Computational Biophysics: Introduction
Bert de Groot, Jochen Hub, Helmut Grubmüller
Max Planck-Institut für biophysikalische Chemie Theoretische und Computergestützte Biophysik Am Fassberg 11 37077 Göttingen
Tel.: 201-2308 / 2314 / 2301 / 2300 (Secr.)
Email: [email protected] [email protected] [email protected] www.mpibpc.mpg.de/grubmueller/
mailto:[email protected]
Chloroplasten, Tylakoid-Membran
Primary steps in photosynthesis
From: X. Hu et al., PNAS 95 (1998) 5935
F-ATP Synthase
20 nm
F1-ATP(synth)ase
ATP hydrolysis drives rotation of γ subunit and attached actin filament
F1-ATP(synth)ase
NO INERTIA!
The Ribosome
30 nm
Proteins are Molecular Nano-Machines !Elementary steps:
Conformational motions
Overview: Computational Biophysics: Introduction
L1/P1: Introduction, protein structure and function, molecular dynamics, approximations, numerical integration, argon
L2/P2: Tertiary structure, force field contributions, efficient algorithms, electrostatics methods,
protonation, periodic boundaries, solvent, ions, NVT/NPT ensembles, analysis
L3/P3: Protein data bank, structure determination by NMR / x-ray; refinement
L4/P4: Bioinformatics: sequence alignment, Structure prediction, homology modelling
L5/P5: Monte Carlo, normal mode analysis, principal components
L6/P6: Charge transfer & photosynthesis, electrostatics methods
L7/P7: Aquaporin / ATPase / Ribosome: examples from current research
Overview: Computational Biophysics: Concepts & Methods
L08/P08: MD Simulation & Markov Theory: Molecular Machines
L09/P09: Free energy calculations: Molecular recognition
L10/P10: Non-equilibrium thermodynamics: Molecular driving forces
L11/P11: Quantum mechanics methods: Enzymatic catalysis
L12/P12: Hartree-Fock, density functional theory
L13/P13: Rate theory: Biomolecular efficiency
a water molecule
an ethanol molecule
a water droplet
a water droplet
water vapor
a salt crystal (NaCl)
bovine pancreatic trypsin inhibitor (BPTI)
20 different amino acids
Alanine
Tyrosine Cysteine
Arginine
Asparagine
Aspartate
Glutamate
Glycine
Threonine
Lysine
Glutamine TryptophaneMethionine
Histidine
Phenylalanine
Valine
Proline
Isoleucine
Serine
Leucine
hexa-peptide
alpha-helix
beta sheet
bovine pancreatic trypsin inhibitor (BPTI)
myoglobin
antibody IGG domain
porin
bacteriorhodopsin
?
Four different nucleotides encode amino acids
(à Uracil)
hemagglutinin (influenza virus)
hemagglutinin (influenza virus)
Molecular Dynamics Simulations
Interatomic interactions
Molecular Dynamics SimulationMolecule: (classical) N-particle system
Newtonian equations of motion:
with
Integrate numerically via the „leapfrog“ scheme:
(equivalent to the Verlet algorithm)
with
Δt ≈ 1fs!
MD-Experiments with Argon Gas
Radial distribution function
300 K 70 K 10 K
distance
i~@t (r, R) = H (r, R)
He e(r;R) = Ee(R) e(r;R)
Molecular Dynamics Simulations
Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical Force field
1
Molecular dynamics-(MD) simulations of Biopolymers• Motions of nuclei are described classically,
• Potential function Eel describes the electronic influence on motions of the nuclei and is approximated empirically à „classical MD“:
approximated
exact
Eibond
|R|ν0
KBT {
Covalent bonds Non-bonded interactions
==R
Molecular Dynamics SimulationMolecule: (classical) N-particle system
Newtonian equations of motion:
with
Integrate numerically via the „leapfrog“ scheme:
(equivalent to the Verlet algorithm)
with
Δt ≈ 1fs!
„Force-Field“
Computational task:
Solve the Newtonian equations of motion:
BPTI: Molecular Dynamics (300K)
8
4 nm
Molecular dynamics simulation, 1s = 2 ·10 -11s ^