O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 1 A Computational Model for Analyzing...

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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY

A Computational Model for Analyzing the Biochemical Pathways of Matrix Metalloproteinase (MMP) 2 & 9 in

Collagen Type IV Proteolysis

Elizabeth O’QuinnWofford College

Research Alliance in Math & Science

Summer 2005

Mentor: Kara KruseComputational Sciences & Engineering Division

AAA

www.southfloridacardio.com

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Matrix Metalloproteinase Modeling

Background Modeling Approach Biochemical Pathways Model implementation Experimental analysis Future research delphi.phys.univ-tours.fr/ Prolysis

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What is an AAA? ABDOMINAL — occurs in abdomen AORTIC — pertains to aorta, the largest artery ANEURYSM — abnormal ballooning of a blood vessel

The Consequences “Silent Killer” Kills 15,000 people in US

more each year than AIDS Mortality from ruptured AAA ~ 80%

How does an AAA develop?

Abdominal Aortic Aneurysms (AAA)

www.oakridger.com

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Aneurysm Development Arterial walls composed of proteins

Elastin for elasticity Collagen for strength

Matrix metalloproteinases breakdown collagen & elastin Complex interactions involving up to 25 MMPs MMP-2 & MMP-9 most important

Inhibitors block proteinases TIMP – Tissue Inhibitor Metalloproteinase

Imbalance between proteinases & inhibitors Elastin degradation – artery balloons Collagen degradation – artery ruptures

How is this balance regulated?

www.lab.anhb.uwa.edu

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3 Levels of Regulation

1. Gene Transcription Marfan’s Syndrome Kawasaki Disease Symptoms appear at early ages

2. Activation of latent form of enzyme

3. Inactivation by specific endogenous inhibitors

All affected by environmental factors

• Smoking (80% of patients)

• Diet

Focus primarily on #’s 2 & 3 OULU 2003

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Approach Develop math model of complex biochemistry

Collagen type IV proteolysis MMP-2 & MMP-9 kinetics Reaction rates from:

Literature Experiments (UTMCK)

Model developed by: Separate studies of individual reactions In vitro controlled conditions

Validate model Simulate integrated system behavior Design experimental procedures Compare experimental results to math model predictions

Update model

MathBiomedical Sciences

Computer Science

Computational Science

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Summer Project Goals

Evaluate related model from literature Collagen type I proteolysis by MMP-2 (Karagiannis, E. D. and Popel, A. S., “A Theoretical Model of Type I Collagen Proteolysis by Matrix

Metalloproteinase (MMP) 2 and Membrane Type 1 MMP in the Presence of Tissue Inhibitor of Metalloproteinase 2,” Journal of Biological Chemistry, Vol. 279, No. 37, pp.39105-39114, 2004.)

Implement literature model in JSim simulation

Examine literature Collagen type IV proteolysis by MMP-2 Collagen type IV proteolysis by MMP-9

Develop pathways for MMP-2 & MMP-9

Design experiments to measure unknown reaction rates

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Matrix Metalloproteinase Pathways

proMMP

TIMP

MMP+

Active

TIMP

CollagenDenatured Collagen

MMP

Inhibited

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MMP-2 MMP-9

Enzyme Complexity

MMP-9 pathway is more complex than MMP-2 pathway because:

• MMP-2 has 2 binding sites

• MMP-9 has at least 7 binding sites

© RCSB© RCSB

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JSim

Provides model development tools for:1. Mathematical Modeling Language (MML) for specifying

equation sets2. Model parameters can be input or derived from

experimental data3. Compute engine for solving equations sets4. Optimizer solves model for range of parameters5. Graphical display of results6. Project management

Free software environment for scientific modeling developed by the University of Washington

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JSim

"JSim is a software environment for scientific modeling that provides tools for development of models, for their run-time control, and for analysis of their behavior."

