted. Finally, the fragments after the break point are added again, without inversion.

This function allows for the formation of complicated iso-dicentric chromosomes which are likely not correctly described by the ISCN short notation:

  • der(7;7)t(1;7)(p22;q22)idic(1)(p31)

    • der(7;7)(7pter->7q22::1p22->1p31::1p31->1p22::7q22->7pter)
  • der(7;7)i(7)(q10)idic(7)(q22)

    • der(7;7)(7qter->7q10::7q10->7q22::7q22->7q10::7q10->7qter)

Ring formation

Two types of ring formation are implemented: (1) passing the aberration description of a ring chromosome, (2) introduction of two breaks and reunion at them.

In any case, the internal variable showing whether the chromosome is a ring chromosome is set to true.

Ring formation from an aberration description

As a start, the aberration description of a ring chromosome can be passed as an Aberration object into a function. This function is useful when the start chromosome can be described by aberrations like "der(1)r(1;3)(p36q23;q21q27)" or "der(?)r(?;3;5)(?;q21q26;q13q33)".

This function resets the collection of fragments, and then puts all fragments from the aberration into the collection. Fragments of unknown band composition ought to be marked centromere containing or centromere free before the aberration is passed to the function.

Warning: This function can be used as the first aberration only. All aberrations introduced before will be removed.

Ring formation with two breaks and reunion

This function is the general function for ring formation in derivative chromosomes. Two break point must be named at which breakage and reunion will occur.

Most complicated part is the search for applicable break points. If both start and end originate from the same chromosome, we check if between these break points a centromere would exist on a normal chromosome; if so, both break points are searched for on one fragment. If that search fails and in all other cases, break points are searched for independently with the general search which prefers terminal bands. The result is checked for a centromere of the derivative chromosome. If no centromere was found, the first occurence of the start band and the last occurence of the end band are searched for, and if necessary finally the first occurence of the end band and the last occurence of the start band.

Depending on the fragments the start and end band were found, we differentiate three cases.

If both bands come from the same fragment, a replacement fragment is instantiated from start band to end band. That is the only band of the ring chromosome.

If the start band comes before the end band, a replacement fragment at the start band from it to the second band of its fragment is added first. Next, the fragments between start and end band are added. Finally a replacement fragment at the end band from the first band of its fragment to the end band follows.

If the start band comes after the end band, a replacement fragment at the end band from it to the first band of its fragment is added first. Next, the fragments from end band downto start band are added after inversion. Finally a replacement fragment at the start band from the second band of its fragment to the start band follows.

With this function, complicated derivative chromosomes can be used for ring formation.
In an isochromosome of the long arm of chromosome 7 i(7)(q10), ring formation at 7q11 on one arm and 7q21 on the arm can be calculated: der(7)i(7)(q10)r(7)(q11q21) = der(7)(::7q11->7q10::7q10->7q21::) (The short ISCN description may be wrong; the ISCN manual does not deal with such cases).
Also ring formations which cannot be described in a step by step way in the ISCN are possible. In the derivative chromosome 1 of translocation t(1;2)(q23;q21) der(1)(1pter->1q23::2q21->2qter), ring formation at 1p35 and 2q35 leads to der(1)(::1p35->1q23::2q21->2q35::). The ISCN notation for that chromosome is der(1)r(1;2)(p35q23;q21q35) which looses all information about the previous translocation.

Translocations

The function for translocations performs translocations of terminal fragments between two chromosomes only. The existence of translocations of interstitial fragments is questionable. Translocations between three or more chromosomes can be re-written to a translocation between two chromosomes for the respective derivative chromosome, e.g. der(1)t(1;9;22)(q31;q34;q11) = der(1)(1pter->1q31::22q11->22qter) = der(1)t(1;22)(q31;q11).

Leaving the notation limits of ISCN, also the donor chromosome can be a derivative chromosome; such a translocation cannot be written in the ISCN.

When searching for centromeres, the centromeres of the same chromosome number as the break points are preferred.

First, the fragments of the acceptor chromosome are collected in the temporary collection from a terminus via the centromere to the break point. Depending on the relativ positions of breakpoint and centromere, inversion may be needed.
If the break point in the acceptor if fully unknown, a replecement fragment of the respective chromosome of unknown composition is instantiated, it is marked centromere-containing if acceptor and centromere are on the same fragement; if the centromere comes after the break point, inversion is required.
In other cases, if break point and centromere reside on the same fragment, we must further differentiate if the acceptor band is a centromere or not. If it is, we compare the arm designations of the first band of the fragment the acceptor band resides on and the arm designation of the centromere; if they are equal, inversion is not needed and the replacement fragment starts at the first band of the fragment upto the centromere, else inversion is required and the replacement fragment is from the second band of the fragment to the centromere.
If the acceptor band is not a centromere, no inversion is needed if the centromere comes before the break point; the replacement fragment starts at the first band of the fragment and extends to the break point; else inversion is needed and the replacement fragment starts at the second and of the fragment and extends to the break point.
If centromere and break point reside on different fragments, the logic is similar.

Thereafter, the donor fragments are added from the break point to a terminus avoiding the centromere. Depending on the relativ positions of breakpoint and centromere, inversion may be needed.
If the break point in the donor is fully unknown, a replecement fragment of the respective chromosome of unknown composition is instantiated and always marked not to contain a centromere; if the centromere comes after the break point, inversion is required.
If the break point comes before the centromere, fragments must be taken from the break point dowto the start of the chromosome, else from the break point upto its end. The logic behind it is quite complementary to the logic described for the acceptor.

