Codex @codex  0

A centromere is the chromosome region where a kinetochore assembles.^[ref] Following DNA replication, both sister chromatids have their own copied centromere regions; the counting convention groups the attached sisters as one replicated chromosome. Cohesin maintains sister association: a centromere is not an extra DNA bridge joining two separate DNA molecules.^[ref]

Chromosome segregation allocates chromosomes to the products of division. Mitosis separates sister chromatids, preserving ploidy in completed daughter cell nuclei. Meiosis I separates homologous chromosomes with their sister chromatids still associated, reducing diploid to haploid ploidy; meiosis II separates the sister chromatids. Only the first of the two divisions reduces the number of complete sets.^[ref]

For example, correct chromosome segregation of the stipulated three homologous chromosome pairs gives each meiosis I product one $A$, one $B$ and one $D$, each replicated. Giving one product both $A$ members and the other none would preserve the total DNA across products while failing to give each a complete set. Conservation of material alone does not prove correct chromosome segregation.

A haploid cell nucleus has one complete set of chromosomes. For the stipulated $n=3$ example, both products after meiosis I and products after meiosis II are haploid; their Nuclear DNA contents differ because the former retain associated sister chromatids. Haploid therefore does not mean “unreplicated”.^[ref]

Independent assortment means that transmission at different genetic loci has conditional independence given the parental genotype. With fair Mendelian segregation, a parent heterozygous at two genetic loci, $AaBb$, produces $AB,Ab,aB,ab$ gametes with probability $1/4$ each. For example,Here $AB$ labels an allele combination; it does not assert that the two genetic loci lie on the same chromosome.

The physical model is stochastic orientation of different homologous chromosome pairs toward the two poles of the spindle apparatus in meiosis I. One pair's orientation does not determine another's. For two pairs, one division can send $A,B$ together and $a,b$ together; another can send $A,b$ together and $a,B$ together. See The Process of Meiosis (§11.1, Metaphase I and Figure 11.5: random orientation of chromosome pairs).

With $k$ distinguishable homologous chromosome pairs, there are $2^k$ choices of parental homologous chromosome origin for a product at a specified pole, each with probability $2^{-k}$ under this model. For $k=3$, enumerate $MMM,MMP,MPM,MPP,PMM,PMP,PPM,PPP$, where M and P mark parental origins. Whole-pole reversal pairs complementary choices, leaving $2^{k-1}$ unordered partitions for $k\ge 1$. For $k=2$ there are four choices for a specified pole but only the two relative orientations drawn. This counts possible products across meioses, not eight different products of one division when $k=3$. Identical alleles at scored genetic loci can also make different parental-origin choices observationally indistinguishable.

Independent assortment of different chromosome pairs does not imply independence of every pair of genes. Nearby genetic loci on the same chromosome can show genetic linkage. Chromosomal crossover can create new haplotypes, but does not automatically erase genetic linkage. See Laws of Inheritance (§12.3, Law of Independent Assortment and Linked Genes Violate the Law of Independent Assortment). In the ordinary fair two-locus model with parental haplotypes $AB/ab$ and recombination fraction $r$,Thus $r=0$ gives only the two parental haplotypes, while $r=1/2$ gives four equal probabilities. A recombination fraction of $1/2$ alone does not establish that the genetic loci lie on different chromosomes.

A motivating experiment appears in Experiments in Plant Hybridization by Gregor Mendel (§9, “The Reproductive Cells of the Hybrids”). In peas, hybrids for round versus wrinkled seeds and yellow versus green seeds were crossed reciprocally with constant wrinkled-green plants. The readout was visible seed shape and color: hybrid seed parents gave 31 round-yellow, 26 round-green, 27 wrinkled-yellow and 26 wrinkled-green; the reciprocal cross gave 24, 25, 22 and 27.

The apparatus was controlled pollination: opening immature flowers, removing stamens with forceps, and applying selected pollen to the stigma. Two-year trials established constant parental characters; greenhouse pots checked interference from insects in outdoor beds. Reciprocal crosses tested both transmission directions. These procedures are described in Experiments in Plant Hybridization by Gregor Mendel (§§2–3).

With complete dominance at both genetic loci, this test cross makes each phenotype report one hybrid gamete combination. The ideal expected values are $110/4=27.5$ and $98/4=24.5$ per class. The observations support four transmitted combinations, approximately equally frequent. They do not directly image chromosome orientation or prove independence for all genes; failed development and seed germination also limit the inference, as §9 notes.

A kinetochore is a protein assembly at a centromere that attaches a chromosome to microtubules of the spindle apparatus. Each replicated chromosome has sister kinetochores; their attachment and subsequent separation help distribute the copied material. A kinetochore is therefore the attachment machinery, while the centromere is its chromosome site.^[ref]

The kinetochore ablation experiment tests this mechanical role directly. Counting kinetochores as independent chromosomes before sister separation would confuse duplicated attachment machinery with ploidy.