But what if we test more than one locus?
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But what if we test more than one locus?
The future of genetic studies of complex human diseases. Ref (Note above graphs are active spreadsheets -- just click)
Y= Number of Sib Pairs (Association)X= Population frequency (p)
GRR=1.5, #alleles=1E6
1E+2
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
1E+9
1E+10
1E-091E-081E-071E-060.000010.00010.0010.010.11
[based on Risch & Merikangas (1996) Science 273: 1516]
| Y= Number of Sib Pairs (Association)X= Genotypic Relative Risk (GRR)
#alleles=1E6, p=0.5 (population frequency)
1E+1
1E+2
1E+3
1E+4
1E+5
1E+6
1E+7
1E+8
0.001 0.01 0.1 1 10 100 1000 10000
1.001 1.01 1.1 2 11 101 1,001 10,001
1-GRRGRR
[based on Risch & Merikangas (1996) Science 273: 1516]|
|
Y= Number of Sib Pairs (Assocation)X= Number of Alleles (Hypotheses) Tested
GRR=1.5, p= 0.5 (population frequency)
0
200
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800
1,000
1,200
1,400
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1E+4 1E+6 1E+8 1E+10 1E+12 1E+14 1E+16 1E+18 1E+20 1E+22
[based on Risch & Merikangas (1996) Science 273: 1516]|
GRR = Genotypic relative risk
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Why multiple genes? alleles?
covariance
cis & trans
Haplotyping
Multiple loci models(additive, multiplicative, mean…)
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SNPs & Covariance in proteins
ApoE e4 RRR e3 RCR e2 RCC
Ancestral = Thr 61 Arg 112
Genotype
frequencies
Allele e2 e3 e4
10.0% e2 1.7% 15.0% 1.7% 18.3%
75.0% e3 15.0% 55.0% 25.0% 95.0%
15.0% e4 1.6% 25.0% 1.7% 28.3%
100.0% 18.3% 95.0% 28.4% 100.0%
(61 112 158)
Risk ratio: e2/3=0.5 ; e3/3=1; e3/4=2.5 ; e4/4=15
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Covariance in RNA
ref
" "
1 72
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Covariance
Mij= fxixjlog2[fxixj/(fxifxj)] M=0 to 2 bits; x=base type
xixj see Durbin et al p. 266-8.
D-stem
anticodonTC
3’acc
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Mutual Information
ACUUAU M1,6= = fAU log2[fAU/(fA*fU)]...CCUUAG x1x6
GCUUGC =4*.25log2[.25/(.25*.25)]=2UCUUGAi=1 j=6 M1,2= 4*.25log2[.25/(.25*1)]=0
Mij= fxixjlog2[fxixj/(fxifxj)] M=0 to 2 bits; x=base type
xixj see Durbin et al p. 266-8.
See Shannon entropy, multinomial Grendar
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Dulbecco R. (1986) A turning point in cancer research: sequencing the human genome. Science 231:1055-6
Mutations G719S, L858R, Del746ELREA in red.
EGFR Mutations in lung cancer: correlation with clinical response to Gefitinib [Iressa] therapy.
Paez, … Meyerson (Apr 2004) Science 304: 1497
Lynch … Haber, (Apr 2004) New Engl J Med. 350:2129.
Pao .. Mardis,Wilson,Varmus H, PNAS (Aug 2004) 101:13306-11.
Trastuzumab[Herceptin], Imatinib[Gleevec] : Normal, sensitive, & resistant alleles
Wang Z, et al. 2004 Science 304:1164. Mutational analysis of the tyrosine phosphatome in colorectal cancers.
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Pharmacogenomic tests
Abacavir HIV-AIDS HLA B5701 & 1502Warfarin Anti-Clot CYP2C9 & VKCoRImatinib Cancer BCR-ABLIrinotecan Cancer UGT1A15Fluorouracil Cancer DPYD-TYMSTamoxifen Cancer CYP2D6Long-QT Cardiac FamilionMercaptopurine Cancer TPMTClozapine Anti-psychotic HLA-DQB1Clopidogrel Anti-Clot CYP2C19
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Nutrigenomics/pharmacogenomics
Lactose intolerance: C/T(-13910) lactase persistence/non functions in vitro as a cis element 14kbp upstream enhancing the lactase promoter
http://www.genecards.org/cgi-bin/carddisp.pl?gene=LCT
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Nutrigenomics/pharmacogenomics
Thiopurine methyltransferase (TPMT) metabolizes 6-mercaptopurine and azathiopurine, two drugs used in a range of indications, from childhood leukemia to autoimmune diseases
CYP450 superfamily: CYP2D6 has over 75 known allelic variations, 30% of people in parts of East Africa have multiple copies of the gene, not be adequately treated with standard doses of drugs, e.g. codeine (activated by CYP2D6).
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Human metabolic Network (Recon 1)
Duarte et al. reconstruction of the human metabolic network based on genomic and bibliomic data. PNAS 2007 104:1777-82.
