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accurate calculation of large map distances mapping function
analysis of single meioses ordered: gene centromere unordered: gene gene
LECTURE 07: EUKARYOTE CHROMOSOME MAPPING AND RECOMBINATION II
CHAPTER 4: FURTHER IDEAS
double & higher multiple crossovers underestimates of map distances calculated from recombination
specialized mapping formulae accurate map distance corrected for multiple crossovers
analysis of single meioses (in Fungi) can... position centromeres on genetic maps (~ genes) mechanisms of segregation and recombination
crossovers occur occasionally in mitotic diploid cells
ACCURATE MAPPING
mapping large distances is less accurate
best estimate of map distance obtained by adding distances calculated for shorter intervals
if possible, include more genes in the map
ACCURATE MAPPING
problems occur when you have ...
no intervening genes
genes very close together
ACCURATE MAPPING
account for multiple crossovers ?
need mapping function to correct for multiple events and accurately relate recombination to map distance
POISSON DISTRIBUTION
low #s sampled from large population
possible numbers obtainable are large, but most samples are small
e.g. random distribution of 100 x 1$ in class of 100 students... few students receive many bills...
POISSON DISTRIBUTION
e.g. random distribution of 100 x 1$ in class of 100 students
POISSON DISTRIBUTION
here, average is 1 bill/student... m = 1 # for a particular class... i = 0, 1, 2... 100
POISSON DISTRIBUTION
here, mean is 1 bill/student... m = 1 because 100 bills & 100 students
# for a particular class... i = 0, 1, 2... 100
how many students are predicted to capture 3 bills?
POISSON DISTRIBUTION
here, mean is 1 bill/student... m = 1 because 100 bills & 100 students
# for a particular class... i = 0, 1, 2... 100
how many students are predicted to capture 3 bills?
f(i) = ————
e-m mi
i !
POISSON DISTRIBUTION
POISSON DISTRIBUTION
f(0) = 0.368
f(1) = 0.368
f(2) = 0.184
f(3) = 0.061
f(4) = 0.015
f(5) = . . .
POISSON DISTRIBUTION
proportion of class with i items different m values
MAPPING FUNCTION
use Poisson to describe distribution of crossovers along chromosome
if... crossovers are random, we know mean # / region on chromosome
then we can calculate distribution of meioses with 0, 1, 2... n multiple crossovers
recombination frequency (RF) = % recombinants meiosis with 0 crossovers RF of 0%
MAPPING FUNCTION
meiosis with 1 crossover RF of 50%
MAPPING FUNCTION
meioses with 0 crossovers RF of 0%
meioses with > 0 crossovers RF of 50%
compare the non-recombinantchromatids
recombinantsshown darker
MAPPING FUNCTION
recombinants make up half of the products of meioses with 1 or more crossovers
0 crossover class is the only critical one
proportion of meioses with at least one crossover is 1 – 0 class; the 0 class is...
f(0) = ———— = e-me-m m0
0 !
MAPPING FUNCTION
proportion of meioses with at least one crossover is 1 – 0 class, which is...
f(0) = ———— = e-m
so the mapping function can be stated as...
RF = ½ (1 – e-m)
e-m m0
0 !
MAPPING FUNCTION
for low m...
m = 0.05, RF = ½ mm = 0.1, RF = ½ mm = 1, RF = 50
... RF = m / 2 at the dashed line
RF = ½ (1 – e-m)
or
use the equation... ~40
RF = ½ (1 – e-m)
RF = 27.5 cM ?
0.275 = ½ (1 – e-m)0.55 = 1 – e-m
e-m = 1 – 0.55 = 0.45
MAPPING FUNCTION
m 0.8 (mean # of crossovers / meiosis)corrected RF = m/2 = 0.4 = 40 % or 40 cM
MAPPING FUNCTION
for low m...
m = 0.05, RF = ½ mm = 0.1, RF = ½ mm = 1, RF = 50
... RF = m / 2 at the dashed line
RF = ½ (1 – e-m) = 40 cM
or
use the equation... ~40
mapping large distances is less accurate
best estimate of map distance obtained by adding distances calculated for shorter intervals
if possible, include more genes in the map
put RF values through a mapping function
MAPPING FUNCTION
ANALYSIS OF SINGLE MEIOSES products of meiosis remain together groups of haploid cells... either 4 (tetrads) or 8 (octads)
ANALYSIS OF SINGLE MEIOSES Neurospora crassa (we use Sordaria fimicola in Lab 5) note pigment phenotypes of the ascospores
ANALYSIS OF SINGLE MEIOSES meiosis & post-meiotic mitosis in linear tetrad / octad
ANALYSIS OF SINGLE MEIOSES
2 kinds of mapping with tetrads / octads:
ordered analysis to map gene centromere
unordered analysis to map gene gene
ORDERED ANALYSIS no crossing over between gene A and centromere
A & a segregateto different poles
“MI” segregation
ORDERED ANALYSIS crossing over between gene A and centromere
A & a segregateto different poles
“MII” segregation
ORDERED ANALYSIS
4 types of MII patterns equal frequencies
ORDERED ANALYSISOCTADS
A a A a A a A a A a A a
A a a A a A A a a A a A
a A A a a A
a A A a a A a A a A A a
a A a A A a
126 132 9 11 10 12 300 MII MII
MI
ORDERED ANALYSIS
# MI = 126 + 132 = 258 = 86 %
# MII = 9 + 11 + 10 + 12 = 42 = 14 %
OCTADS
A a A a A a A a A a A a
A a a A a A A a a A a A
a A A a a A
a A A a a A a A a A A a
a A a A A a
126 132 9 11 10 12 300 MII MII
MI
ORDERED ANALYSIS
divide by 2
ORDERED ANALYSIS
# MII = 9 + 11 + 10 + 12 = 42 = 14 %
A centromere = 14 / 2 = 7 cM
OCTADS
A a A a A a A a A a A a
A a a A a A A a a A a A
a A A a a A
a A A a a A a A a A A a
a A a A A a
126 132 9 11 10 12 300 MII MII
MI
ORDERED ANALYSIS
3 possibilities:1. the genes are on separate
chromosomes2. the genes are linked but on opposite
sides of the centromere3. the genes are linked and on the same
side of the centromere
a b
a b
a b
now consider 2 genes...