(National Simulation Resource, Univ. of Washington)

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Model Implementation

Model Assumptions

1. Reaction occurs in a well mixed system

2. Temperature is constant

3. Volume of the system is constant allows use of concentrations in rate laws

€

E + S k1 ⏐ → ⏐k2

← ⏐ ⏐ ES k3 ⏐ → ⏐k4

← ⏐ ⏐ E + P

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Model EquationsSource Code of Model

JSim v1.1import nsrunit;unit conversion on;math uncatCrev{realDomain t hour; // timet.min=0.0; t.max=20.0; t.delta=0.2;real kIso=33 1/sec; // Reaction rate parametersreal kNegIso=2*10^-8 1/sec;real kOnM2T2=5.9*10^6 M^(-1)*sec^(-1); real kOffM2T2=6.3 1/sec;

real M2T2L(t) pM, M2T2S(t) pM, M2(t) pM, T2(t) pM; // State Variables

// Initial Conditionswhen(t=t.min) {M2T2L=0; M2T2S=0; M2=30; T2=300; } // Ordinary Differential Equations:M2:t = kOffM2T2*M2T2L-kOnM2T2*M2*T2;T2:t = kOffM2T2*M2T2L-kOnM2T2*M2*T2;M2T2L:t = kNegIso*M2T2S+kOnM2T2*M2*T2-kIso*M2T2L-kOffM2T2*M2T2L; M2T2S:t = kIso*M2T2L-kNegIso*M2T2S;}

Equations Used in Model

The behavior of MMP-2/TIMP-2 isoforms

To solve the ordinary differential equations for the following system in which MMP2 & TIMP2 bind to form MMP2-TIMP2 complex isomers

kOnM2T2 kIso M2 + T2 <--> M2T2(L) <--> M2T2(S) kOffM2T2 kNegIso

[M2](t) = kOffM2T2*[M2T2L]-kOnM2T2*[M2]*[T2]

[T2](t) = kOffM2T2*[M2T2L]-kOnM2T2*[M2]*[T2]

[M2T2L](t) = kNegIso*[M2T2S]+kOnM2T2*[M2]*[T2] -kIso*[M2T2L]-kOffM2T2*[M2T2L]

[M2T2S] (t) = kIso*[M2T2L]-kNegIso*[M2T2S]

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Verification of JSim Implementation

Behavior of MMP2/TIMP2 Isoforms

• Initial concentration of MMP2 while the TIMP2 concentration varies

• With ratios 1/10, 1/5,1/3, 1/2, 1/1 of MMP-2/TIMP-2

JSim Model MatLab ModelKaragiannis ED, Popel AS (2004)

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Reaction Rates Several Techniques

ELISA, Western Blot, & HPLC Rate Analysis Optimization

Incorporate measured rates into JSim model

Western Blot

ELISA

Antibody Binding

http://boneslab.bio.ntnu.no

http://www.chemicon.com/

http://boneslab.bio.ntnu.no

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Current StatusKaragiannis collagen type I / MMP-2 Model

Implemented in JSim

JSim results match literature results

Collagen type IV / MMP-2 modelPathway modifications from collagen type I defined

Pathway implemented in JSim

Need type IV specific reaction rates

Collagen type IV / MMP-9 modelPathway partially defined from literature

Last portion of MMP-9 activation pathway needs further study

Not yet implemented in JSim

Need numerous reaction rates

Experimental measurement of reaction ratesChose Western Blot method

UTMCK commencing experiments

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Future Research/ApplicationsExpand model to study MMP involvement in:

• Arteriosclerosis

• Aneurysm formation

• Hormone replacement therapy promotes vascular health

• Effects of smoking on collagen degradation

• Nitrous oxide – a vasodilator

Other applications:

• Angiogenesis in tumor formation

• Orthopedic diseases

J Clin Invest. 2004 July 15; 114(2): 168–171

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Acknowledgements

University of Tennessee Medical Center /

Graduate School of Medicine, Knoxville:

Drs. Oscar Grandas, M.D., Michael Freeman, M.D., Mitchell Goldman, M.D.

Richie Reece, Stacy Kirkpatrick, Wendy Packan, Eva Bukovska

Research Alliance in Math and Science

Mathematical, Information, and Computational Science, OASCR, DOE

ORNLKara Kruse, M.S.E., Richard Ward, Ph.D.

Computational Sciences and Engineering Division

University of Washington, for JSim Code

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Questions?

MMP-2 MMP-9

© RCSB© RCSB

www.pennhealth.com/

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O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 1 A Computational Model for Analyzing...

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