Unit 4: Linkage, Chromosome Mapping and Bacterial Genetics

Genes located on the same chromosome tend to be inherited together, violating Mendel's law of independent assortment. This unit builds on that single fact: measuring how often such genes are separated by recombination lets geneticists order genes and estimate distances, first in eukaryotes and then in bacteria and viruses.

I. Orientation: The Basis of Linkage

Linkage was established by Bateson and Punnett (1905) in sweet peas, where certain trait combinations appeared more often than expected, and explained by Morgan (1910) using Drosophila.

• Chromosome theory: genes are physical loci arranged linearly on chromosomes; alleles on the same chromosome form a linkage group.
• Linkage group: the number of linkage groups equals the haploid chromosome number (e.g. Drosophila = 4).
• Recombination frequency (RF): the proportion of recombinant offspring; used as the unit of genetic distance.
• Map unit (m.u.) / centiMorgan (cM): 1 m.u. = 1% recombinants; an operational, not physical, distance.
• Coupling vs repulsion: in cis (coupling) both dominant alleles lie on one homolog (AB/ab); in trans (repulsion) they are split (Ab/aB).

II. Linkage and Crossing Over

Mechanics of joint inheritance and its breakdown

The tendency of alleles to stay together is opposed by crossing over, which reshuffles them; the balance between the two determines observed ratios.

A. Definition

• Linkage: the physical association of genes on the same chromosome so they are transmitted as a unit.
• Crossing over: reciprocal exchange of segments between non-sister chromatids of homologous chromosomes during pachytene of meiosis I, producing recombinant chromatids.
• Chiasma: the visible cytological point of exchange; each crossover corresponds to one chiasma involving two of the four chromatids.

B. Complete and Incomplete Linkage

Whether recombinants appear at all depends on whether crossing over occurs between the loci.

1. Complete linkage: no recombinants produced (RF = 0).
   • Cause: genes so close, or crossing over suppressed, that no exchange separates them.
   • Example: male Drosophila and female silkworm show no crossing over, so only parental types arise.
   • Testcross output: AB/ab × ab/ab → only AB and ab, in ~1:1.
2. Incomplete (partial) linkage: both parental and recombinant types produced (0 < RF < 50%).
   • Cause: crossing over occurs in some meiocytes but not all.
   • Signature: parentals in majority, recombinants in minority.
   • Example testcross: AB/ab × ab/ab → AB and ab abundant, Ab and aB rare; RF = (Ab + aB) / total × 100.

• Upper limit: RF cannot exceed 50%; genes far apart or on different chromosomes give 50% recombinants, indistinguishable from independent assortment.

C. Molecular Mechanism of Crossing Over

Crossing over is enzymatic breakage and rejoining of DNA, described by the Holliday model (1964) and its double-strand-break refinements.

• Initiation: a double-strand break (or single-strand nicks) forms in one duplex, catalysed in meiosis by Spo11.
• Strand invasion: a free 3′ end invades the homologous duplex, forming a displacement (D) loop and a heteroduplex region.
• Holliday junction: the crossed strands create a four-way branched structure that migrates along the DNA (branch migration).
• Resolution: resolvase enzymes cut the junction.
  • Horizontal cut: yields non-crossover (patch) products.
  • Vertical cut: yields crossover (splice) products with recombinant flanking markers.
• Repair proteins: RecA (bacteria) / Rad51 (eukaryotes) mediate strand exchange; mismatch repair of heteroduplex explains gene conversion, non-reciprocal transfer seen in fungal tetrads.

III. Chromosome Mapping

Converting recombination into linear gene order

Because RF rises with distance, recombinant proportions from controlled crosses reconstruct the sequence and spacing of loci.

A. Two and Three Factor Crosses

Testcrosses to a fully recessive parent expose gamete genotypes directly as phenotypes.

1. Two-point cross: measures distance between two loci.

   • Distance: map distance (m.u.) = RF% = recombinants / total × 100.
   • Limitation: underestimates true distance over long intervals because double crossovers restore parental arrangement and go undetected.

2. Three-point cross: orders three genes and detects double crossovers in one experiment.

   • Setup: trihybrid testcross, e.g. ABC/abc × abc/abc, giving eight phenotypic classes.
   • Reading the classes:
     • Parentals: two most frequent classes.
     • Double crossovers (DCO): two rarest classes.
   • Gene order: compare a parental with a DCO class; the gene whose allele has switched relative to the other two is the middle gene.
   • Distances: for each interval, RF = (single crossovers in that interval + DCO) / total × 100.