E.coli: 1200 ORFs http://gcrg.ucsd.edu/organisms
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Steady-state flux optima
A BRA
x1
x2
RB
D
C
Feasible fluxdistributions
x1
x2
Max Z=3 at (x2=1, x1=0)
RC
RD
Flux Balance Constraints:
RA < 1 molecule/sec (external)RA = RB (because no net increase)
x1 + x2 < 1 (mass conservation) x1 >0 (positive rates)
x2 > 0
Z = 3RD + RC
(But what if we really wanted to select for a fixed ratio of 3:1?)
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Applicability of LP & FBA
• Stoichiometry is well-known• Limited thermodynamic information is required
– reversibility vs. irreversibility• Experimental knowledge can be incorporated in to the
problem formulation• Linear optimization allows the identification of the reaction
pathways used to fulfil the goals of the cell if it is operating in an optimal manner.
• The relative value of the metabolites can be determined• Flux distribution for the production of a commercial
metabolite can be identified. Genetic Engineering candidates
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Precursors to cell growth
• How to define the growth function.– The biomass composition has been determined
for several cells, E. coli and B. subtilis.• This can be included in a complete metabolic
network
– When only the catabolic network is modeled, the biomass composition can be described as the 12 biosynthetic precursors and the energy and redox cofactors
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in silico cells E. coli H. influenzae H. pylori
Genes 695 362 268Reactions 720 488 444Metabolites 436 343 340
(of total genes 4300 1700 1800)
Edwards, et al 2002. Genome-scale metabolic model of Helicobacter pylori 26695. J Bacteriol. 184(16):4582-93.
Segre, et al, 2002 Analysis of optimality in natural and perturbed metabolic networks. PNAS 99: 15112-7. (Minimization Of Metabolic
Adjustment ) http://arep.med.harvard.edu/moma/
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EMP RBC, E.coli KEGG, Ecocyc
Where do the Stochiometric
matrices (& kinetic parameters) come
from?
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0 5 10 15 20 25 30 35 40 4510
-6
10-4
10-2
100
102
ACCOA
COA
ATP
FAD
GLY
NADH
LEU
SUCCOA
metabolites
coef
f. in
gro
wth
rea
ctio
nBiomass Composition
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Flux ratios at each branch point yields optimal polymer composition for replication
x,y are two of the 100s of flux dimensions
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Minimization of Metabolic Adjustment
(MoMA)
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Flux Data
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0 50 100 150 2000
20
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60
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100
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1
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456
78
9
10
11121314
15
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17 18
-50 0 50 100 150 200 250-50
0
50
100
150
200
250
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2
3456
78
910
11121314
1516
17
18
Experimental Fluxes
Pre
dic
ted
Flu
xes
-50 0 50 100 150 200 250-50
0
50
100
150
200
250
1
2
3
456
78
910
111213
14
15
16
1718
pyk (LP)
WT (LP)
Experimental Fluxes
Pre
dic
ted
Flu
xes
Experimental Fluxes
Pre
dic
ted
Flu
xes
pyk (QP)
=0.91p=8e-8
=-0.06p=6e-1
=0.56P=7e-3
C009-limited
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Competitive growth data: reproducibility
Correlation between two selection experiments
Badarinarayana, et al. Nature Biotech.19: 1060
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Essential 142 80 62Reduced growth 46 24 22
Non essential 299 119 180 p = 4∙10-3
Essential 162 96 66Reduced growth 44 19 25
Non essential 281 108 173 p = 10-5
MOMA
FBA
Competitive growth data
2 p-values
4x10-3
1x10-5
Position effects Novel redundancies
On minimal media
negative small selection effect
Hypothesis: next optima are achieved by regulation of activities.
LP
QP
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Co-evolution of mutual biosensors/biosynthesissequenced across time & within each time-point
Independent lines of Trp & Tyr co-culture
5 OmpF: (pore: large,hydrophilic > small)
42R-> G,L,C, 113 D->V, 117 E->A
2 Promoter: (cis-regulator) -12A->C, -35 C->A
5 Lrp: (trans-regulator) 1b, 9b, 8b, IS2 insert, R->L in
DBD.
Heterogeneity within each time-point .
Reppas, Shendure, Porecca
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Reconstructing evolved strains
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Non-optimal evolves to optimal
Ibarra et al. Nature. 2002 Nov 14;420(6912):186-9. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth.
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Metabolic optimization readings
Duarte et al. reconstruction of the human metabolic network based on genomic and bibliomic data. Proc Natl Acad Sci U S A. 2007 Feb 6;104(6):1777-82.
Joyce AR, Palsson BO. Toward whole cell modeling and simulation: comprehensive functional genomics through the constraint-based approach. Prog Drug Res. 2007;64:265, 267-309. Review.
Herring, et al. Comparative genome sequencing of Escherichia coli allows observation of bacterial evolution on a laboratory timescale. Nat Genet. 2006 38:1406-12.
Desai RP, Nielsen LK, Papoutsakis ET. Stoichiometric modeling of Clostridium acetobutylicum fermentations with non-linear constraints. J Biotechnol. 1999 71:191-205.
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.