Structural Control of Motions?

Robert JerniganLH Baker Center for Bioinformatics and Biological Statistics

Department of Biochemistry, Biophysics and Molecular Biology

Iowa State University

Coarse-Graining Structures

Complexity requires use of simple approaches –a network view of molecular structure (hydrophobicity cohesiveness)Identification of physical interactions (proximity)Usually no chemical identities of atoms or residuesA physics/materials/polymers/engineering based approachEssential to represent the cohesiveness of structures

Simplifying Structures for Simulations of Larger Structures

Intrinsic Regularities for Packing inside Proteins

Face-centeredCubic lattice

Actual proteingeometry between neighbors

Preferred Orientations:

Icosahedra

Order parameter

2

1

cosm

iiOP

m

α=

Δ=

∑

Superimpositions of coordination clusters with directional vectors pointing from the centers of the icosahedra to their 12 vertices give OP = 0.91

The 12 directions of the fcc lattice give OP = 0.82

4-Body Potentials

Improvements over 2-body potentials in gapless threading

Indicates the Importance of Packing Density

Correlation of Sequence Entropy with Inverse of Packing Density

sequence entropyΣ p ln p

residue packing densityaverage over many occurrencesother amino acid properties correlated with sequence entropy also

Liao, et al Prot. Eng. Des. Select., 2005

Elastic network models

Rubber elasticity (polymers - Flory)Intrinsic motions of structures (Tirion 1996) Simple elastic networks of uniform material – a packing modelAppropriate for largest, most important domain motions of proteins - independent of structural detailsImplies high resolution structures not always needed to learn about important motions

Rubbery Bodies with Well Defined, Highly Controlled Motions

Protein MechanicsFunctional part can be a small part –what’s the rest of the structure for?How do effects at a distance work (allostery)?Understanding protein control – reactions and processingHow cooperative are proteins in their motions?A parts list?

Protein Structure Controls Functional Motions

Supporting evidence for elastic network models

Reproduce X-ray B-Factors Often Better than Atomic Molecular DynamicsReproduce Motions Represented in NMR Ensembles Even BetterGood Agreement with Molecular DynamicsMotions Relate Closely to Observed Structure Changes, Including LigandBinding

Strong Experimental Support for Elastic Models

Elastic Network Models

Calculating Protein Position Fluctuations

Vtot(t) = (γ/2) tr [ΔR(t)T Γ ΔR(t)]

<ΔRi . ΔRj> = (1/ZN) ∫ (ΔRi . ΔRj) exp {-Vtot/kT} d{ΔR}= (3kT/γ) [Γ-1]ij

Γ = Kirchhoff matrix of contacts

=Γ =

Compute Normal Modes for Fluctuations and Correlations

Validation from X-ray Temperature Factors

0

25

50

75

100

0 50 100 150 200 250 300 350

(b) 1omfcalculated

experimental

0

20

40

60

80

0 20 40 60 80 100 120

(a) 2ccya

Debye-Waller factors:

Bk = 8 π2 <ΔRk • ΔRk> /3

Usually Slightly Better than from Atomic MD

Effects of Gln Synthetase Binding tRNA

0 10 20 30 40 50 60 70 80

Bound calculatedBound experimentalUnbound calculatedUnbound experimental

nucleotide number

T em

pera

tur e

F ac t

or

Major Changes upon Binding Are Reproduced

tRNA Motions

These Are Known Motions

Reverse Transcriptase Mechanism fromModes

1. Push-pull hinge

2. Clamp-release hinge

Two Enzyme Sites – NA Copy & Cut

Two Slowest Modes of Motion Relate to the Coordinated Processing Motion between Two Sites

Combine for Mechanism

HIV Reverse Transcriptase – Slowest Motion

Push-pull Hinge

Modes of Motion – HIV Protease

Mode 1 Mode 2 Mode 3

Three Ways to Open the Flaps

NMR Structures Fit Elastic Networks Better than X-Ray Structures

Results for 164 X-ray and 28 NMR HIV Protease Structures

HIV ProteaseOverlaps between directions of motions

(dot products of vectors)

Includes Many Drug Bound Structures

Distortions for Drug Binding Are Intrinsic to Protein Structure

Cumulative Overlaps with NMR Motions

NMR Agreement Better than X-ray

Analyses of the conformational transitions by the motion types

Motion Type

Shear Hinge Other Larger Motions

Number of Pairs

27 59 18 18

Reduced DOF

107 68 79 113

Maximum Overlap

0.58 0.67 0.46 0.50

Hinges and Shears Represented Best by ENMs

Prediction of directions of conformational transitions with ENM

New overlap – infinitesimal changes compared – important for rotational motions

Infinitesimal Rotations for Initial Directions

•Directions change during rotation, so need initial infinitesimal direction•Improved overlaps!

Rigid Body RotationFrom A to B

Generating a transition pathway from the “closed”monomer to the “open” domain-swapped dimer1. Begin with the `closed' form and solve for internal modes

6-12 - the important relative rigid body motions of the two domains

2. Pick the mode that decreases the number of contacts between the domains

3. