Upload
others
View
5
Download
0
Embed Size (px)
Citation preview
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