Combinatorially Complex Combinatorially Complex Equilibrium Model Equilibrium Model

SelectionSelection

Tom RadivoyevitchAssistant ProfessorEpidemiology and BiostatisticsCase Western Reserve University

Email: txr24@case.eduWebsite: http://epbi-radivot.cwru.edu/

Combinatorially Complex Combinatorially Complex Equilibrium Model Equilibrium Model

SelectionSelection(overview/title breakdown)(overview/title breakdown)

• Combinatorially Complex Equilibria:Combinatorially Complex Equilibria:few reactants => many possible complexesfew reactants => many possible complexes

• Generate the possible models + Select or average the Generate the possible models + Select or average the best best

• Selection/Averaging: Akaike Information Criterion (AIC)Selection/Averaging: Akaike Information Criterion (AIC)• AIC decreases with P and then increasesAIC decreases with P and then increases• Billions of models, but only thousands near AIC upturnBillions of models, but only thousands near AIC upturn

• Challenge: Generate 1P, 2P, 3P model space chunks Challenge: Generate 1P, 2P, 3P model space chunks sequentially sequentially

• 8GB RAM => max of ~5000 models at a time8GB RAM => max of ~5000 models at a time• Models = Hypotheses Models = Hypotheses • Spurs: complete K = ∞ Spurs: complete K = ∞ [Complex]=0 [Complex]=0• Grids: binary K equal each otherGrids: binary K equal each other• R package ccems (CRAN) implements the methodsR package ccems (CRAN) implements the methods

Center RelevanceCenter Relevance

• StructuresStructures constrain minimal simplicity and maximal constrain minimal simplicity and maximal complexity of possible complexes and models in the complexity of possible complexes and models in the model space model space

• Move prior knowledge of structures into enzyme Move prior knowledge of structures into enzyme models models

• System BiologySystem Biology models integrate enzyme models models integrate enzyme models

• Protein-Protein Protein-LigandProtein-Protein Protein-Ligand I Interactionnteraction readouts: readouts:• Enzyme activities and DLS mass (i.e. average Enzyme activities and DLS mass (i.e. average

measures)measures)• Mass distributions of complexes (e.g. SEC and Mass distributions of complexes (e.g. SEC and

GEMMA)GEMMA)• Validate omic-predicted interactions and model themValidate omic-predicted interactions and model them• PEPCC (Harry Gill): Systematically express, purify and PEPCC (Harry Gill): Systematically express, purify and

characterize interaction suspects (e.g. of core wnt characterize interaction suspects (e.g. of core wnt signaling proteins) signaling proteins)

Ultimate GoalUltimate Goal

EXPERIMENTALBIOLOGY

COMPUTERMODELING

CONTROLTHEORY

models

control lawsdata

hypotheses

proposed clinical trial

validated process model development

control system design methods development

Present Future

• Safer flying airplanes with autopilotsSafer flying airplanes with autopilots• Ultimate Goal: individualized, state feedback based Ultimate Goal: individualized, state feedback based

clinical trialsclinical trials

• Better understanding => better controlBetter understanding => better control• Conceptual models help trial designs today Conceptual models help trial designs today • Computer models of airplanes help train pilots and Computer models of airplanes help train pilots and

autopilotsautopilots

Radivoyevitch et al. (2006) BMC Cancer 6:104

dNTP Supply System

Figure 1. dNTP supply. Many anticancer agents act on or through this system to kill cells. The most central enzyme of this system is RNR.

UDP

CDP

GDP

ADP

dTTP

dCTP

dGTP

dATP

dT

dC

dG

dADNA

dUMP

dU

TS

DCTD

dCK

DN

A p

olym

eras

eTK1

cytosol

mitochondria

dT

dC

dG

dA

TK2

dGK

dTMPdCMP

dGMP

dAMP

dTTPdCTP

dGTP

dATP

5NT

NT2

cytosol

nucleus

dUDP

dUTPdUTPase dN

dN

dCK

flux activation inhibition

ATPordATP

RN

R

dCK

R1

R2 R2

R1 R1

R1 R1

R1 R1

R1 R1 R1

R1

R1 R1

R1 R1 R1

R1

R2 R2

UDP, CDP, GDP, ADP bind to catalytic site

ATP, dATP, dTTP, dGTP bind to selectivity site

dATP inhibits at activity site, ATP activates at activity site?

5 catalytic site states x 5 s-site states x 3 a-site states x 2 h-site states = 150 states

(150)6 different hexamer complexes => 2^(150)6 models ~ 1 followed by a trillion zeros

ATP activates at hexamerization site??

