Download - Mathematical modeling of apoptosis: the death-inducing ...klho.github.io/pres/docs/ho-2009-nyu-biomath.pdf · Introduction Model formulation Results Conclusion Mathematical modeling

Introduction Model formulation Results Conclusion

Mathematical modeling of apoptosis: thedeath-inducing signaling complex

Kenneth L. Ho

Courant Institute, New York University

NYU Biomathematics Seminar (2009 Feb 3)


What is apoptosis?

Apoptosis is a conserved, highly regulated cell death program inmulticellular organisms.

Involved in many physiological processes

Dysregulation associated with pathological conditions

Characteristic cell death morphology


Biochemistry of apoptosis

Hengartner (2000)


Motivation for a detailed model

Previous models of apoptosis

Complete but unstable

Harrington et al. (2008)Hua et al. (2005)Okazaki et al. (2008)

Stable but incomplete

Bagci et al. (2006)Eissing et al. (2004)Legewie et al. (2006)

How to achieve a complete and stable model?

1 Mechanistic description of oligomerization

2 Inclusion of inhibitors (IAP, BAR, cFLIP)

3 Synthesis and degradation


Role of cFLIP: a toy model

Toy model:

Reactions:

DISC + cFLIPk1−−⇀↽−−k−1

DISC:cFLIP,

DISC + Casp8k2−→ DISC + Casp8∗,

∅ α−⇀↽−β

Casp8 , Casp8∗γ−→ ∅

Steady state:

[Casp8∗]ss =α/γ

1 + β/ (k2 [DISC]ss),


Role of cFLIP: a toy model

10−2

100

102

0

10

20

30

[DISC]0 (nM)

[Cas

p8*]

ss (

nM)

[cFLIP]0 = 81 nM

0 50 100 150 2000

5

10

15

[cFLIP]0 (nM)

[Cas

p8*]

ss (

nM)

[DISC]0 = 1 nM

[DISC]0 (nM)

[cF

LIP

] 0 (nM

)

[Casp8*]ss

(nM)

10−2

10−1

100

101

102

0

50

100

150

200

5

10

15

20

cFLIP

no cFLIP

B

C

A


Goals

Focus on the extrinsic pathway of apoptosis

DISC formation and its downstream interactions

Goals1 To construct a biologically relevant model

Bistability at physiological parametersMeaningful input-output map (FasL→ Casp3∗)

2 To study the function of cFLIP

How does it affect the apoptotic threshold?Does it confer robustness to the system?


DISC model

Important features

1 Fas trimerization

2 Stepwise recruitment

3 Regulation by cFLIP

4 Pairwise Casp8 activation

Reactions [with (i , j , k, l) ≡FasL:Fasi :FADDj :cFLIPk :Casp8l ]:

(i , j , k, l) + Fas −−−⇀↽−−− (i + 1, j , k, l)

(i , j , k, l) + FADD −−−⇀↽−−− (i , j + 1, k, l)

(i , j , k, l) + cFLIP −−−⇀↽−−− (i , j , k + 1, l)

(i , j , k, l) + Casp8 −−−⇀↽−−− (i , j , k, l + 1)

(i , j , k, l) −−→ (i , j , k, l − 2) + 2Casp8∗

Model parameters(δ, σcFLIP, σCasp8):

1 Death domain clustering(δ = 1, 2, 3)

2 cFLIP stoichiometry(σcFLIP = 1, 2, 3)

3 Casp8 stoichiometry(σCasp8 = 2, 3)


Extrinsic caspase model

Couple to DISC model, map from Casp8→ Casp3:

Reactions:

Casp8∗ + Casp3 −−→ Casp8∗ + Casp3∗

Casp3∗ + Casp8 −−→ Casp3∗ + Casp8∗

Casp8∗ + BAR −−⇀↽−− Casp8∗:BAR

Casp3∗ + IAP −−⇀↽−− Casp3∗:IAP


DISC model (3,3,3)

10−2

100

2

4

6

8

10

12

[FasL]0 (nM)

[Cas

p8*]

ss (

nM)

[cFLIP]0 = 81 nM

0 50 100 150 2000.5

1

1.5

2

2.5

[cFLIP]0 (nM)

[Cas

p8*]

ss (

nM)

[FasL]0 = 0.1 nM

[FasL]0 (nM)

[cF

LIP

] 0 (nM

)

[Casp8*]ss

(nM)

10−2

10−1

100

101

0

50

100

150

200

2

4

6

8

10

12

cFLIP

no cFLIP

C

A B


Comparison of DISC models

2 4 6 8 10 12 14 16 1810

−2

10−1

100

101

Model variant number

[Fas

L]0 (

nM)

[Casp8*]ss

(nM) at [cFLIP]0 = 81 nM

2

4

6

8

10

2 4 6 8 10 12 14 16 180

50

100

150

200


[cF

LIP

] 0 (nM

)

[Casp8*]ss

(nM) at [FasL]0 = 0.1 nM

1

1.5

2

B

A


Coupled extrinsic caspase model (3,3,3)

10−4

10−3

10−2

0

20

40

60

80

αFasL

(nM/min)

[Cas

p3*]

ss (

nM)

[cFLIP]0 = 81 nM

10−4

10−2

0

100

2000

50

100

αFasL

(nM/min)[cFLIP]0 (nM)

[Cas

p3*]

ss (

nM)

αFasL

(nM/min)

[Cas

p3*]

(nM

)

