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

400

600

800

1,000

1,200

1,400

1,600

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

Why multiple genes? alleles?

covariance

cis & trans

Haplotyping

Multiple loci models(additive, multiplicative, mean…)

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

Covariance in RNA

ref

" "

1 72

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

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

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.

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

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

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).

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

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?)

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

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

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/

EMP RBC, E.coli KEGG, Ecocyc

Where do the Stochiometric

matrices (& kinetic parameters) come

from?

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

Flux ratios at each branch point yields optimal polymer composition for replication

x,y are two of the 100s of flux dimensions

Minimization of Metabolic Adjustment

(MoMA)

Flux Data

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

1

2

3

456

78

9

10

11121314

15

16

17 18

-50 0 50 100 150 200 250-50

0

50

100

150

200

250

1

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

Competitive growth data: reproducibility

Correlation between two selection experiments

Badarinarayana, et al. Nature Biotech.19: 1060

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

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

Reconstructing evolved strains

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.

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.

.