Ribonucleotide Reductase (RNR)Ribonucleotide Reductase (RNR)

R2 R2

RNR is Combinatorially Complex

Michaelis-Menten ModelMichaelis-Menten Model

RNR: no NDP and no R2 dimer => kcat of complex is zero,else different R1-R2-NDP complexes can have different kcat values.

m

Tmm

mT

TT

TT

KSSVv

kEKSKS

KSkEv

kEEES

EEES

ESkEv

EPEESPEkvEESkv

][][

][1/][

101/][

/][][

][][][

][0][][

][][

)(][0)(][][0][

max

1

1

1

1

E + S ES

0.005 0.010 0.020 0.050 0.100 0.200 0.500

020

4060

8010

0

Total [r] (uM)

Per

cent

Act

ivity solid line = Eqs. (1-2)

dotted = Eq. (3)

Data from Scott, C. P., Kashlan, O. B., Lear, J. D., and Cooperman, B. S. (2001) Biochemistry 40(6), 1651-166

Model Parameter Initial Value Optimal Value Confidence Interval RRGGttr1.1.0 RRGGtt_r 0.020 0.012 (0.007, 0.024) SSE 1070.252 823.793 AIC 45.006 42.650

MM Kd 0.020 0.033 (0.022, 0.049) SSE 2016.335 1143.682 AIC 50.706 45.603

R=R1 r=R22G=GDP t=dTTP

)2(]][[][][0

)1(]][[][][0

_

_

SET

SET

KSESS

KSEEE

SE

T

SE

T

T

SE

SET

SE

TSE

T

KS

KS

EESversus

KS

KS

EES

KS

EEKSEE

_

_

_

_

_

_ ][1

][

][][][1

][

][][][1

1][][][1][][

Substitute this in here to get a quadratic in [S] which solves as

Bigger systems of higher polynomials cannot be solved algebraically => use ODEs (above)

][4][][(][][(5.][][ _2

__ TSETTSETTSET SKESKESKSES

0)0]([,0)0]([

]][[][][][

]][[][][][

_

_

SE

KSESS

dSd

KSEEE

dEd

SET

SET

Michaelis-Menten ModelMichaelis-Menten Model [S] vs. [S[S] vs. [STT] ]

(3)

E ES

EI ESI

E ES

EI ESISEIIEIE

T

SEIIESET

SEIIEIESET

KKSIE

KIEII

KKSIE

KSESS

KKSIE

KIE

KSEEE

___

___

____

]][][[]][[][][0

]][][[]][[][][0

]][][[]][[]][[][][0

E ES

EI

EIT

EST

EIEST

KIEII

KSESS

KIE

KSEEE

]][[][][0

]][[][][0

]][[]][[][][0

ESIEIT

ESIEST

ESIEIEST

KISE

KIEII

KISE

KSESS

KISE

KIE

KSEEE

]][][[]][[][][0

]][][[]][[][][0

]][][[]][[]][[][][0

E ES

EI ESI

E

EI ESI

E ES

ESI

E

EI ESI

E ES

ESI

=

=E

EI

E

ESI

E ES E

Competitive inhibition

uncompetitive inhibition if kcat_ESI=0

E | ES

EI | ESI

noncompetitive inhibition Example of K=K’ Model

==

Enzyme, Substrate and InhibitorEnzyme, Substrate and Inhibitor

Total number of spur graph models is 16+4=20 Radivoyevitch, (2008) BMC Systems Biology 2:15

Rt Spur Graph ModelsRt Spur Graph Models

RRttRRtRt

T

RRttRRtRRRtT

KtR

KtR

KtRtt=

KtR

KtR

KR

KtRRRp=

222

2222

20

2220

.0)0(;0)0(

2

222

222

2222

tRKtR

KtR

KtRtt=

dtd

KtR

KtR

KR

KtRRRp=

dRd

RRttRRtRtT

RRttRRtRRRtT

R RR

RRtt

RRt Rt

R

RRtt

RRt Rt

R RR

RRtt

Rt

R RR

RRt Rt

R RR

RRtt

RRt

R

RRtt

Rt

R

RRt Rt

R RR

Rt

IJJJJJIJ JJJI JIJJ

IJIJ IJJI JJII

JJJJ

R

RRtt

RRt

R RR

RRtt

R RR

RRt

R

Rt

R

RRtt

R

RRt

JIIJIIJJ JIJI

R RR RIJII IIIJ IIJI JIII IIII

R

Rt

R

RRtt

R

RRt

R RRI0II III0 II0I 0III

R = R1 t = dTTP

for dTTP induced R1 dimerization(RR, Rt, RRt, RRtt)

R Rt t

RRt t

Rt R t

RRt t

Rt Rt RRtt

Kd_R_R

Kd_Rt_R

Kd_Rt_Rt

Kd_R_t

Kd_R_t Kd_RRt_t

Kd_RR_t=

=

=

=

|

|

|

Rt Grid Graph ModelsRt Grid Graph Models

R Rt t

RRt t

Rt R t

RRt t

RRtt

KR_R

KR_t

KRRt_t

KRR_t=

=

===

== ===

=

==

===

==

=

R Rt t

RRt t

Rt R t

RRt t

Rt Rt RRtt

KR_R

KRt_R

KRt_Rt

KR_t

KR_t

|

|

|

|

|

|

| |

|

|

|

|

| |

|

?

?

HIFF

HDFFHDDD

=

][][2][2][22

][)1]([][)(

)(

11TT

T

RRRttRRtRRM

RpRRMyE

yEy

AICc = N*log(SSE/N)+2P+2P(P+1)/(N-P-1)

Scott, C. P., Kashlan, O. B., Lear, J. D., and Cooperman, B. S. (2001) Biochemistry 40(6), 1651-166

Radivoyevitch, (2008) BMC Systems Biology 2:15

Application to DataApplication to Data

HDFF==

R

RRtt

IIIJ

5 10 15

100

120

140

160

180

Total [dTTP] (uM)

Ave

rage

Mas

s (k

Da)

III0mIIIJHDFF

III0m

Model Parameter Initial Value

Optimal Value

Confidence Interval

1 III0m m1 90.000 82.368 (79.838, 84.775)

  SSE 4397.550 525.178

  AIC 71.965 57.090

2 IIIJ R2t2 1.000^3 2.725^3 (2.014^3, 3.682^3)

  SSE 2290.516 557.797

  AIC 67.399 57.512

27 HDFF R2t0 1.000 12369.79 (0, 1308627507869)

  R1t0_t 1.000 1.744 (0.003, 1187.969)

  R2t0_t 1.000 0.010 (0.000, 403.429)

  SSE 25768.23 477.484

  AIC 105.342 77.423

RRttRRtRt

T

RRttRRtRRRtT

KtR

KtR

KtRtt=

KtR

KtR

KR

KtRRRp=

222

2222

20

2220

.0)0(;0)0(

2

222

222

2222

tRKtR

KtR

KtRtt=

dtd

KtR

KtR

KR

KtRRRp=

dRd

RRttRRtRtT

RRttRRtRRRtT

jitR

ji

KtR=tR

ji

2+5+9+13 = 28 parameters => 228=2.5x108 spur graph models via Kj=∞ hypotheses

28 models with 1 parameter, 428 models with 2, 3278 models with 3, 20475 with 4

R = R1X = ATP

18

6

612

4

46

2

22

1

18

6

612

4

46

2

22

1

642

642

0

6420

i XR

i

i XR

i

i XR

i

i RX

i

T

i XR

i

i XR

i

i XR

i

i RX

i

T

iiii

iiii

KXRi

KXRi

KXRi

KXRiXX=

KXR

KXR

KXR

KXRRR=

Yeast R1 structure. Dealwis Lab, PNAS 102, 4022-4027, 2006

ATP-induced R1 Hexamerization

Kashlan et al. Biochemistry 2002 41:462

==

==

==

= ====

==

= ====

======

====

----

====

==

====

======

==

= ====

------------

==

====

------------

X ====

------------

==

====

------------

X

====

======

XX

====

======

XX

X

====

------------

XX

X

====

======

XX

====

======

==

====

==

====

==

====

======

------------

XX

X

X ====

------------

X====

------------

====

======

X ------------

X

====

------------

------------

X ------------

X------------

X ====

X====

====

XX

X XX

X

Kolmogorov-Smirnov Test p < 10-16 28 of top 30 did not include an h-site term; 28/30 ≠ 503/2081 with p < 10-16

This suggests no h-site. Top 13 included R6X8 or R6X9, save one, single edge model R6X7 This suggests that less than 3 a-sites are occupied in hexamer.

2088 Models with SSE < 2 min (SSE)

142 144 146 148 150 152 154

0.00

0.05

0.10

0.15

0.20

0.25

AIC

dens

ity

no h site (508)h site (1580)

A

142 144 146 148 150

0.05

0.15

0.25

AICde

nsity

no h site (77)h site (78)

B

146 148 150 152 154

0.00

0.05

0.10

0.15

0.20

0.25

0.30

AIC

dens

ity

no h site (287)h site (1174)

C

148 150 152 154

0.0

0.1

0.2

0.3

0.4

0.5

AIC

dens

ity

no h site (146)h site (329)

D

50 100 200 500 1000 2000

100

200

300

400

500

[ATP] (uM)

Mas

s (k

Da)

R6X8 141.23R6X9 142.88R6X7 143.12R6X10 146.12R6X6 148.92R6X11 149.60R6X12 152.82R6X13 155.68R6X14 158.17R6X15 160.33R6X16 162.20R6X17 163.84R6X18 165.26

