Beating heart simulation driven by three dimensional molecular

dynamics model

Takumi Washio (UT-Heart Inc.) Ryo Kanada (RIKEN)

Xiaoke Cui (UT-Heart Inc.) Seiryo Sugiura (UT-Heart Inc.)

Yasushi Okuno (Kyoto Univ.) Toshiaki Hisada (UT-Heart Inc.)

Pflop/s % of peak model∖#nodes 20736 41472 82944 20736 41472 82944

49KDOF 0.72 1.39 2.74 28.10 27.43 27.72

macro #myocardial elements 659456 micro #myofibril elements of a cell 5796

NDOF of a cell 49245 NDOF of a z disk 230

#motor proteins 160

Heart + Cell + Motor proteins Multiscale Challenge on K-computer (2012) FEM FEM MonteCarlo Model size

Performance

600K elements

5K elements 50K #DOF

160 motor proteins

Fiber direction f

Contraction force

Length change in the fiber direction f

XxF

∂∂

=t

t Fftt SLSL 0=

Sarcomere model

Strain tensor Sarcomere length

Ttt

Sact

t TC FffFf

Π ⋅⊗=

Stress tensor

∑=

=n

ii

tMiAS

t xkT1

,δ

Conventional Multiscale Approach Heart –Sarcomere Coupling Model

Filament sliding changes the mechanical load, thereby affects the lever arm swing and the detachment .

Research directions for Post-K : from 1d MC to 3d MD

Cafemol (Takada Lab., Kyoto Univ.) Focusing on inside of the molecular motor

Super Coarse grained (UT-Heart Inc. ) Focusing on 3D sarcomere structure

K

Post-K

1D Monte Carlo Load dependent state Transition

3D Molecular Dynamics Deformation potentials

-40 -20 0 20 400

50

100

150

Lever arm angle [degree]pow

er s

troke

ene

rgy

[pN

nm

]

Thin filament (modeled by a rigid bar)

Switch the potentials at the state transitions

0 50 100 mmHg

Preliminary test using Cafemol-Ring Coupling model

Blood pressure

Micro-Macro interaction through the thin filament sliding

0.2 0.21 0.22 0.23100

110

120

130

140

150

160

Time [s]

Thin

fila

men

t slid

ing

dist

ance

[Å]

Time[s]

sw1-

sw2[

A]

ploo

p-sw

1[A]

For

ce[p

N]

LA-s

win

g[A]

Rigor ADP Pi-release ADP・Pi (weak bind) ATP (detachment)

No contribution

Behavior of the molecular motor under physiological condition

-202468

050100

0 0.1 0.2 0.3102030

sw1-sw2distance [Å]

ploo

p-sw

1 di

stan

ce [Å

]

Increase the rate ADP=>Pi-release by 10

Verification of Pocket Deformation Feedback Model

ADP・Pi (Detachment)

Pi-release (Weak bind)

Pi-release ADP Rigor (Strong bind)

ATP bind

Red: : successful cycles Blue : unsuccessful cycles

Contour of the pocket deformation of the basic model

10

15

20

25

30

35

40

0 5 10 15 20 25 30

60 80 100 120 1400

50

100

0 0.1 0.2 0.3 0.4 0.50

500

1000

Time[s] Volume[ml]

Bloo

d pr

essu

re[m

mHg

]

Basic model Feedback model

Basic model Feedback model A

TP c

onsu

mpt

ion

Benefits of the feedback mechanism

Pressure Volume loop Energy consumption

1. ３% increase of blood ejection 2. 10% reduction of ATP consumption

Verification of Pocket Deformation Feedback Model

Time

∆𝑡𝑡 ∶ micro step

∆𝑇𝑇: macro step

100 101 102 1030

100

200

300

∆𝑇𝑇/∆𝑡𝑡

Elap

sed

time(

s)/0

.1M

mic

ro st

eps

Time average of contraction force and stiffness ∆𝑇𝑇 ∆𝑡𝑡

Macro Micro

Overhead reduction

Coupling technique : Efficiency & Stability 1. Reduction of communication overheads by the multiple time step method 2. Stability by taking the active stiffness

