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Computational systems biophysics in health and disease at the molecular, cellular, and cell-

population levels

Jose Vilar

Biofisika Institute (CSIC, UPV/EHU), University of the Basque Country,

Bilbao, Spain

1998-2004: Physics & Biology ( Postdoc at Princeton U./HHMI & Rockefeller U.) 2004-2008: Computational Biology (Lab Head & Asst. Member at MSKCC) 2008- : Biophysics (Ikerbasque Prof. at U. Basque Country)

Goal: To understand and accurately predict the molecular, cellular, and cell-population behavior in terms of the interactions of the components and vice versa

Outline: •  Relevance of quantitative biophysical models •  Molecular level:

lac operon DNA looping, macromolecular assembly, and gene regulation phage-λ RXR

•  Cellular level: TGF-beta pathway

•  Cell-population level: T-cell apoptosis Accurate diagnosis of acute myeloid leukemia

Goal: To understand and accurately predict the molecular, cellular, and cell-population behavior in terms of the interactions of the components and vice versa

Outline: •  Relevance of quantitative biophysical models •  Molecular level:

lac operon DNA looping, macromolecular assembly, and gene regulation phage-λ RXR

•  Cellular level: TGF-beta pathway

•  Cell-population level: T-cell apoptosis Accurate diagnosis of acute myeloid leukemia

O3 O1 O2

PlacZYA

92bp 401bp

lac operon

OL1 2 3

OR3 2 1 PR / cro

PRM / cI

2kbphage

O3 O1 O2

PlacZYA

92bp 401bp

lac operon

OL1 2 3

OR3 2 1 PR / cro

PRM / cI

2kbphage

Molecular Biology of THE CELL, 3th ed (1994)

A physicist getting into biology: read the Alberts, let’s model the lac operon

How come that O2 and O3 increase the repression level by a factor 60? Increase in the repressor local concentration around O1? But O2 and O3 are 10 and 300 times weaker than O1!

Vilar & Leibler, J. Mol. Biol. 2003 Figure from Alberts et al., Molecular Biology of THE CELL, 5th ed (2008)

Intuitive idea:

- Bacteria: lac, ara, gal… (~200 bp) - Viruses: λ-phage (~2,000 bp) - Eukaryotes: transcription (~5,000 bp) p53, NF-κB, RXR mating type switching (~100,000 bp) (telomere)T-loops (~10,000bp)

p53

Stenger et al., EMBO J 1994

100 nm λcI

Revet et al., 1999

T-loops

Griffith et al., 1999

DNA looping

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Saiz & Vilar, Mol. Syst. Biol. 2006 Vilar & Leibler, J. Mol. Biol. 2003

on

on

off

off

off

(i)

(ii)

(iii)

(iv)

(v)

/1 [ ]okn G RTk

kP N eZ

−Δ=

1

2

L

1

2

L

p+e2

-pcL

p+e1

1

1 2

21 2( ) ( ) ( )( ) LL

G p e p ec p

s s ss s s

Δ = + + ++ −

( ) /1 G Rs TsP eZ

−Δ=

State-oriented Domain-oriented

Modeling of DNA looping and transcription regulation (2 sites, 1 loop)

ln[ ]op p RT N= −

1max (1 )sτ −

Key idea: ΔGiv= ΔGbinding1 + ΔGbinding2 + ΔGlooping

Repressor concentration (nM) Saiz &Vilar, Nuc. Acids Res. 2008

Rep

ress

ion:

τ max

/τ

Free energy:

O3 O1 O2

PlacZYA

92bp 401bp

Exps. (symbols) by Oehler et al., 1990

lac operon model:

There are no free parameters!