Worked example (total = 1000 progeny):

Class          Count   Type
+ + +   / a b c   parental   405 / 400
+ + c / a b +    SCO region II  45 / 48
+ b c / a + +    SCO region I   45 / 51
+ b + / a + c    DCO             3 / 3

Region I  (gene1–gene2) = (45+51+3+3)/1000 = 10.2 m.u.
Region II (gene2–gene3) = (45+48+3+3)/1000 =  9.9 m.u.

• Interference (I): crossovers suppress nearby crossovers.
  • Coefficient of coincidence (c.o.c.): observed DCO / expected DCO, expected = RF(I) × RF(II) × total.
  • Interference: I = 1 − c.o.c.; I = 1 means complete interference (no DCO), I = 0 means independence.

B. Tetrad Analysis

In fungi such as Neurospora and yeast, all four meiotic products stay together, so recombination is scored per meiosis rather than per gamete.

• Tetrad types (two-gene cross AB × ab):
  • Parental ditype (PD): all four spores parental (2 AB, 2 ab).
  • Non-parental ditype (NPD): all four recombinant (2 Ab, 2 aB).
  • Tetratype (TT): one each of all four genotypes.
• Linkage test: genes are linked when PD ≫ NPD; unlinked when PD ≈ NPD.
• Map distance: corrected for double crossovers,
  
  TEXT

    RF = [ (½ TT) + (3 × NPD) ] / total tetrads × 100

• Ordered tetrads (Neurospora): the ascus preserves spore order, so the centromere–gene distance can be mapped.
  • First-division segregation (MI): alleles separate at meiosis I → no crossover between gene and centromere.
  • Second-division segregation (MII): alleles separate at meiosis II → a crossover occurred.
  • Centromere distance: = ½(MII asci) / total × 100.

IV. Bacterial Genetics

Mapping without meiosis

Bacteria lack meiotic crossing over; genes are mapped by three modes of DNA transfer, each with its own distance metric.

A. Transformation and Mapping

Uptake of free DNA from the medium by a competent recipient cell, discovered by Griffith (1928) and shown to be DNA by Avery, MacLeod and McCarty (1944).

• Process: donor DNA fragments enter the cell and recombine into the chromosome by homologous recombination.
• Co-transformation: two genes taken up and integrated together must lie close on the chromosome.
• Mapping principle: the higher the frequency of co-transformation, the tighter the linkage.
  • Metric: compare frequency of double transformants to the product of single-transformant frequencies; excess over the product indicates linkage.

B. Transduction and Mapping

Transfer of bacterial DNA from donor to recipient via a bacteriophage, discovered by Zinder and Lederberg (1952).

1. Generalized transduction: any chromosomal fragment is mistakenly packaged into a phage head during lytic assembly.
   • Co-transduction: two genes carried in one phage particle must lie within the length of DNA a phage head holds (~1–2 min of the map).
   • Mapping: co-transduction frequency falls as gene separation rises; used for fine-scale ordering.
2. Specialized transduction: a temperate phage (e.g. λ) excises imprecisely from its integration site and carries only adjacent genes (e.g. gal, bio for λ).
   • Use: confirms genes flanking the prophage attachment site.

C. Conjugation and Mapping

Direct cell-to-cell transfer of DNA through a pilus, requiring the F (fertility) plasmid; described by Lederberg and Tatum (1946) and refined by Wollman and Jacob.

• Cell types:
  • F⁺: carries free F plasmid; transfers plasmid only.
  • Hfr: F integrated into the chromosome; transfers chromosomal genes in a fixed order.
  • F′: F carrying a piece of chromosome after imprecise excision.
• Interrupted mating (Wollman–Jacob): mating pairs are broken at timed intervals in a blender; the time at which each donor gene first appears in recipients gives its map position.
  • Metric: map distance measured in minutes of transfer time; the E. coli map is 100 minutes, calibrated by origin of transfer.
  • Gradient: genes near the origin enter early and appear in most recombinants; distal genes enter late and rarely, because the mating filament usually breaks before transfer completes.
• Complementary approach: overlapping Hfr strains with different origins allow the circular chromosome to be assembled into one continuous map.