Data from Kashlan et al. Biochemistry 2002 41:462

Conclusions (so far)1. The dataset does not support the existence of an h-site

2. The dataset suggests that ~1/2 of the a-site are not occupied by ATP

R1

R1

R1 R1

R1 R1

aa

[ATP]=~1000[dATP]So system prefers to have 3 a-sites empty and ready for dATPInhibition versus activation is partly due to differences in pockets

a

a

a

a

UDP

CDP

GDP

ADP

dTTP

dCTP

dGTP

dATP

dT

dC

dG

dADNA

dUMP

dU

TS

DCTD

dCK

DN

A p

olym

eras

e

TK1

cytosol

mitochondria

dT

dC

dG

dA

TK2

dGK

dTMPdCMP

dGMP

dAMP

dTTPdCTP

dGTP

dATP

5NT

NT2

cytosol

nucleus

dUDP

dUTPdUTPase dN

dN

dCK

flux activation inhibition

ATPordATP

RN

R

dCK

== =

=

==_=

=

==

=

=

==

==

== _

EESES2

ES3

ES4

X

8 K Models x 8 k Models => 64 Models

Tetrameric Enzyme Models (e.g. Thymidine Kinase 1)

4

1

4

1

4

1

4

1

4

1

][14

][

][1][4

]][[

][4

][

i ES

iT

i ES

iT

i

i ES

iT

i ES

iT

i

T

i

ii

i

i

i

i

KS

KSik

KSE

KSEik

E

ESikk

4321

4321

432

432

]][[4]][[3]][[2]][[][][0

]][[]][[]][[]][[][][0

ESESESEST

ESESESEST

KSE

KSE

KSE

KSESS

KSE

KSE

KSE

KSEEE

4,3,2,1]][[][ iKSEESiES

ii

][4

][4

1

T

i

ii

E

ESikk

== =

=

==_=

=

===

===

==== _

ESES2

ES3

ES4

If [S] ≈ [ST]

44

][]][[4]][[4][ _

_SE

ESESon

offSEonoff

KKK

ESSE

kk

KSEkESk

66

][]][[6

][2]][[3

][]][[4 __

222

2

2__SESSE

ESESSESSE

KKKK

ESSE

ESSES

ESSEKK

4][3]][[2

][2]][[3

][]][[4 ___

33

2

2___

2

2

SESSESSE

ESSESSESSE

KKKK

ESSES

ESSES

ESSEKKK

SESSESSESSEES

SESSESSESSE

KKKKKESSES

ESSES

ESSES

ESSEKKKK

____4

4

3

3

2

2____

32

32][4]][[

][3]][[2

][2]][[3

][]][[4

Complete K vs. Binary K

0.05 0.20 1.00 5.00 50.00

0.2

0.5

1.0

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.79, 1.84, 2.34, 2.24 k = 7.04, 5.92, 5.91, 3.62

1 2 3

-0.0

6-0

.02

0.02

0.06

Model Average

Fitted Value

Tran

sfor

med

Res

idua

l

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Berenstein 2000

Total [dT]k

(1/s

ec)

K = 0.76, 0.78, 0.74, 0.20 k = 7.10, 6.98, 7.01, 7.02

1 2 3 4 5 6 7

-0.2

-0.1

0.0

0.1

0.2

0.3

Model Average

Fitted Value

Tran

sfor

med

Res

idua

l

0.2 0.5 1.0 2.0 5.0

0.5

1.0

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 0.73, 0.51, 0.49, 0.49 k = 1.97, 3.16, 3.90, 3.89

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-0.1

5-0

.05

0.05

0.15

Model Average

Fitted ValueTr

ansf

orm

ed R

esid

ual

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Li 2004

Total [dT]

k (1

/sec

)

K = 0.70, 0.56, 0.54, 0.56 k = 5.21, 4.77, 4.70, 4.69

1 2 3 4

-0.2

-0.1

0.0

0.1

0.2

0.3

Model Average

Fitted Value

Tran

sfor

med

Res

idua

l

0.1 0.2 0.5 1.0 2.0 5.0

0.02

0.05

0.10

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 1.19, 0.64, 0.49, 0.47 k = 0.20, 0.27, 0.27, 0.27

0.05 0.10 0.15 0.20 0.25

-0.0

15-0

.005

0.00

5

Model Average

Fitted Value

Tran

sfor

med

Res

idua

l

K = (0.85, 0.69, 0.65, 0.51) µM k = (3.3, 3.9, 4.1, 4.1) sec-1

kmax = 4.1/sec S50 = 0.6 µM h = 1.1

h

T

h

T

SS

SSk

k

50

50max

1

DFFF.DDDD DDLL.DDDD DDDM.DDDD DDDD.DFFFDDDD.DDLL DDDD.DDDM

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 0.72, 0.72, 0.72, 0.72 k = 2.91, 2.91, 4.18, 4.18