1 2 3

1 2

1 2

12

1 3 13

2 3 23

3

12

13

23

( ) ( ) ( ) ( )( )( )( )

L

L

L

L

L

L

s s sG p e p e ss s ss s ss s s

p ec pc pc p

Δ = + + + + ++ −+ −+ −

( ) /m 1 3ax 3

1 (1 )( 1 ) sG RT

ss s s e

Zτ τ χ −Δ= − + −∑Transcription:

ΔG

l in k

cal/m

ol

Operator distance in bp

In vivo properties of DNA

Free energy of looping

Muller et al., 1996

(± 0.15 kcal/mol)

Saiz, Rubi, and Vilar, PNAS 2005 ; Saiz &Vilar, COSB 2006 & PLoS One 2007

ΔGl = −RT ln

Rloop − Rnoloop

Rnoloop −1[N ]

The octamer does not exist in solution!

cI & cro 2*36= 1458 states 1458*13= 18,954 reactions

cI2

cro2

1/kdegradation (min)#

mol

ecul

es

2 kb

Combinatorial complexity in phage-λ

Saiz & Vilar, Mol. Syst. Biol. 2006

Implementation in C++double H(long *s) { return ( -0.6*mylog((lci2f(s)*1.47e-9)/nsbfactorCI2)*(s[o1ri]+s[o2ri]+s[o3ri]+s[o1li]+s[o2li]+s[o3li]) -12.7*s[o1ri]-10.7*s[o2ri]-10.2*s[o3ri]-3*s[o1ri]*s[o2ri]-3*(1-s[o1ri])*s[o2ri]*s[o3ri] -13.8*s[o1li]-12.1*s[o2li]-12.4*s[o3li]-2.5*s[o1li]*s[o2li]-2.5*(1-s[o1li])*s[o2li]*s[o3li] +(eloop-21.5*s[o1ri]*s[o2ri]*s[o1li]*s[o2li]-3*s[o3ri]*s[o3li])*s[loop] -0.6*mylog((cro2f(s)*1.47e-9)/nsbfactorcro)*(s[o1rc]+s[o2rc]+s[o3rc]+s[o1lc]+s[o2lc]+s[o3lc]) -12.0*s[o1rc]-10.8*s[o2rc]-13.4*s[o3rc]-1.0*s[o1rc]*s[o2rc]*(1-s[o3rc])-0.6*s[o2rc]*s[o3rc]*(1-s[o1rc])-0.9*s[o1rc]*s[o2rc]*s[o3rc] -12.0*s[o1lc]-10.8*s[o2lc]-13.4*s[o3lc]-1.0*s[o1lc]*s[o2lc]*(1-s[o3lc])-0.6*s[o2lc]*s[o3lc]*(1-s[o1lc])-0.9*s[o1lc]*s[o2lc]*s[o3lc] +infinito*(s[o1ri]*s[o1rc]+s[o2ri]*s[o2rc]+s[o3ri]*s[o3rc]+s[o1li]*s[o1lc]+s[o2li]*s[o2lc]+s[o3li]*s[o3lc]) )/0.6; };

double logkon(long i, long *s) { switch(i) { case o1ri: case o2ri: case o3ri: case o1li: case o2li: case o3li: return mylog(0.1*lci2f(s)/nsbfactorCI2); case o1rc: case o2rc: case o3rc: case o1lc: case o2lc: case o3lc: return mylog(0.1*cro2f(s)/nsbfactorcro); case loop: return log(1); } };

Free energy

ln(on rate) double singlerate(long i, long *s) { double Hchan; switch(s[i]) { case 0: return myexp(logkon(i,s)); case 1: s[i]=0; Hchan=H(s); s[i]=1; return myexp(H(s)-Hchan+logkon(i,s)); } };

on rate: 0 → 1

off rate: 1 → 0 using detailed balance

1,458 states 18,954 reactions

Modulated    self-­‐assembly    

[n4 ] =

[n2 ]2

Kdim

[n2 ]

[n2*] = [n2 ] f ([s])

