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/ Chloroplasten, Tylakoid-Membran From: X. Hu et al., PNAS 95 (1998) 5935
Primary steps in photosynthesis 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! 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: Monte Carlo, normal mode analysis, principal components
L5/P5: Bioinformatics: sequence alignment, Structure prediction, homology modelling
L6/P6: Charge transfer & photosynthesis, electrostatics methods
L7/P7: Aquaporin / ATPase: two 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
Threonine Asparagine Glutamate
Alanine Proline
Histidine Isoleucine Arginine Valine
Lysine Glycine Serine Phenylalanine Aspartate
Leucine Glutamine Methionine Tyrosine Tryptophane Cysteine 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 Simulation
Molecule: (classical) N-particle system
Newtonian equations of motion:
with
Integrate numerically via the „leapfrog“ scheme:
with Δt ≈ 1fs!
(equivalent to the Verlet algorithm) MD-Experiments with Argon Gas Radial distribution function
distance
300 K 70 K 10 K Molecular Dynamics Simulations
Schrödinger equation
i~@t (r, R)=H (r, R) Born-Oppenheimer approximation
He e(r; R)=Ee(R) e(r; R)
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“:
Covalent bonds Non-bonded interactions
bond Ei approximated
exact = K T { B R= ν0 |R| Molecular Dynamics Simulation
Molecule: (classical) N-particle system
Newtonian equations of motion:
with
Integrate numerically via the „leapfrog“ scheme:
with Δt ≈ 1fs!
(equivalent to the Verlet algorithm) „Force- Field“ Computational task:
Solve the Newtonian equations of motion: BPTI: Molecular Dynamics (300K)
8 4 nm
Molecular dynamics simulation, 1s = ^ 2 ·10 -11s