DD

DD

.DD

LL

5e-02 5e+00

0.5

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 0.39, 0.39, 0.39, 0.39 k = 3.58, 3.58, 7.14, 7.14

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 0.36, 0.36, 0.36, 0.36 k = 1.35, 1.35, 3.80, 3.80

5e-02 5e+00

0.5

5.0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.45, 0.45, 0.45, 0.45 k = 3.89, 3.89, 4.66, 4.66

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 0.35, 0.35, 0.35, 0.35 k = 0.07, 0.07, 0.27, 0.27

Total [dT]

k (1

/sec

)

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.28, 1.28, 1.28, 1.28 k = 4.99, 4.99, 4.99, 4.11

DD

DD

.DD

DM

5e-02 5e+000.

55.

0

Berenstein 2000

Total [dT]

k (1

/sec

) K = 0.15, 0.15, 0.15, 0.15 k = 1.69, 1.69, 1.69, 7.18

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 1.20, 1.20, 1.20, 1.20 k = 5.51, 5.51, 5.51, 3.44

5e-02 5e+00

0.5

5.0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.60, 0.60, 0.60, 0.60 k = 5.01, 5.01, 5.01, 4.67

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 1.43, 1.43, 1.43, 1.43 k = 0.41, 0.41, 0.41, 0.20

Total [dT]

k (1

/sec

)

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 0.95, 0.95, 0.95, 0.95 k = 3.56, 4.29, 4.29, 4.29

DD

DD

.DFF

F

5e-02 5e+00

0.5

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 0.54, 0.54, 0.54, 0.54 k = 3.93, 7.22, 7.22, 7.22

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]k

(1/s

ec)

K = 0.53, 0.53, 0.53, 0.53 k = 0.96, 3.93, 3.93, 3.93

5e-02 5e+00

0.5

5.0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.48, 0.48, 0.48, 0.48 k = 3.50, 4.67, 4.67, 4.67

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 0.56, 0.56, 0.56, 0.56 k = 0.06, 0.28, 0.28, 0.28

Total [dT]

k (1

/sec

)

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.08, 1.08, 0.85, 0.85 k = 4.23, 4.23, 4.23, 4.23

DD

LL.D

DD

D

5e-02 5e+00

0.5

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 0.83, 0.83, 0.42, 0.42 k = 7.14, 7.14, 7.14, 7.14

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 0.90, 0.90, 0.41, 0.41 k = 3.80, 3.80, 3.80, 3.80

5e-02 5e+00

0.5

5.0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.57, 0.57, 0.48, 0.48 k = 4.66, 4.66, 4.66, 4.66

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 1.08, 1.08, 0.32, 0.32 k = 0.26, 0.26, 0.26, 0.26

Total [dT]

k (1

/sec

)

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.02, 1.02, 1.02, 0.56 k = 4.12, 4.12, 4.12, 4.12

DD

DM

.DD

DD

5e-02 5e+00

0.5

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 0.76, 0.76, 0.76, 0.20 k = 7.02, 7.02, 7.02, 7.02

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 0.77, 0.77, 0.77, 0.19 k = 3.69, 3.69, 3.69, 3.69

5e-02 5e+000.

55.

0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.54, 0.54, 0.54, 0.51 k = 4.69, 4.69, 4.69, 4.69

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 0.90, 0.90, 0.90, 0.08 k = 0.25, 0.25, 0.25, 0.25

Total [dT]

k (1

/sec

)

0.05 0.50 5.00

0.2

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.15, 0.97, 0.97, 0.97 k = 4.31, 4.31, 4.31, 4.31

DFF

F.D

DD

D

5e-02 5e+00

0.5

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 0.98, 0.55, 0.55, 0.55 k = 7.23, 7.23, 7.23, 7.23

0.2 1.0 5.0

0.5

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 1.32, 0.54, 0.54, 0.54 k = 3.92, 3.92, 3.92, 3.92

5e-02 5e+00

0.5

5.0 Li 2004

Total [dT]

k (1

/sec

)

K = 0.65, 0.49, 0.49, 0.49 k = 4.67, 4.67, 4.67, 4.67

0.1 0.5 2.0

0.02

0.20

Birringer 2006

Total [dT]k

(1/s

ec)

K = 1.62, 0.53, 0.53, 0.53 k = 0.27, 0.27, 0.27, 0.27

Total [dT]

k (1

/sec

)

0.05 0.20 1.00 5.00 50.00

0.2

0.5

1.0

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.32, 0.72, 1.18, 2.38 k = 5.16, 2.92, 5.99, 3.63