...independent
...independent
...???
ORDERED ANALYSIS crossover between centromere and both genes...
ANALYSIS OF SINGLE MEIOSES
2 kinds of mapping with tetrads / octads:
ordered analysis to map gene centromere
unordered analysis to map gene gene
ORDERED ANALYSIS
lots of crossovers between gene & centromere... appear to be unlinked
ORDERED ANALYSIS
MII frequency never reaches 100% theoretical maximum RF = 2/3 or 66.7% theoretical maximum calculated map distance = 33.3% >1 crossovers with distance... especially, DCO look like SCO
ORDERED ANALYSIS
second allele determines pattern
maximum MII = 2/3 = 33.3 % = 33.3 cM
multiple crossovers !
UNORDERED ANALYSIS
meioses with 0 crossovers RF of 0%
meioses with > 0 crossovers RF of 50%
UNORDERED ANALYSIS
parental ditypes
non-parenal ditypes
tetratypes
= NCO + 1/4 DCO
= 1/4 DCO
= SCO + 1/2 DCO
UNORDERED ANALYSIS
NCO = PD – NPD
= P score 1x
PD but not NCO
UNORDERED ANALYSIS
SCO = TT – 2NPD
= 2P score 2x
T but not SCO
UNORDERED ANALYSIS
DCO = 4NPD
= 4P score 4x
DCO but not NPD
UNORDERED ANALYSIS
corrected map distance (cM) between genes
= RF × 100 cM
= [ ½ single events + double events ] / total × 100 cM
= [ ½ ( TT – 2NPD ) + 4NPD ] / total × 100 cM
= ½ [ TT + 6NPD ] / total × 100 cM
ANALYSIS OF SINGLE MEIOSES
2 kinds of mapping with tetrads / octads:
ordered analysis to map gene centromere
unordered analysis to map gene gene
e.g., ORDERED & UNORDERED ANALYSIS
P r + × + t
r + F1 + t F2
or
e.g., ORDERED & UNORDERED ANALYSIS
P r + × + t
r + F1 +
; t
F2
e.g., ORDERED & UNORDERED ANALYSIS r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200
ORDERED & UNORDERED ANALYSIS r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
ordered analysis to map gene centromere MI ... no recombination
MII ... recombination
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
ordered analysis to map gene centromere MI ... no recombination
MII ... recombination
RF = ½ (MII / TOTAL)
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
ordered analysis to map gene centromere MI ... no recombination
MII ... recombination
RF = ½ (MII / TOTAL)
RF x 100 = map distance (cM)
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
RF = ½ (MII / TOTAL)
RF x 100 = map distance (cM)r cent. = ½ [(1+2+1+2+1)/200] x 100 = 1.75 cM
t cent. = ½ [(1+2+1+15+13+17+1)/200] x 100 = 16.75 cM
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
unordered analysis to map gene gene consider all possible gene pairs (here only 1) PD NPD?, unlinked or PD >> NPD, linked PD = NCO + 2-strand DCO TT = SCO + 3-strand DCO (x2) NPD = 4-strand DC) (¼ of all DC0)
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
unordered analysis to map gene geneRF = ½ [ TT + 6NPD ] / TOTAL
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
unordered analysis to map gene geneRF = ½ [ TT + 6NPD ] / TOTALRF x 100 = map distance (cM)
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
unordered analysis to map gene geneRF = ½ [ TT + 6NPD ] / TOTALRF x 100 = map distance (cM)
PD (133) >> NPD (2) linkedr t = ½ [ 65 + 6(2) / 200 ] x 100 = 19.25 cM
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
r 1.75 16.75 t
19.25
ORDERED & UNORDERED ANALYSIS
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
r 1.75 16.75 t
19.25
ORDERED & UNORDERED ANALYSIS
but... 1.75 + 16.75 = 18.5 ??
r + + t r + r + r t r t r + r + r + r t + + r + r + + t + t r + r + r t r t + + + + + + + t r + r + + t + + + t + + + t r t r + r t + t + t + t r + + t + + + t + + + t + t r t 129 1 2 1 15 13 17 17 2 1 2 200 r M1 M2 M2 M2 M1 M1 M1 M1 M2 M2 M1 t M1 M2 M2 M2 M2 M2 M2 M2 M1 M2 M1
r&t PD PD PD PD TT TT TT TT TT TT N PD
r 1.75 16.75 t
19.25
ORDERED & UNORDERED ANALYSIS
more accurate... calculation includes DCOs
EUKARYOTE CHROMOSOME MAPPING AND RECOMBINATION: PROBLEMS
in Griffiths chapter 4, beginning on page 141, you should be able to do questions #1-30
begin with the solved problems on page 138 if you are having difficulty
look at the way Schaum’s Outline discusses linkage and mapping for alternative explanations - especially tetrad analyses
try Schaum’s Outline questions in chapter 4, beginning on page 208