# Presentation: 388848

## A Computational Model for Analyzing the Biochemical Pathways of Matrix Metalloproteinase (MMP) 2 & 9 in Collagen Type IV Proteolysis 

**Elizabeth O’Quinn**
- Wofford College
**Research Alliance in Math & Science**
- Summer 2005
**Mentor: Kara Kruse**
- Computational Sciences & Engineering Division

- AAA

- www.southfloridacardio.com

## Matrix Metalloproteinase Modeling

**Background**
**Modeling Approach **
**Biochemical Pathways**
**Model implementation**
**Experimental analysis**
**Future research **

- delphi.phys.univ-tours.fr/ Prolysis

**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

## 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?**

- Aorta
- Histology

**www.lab.anhb.uwa.edu**

## 3 Levels of Regulation
Gene Transcription
Marfan’s Syndrome 
Kawasaki Disease 
Symptoms appear at early ages
Activation of latent form of enzyme
Inactivation by specific endogenous inhibitors

All affected by environmental factors
Smoking (80% of patients)
Diet 

**Gene Transcription**
**Marfan’s Syndrome **
**Kawasaki Disease **
**Symptoms appear at early ages**
**Activation of latent form of enzyme**
**Inactivation by specific endogenous inhibitors**
**All affected by environmental factors**
**Smoking (80% of patients)**
**Diet **

** ****Focus primarily on #’s 2 & 3**

- OULU 2003

## 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**

- Math

- Biomedical Sciences

- Computer Science

- Computational Science

## 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**

## Matrix Metalloproteinase Pathways

- proMMP

- TIMP

- MMP

- +

**Active**

- TIMP

- Collagen

- Denatured Collagen

- MMP

**Inhibited**

## Enzyme Complexity

- MMP-2

- MMP-9

**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*

## JSim

**Provides model development tools for:**
- Mathematical Modeling Language (MML) for specifying equation sets
- Model parameters can be input or derived from experimental data
- Compute engine for solving equations sets
- Optimizer solves model for range of parameters
- Graphical display of results
- Project management

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

## 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*****) **

## Model Implementation

**Model Assumptions**
- Reaction occurs in a well mixed system
- Temperature is constant
- Volume of the system is constant
- allows use of concentrations in rate laws

## Model Equations

**Source Code of Model**
- JSim v1.1
- import nsrunit;
- unit conversion on;
- math uncatCrev
- {realDomain t hour; // time
- t.min=0.0; t.max=20.0; t.delta=0.2;
- real kIso=33 1/sec; // Reaction rate parameters
- real 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 Conditions
- when(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]

## 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 Model
- Karagiannis ED, Popel AS (2004)

## Reaction Rates 

- 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

## Current Status

**Karagiannis collagen type I / MMP-2 Model**
**Implemented in JSim**
**JSim results match literature results**
**Collagen type IV / MMP-2 model**
**Pathway modifications from collagen type I defined **
**Pathway implemented in JSim**
**    ****Need type IV specific reaction rates**
**Collagen type IV / MMP-9 model**
**Pathway 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 rates**
**Chose Western Blot method**
**UTMCK commencing experiments**

## Future Research/Applications

**Expand 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

## 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
**ORNL**
- Kara Kruse, M.S.E., Richard Ward, Ph.D.
- Computational Sciences and Engineering Division

- University of Washington, for JSim Code

## Questions?

- MMP-2

- MMP-9

*© RCSB*

*© RCSB*

- www.pennhealth.com/