[cFLIP]0 = 81 nM

0 1 2 3 4

x 10−4

0

20

40

60

80

100

apoptosis

stable

unstable

αFasL

(nM/min)

[Cas

p3*]

(nM

)

[cFLIP]0 = 0 nM

0 1 2 3 4

x 10−4

0

20

40

60

80

100

apoptosis

stable

unstable

cFLIP

no cFLIP

A B

C D


Apoptotic threshold

[cFLIP]0 (nM)

α Fas

L* (n

M/m

in)

0 20 40 60 80 100 120 140 160 180 2001

1.5

2

2.5

3

3.5

4

4.5x 10

−4

(<3,1,⋅)

(3,1,⋅)

(<3,2,⋅)

(3,2,⋅)

(<3,3,⋅)

(3,3,⋅)

2 4 6 8 10 12 14 16 180

2

4x 10

−4


α Fas

L* (n

M/m

in)

cFLIP

no cFLIP

B

A


DISC model time courses

Time (min)

[Cas

p8*]

(nM

)

0 50 100 150 200 250 300 350 400 450 5000

2

4

6

8

10

12

σcFLIP

= 1

σcFLIP

> 1

[FasL]0 = 0.1 nM

[FasL]0 = 2 nM


Robustness with FasL

β: minimum fractional inhibitor reduction for apoptosis

[IAP]0 7→ (1− β) [IAP]0 and [BAR]0 7→ (1− β) [BAR]0β is a measure of robustness


Robustness with FasL

β: minimum fractional inhibitor reduction for apoptosis

[IAP]0 7→ (1− β) [IAP]0 and [BAR]0 7→ (1− β) [BAR]0β is a measure of robustness

αFasL

(nM/min)

β

10−6

10−5

10−4

10−3

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

σcFLIP

= 1

σcFLIP

> 1

no cFLIP


Robustness with cFLIP

[cFLIP]0 (nM)

β

αFasL

= 5 × 10−5 nM/min

0 20 40 60 80 100 120 140 160 180 2000.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

(<3,1,⋅)

(3,1,⋅)

(<3,2,⋅)

(3,2,⋅)

(<3,3,⋅)

(3,3,⋅)

2 4 6 8 10 12 14 16 180

0.1

0.2

0.3


β

cFLIP

no cFLIP

A

B


Conclusion

1 Model exhibits irreversible bistability

Mechanistic descriptionSynthesis and degradation

2 Only significant parameter is σcFLIP; otherwise, degenerate3 cFLIP protects cell survival and robustness (σcFLIP > 1)

Increases apoptotic thresholdMaintains robustness of bistability

But the only truly significant result is bistability; the rest is justminor details if we’re interested in bigger questions...


Conclusion



2 Only significant parameter is σcFLIP; otherwise, degenerate

3 cFLIP protects cell survival and robustness (σcFLIP > 1)




Conclusion



2 Only significant parameter is σcFLIP; otherwise, degenerate3 cFLIP protects cell survival and robustness (σcFLIP > 1)




Ideas!

Use the DISC model as a component in a larger model to achieve asystems-level description that is complete and stable

1 What are the determinants of cell survival or death?

Linear classifier: y = θ(∑

i wixi )SVD (principal components)GSVD as a comparison tool (Alter et al., 2003)

2 Similarly, study how bistability is maintained3 What controls the apoptotic threshold?

Linear regression

Any suggestions?


Ideas!





2 Similarly, study how bistability is maintained

3 What controls the apoptotic threshold?

Linear regression

Any suggestions?


Ideas!





2 Similarly, study how bistability is maintained3 What controls the apoptotic threshold?

Linear regression

Any suggestions?


References

Alter O, Brown PO, Botstein D (2003) Generalized singular value decomposition for comparative analysis ofgenome-scale expression data sets of two different organisms. Proc Natl Acad Sci USA 100(6):3351–3356.

Bagci EZ, Vodovotz Y, Billiar TR, Ermentrout GB, Bahar I (2006) Bistability in Apoptosis: Roles of Bax,Bcl-2, and Mitochondrial Permeability Transition Pores. Biophys J 90(5):1546–1559.

Eissing T, Conzelmann H, Gilles ED, Allgower F, Bullinger E, Scheurich P (2004) Bistability Analyses of aCaspase Activation Model for Receptor-induced Apoptosis. J Biol Chem 279(35):36892–36897.

Harrington HA, Ho KL, Ghosh S, Tung KC (2008) Construction and analysis of a modular model ofcaspase activation in apoptosis. Theor Biol Med Model 5(1):26.

Hengartner MO (2000) The biochemistry of apoptosis. Nature 407(6805):770–776.

Hua F, Cornejo MG, Cardone MH, Stokes CL, Lauffenburger DA (2005) Effects of Bcl-2 Levels on FasSignaling-Induced Caspase-3 Activation: Molecular Genetic Tests of Computational Model Predictions. JImmunol 175(2):985–995.

Lai R, Jackson TL (2004) A Mathematical Model of Receptor-Mediated Apoptosis: Dying to Know WhyFasL is a Trimer. Math Biosci Eng 11(2):325–338.

Legewie S, Bluthgen N, Herzel H (2006) Mathematical Modeling Identifies Inhibitors of Apoptosis asMediators of Positive Feedback and Bistability. PLoS Comput Biol 2(9):e120.

Okazaki N, Asano R, Kinoshita T, Chuman H (2008) Simple computational models of type I/type II cellsin Fas signaling-induced apoptosis. J Theor Biol 250(4):621–633.