NAMD Tutorial (Part 2)
Transcript of NAMD Tutorial (Part 2)
![Page 1: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/1.jpg)
NAMD Tutorial (Part 2)NAMD Tutorial (Part 2)
2 Analysis 2.1 Equilibrium
2.1.1 RMSD for individual residues2.1.2 Maxwell-Boltzmann Distribution2.1.3 Energies2.1.4 Temperature distribution2.1.5 Specific Heat
2.2 Non-equilibrium properties of protein2.2.1 Heat Diffusion2.2.2 Temperature echoes
![Page 2: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/2.jpg)
Organization of NAMD Tutorial FilesOrganization of NAMD Tutorial Files
![Page 3: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/3.jpg)
Simulated Cooling of UbiquitinSimulated Cooling of Ubiquitin• Proteins function in a narrow (physiological)
temperature range. What happens to them when the temperature of their surrounding changes significantly (temperature gradient) ?
• Can the heating/cooling process of a protein be simulated by molecular dynamics ? If yes, then how?
0T
1T• What can we learn from the
simulated cooling/heating of a protein ?
![Page 4: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/4.jpg)
Nonequilibrium (Transport) Nonequilibrium (Transport) PropertiesProperties
macromolecular properties of proteins, which are related to their biological functions, often can be probed by studying the response of the system to an external perturbation, such as thermal gradient“small” perturbations are described by linear response theory (LRT), which relates transport (nonequilibrium) to thermodynamic (equilibrium) propertieson a “mesoscopic” scale a globular protein can be regarded as a continuous medium ⇒ within LRT, the local temperature distribution T(r,t) in the protein is governed by the heat diffusion (conduction) equation
2( ) ( )T t D T tt
∂ ,= ∇ ,
∂r r
![Page 5: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/5.jpg)
Atomic Atomic vsvs MesoscopicMesoscopic
• each atom is treated individually
• length scale ~ 0.1 Ǻ
• time scale ~ 1 fs
• one partitions the protein in small volume elements and average over the contained atoms
• length scale ≥ 10 Ǻ = 1nm
• time scale ≥ 1 ps
![Page 6: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/6.jpg)
Heat Conduction EquationHeat Conduction Equation2( ) ( )T t D T t
t∂ ,
= ∇ ,∂r r
D K cρ= /thermal diffusion coefficient
thermal conductivityspecific heat
mass density
• approximate the protein with a homogeneous sphere of radius R~20 Ǻ
• calculate T(r,t) assuming initial and boundary conditions:
0( ,0)( , ) bath
T r T for r RT R t T
= <
=
R0r
![Page 7: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/7.jpg)
Solution of the Heat EquationSolution of the Heat Equation
( )2 22 2
12
6 1( ) (0) exp
( ) ( ) ,n
bath
T t T n tn
T t T t T R D
π τπ
τ
∞
0=
0
∆ = ∆ × − /
∆ ≡ − = /
∑where
0 0.2 0.4 0.6 0.8 1
0.2
0.4
0.6
0.8
1.0
( , )(0, )T t rT r
∆∆
rR
time
protein
coola
nt
averaged over the entire protein!averaged over the entire protein!
![Page 8: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/8.jpg)
How to simulate cooling ?How to simulate cooling ?• In laboratory, the protein is immersed in a coolant and the
temperature decreases from the surface to the center
• Cooling methods in MD simulations:
1.1. Stochastic boundary methodStochastic boundary method
2. Velocity rescaling (rapid cooling, biased velocity autocorrelation)
3. Random reassignment of atomic velocities according to Maxwell’s distribution for desired temperature (velocity autocorrelation completely lost)
2
1( )
dN
i ii new
i isimd B old
m vTT t v v
N k T= ′= ⇒ =∑
![Page 9: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/9.jpg)
Stochastic Boundary MethodStochastic Boundary Method
2R δ
coolant layer of atomscoolant layer of atomsmotion of atoms is subject to stochastic Langevindynamics
FF H f L
FF
H
f
L
m = + + +
→→→→
r F F F FFFFF
force fieldharmonic restrainfriction Langevin force
FFm =r F
Heat transfer through mechanical coupling between atoms in the two regions
atoms in the inner region follow Newtonian dynamics
![Page 10: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/10.jpg)
Determine D by Fitting the DataDetermine D by Fitting the Data
0 0.2 0.4 0.6 0.8 1
220
240
260
280
300
Tem
pera
ture
[K]
time [x10ps]
( )22 2
1
2
00
( ) 6 1 exp(0)
10 , ,
n
T tn x t t
T n
R xt ps x fitting parameter Dt
π
π
∞
0=
∆= − /
∆
= = =
∑
3 21.41 0.97 10x D cm s−≈ ⇒ ≈ × /
(use the first 100 terms in the series ! )
![Page 11: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/11.jpg)
Thermal Conductivity of UBQThermal Conductivity of UBQ
K D cρ=
( )2 2 2 2 2/ /V B BC E k T E E k Tδ= ⟨ ⟩ = ⟨ ⟩ − ⟨ ⟩
3 20.97 10D cm s−≈ × /3 31 10 kg mρ ≈ × /
![Page 12: NAMD Tutorial (Part 2)](https://reader034.fdocuments.net/reader034/viewer/2022042609/62635e6ab86a0f63d65046fa/html5/thumbnails/12.jpg)
NAMD Tutorial (Part 2)NAMD Tutorial (Part 2)
2 Analysis 2.1 Equilibrium
2.1.1 RMSD for individual residues2.1.2 Maxwell-Boltzmann Distribution2.1.3 Energies2.1.4 Temperature distribution2.1.5 Specific Heat
2.2 Non-equilibrium properties of protein2.2.1 Heat Diffusion2.2.2 Temperature echoes