Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Nonequilibrium effects in DNA microarrays:a multiplatform study

Jean-Charles WalterKU Leuven, Belgium

Collaborators :Myriam Kroll, Jef Hooyberghs and Enrico Carlon

LAFNES11, DresdenJuly 14

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Outline

1 Introduction : DNA and microarrays

2 Two- and Three-state models

3 Analysis of experimental data

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

DNA double helix

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Information in the cell

DNAtranscription

RNAtranslation

Proteine

replication

Antisense strand RNA polymerase

mRNA Transcript

Sense Strand

AG CG

UAC

G CG

CG

UAT

ACGU

ACGC

GCG

CGC

GUA

UAT

T T T TT TT T T TTA A AA A

AAAAAA TT TC G GG GG G

GGGGGGGG

C C C

CCCCCCCCCCC G

3' 5'

3'5'

5'3'

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

DNA microarrays : principle

Strands on the surface : probes

Strands labelled in solution : targets

Gene expression, detection of mutations...

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Two-state model

dθdt

= ck1(1 − θ)− k−1θ

k1/k−1 = e−∆G/RT

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Two-state model

θeq =ce−∆G/RT

1 + ce−∆G/RT≈

c,−∆G≪1ce−∆G/RT

θ(t) = θeq(1 − e−t/τ ) (θ(0) = 0)

{

k1 = Cst = α

k−1 = α · e∆G/RT

τ =1

ck1 + k−1=

1α(c + e∆G/RT )

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Two-state model

5 10 15 20 25 30 35 40-∆G (kcal/mol)

10-8

10-6

10-4

10-2

100

θdynamical saturation

Langmuir chemical saturation

isotherm

t=4ht=17ht=86h

~1/RT

T = 337K, c = 5pM and k1 = 104s−1M−1.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Three-state model

G∆G∆ G∆= γ’

θ1 θ2

k

k

k

−2

2

1

k−1

Hooyberghs, Baiesi, Ferrantini and Carlon (PRE, 2010)

JCW, Kroll, Hooyberghs and Carlon (J.Phys.Chem.B, 2011)

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Three-state model

dθ1dt = ck1(1 − θ1 − θ2) + k−2θ2 − (k−1 + k2)θ1,

dθ2dt = k2θ1 − k−2θ2,

k1/k−1 = e−∆G′/RT k2/k−2 = e−(∆G−∆G′)/RT ,

k1 = α; k−1 = αe∆G′/RT ,

k2 = ω; k−2 = ωe(∆G−∆G′)/RT .

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Three-state model

5 10 15 20 25 30 35 40-∆G (kcal/mol)

10-8

10-6

10-4

10-2

100

θ

regime

Langmuir isotherm ~ 1/RTexp

intermediate

dynamical saturation

chemical saturation

~1/RTeff

t=86ht=17ht=4h

T = 337K, c = 5pM, k1 = 105s−1M−1, k2 = 1s−1 andγ = 1/3.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Agilent microarrays

(a)

(c)

(d)

(b)

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Agilent microarrays

Design :

1 single Target :3’ ATTCGCCTATTGGACTACGTATTGCTCAGC 5’

Perfect Match Probe :5’ TAAGCGGATAACCTGATGCATAACGAGTCG 3’

One Mismatch Probes :5’ TAACCGGATAACCTGATGCATAACGAGTCG 3’

Two Mismatches Probes :5’ TAAGCTGATAACCTGATGCATCACGAGTCG 3’

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Agilent microarrays

t

-8 -6 -4 -2 0-∆∆Gµarray

(kcal/mol)10

0

102

104

106

I

L=30 nt, 50 pM, 65°C, 17h

(a)L

-8 -6 -4 -2 0-∆∆Gµarray

(kcal/mol)10

0

102

104

106

I

L=30 nt, 50 pM, 65°C, 86h

(b)

-8 -6 -4 -2 0-∆∆Gµarray

(kcal/mol)10

0

102

104

106

I

L=25 nt, 500 pM, 65°C, 17h

(c)

Fit : k1 = 5 · 103s−1M−1, k2 = 1s−1 and γ = 1/3.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Affymetrix microarrays

Data from Suzuki et al (BMC Genomics, 2007)Design :

150 6= Targets (L = 25nt) :3’ ATTCGCCTATTGGACTACGTATTGCTCAGC 5’

Probes with varying length :Perfect Match :

5’ TAAGCGGATAACCTGATGCATAACGAGTCG 3’ (L = 25nt)5’ AAGCGGATAACCTGATGCATAACGAGTCG 3’ (L = 24nt)

· · ·

5’ TGCATAACGAGTCG 3’(L = 14nt)One Mismatch :

5’ TAAGCGGATAACCTGATGCATAACGAGTCG 3’ (L = 25nt)5’ AAGCGGATAACCTGATGCATAACGAGTCG 3’ (L = 24nt)

· · ·

5’ CCTGATGCATAACGAGTCG 3’ (L = 14nt)

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Affymetrix microarrays

15 20 25 30-∆G (kcal/mol)

10

103

105

I

1.4fM14fM140fM1.4pM14pM140pM1.4nM

~1/RTexp

~1/RTeff

t = 16h, Texp = 318K, Teff = 850K= 2.7Texp

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Affymetrix microarrays

10 15 20 25 30 35-∆G (kcal/mol)

10

103

105

I

14fM140fM1.4pM

k1 = 105s−1M−1, k2 = 1s−1 and γ = 0.374

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Conclusion

Thermodynamics of DNA µarray still poorly understood.

Discrepancy between experiments and the two-statemodel : nonequilibrium effects.

Weaker slope : effective temperature.

Saturation of the signal at a lower value :dynamical saturation.

Consequences on the behavior of the devices.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Agilent microarrays

-8 -6 -4 -2 0-∆∆Gµarray

(kcal/mol)10

0

102

104

106

I c=2pM

c=10pM

c=50pM

c=250pML=30, 65°C, 17h

Intensity proportional to the concentration :far from saturation.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Agilent microarrays

14 16 18 20 22 24 26 28 30-∆G

sol (kcal/mol)

100

102

104

106

I

c=50pM

c=500pM

c=5000pMequilibrium

region

non-equilibrium region

L=30, T=55°C, 17h

T

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

DNA double helix

Estimation of the Gibbs free energy :

∆G = ∆H − T∆S

with the nearest-neighbor model :

∆G(

T A CA T G

)

= ∆G(

T AA T

)

+∆G(

A CT G

)

,

where the values are estimated in solution.

DNA Microarrays

Introduction : DNA and microarraysTwo- and Three-state modelsAnalysis of experimental data

Affymetrix microarrays

0 10 20 30 40-∆G (kcal/mol)

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

θ 5.105pM

5.103pM

5.101pM

5.10-1

pM

5.10-3

pM

T = 337K, t = 17h, k1 = 105s−1M−1, k2 = 1s−1 andγ = 1/3.

DNA Microarrays