Instructor: Prof. Jesús A. Izaguirre
Textbook: Tamar Schlick, Molecular Modeling and Simulation: An Interdisciplinary Guide, Springer-Verlag, Berlin-New York, 2002, Chapters 2-4
References:
C. Brooks, M. Karplus, B. Pettitt, Proteins: A Theoretical Perspective of Dynamics, Structure, and
Thermodynamics, Wiley, 1988
Various websites indicated in the text
Computational Biophysics & Systems Biology
Biomolecular modeling of proteins
Outline
1. Historical perspective
2. Review of protein structure
3. Review of protein dynamics
What is biomolecular modeling?
• Application of computational models to understand the structure, dynamics, and thermodynamics of biological molecules
• The models must be tailored to the question at hand: Schrodinger equation is not the answer to everything! Reductionist view bound to fail!
• This implies that biomolecular modeling must be both multidisciplinary and multiscale
Historical Perspective
1. 1946 MD calculation
2. 1960 force fields
3. 1969 Levinthal’s paradox on protein folding
4. 1970 MD of biological molecules
5. 1971 protein data bank
a. 1998 ion channel protein crystal structure
b. 1999 IBM announces blue gene project
Theoretical Foundations
1. Born-Oppenheimer approximation (fixed nuclei)
2. Force field parameters for families of chemical compounds
3. System modeled using Newton’s equations of motion
4. Examples: hard spheres simulations (alder and Wainwright, 1959); Liquid water (Rahman and Stillinger, 1970); BPTI (McCammon and Karplus); Villin headpiece (Duan and Kollman, 1998)
Experimental Foundations I
1. X-ray crystallography• Analysis of the X-ray diffraction pattern produced when a
beam of X-rays is directed onto a well-ordered crystal. The phase has to be reconstructed.
• Phase problem solved by direct method for small molecules
• For larger molecules, sophisticated Multiple Isomorphous Replacement (MIR) technique used
• Current resolution below 2 \AA
2. Protein crystallography• Difficult to grow well-ordered crystals• Early success in predicting alpha helices and beta sheets
(Pauling, 1950s)
Experimental Foundations II
3. NMR Spectroscopy• Nuclear Magnetic Resonance provides
structural and dynamic information about molecules. It is not as detailed as X-ray, somewhat limited in size
• Distances between neighboring hydrogens are used to reconstruct the 3D structure using global optimization
• Relaxation rates give dynamics (slow and fast)
Proteins I
• Polypeptide chains made up of amino acids or residues linked by peptide bonds– Peptide bond is a partial double bond; limited
rotation – 2kcal/mole for rotations 10°-20°; 3.2 kcal/mole for rotations 20° out of the plane
• 20 aminoacids
Proteins I
• 50-500 residues, 1000-10000 atoms
• Native structure believed to correspond to energy minimum, since proteins unfold when temperature is increased
Protein Functions
• Enzymes – synthetic and degradative• Hormones• Receptors• Membrane structural proteins
– Aquaporin and Ion Channels– Transporters – Photosynthesis– APT/energy generators– Photoreceptors
Protein Functions
• Replicases and polymerase
• Globular structural proteins – tubulin, flagellin
• Fibrous structural proteins – collagens, keratin
• Motor proteins – kinesins, myosin
Source: MIT OCW (MIT 791)
Protein Structure
Protein Structure
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Source: MIT OCW (MIT 791)
Model Molecule: Hemoglobin
Heme Groups in Hemoglobin
Hemoglobin: Background
• Protein in red blood cells
• Composed of four subunits, each containing a heme group: a ring-like structure with a central iron atom that binds oxygen
• Picks up oxygen in lungs, releases it in peripheral tissues (e.g. muscles)
Hemoglobin – Quaternary Structure
Two alpha subunits and two beta subunits(141 AA per alpha, 146 AA per beta)
Hemoglobin – Tertiary Structure
One beta subunit (8 alpha helices)
Proteins III
• Protein motions of importance are torsional oscillations about the bonds that link groups together
• Substantial displacements of groups occur over long time intervals
• Collective motions either local (cage structure) or rigid-body (displacement of different regions)
• What is the importance of these fluctuations for biological function?
• See http://www.molmovdb.org
Proteins IV
• Effect of fluctuations:– Thermodynamics: equilibrium behavior
important; examples, energy of ligand binding– Dynamics: displacements from average
structure important; example, local sidechain motions that act as conformational gates in oxygen transport myoglobin, enzymes, ion channels
Proteins V: Local Motions
• 0.01-5 AA, 1 fs -0.1s• Atomic fluctuations
– Small displacements for substrate binding in enzymes– Energy “source” for barrier crossing and other
activated processes (e.g., ring flips)
• Sidechain motions– Opening pathways for ligand (myoglobin)– Closing active site
• Loop motions– Disorder-to-order transition as part of virus formation
Proteins VI: Rigid-Body Motions
• 1-10 AA, 1 ns – 1 s• Helix motions
– Transitions between substrates (myoglobin)
• Hinge-bending motions– Gating of active-site region (liver alcohol
dehydroginase)– Increasing binding range of antigens
(antibodies)
Proteins VII: Large Scale Motion
• > 5 AA, 1 microsecond – 10000 s• Helix-coil transition
– Activation of hormones
• Dissociation– Formation of viruses
• Folding and unfolding transition– Synthesis and degradation of proteins
Role of motions sometimes only inferred from two or more conformations in structural studies
Study of Dynamics I
• The computational study of atomic fluctuations in BPTI and other proteins has shown that :– Directional character of active-site fluctuations
in enzymes contributes to catalysis– Small amplitude fluctuations are “lubricant”– It may be possible to extrapolate from short
time fluctuations to larger-scale protein motions
Study of Dynamics II
• Collective motions particularly important for biological function, e.g., displacements for transition from inactive to active – Extended nature of these motions makes
them sensitive to environment: great difference between vacuum and solution simulations
– Collective motions transmit external solvent effects to protein interior
Study of Dynamics III
• For the related storage protein, myoglobin:– Fluctuations in the globin are essential to
binding: the protein matrix in X-ray is so tightly packed that there is no low energy path for the ligand to enter or leave the heme pocket
– Only through structural fluctuations can the barriers be lowered sufficiently
– Demonstrated through energy minimization and molecular dynamics
Study of Dynamics IV
• For the transport protein hemoglobin there are several important motions:– Oxygen binding produces tertiary structural change– A quaternary structural change from deoxy (low
oxygen affinity) to oxy configuration takes place. This transmits information over a long distance
– From the X-ray deoxy and oxy structures, a stochastic reaction path has been found. Detailed ligand binding has been performed using MD. A statistical mechanical model has provided coupling between these two processes
Lengthening Scales: SRP
• Enzyme simulation of a ms using stochastic reaction path – disadvantage: need initial and final configuration
• Finds a trajectory where “global energy” is minimized
Protein Folding
Source: Folding@Home
Source: Gruebele 2002, Fig. 1
Folding from SimulationPredicting kinetic rates Atomistic simulations (MD)
microsecond resolution
so far for 2 state folders Solvent representation
Ensemble kinetics
Transition state identification e.g. Unfolding simulations
reaction coordinates
transition path sampling
reaction path methods
Free energy landscape F(q) = -ln P(q)
replica exchange
thermodynamic integration
Folding Coordinates
• Fraction of native contacts (difficult experimentally)
• Radius of gyration (not universal)
• Global coordinates
• Local coordinates
• Thermodynamic coordinates (measure barrier changes w. small change in T, etc.)
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