19/05/16 - indico.cern.ch
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19/05/16
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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
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%&$
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%&$
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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.