1 2 3

-0.0

8-0

.04

0.00

0.04

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3

-0.1

0-0

.05

0.00

0.05

Fitted Values

Res

idua

ls

CV = 0.014

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 1.18, 0.44, 0.69, 0.10 k = 11.94, 3.19, 4.10, 7.03

1 2 3 4 5 6 7

-0.2

-0.1

0.0

0.1

0.2

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3 4 5 6 7

-0.3

-0.1

0.1

0.3

Fitted Values

Res

idua

ls

CV = 0.04

0.1 0.5 2.0 5.0

0.2

0.5

1.0

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 1.65, 0.30, 8.94, 0.19 k = 1.14, 5.42, 8.50, 3.56

0.5 1.5 2.5 3.5

-0.1

5-0

.05

0.05

Fitted Values

Tran

sfor

med

Res

idua

ls

0.5 1.5 2.5 3.5

-0.2

0-0

.10

0.00

0.10

Fitted Values

Res

idua

ls

CV = 0.06

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Li 2004

Total [dT]

k (1

/sec

)

K = 1.69, 2.01, 0.10, 0.52 k = 12.81, 6.05, 3.52, 4.76

1 2 3 4

-0.1

0.0

0.1

0.2

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3 4

-0.2

-0.1

0.0

0.1

0.2

Fitted Values

Res

idua

ls

CV = 0.039

0.1 0.2 0.5 1.0 2.0 5.0

0.02

0.05

0.10

0.20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 104.58, 0.88, 0.01, 0.20 k = 21.33, 3.32, 0.01, 0.29

0.05 0.10 0.15 0.20 0.25

-0.0

100.

000

0.00

5

Fitted Values

Tran

sfor

med

Res

idua

ls

0.05 0.10 0.15 0.20 0.25

-0.0

15-0

.005

0.00

5

Fitted Values

Res

idua

ls

CV = 0.062

0.05 0.20 1.00 5.00 50.00

0.2

0.5

1.0

2.0

MunchPetersen 1993

Total [dT]

k (1

/sec

)

K = 1.32, 0.72, 1.18, 2.38 k = 5.16, 2.92, 5.99, 3.63

1 2 3

-0.0

8-0

.04

0.00

0.04

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3

-0.1

0-0

.05

0.00

0.05

Fitted Values

Res

idua

ls

CV = 0.014

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Berenstein 2000

Total [dT]

k (1

/sec

)

K = 1.18, 0.44, 0.69, 0.10 k = 11.94, 3.19, 4.10, 7.03

1 2 3 4 5 6 7

-0.2

-0.1

0.0

0.1

0.2

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3 4 5 6 7

-0.3

-0.1

0.1

0.3

Fitted Values

Res

idua

ls

CV = 0.04

0.1 0.5 2.0 5.0

0.2

0.5

1.0

2.0

Frederiksen 2004

Total [dT]

k (1

/sec

)

K = 1.65, 0.30, 8.94, 0.19 k = 1.14, 5.42, 8.50, 3.56

0.5 1.5 2.5 3.5

-0.1

5-0

.05

0.05

Fitted Values

Tran

sfor

med

Res

idua

ls

0.5 1.5 2.5 3.5

-0.2

0-0

.10

0.00

0.10

Fitted Values

Res

idua

ls

CV = 0.06

5e-02 5e-01 5e+00 5e+01

0.5

1.0

2.0

5.0

Li 2004

Total [dT]

k (1

/sec

)

K = 1.69, 2.01, 0.10, 0.52 k = 12.81, 6.05, 3.52, 4.76

1 2 3 4

-0.1

0.0

0.1

0.2

Fitted Values

Tran

sfor

med

Res

idua

ls

1 2 3 4

-0.2

-0.1

0.0

0.1

0.2

Fitted Values

Res

idua

ls

CV = 0.039

0.1 0.2 0.5 1.0 2.0 5.00.

020.

050.

100.

20

Birringer 2006

Total [dT]

k (1

/sec

)

K = 104.58, 0.88, 0.01, 0.20 k = 21.33, 3.32, 0.01, 0.29

0.05 0.10 0.15 0.20 0.25

-0.0

100.

000

0.00

5

Fitted Values

Tran

sfor

med

Res

idua

ls

0.05 0.10 0.15 0.20 0.25

-0.0

15-0

.005

0.00

5

Fitted Values

Res

idua

ls

CV = 0.062

8-parameter model fits to the datasets

1e-08 1e-04 1e+00 1e+04

05

1015

2025

30

DFLM.DFLM

Total [S]

k (1

/sec

)A

1e-08 1e-04 1e+00 1e+04

020

4060

8010

0

DFLM.DFLM

Total [S]

k (1

/sec

)

B

K = (10-6, 10-3, 1, 103) A) k = (100, 10, 40, 10) B) k = (10, 10, 40, 100)

With parameters initially at ½ their true values, A identified itself, B had difficulties (its 1st two K estimates were off 2-5-fold).