Strain in the fiber direction

Passive stiffness

Active stiffness

Passive stiffness

Active stiffness

Relaxation phase

Contraction phase

Micro Macro

Force 𝑭𝑭�𝑎𝑎𝑎𝑎𝑎𝑎𝑇𝑇,∆𝑇𝑇 Stiffness 𝑲𝑲�𝑎𝑎𝑎𝑎𝑎𝑎𝑇𝑇,∆𝑇𝑇

Strain in the fiber direction 𝜖𝜖𝑇𝑇

𝑪𝑪 𝒖𝒖𝑇𝑇+∆𝑇𝑇 − 𝒖𝒖𝑇𝑇

∆𝑇𝑇= 𝑭𝑭𝑝𝑝𝑎𝑎𝑝𝑝( 𝒖𝒖𝑇𝑇+∆𝑇𝑇 )+𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎( 𝒖𝒖𝑇𝑇+∆𝑇𝑇 )

𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎 𝒖𝒖𝑇𝑇+∆𝑇𝑇 = 𝑭𝑭�𝑎𝑎𝑎𝑎𝑎𝑎𝑇𝑇,∆𝑇𝑇 + 𝑲𝑲�𝑎𝑎𝑎𝑎𝑎𝑎𝑇𝑇,∆𝑇𝑇 𝒖𝒖𝑇𝑇+∆𝑇𝑇 − 𝒖𝒖𝑇𝑇

𝑧𝑧 =𝑇𝑇−Δ𝑇𝑇+𝜔𝜔∆𝑇𝑇𝑆𝑆𝑆𝑆0

21 − 𝜔𝜔 𝜖𝜖𝑇𝑇−∆𝑇𝑇 + 𝜔𝜔 𝜖𝜖𝑇𝑇

𝑧𝑧 =𝑇𝑇+𝜔𝜔∆𝑇𝑇𝑆𝑆𝑆𝑆0

21 − 𝜔𝜔 𝜀𝜀𝑇𝑇 + 𝜔𝜔 𝜖𝜖𝑇𝑇+∆𝑇𝑇

Time

𝑇𝑇

𝑇𝑇 + Δ𝑇𝑇 Strain in the fiber direction 𝜖𝜖𝑇𝑇+∆𝑇𝑇

𝑇𝑇 + 2Δ𝑇𝑇

Coupling technique : Efficiency & Stability 1. Reduction of communication overheads by the multiple time step method 2. Stability by taking the active stiffness

𝑧𝑧

0 0.01 0.02 0.03 0.04 0.05-0.0100.010.020.030.040.05

0 0.01 0.02 0.03 0.04 0.050

10

20

30

Stra

in in

the

fiber

dire

ctio

n

時間[秒]

ATP

cons

umpt

ion

Explicit ∆𝑇𝑇 ∆𝑡𝑡⁄ = 1 Explicit ∆𝑇𝑇 ∆𝑡𝑡⁄ = 1000 Implicit ∆𝑇𝑇 ∆𝑡𝑡⁄ = 1000

Oscillation from the instability

Extreme energy consumption

Coupling technique : Efficiency & Stability 1. Reduction of communication overheads by the multiple time step method 2. Stability by taking the active stiffness

Concluding Remarks We constructed a multiscale platform that enables us to analyze the stochastic dynamics of motor proteins under the condition : that is generated by the protein motors themselves that can’t be made from artificial boundary conditions

Big data & AI Huge numerical simulation data of the

molecular behavior Seeking correlations between the

functional parts in the protein motors Optimization of parameters of

numerical models

Central-Body Converter

Lever-arm

Upper-50K

Thin filament

Lower-50K

Beating heart simulation driven by three dimensional molecular dynamics model�スライド番号 2スライド番号 3スライド番号 5スライド番号 6スライド番号 7スライド番号 8スライド番号 9スライド番号 10スライド番号 11スライド番号 12スライド番号 13スライド番号 14