[s]

response R1

signal

response R2

DNA  binding  

1

[n2 ]e−ΔGs1

o

RT

[n2 ]e−ΔGs2

o

RT

[n2 ]2 e−ΔGs1

o +ΔGs2o

RT

[n4 ]e−ΔGs2

o

RT

[n2 ][n4 ]e−ΔGs1

o +ΔGs2o

RT

[n4 ]e−ΔGs1

o

RT

[n2 ][n4 ]e−ΔGs1

o +ΔGs2o

RT

[n4 ]2 e−ΔGs1

o +ΔGs2o

RT

[n4 ]e−ΔGs1

o +ΔGs2o +ΔGC

o

RT

[n2*][n4 ]e

−ΔGs1

o +ΔGs2o

RT

[n2*][n4 ]e

−ΔGs1

o +ΔGs2o

RT

[n2*]e

−ΔGs1

o

RT

[n2*]e

−ΔGs2

o

RT

[n2*]2 e

−ΔGs1

o +ΔGs2o

RT

[n2*][n2 ]e

−ΔGs1

o +ΔGs2o

RT

[n2*][n2 ]e

−ΔGs1

o +ΔGs2o

RT

(17)

(14)

(11)

(8)

(16)

(13)

(10)

(7)

(5) (4)

(15)

(12)

(9)

(6)

(3)

(1) (2)

(state) Zstate

- site 2 --- site 1 -

TranscripAon  control  

enhancer

coactivator

Vilar & Saiz, Nuc. Acids Res. 2011

DNA looping in the nuclear receptor RXR

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[atRA] (nM)

Nor

mal

ized

fold

indu

ctio

n

Response R2 Klig=350

GCo = 10.92

GCo = 10.76

GCo = 9.47

[9cRA] (nM)

Response R2 Klig=8

Response R1 Klig=8

GCo = 8.03

A

B C

100 101 102 103 1040.0

0.5

1.0

100 101 102 103 1040.0

0.5

1.0

100 101 102 103 1040.0

0.5

1.0

10 1 100 101 102 1030.0

0.5

1.0

10 1 100 101 102 1030.0

0.5

1.0

10 1 100 101 102 1030.0

0.5

1.0

0 101 102 103 1040.0

0.5

1.0

Modulated    self-­‐assembly    

[n4 ] =

[n2 ]2

Kdim

[n2 ]

[n2*] = [n2 ] f ([s])

[s]

response R1

signal

response R2

TranscripAon  control  

enhancer

coactivator

Vilar & Saiz, Nuc. Acids Res. 2011

DNA looping in the nuclear receptor RXR Control/intervention points: Modulated self-assembly is a key control point of the transcriptional responses. It is present in transcription factors like p53, NF-κB, STATs, Oct, RXR ...

Zhu et al, Cancer Cell 2005 Receptor trafficking is a key control point of of the TGF-β pathway (NEXT)

Does cancer progression take advantage of it? Acute promyelocytic leukemia resulting from translocation t(15;17)(q24;q21) leads to the formation of PML-RAR/RXR tetramers

Goal: To understand and accurately predict the molecular, cellular, and cell-population behavior in terms of the interactions of the components and vice versa

Outline: •  Relevance of quantitative biophysical models •  Molecular level:

lac operon DNA looping, macromolecular assembly, and gene regulation phage-λ RXR

•  Cellular level: TGF-beta pathway

•  Cell-population level: T-cell apoptosis Accurate diagnosis of acute myeloid leukemia

Signal transduction and receptor trafficking: TGF-β pathway

Vilar, Jansen & Sander, PLoS Comp. Biol. 2006

PT45

HaCaT

Act

ivity

Time (min) TGF-β

0 100 200 300 400 0

50

100

150

200

250

0 100 200 300 400 0

100

200

300

400

500

0 100 200 300 400 0

100

200

300

θ M

θ EE

θ 0θ1

Internal- ization

Degradation Recycling

Production

Degradation

Production

Signal

Signal

Two-compartment model

Trafficking-coordinate model

TβRII

TβRI

complex

Smad

ligand

Same biology + fancier math

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'&%

Time (hours)

Act

ivity

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%&$

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"#!

