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.)