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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

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
Motivation
  • 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

Building Multiscale Heart Models

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
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

slide6

Ca

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
Thin filament is a two-stranded helix of actin monomers

"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
Position of myosin heads on thick filament
  • 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

A. Spatial relationships of actin and myosin

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
Representing compliances in myofilament

Daniel, Trimble & Chase, 1998

K.X = A

representing nearest neighbor interactions

Ca

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

Compute exponent on g

n = 0

n = 1 {

or

n = 2

combining computational models

1N

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

Ca

Ca

Ca

Ca

Ca

Ca

Ca

Must Use Monte Carlo Methods

Relaxed

Activated – Generates Force

sample results variation of gamma
Sample Results - Variation of Gamma

Ca

Ca

n = 0

g

Exponent on

n = 1

n = 2

some results f ca relations
Some Results - F-Ca Relations

Unpublished data from Dobesh et al., 2001, rat skinned fiber, SL = 2.15 mm

representing nearest neighbor interactions20

Ca

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

Compute exponent on g

n = 0

n = 1 {

or

n = 2

combining computational models22

1N

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

Ca

Ca

Ca

Ca

Ca

Ca

Ca

Must Use Monte Carlo Methods

Relaxed

Activated – Generates Force

sample results variation of gamma24
Sample Results - Variation of Gamma

Ca

Ca

n = 0

g

Exponent on

n = 1

n = 2

some results f ca relations25
Some Results - F-Ca Relations

Unpublished data from Dobesh et al., 2001, rat skinned fiber, SL = 2.15 mm

why correct f ca important

Mean Field

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
Need explicit consideration of spatial interactions

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

Mean Field

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

Combine 32 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

processing steps for each d t
Processing steps for each 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

Relaxation is not homogeneous

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
Future directions - Whole heart model with large-scale parallelization on Blue Gene(collaboration with Universität Karlsruhe)
spatial resolution is still too low
Spatial resolution is still too low

~ 200 elements

0.1 mm per cell

1010 elements

full heart and ecg calculation is not feasible
Full heart and ECG calculation is not feasible

F. H. Netter. Thieme. 1990

0.1 mm per cell

1010 elements

Keller et al., 2007

modeling electrophysiology
Cell Models

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
Experimental ventricular wedge preparation

Yan, Shimizu, and Antzelevitch, 1998

Shimizu and Antzelevitch, 1998

constructing a wedge model electrophysiology
Constructing a wedge model: Electrophysiology

Clancy and Rudy, 2005

Silva and Rudy, 2005

slide41

Constructing a wedge model: 1-D cable and computing the ECG

100 mm

-

+

192

191

190

1

3

2

Endocardium

Epicardium

Transumural ECG

transmural ecg of mut a and mut b

Mut A

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
Next step: Move to 3-D wedge model

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
Current approaches do not scale to large numbers of processors

Kharche et al. (2008) in press

Plank et al. (2006)

communication framework
Communication Framework

Send/ReceivePointer

Common Faces

communication cycle

Initialization

Compute Vm

Cycle 1 - Vm

monodomain

Compute I(Vm)

bidomain

Compute e

Cycle 2 - e

Compute I(e)

CommunicationCycle
conclusion
Conclusion
  • 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
IBM

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

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

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

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