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High performance computing in multiscale modeling cardiac contraction: Bridging proteins to cells to whole heart . J. Jeremy Rice. Computational Biology Center Thomas J. Watson Research Center [email protected] Motivation.

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Slide1 l.jpg

High performance computing in multiscale modeling cardiac contraction: Bridging proteins to cells to whole heart

J. Jeremy Rice

Computational Biology Center Thomas J. Watson Research Center [email protected]


Motivation l.jpg
Motivation contraction: Bridging proteins to cells to whole heart

  • Deaths due to cardiovascular diseases remain the largest contributor to premature mortality in most developed societies.

  • The cost of heart disease and stroke in the US is projected to be more than $448 billion in 2008.

  • Amiodarone is the most effective antiarrhythmic drug - but uncertain action and serindipitous discovery.

  • Predictive mathematical models are ideal tools to address the complex nature cardiovascular diseases.

  • Efforts to "customize" cardiac models are pushing towards role as enablers of personalized medicine.


Slide3 l.jpg

Building Multiscale Heart Models contraction: Bridging proteins to cells to whole heart

Heart will allow better therapies for heart disease..

...but will require bridging between organ level and molecular level

Organ level

Cell level

Molecular level

Sarcomere contracts by cyclical interactions of myosin on thick filament (red) and actin in thin filament (green).

In each cell of heart, a lattice of sarcomeres produce contraction on every heart beat.

Reconstruction of whole heart by Peter Hunter, U. of Auckland


Cyclical actin and myosin interactions converts energy in atp to force motion l.jpg
Cyclical actin and myosin interactions converts energy in ATP to force/motion

From the website of the Michael Geeves' Laboratory: http://www.kent.ac.uk/bio/geeves/Research/home.htm


Banded structure of sarcomere l.jpg
Banded Structure of Sarcomere ATP to force/motion


Slide6 l.jpg

Ca ATP to force/motion

Ca

Ca

Building a multiscale model on actin-myosin in muscle

B. Sarcomere component proteins

A. Sarcomere structure

z-line

z-line

thin filament

troponin complex

actin

TnC

TnT

TnI

tropomyosin

myosin head

thick filament

myosin neck

z-line

intertwined myosin tail regions

Single thick and thin filament in half sarcomere


Thin filament is a two stranded helix of actin monomers l.jpg
Thin filament is a two-stranded helix of actin monomers ATP to force/motion

"Pseudo-repeat" 37 nm

"Pseudo-repeat" = 13 units

True repeat = 26 units

5.54 nm

2.77 nm

From http://www.kent.ac.uk/bio/geeves/Research/home.htm


Position of myosin heads on thick filament l.jpg
Position of myosin heads on thick filament ATP to force/motion

  • Pairs of heads emanate 180 degree apart in radial direction at each step

  • Radial direction of heads rotate ~60 degrees at next step in axial direction (distance = ~14.3 nm)

  • a "pseudo-repeat" happens on the 3th steps as heads will be radiate in same radial direction (distance = ~43 nm)

axial direction

radial direction


Slide9 l.jpg

A. Spatial relationships of actin and myosin ATP to force/motion

yj+1

yj

37 nm

C. Markov state model of crossbridging

43 nm

xj+1

xj

B. Mechanical representation

ka= 1743 pN/nm

yj+2

yj

yj-1

yj+2

-7 nm

kxb= 1 pN/nm

xj+2

xj+1

xj

xj-1

km= 2020 pN/nm


Representing compliances in myofilament l.jpg
Representing compliances in myofilament ATP to force/motion

Daniel, Trimble & Chase, 1998

K.X = A



Cardiac muscle physiology l.jpg
Cardiac Muscle Physiology ATP to force/motion


Cardiac muscle physiology13 l.jpg
Cardiac Muscle Physiology ATP to force/motion


Representing nearest neighbor interactions l.jpg

Ca ATP to force/motion

Ca

Representing nearest-neighbor interactions

kon[Ca]

0N

1N

koff

gnknp_1

g-nkpn _1

g-nkpn_0

gnknp_0

k’on[Ca]

1P

0P

k’off

g > 1 for neighbor-to-neighbor cooperativity

n = number of activated neighbors in 0P or 1P state (0, 1 or 2)