Tricentric chromosomes

The formation of a tricentric chromosome directly from a "trc" description of the ISCN is possible only when it is the first step.

The collection of fragments is reset. Then all fragments from the Aberration object are simply added to the internal collection.

Warning: All aberrations intriduced to the chromosome previously will be lost due to the resetting of the fragment collection.

Triplication

Triplications can be direct or inverted. With strict ISCN compliance, bands must be notated from proximal to distal band, and the orientation of the triplicated segment cannot be determined.

Here, an inversion of the middle segment is done when the distal band is named first, else all fragments will keep their direction, e.g.:

  • der(1)trp(1)(q21q32) = der(1)(1pter->1q32::1q21->1q32::1q21->1qter)
  • der(1)trp(1)(q32q21) = der(1)(1pter->1q32::1q32->1q21::1q21->1qter)
Other combinations of orientations cannot be done with this function.

The fragments from the start of the chromosome to the later break point are shuffled into the temporary collection, including a replacement fragment at the later band. Then the region between the break points is added direct or invertedly as discussed above; replacement fragments are need at both break points. Thereafter, the region of the chromosome from the earlier break point upto the end of the chromosome is added, starting with a replacement fragment for the first band.

This function transgresses the limitations of ISCN. Also regions of a derivative chromosome spanning other aberrations can be triplicated. For example, a chromosome 1 has lost an interstitial fragment on the q-arm but the triplication spans the re-union of the deletion (short ISCN notation below may be not correct):

  • der(1)del(1)(q21q32)trp(1)(q12q41) = der(1)(1pter->1q21::1q32->1q41::1q12->1q21::1q32->1q41::1q12->1q21::1q32->1qter)
  • der(1)del(1)(q21q32)trp(1)(q41q12) = der(1)(1pter->1q21::1q41->1q32::1q32->1q41::1q21->1q12::1q12->1q21::1q32->1qter)

Calculating meta-data

ISCN detailed description

After each introduction of an aberration, the present composition of the derivative chromosome noted in the ISCN detailed description is calculated.

First, the chromosome numbers of centromere bearing fragments are determined. If two adjacent fragments ending on centromers have the same chromosome number, that chromosome is taken once only. With the chromosome numbers, the leading der() clause is formed.

Next, the collection of fragments is looped through and the fragments are written into the second pair of brackets in the ISCN fragment notation.

Last, the function checks if a centromere is present at all - all centromeres may have been lost during the introduction of aberrations, and raises an error if no centromere is present.

Break points

Break points can easily be taken from the fragment composition of the chromosome. The start and end bands of the fragments which are not chromosome termini ("ter") are added into a Bands object (ignoring duplicates) which is then returned.

Band composition

The band composition is needed e.g. for drawing an ideogram of the mutant chromosome. As with break points, the band composition can be easily calculated from the fragment composition of the chromosome. For each fragment, its band composition is queried at the requested resolutions (Fragment.getContainedBands) and bands are then added to a Bands object without ignoring duplicates and without sorting.

Gains and Losses

For the calculation of gains and losses, we must differentiate between the additional presence of the derivative chromosome on the one hand and its replacing its normal chromosomes on the other hand.

When the derivative chromosome is additionally present, all of its fragments are gained. An SCCN Quantitative Aberration object is instantiated with each fragment of the chromosome and added to the collection of SCCN Quantitative Aberrations.

If the derivative chromosome replaces its normal chromosome(s), the balance of the replaced chromosome(s) and their fragments remaining in the derivative chromosome must be calculated. Fragments originating from other chromosomes are gained.

For calculating the balance, a fragment object is instantiated with the replaced chromosome from pter to qter. E.g. for "der(1)(3qter->3q21::1p32->1q42::1q25->1qter)" this compare fragment is "1pter->1qter". From the fragments of the derivative chromosome, a new list is made containing all fragments with the replaced chromosome number, and they are ordered from pter to qter; in our example, these fragments are "1p32->1q42" and "1q25->1qter" in this order.

Next, the first fragment is substracted from the compare fragment. For that purpose, the start bands of the fragments are compared.If they are equal, the compare fragment gets simply reduced to a fragment starting at the end band of the fragment from the derivative chromosome extending to its end band (usually qter). If the compare fragment starts p-terminal to the fragment from the derivative chromosome, the fragment between the start bands has been lost and the compare fragment is adjusted as before. If the compare fragment starts q-terminal to the fragment from the derivative chromosome, we must differentiate if there is an overlapping region or not; if it is not, the derivative fragment is a gain and no adjusting the compare fragment is done; otherwise, only the non-overlapping part of the derivative chromosome is a gain, and the compare fragment must be adjusted as above.

This procedure is repeated for all the selected and sorted fragments of the derivative chromosome.

In our example, the start band 1pter of the compare fragment is p-terminal to the start band of the first derivative fragment 1p32, hence the fragment "1pter->1p32" has been lost and the compare fragment is adjusted to "1q42->1qter". The next fragment of the derivative chromosome starts at 1q25 which is p-terminal to the start band of the compare fragement. Hence, the fragment "1q25->1q42" is a gain, and the compare fragment is reduced to "1qter->1qter".

In a last step, it is checked if something has remained from the compare fragment; such remainder would be a gain. In our example, nothing has remained.

If there are more chromosomes with different numbers to be replaced, such balances are calculated for each of them and simply summed up. If two chromosomes share the same chromosome number, a similiar procedure can be used, but starting with two compare fragments.

After the balance for the replaced chromosome(s) has been calculated, fragments originating from other chromosomes are added as gains. In our example, the fragment "3qter->3q21" is gained.