developing modern mathematical methods and computational...
Post on 25-Jul-2020
9 Views
Preview:
TRANSCRIPT
Developing Modern Mathematical Methods and Computational Tools
for Biological Physics
Bo Li Math and CTBP, UCSD
CTBP EAC meeting, Rice Univ., Jan. 10 & 11, 2013
2 fast algorithms
multiscale models surfaces/interface
simulations soln’s of diff. eqns
0 2000 4000 6000 8000 100002
3
4
5
6
7
8
9
10
stochastic models
Projects § Variational implicit solvation (with McCammon) § Electrostatics: Dielectric boundary forces, Ionic
size effects, etc. § A two-scale model: Brownian particles and
diffusion equation (with McCammon) § Diffusion of RNA molecules (with Levine) § Cell shapes and dynamics (with Levine/Rappel) § Fast algorithms: multigrid, GPU computing, etc.
3
4
Free-energy functional
€
r i
€
Ωm
Γ
€
Qi
€
Ωw
€
c j∞,
€
q j , wρG[Γ]= Pvol(Ωm )+γ0 (1− 2τH )dSΓ
∫
€
+ρw ULJ ,ii∑
Ωw
∫ (| r − r i |)dV + Gelec[Γ]
1. Variational Implicit Solvation
(McCammon group, 2006)
The level-set method
5 !! !" # " ! $ % &#"#!
"#$
"#%
"&#
"&"
"&!
"&$
'()*+,
-./010.(
'()*+,23/240+5(627./010.(
0(010542.8219.2/:5442)(3)4.7)0(010542.82.()245*+)2)(3)4.7)
PMF
wall-particle distance
A receptor-ligand system p53/MDM2
uncharged charged
A host-guest system
6
Dielectric boundary force
€
Fn = −δΓGelec[Γ]
€
r i
€
Ωm
Γ
€
Qi
€
Ωw
€
c j∞,
€
q j , wρ€
εm =1
€
εw = 80
€
∇ ⋅εε0∇ψ − χwB'(ψ) = −ρ f
€
Gelec[Γ] = −εε02|∇ψ |2 +ρ fψ − χwB(ψ)
)
* + ,
- . ∫ dV
δΓGelec[Γ]=ε02
1εm
−1εw
#
$%
&
'( |ε∂nψ |
2 +ε02εw −εm( ) (I − n⊗ n)∇ψ 2
+B(ψ)
Electrostatic force points to solutes!
2. Electrostatics
Surface energy vs. electrostatic energy Stability of water-protein interface
7
8R
K: r=u(z)
LO
x
y
z1_
1+ 1 2 3 4 5k
!1.5
!1.0
!0.5
0.5
"2"1"
0 1 2 3 4 5 6
1.342
1.344
1.346
1.348
1.35
1.352
1.354
1.356
1.358
1.36
t = 0
t = 2
t = 4
t = 6
z
r
water
protein
Water molecules inside a protein are unhappy!
8
Ionic size effects: A mean-field model
€
F[c] =12ρψ + β−1 ci ln(ai
3ci)i= 0
M
∑ − µicii=1
M
∑'
( )
*
+ , ∫ dV
€
ρ = ρ f + qicii=1
M
∑
€
∇ ⋅εε0∇ψ = −ρ
€
a03c0 =1− ai
3cii=1
M
∑
€
δiF[c] = 0 Generalized Boltzmann distributions
With a uniform size
€
ci =ci∞e−βqiψ
1+ a3 c j∞ e−βq jψ −1( )j=1
M∑
With nonuniform sizes
€
aia0
"
# $
%
& '
3
ln a03c0( ) − ln ai3ci( ) = β qiψ −µi( )
No explicit formulas. Constrained optimization!
Mean-field Theory and Monte Carlo Simulations
0 5 10 150
5
10
15
20
25
30
35
40
Distance to the charged surface (A)
Rad
ialde
nsity
! i(r
)(M
)
z1=+1, R
1=3.0, N
1=100
z2=+2, R
2=2.5, N
2=100
z3=+3, R
3=3.5, N
3=100
5 10 15 200
5
10
15
20
25
Distance to the charged surface (A)
Radia
ldensity
c i(r)(M
)
z1=+1, R
1=3.0, N
1=100
z2=+2, R
2=2.5, N
2=100
z3=+3, R
3=3.5, N
3=100
" counterion stratification " key parameters:
€
Zi /ai3
9
10
Cluster 1 § Housed in San Diego Supercomputer center § 1500+ processors, ~ 600 nodes § HHMI donation of 200 2-year old nodes in 2012 § Serial and small parallel jobs
Cluster 2 § Housed in the Physics Server Room § 48 cores, 24 GPUs
Software: AMBER, APBS, AutoDock, CHARMM, GAMESS, Gaussian, Gromacs, MMTSB, NAMD, Python, Rasmol, VMD
CTBP Computational Resources at UCSD
11
§ 377th in the Top 500 supercomputer list of June 2012
§ 84 teraflops of performance § 24,576 cores § Massively parallel
IBM Blue Gene/P at Rice University
6 racks 192 cards 6,144 cards 24,576 cores
MBB (Math & Biochem-Biophys) Group § Initiated in 2007. § Current: 4 graduate students, 2 postdocs, and 2
visitors, 2 faculty members. § Former members: postdocs, graduate students,
2 undergrads, and 2 high school students. § Graduate students: San Diego Fellowship
through CTBP, UCOP Computational Science Fellowship, HHMI Fellowship UCSD nominee.
§ Weekly MBB seminars. § Brainstorming workshops (with CTBP groups).
12
Thank you !
13
top related