Slide15 l.jpg

Compute exponent on ATP to force/motion g

n = 0

n = 1 {

or

n = 2


Combining computational models l.jpg

1N ATP to force/motion

0N

Ca

Ca

Ca

1N

0N

Ca

1P

0P

Ca Regulation

Ca

1P

0P

Ca

1PreF

0PreF

P

0F

1F

PreF

F

Ca regulation and XB Cycle

XB Cycle

Combining computational models


Must use monte carlo methods l.jpg

Ca ATP to force/motion

Ca

Ca

Ca

Ca

Ca

Ca

Must Use Monte Carlo Methods

Relaxed

Activated – Generates Force


Sample results variation of gamma l.jpg
Sample Results - Variation of Gamma ATP to force/motion

Ca

Ca

n = 0

g

Exponent on

n = 1

n = 2


Some results f ca relations l.jpg
Some Results - F-Ca Relations ATP to force/motion

Unpublished data from Dobesh et al., 2001, rat skinned fiber, SL = 2.15 mm


Representing nearest neighbor interactions20 l.jpg

Ca ATP to force/motion

Ca

Representing nearest-neighbor interactions

kon[Ca]

0N

1N

koff

gnknp_1

g-nkpn _1

g-nkpn_0

gnknp_0

k’on[Ca]

1P

0P

k’off

g > 1 for neighbor-to-neighbor cooperativity

n = number of activated neighbors in 0P or 1P state (0, 1 or 2)


Slide21 l.jpg

Compute exponent on ATP to force/motion g

n = 0

n = 1 {

or

n = 2


Combining computational models22 l.jpg

1N ATP to force/motion

0N

Ca

Ca

Ca

1N

0N

Ca

1P

0P

Ca Regulation

Ca

1P

0P

Ca

1PreF

0PreF

P

0F

1F

PreF

F

Ca regulation and XB Cycle

XB Cycle

Combining computational models


Must use monte carlo methods23 l.jpg

Ca ATP to force/motion

Ca

Ca

Ca

Ca

Ca

Ca

Must Use Monte Carlo Methods

Relaxed

Activated – Generates Force


Sample results variation of gamma24 l.jpg
Sample Results - Variation of Gamma ATP to force/motion

Ca

Ca

n = 0

g

Exponent on

n = 1

n = 2


Some results f ca relations25 l.jpg
Some Results - F-Ca Relations ATP to force/motion

Unpublished data from Dobesh et al., 2001, rat skinned fiber, SL = 2.15 mm


Why correct f ca important l.jpg

Mean Field ATP to force/motion

Spatially Explicit

Force

Force

Force

Force

30x

Residual force = incomplete relaxation

[Ca]

[Ca]

10x

10x

Why correct F-Ca important?

  • [Ca] changes by ~10x while force changes by ~1000x in real muscle

  • Incorrect Force-Ca relationship leads to muscle that can not fully relax

  • In whole heart, muscle must relax to fill completely and pump efficiently

1000x


Need explicit consideration of spatial interactions l.jpg
Need explicit consideration of spatial interactions ATP to force/motion

Mass-action, mean-field model

Spatially-explicit model

Y. Yaniv, R. Sivan & A. Landesberg, Am J Physiol Heart Circ Physiol. 288, No. 1, H389-99. (2005).

Rice et al., Pacific Symposium on Biocomputing, 2008


Why correct f ca important28 l.jpg

Mean Field ATP to force/motion

Spatially Explicit

Force

Force

Force

Force

30x

Residual force = incomplete relaxation

[Ca]

[Ca]

10x

10x

Why correct F-Ca important?

  • [Ca] changes by ~10x while force changes by ~1000x in real muscle

  • Incorrect Force-Ca relationship leads to muscle that can not fully relax

  • In whole heart, muscle must relax to fill completely and pump efficiently

1000x


Slide29 l.jpg

Combine 32 ATP to force/motion full sarcomeres into 1 myofibril which is a cell-level structure

Moving to a terascale model of a myofibril

1 full 3-D sarcomere with hexagonal lattice

Thick and thin filaments at molecular level



Decomposition scheme l.jpg
Decomposition scheme ATP to force/motion


Processing steps for each d t l.jpg
Processing steps for each ATP to force/motion Dt

If no D XB attachment

Build A and K matrices in distributed manner with PETSc

Update Markov states in each partition

If D XB attachment

Update locations by solving A.X=K with PETSc


Slide33 l.jpg

Relaxation is not homogeneous ATP to force/motion

Relaxation of myofibril showing inhomogeneity and spontaneous oscillations (unpublished data from B. Iorga and R. Stehle, 2006).