"#$

"#%

"#&

'#"

!"# !"$ !"% !"& '"! '"#

!"#

!"$

!"%

!"&

'"!

+cycloheximide

Accurate modeling and prediction

Experimental data from: Inman et al., Mol. Cell, 2002

Vilar & Saiz, Biophys. J. 2011

19/05/16  

4  

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Time (hours)

Act

ivity

HaCaT

PT45

Panc-1

BxPC3

Trafficking control of

transient-permanent responses

Experimental data from: Nicolas & Hill, Oncogene, 2003

Macromolecular assembly on DNA and membranes share the same physical principles

Macromolecular assembly at membranes

Goal: To understand and accurately predict the molecular, cellular, and cell-population behavior in terms of the interactions of the components and vice versa

Outline: •  Relevance of quantitative biophysical models •  Molecular level:

lac operon DNA looping, macromolecular assembly, and gene regulation phage-λ RXR

•  Cellular level: TGF-beta pathway

•  Cell-population level: T-cell apoptosis Accurate diagnosis of acute myeloid leukemia

Coupling of metabolism with apoptosis in T-cells

ATP Apoptosis ↑ ↓ATP Apoptosis ↓ ↑

Threshold model: ATP < ATP*: cell dies ATP > ATP*: cell survives

1 2 3 4

0.5

1.0

1.5

2.0

ATP

1 2 3 4

0.5 Th

resh

old

dist

ribut

ion

ATP*

Survival Death

Why do some cells die and others don’t?

Implications: the death rate is strongly dependent on CHANGES in ATP

0 25 50 75 100 125 1500.0

0.2

0.4

0.6

0.8

1.0

0 25 50 75 100 125 1500

1

2

3

4

0 12

34

0

1

2

3

0 12

34

Exps. by Rathmell et al., 2000

Neo

Bcl-xL 1E1

Bcl-xL 4.1

ATP

(nM

ol/1

06C

ells

)

Time – IL-3 (hours)

Nor

mal

ized

sur

viva

l

Time – IL-3 (hours)

Thre

shol

d di

strib

utio

ns

ATP* (nMol/106Cells)

Neo

Bcl-xL 1E1

Bcl-xL 4.1

Experiments (symbols) vs. model results (black lines)

Vilar, BMC Syst. Biol. 2010

The goal of this challenge is to diagnose Acute Myeloid Leukemia from patient samples using flow cytometry data The samples consist of 43 AML positive patients and 316 healthy donors. Samples from peripheral blood or bone marrow aspirate were collected over a one year period Information for about half of the donors on whether they are healthy or AML positive is provided as training set The challenge is to determine the state of health of the other half, based only on the provided flow cytometry data

Best Performer method at the DREAM6/FlowCAP2 Molecular Classification of Acute Myeloid

Leukemia Challenge

Vilar, Phys. Rev. X 2014

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DREAM6/FlowCAP2 AML diagnosis challenge

  FL1 FL2 FL3 FL4 FL5

Tube 1 IgG1-FITC IgG1-PE CD45-ECD IgG1-PC5 IgG1-PC7

Tube 2 Kappa-FIT Lambda-PE CD45-ECD CD19-PC5 CD20-PC7

Tube 3 CD7-FITC CD4-PE CD45-ECD CD8-PC5 CD2-PC7

Tube 4 CD15-FITC CD13-PE CD45-ECD CD16-PC5 CD56-PC7

Tube 5 CD14-FITC CD11c-PE CD45-ECD CD64-PC5 CD33-PC7

Tube 6 HLA-DR-FITC CD117-PE CD45-ECD CD34-PC5 CD38-PC7

Tube 7 CD5-FITC CD19-PE CD45-ECD CD3-PC5 CD10-PC7

Tube 8 Non Specific Non Specific Non Specific Non Specific Non Specific

Key points to distinguish between AML and Normal cases:

1) How to look at the distributions

2) What to look at

Entropies for comparing distributions

Si,AML

= − Pi(Γ)ln

Pi(Γ)