Horizontal lines are k1/4, 2k2/4, 3k3/4 and 4k4/4 Vertical lines are K1/4, 2K2/3, 3K3/2 and 4K4

Combinatorially Complex Equilibrium Model

Selection (ccems, CRAN 2009)

Systems Biology Markup Language

interface to R (SBMLR, BIOC 2004)Model networks of enzymes

Model individual enzymes

SUMMARYSUMMARY

R1

R2 R2

R1 R1

R1 R1

R1 R1

R1 R1 R1

R1

R1 R1

R1 R1 R1

R1

R2 R2

R2 R2

Figure 8. T. Thorsen et al. (S. R. Quake Lab) Science 2002

Figure 9. J. Melin and S. R. Quake Annu. Rev. Biophys. Biomol. Struct. 2007. 36:213–31

Background: Quake Lab MicrofluidicsBackground: Quake Lab Microfluidics

Figure 9 shows how a peristaltic pump is implemented by three valves that cycle through the control codes 101, 100, 110, 010, 011, 001, where 0 and 1 represent open and closed valves; note that the 0 in this sequence is forced to the right as the sequence progresses.

Adaptive Experimental DesignsAdaptive Experimental DesignsFind best next 10 measurement Find best next 10 measurement conditions given models of data conditions given models of data collected.collected.

Need automated analyses in feedback Need automated analyses in feedback loop of automatic controls of microfluidic loop of automatic controls of microfluidic chips chips

µFluidic M-inputCMPM

C1

Mixing Control bits

C2C3

CM

…

TPC1 …C2 C2 C3 buff buff buff

N-plug stream (C1:2C2:C3:C4)/N

Output

Output

C4

Streams of pulses

Filtered output

(a)

(b)

Output

Output Mixer

Dye-3 (C3)Dye-2 (C2)

Solvent Dye-1 (C1)

0b

2b

1b

3b

Flow velocity = 2 cm/sTP=100 ms, M=4N=20, Levels = 64

Dye-3

C3

Dye-1

Dye-2

C2

Water

C1

Mixing Channel

Output

Control Lines

3 mm C1

C2

C3

5

0

10

-5 0 5 10 15 20

2535

45

minuteste

mpe

ratu

re (C

)

-5 0 5 10 15 20

01

23

45

minutes

cont

rol e

ffort

-5 0 5 10 15 20

2535

45

minutes

tem

pera

ture

(C)

-5 0 5 10 15 20

02

46

8

minutes

cont

rol e

ffort

+-

setpointKp

Ki∫ Σ hot plate water temperature

Simple example of a control system for a single-input single-output (SISO) system

Emphasis is on the stochastic component of the model.

Is there something in the black box or are the input wires disconnected from the output wires such that only thermal noise is being measured? Do we have enough data?

Model components: (Deterministic = signal) + (Stochastic = noise)Statistics Engineerin

gEmphasis is on the deterministic component of the model

We already know what is in the box, since we built it. The goal is to understand it well enough to be able to control it.

Predict the best multi-agent drug dose time course schedules

Increasing amounts of data/knowledge

Why Systems BiologyWhy Systems Biology

dNTPs + AnalogsdNTPs + Analogs DNA + Drug-DNADNA + Drug-DNA

Damage DrivenDamage Drivenor or

S-phase DrivenS-phase Driven

dNTP demand dNTP demand is eitheris either

DNA repairDNA repair

SalvageSalvage

De novoDe novo

MMRMMR-- Cancer Treatment Cancer Treatment Strategy Strategy

IUdRIUdR

ConclusionsConclusions

For systems biology to succeed:For systems biology to succeed:– move biological research toward move biological research toward

systems which are best understoodsystems which are best understood– specialize modelers to become experts specialize modelers to become experts

in biological literatures (SB is not a in biological literatures (SB is not a service)service)

AcknowledgementsAcknowledgements Case Comprehensive Cancer CenterCase Comprehensive Cancer Center NIH (K25 CA104791)NIH (K25 CA104791) Chris Dealwis (CWRU Pharmacology)Chris Dealwis (CWRU Pharmacology) Anders Hofer (Umea) Anders Hofer (Umea) Thank you Thank you

Indirect Approach Indirect Approach pro-B Cell Childhood ALLpro-B Cell Childhood ALL

TT: TEL-AML1 with HR : TEL-AML1 with HR tt : TEL-AML1 with CCR : TEL-AML1 with CCR tt : other outcome : other outcome