time

R. Stehle, M. Krüger, and G. Pfitzer

Biophys J, October 2002, p. 2152-2161, Vol. 83, No. 4


Slide34 l.jpg
Future directions - Whole heart model with large-scale parallelization on Blue Gene(collaboration with Universität Karlsruhe)


Spatial resolution is still too low l.jpg
Spatial resolution is still too low parallelization on Blue Gene

~ 200 elements

0.1 mm per cell

1010 elements



Full heart and ecg calculation is not feasible l.jpg
Full heart and ECG calculation is not feasible parallelization on Blue Gene

F. H. Netter. Thieme. 1990

0.1 mm per cell

1010 elements

Keller et al., 2007


Modeling electrophysiology l.jpg

Cell Models parallelization on Blue Gene

High degree of complexity

Computation of potentials and concetrations

Long simulation times

Cellular Automaton

Rule–based

Pre–calculated potentials

Short simulations times

Modeling Electrophysiology

Courtemanche et al. Cardiovasc Res. 1998


Experimental ventricular wedge preparation l.jpg
Experimental ventricular wedge preparation parallelization on Blue Gene

Yan, Shimizu, and Antzelevitch, 1998

Shimizu and Antzelevitch, 1998


Constructing a wedge model electrophysiology l.jpg
Constructing a wedge model: Electrophysiology parallelization on Blue Gene

Clancy and Rudy, 2005

Silva and Rudy, 2005


Slide41 l.jpg

Constructing a wedge model: 1-D cable and computing the ECG parallelization on Blue Gene

100 mm

-

+

192

191

190

1

3

2

Endocardium

Epicardium

Transumural ECG


Sample ecg signals for the wt case l.jpg
Sample ECG signals for the WT case parallelization on Blue Gene

M Cell

Endo

Epi


Slide43 l.jpg

WT vs. Mut A vs. Mut B versions of I parallelization on Blue GeneKs


Transmural ecg of mut a and mut b l.jpg

Mut A parallelization on Blue Gene

Transmural ECG of Mut A and Mut B

M Cell

M Cell

Endo

Endo

Epi

Epi

QT interval: 224ms(WT) 236ms(Mut A)


Next step move to 3 d wedge model l.jpg
Next step: Move to 3-D wedge model parallelization on Blue Gene

Epi

M-Cell

Endo

Torsade de pointe

  • 50x50x100 elements (=250 K)

  • Slow conduction velocity

  • Realistic size = 32 M elements

Carruth and Silverman, 1980


Current approaches do not scale to large numbers of processors l.jpg
Current approaches do not scale to large numbers of processors

Kharche et al. (2008) in press

Plank et al. (2006)


Decomposition for blue gene computer l.jpg
Decomposition for Blue Gene computer processors

1

0

3

2

1

0

3

2


Communication framework l.jpg
Communication Framework processors

Send/ReceivePointer

Common Faces


Communication cycle l.jpg

Initialization processors

Compute Vm

Cycle 1 - Vm

monodomain

Compute I(Vm)

bidomain

Compute e

Cycle 2 - e

Compute I(e)

CommunicationCycle



Conclusion l.jpg
Conclusion processors

  • The spatial aspects are at the molecular level are reflected up to organ level.

  • Spatial protein interactions are important for the emergent behavior at cell and tissue levels.

  • Multiple models with different levels of abstraction are developed - detailed models guided the ODE-based models.

  • Electromechanical whole heart models are still in development but increased spatial resolution is needed.


Collaborators l.jpg

IBM processors

Jagir Hussan

Matthias Reumann

Gustavo Stolovitzky

Yuhai Tu

Blake Fitch

Aleksandr Rayshubskiy

Michael C. Pitman

University of Illinois Chicago

Pieter De Tombe

John Hopkins University

Viatcheslav Gur'ev

Fijoy Vadakkumpadan

Natalia Trayanova

Universität Karlsruhe

Gunnar Seemann

Daniel Weiss

David U. Keller

Olaf Dössel

Collaborators


Slide53 l.jpg

IBM Thomas J. Watson Research Center, Yorktown Heights, NY processors

IBM Computational Biology Center www.research.ibm.com/compsci/compbio


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