PAML(Γ)dΓ∫ S

i,Normal= − P

i(Γ)ln

Pi(Γ)

PNormal(Γ)dΓ∫

ΔSi= S

i,Normal− S

i,AML= P

i(Γ)ln

PNormal(Γ)

PAML(Γ)dΓ∫

S = Seq− k

BP(Γ)ln P(Γ)

Peq(Γ)dΓ∫

Gibbs entropy formula: Entropy is maximum when P=Peq

Entropies with respect to AML and Normal states:

Entropy difference:

It is positive for P=PNormal and negative for P=PAML

4D entropies (FL 2,3,4,5),(FL 1,2,3,4)x(Tb 3,4,5,6)

AML Normal

ΔS = Si,Normal

− Si,AML( )

i∑ Training set

AML Normal

Prediction

205205314314262262211211227227326326269269219219284284344344

221221348348285285261261299299239239236236203203

337337340340

274274328328357357250250339339187187251251222222301301359359200200264264238238252252181181256256220220325325319319354354224224

270270312312310310245245188188288288182182289289341341254254263263268268333333212212185185279279258258273273186186184184202202249249334334277277311311230230335335247247315315193193308308183183331331355355237237304304232232204204233233327327345345201201343343307307302302296296

226226272272303303292292199199347347266266231231309309291291234234287287217217323323321321317317316316209209243243281281313313260260190190346346358358297297215215267267216216210210208208298298191191207207228228253253242242294294192192213213214214290290305305318318180180241241278278246246223223189189229229332332351351300300352352329329330330195195196196244244198198257257240240306306206206286286283283276276350350282282

324324353353248248194194197197265265349349255255356356338338218218225225280280336336293293275275235235295295320320259259

322322342342271271

50 100 150

-10

-5

5

10

1341345858151151165165959526269989891741743737494910510510310367673333888817217260601011015577117117167167122122939394946363127127178178

2525148148202016316384846262414147474444616199998181102102119119149149170170126126353532326464162162141141242446461381381111137137166166155155686821213131130130424212121311317070

159159909036361251253838161161177177808012912915315312312310810843431711711281281391392323160160106106717116816815151421426969881431437979152152169169272744157157454512412497971201201181181581581751757575535333154154767696961361369191104104666617917930302222161655555757112828661161163939110110787886865959107107929210910910010015015017172273733434146146

131313513515615640405151113113545472721331331641645050144144828229298585140140656548481141141211218787115115147147191998981321321818176176838374741010173173777711211214145656

1111111451455252

50 100 150

-15

-10

-5

5

10

Scores

262262211211227227314314205205299299221221284284269269219219337337285285348348344344203203261261236236326326239239

340340

222222

26326325025018818818318321321319419435735732832825625626826824524531531527027032332330130118418420120122622634634622422419819834534530430422822822522533233218118121721732432433133128828819519524324326726720020027427426626623223233933931731728728724624625225223823818718730730735535529529534934921521535335330530534134133533519719724124132132122322321821832532522922935135133033022022027327319919921221227227235935931031028328320920918218220220231331318018026426428928920420423023023323333633619019018618630030031931931231229329335635629129118518524924929229225725720620624224235435429429429729720720725825830230219619628128118918932232235835831131129629630630634234225125132732724824819319325525527927921021021621628228223723735035026526524024019119130830824424428628627727730330323523523123128028034334327827835235220820830930933333319219229829826026033433434734724724733833825925927627631831832932921421431631625325332032029029027127125425427527523423450 100 150

0.2

0.4

0.6

0.8

1.0

PAML

= 1eΔS + 1

Probability AML

Take-home messages: Piecing back together all the genetic, biochemical, molecular, and structural information into a physiologically relevant description of the cell, needs "constructive" methods. Computational biophysics has emerged as a promising tool for transforming molecular detail into a more integrated form of understanding complex behavior. Having a global view of the processes involved and their effects through all relevant levels of biological organization is crucial to identify and characterize the key control elements of the system.