BB: BCR-ABL with CCR: BCR-ABL with CCR bb: BCR-ABL with HR: BCR-ABL with HR bb: censored, missing, : censored, missing,

or other outcome or other outcome

B

b

b

b

b

b

b

b

bb

bb

b

b

b

b

tt t

tt

t

t t

ttt

tt

t

t

t

t

t

t

t

t

t

tt

t

t

t

t

t

t

tt

t

t

t

t

t

t

t

t

t

tt

t

t

tt

t

t

t

t

t

tt

tt

t

T

T

T

t

t

t

t

t

tt

t

t t

tt

t

tt

t

t

t

t

0 2 4 6 8 10 12 140

200

400

600

800

1000

1200

DNTS Flux (uM/hr)

DN

PS

Flu

x (u

M/h

r)

Ross et al: Blood 2003, 102:2951-2959 Yeoh et al: Cancer Cell 2002, 1:133-143 Radivoyevitch et al., BMC Cancer 6, 104 (2006)

THF

CH2THF

CH3THF

CHOTHF

DHF

CHODHFHCHO

GAR

FGAR

AICAR

FAICAR

dUMP dTMP

NADP+ NADPHNADP+ NADPH

NADP+ NADPH

MetHcys

Ser

Gly

GART

ATICATIC

TS

ATP

ADP

11R

2R 2

3

4

10

9 8

5 6

7

12 11

13

HCOOH

MTHFDMTHFR

MTR

DHFR

SHMT

FTS

FDS

Morrison PF, Allegra CJ: Folate cycle kinetics in human breast cancer cells. JBiolChem 1989, 264:10552-10566.

library(ccems) # Thymidine Kinase Example topology = list( heads=c("E1S0"), # E1S0 = substrate free E sites=list( c=list( # c for catalytic site t=c("E1S1","E1S2","E1S3","E1S4") ) # t for tetramer ) ) # TK1 is 25kDa = 25mg/umole, so 1 mg = .04 umoles g = mkg(topology, activity=T,TCC=F)dd=subset(TK1,(year==2000),select=c(E,S,v))dd=transform(dd, ET=ET/4,v=ET*v/(.04*60))# now uM/sectops=ems(dd,g,maxTotalPs=8,kIC=10,topN=96)#9 min on 1 cpu

library(ccems) # Ribonucleotide Reductase Exampletopology <- list( heads=c("R1X0","R2X2","R4X4","R6X6"), sites=list( # s-sites are already filled only in (j>1)-mers a=list( #a-site thread m=c("R1X1"), # monomer 1 d=c("R2X3","R2X4"), # dimer 2 t=c("R4X5","R4X6","R4X7","R4X8"), # tetramer 3 h=c("R6X7","R6X8","R6X9","R6X10", "R6X11", "R6X12") # hexamer 4 ), # tails of a-site threads are heads of h-site threads h=list( # h-site m=c("R1X2"), # monomer 5 d=c("R2X5", "R2X6"), # dimer 6 t=c("R4X9", "R4X10","R4X11", "R4X12"), # tetramer 7 h=c("R6X13", "R6X14", "R6X15","R6X16", "R6X17", "R6X18")# hexamer 8 ) ))g=mkg(topology,TCC=TRUE) dd=subset(RNR,(year==2002)&(fg==1)&(X>0),select=c(R,X,m,year))cpusPerHost=c("localhost" = 4,"compute-0-0"=4,"compute-0-1"=4,"compute-0-2"=4)top10=ems(dd,g,cpusPerHost=cpusPerHost, maxTotalPs=3, ptype="SOCK",KIC=100)

K = e∆G/RT => K = (0, ∞) maps to ∆G = (-∞, ∞)

Model weights e∆AIC/∑e∆AIC

Fast Total Concentration Constraint (TCC; i.e. g=0) solvers are critical to model

estimation/selection. TCC ODEs (#ODEs = #reactants) solve TCCs faster than kon =1 and koff = Kd systems (#ODEs = #species = high # in combinatorially complex situations)

Semi-exhaustive approach = fit all models with same number of parameters as parallel batch, then fit next batch only if current shows AIC improvement over previous batch.

Comments on Methods

50 100 200 500 2000

100

200

300

400

500

[ATP] (uM)

Mas

s (k

Da)

A

R6X8R2X4.R6X8R6X9

100 200 300 400 500

-20

020

40

Fitted Value

Res

idua

l

B

1e+02 1e+03 1e+04 1e+05 1e+06

010

020

030

040

050

0

[ATP] (uM)

Mas

s (k

Da)

R2X4.R6X8R2X3.R6X9R2X3.R6X12

Conjecture

Greater X/R ratio dominates at highLigand concentrations

In this limit the system wants to partition As much ATP into a bound form as possible

Bias in 1st four residuals=> Do not weight errors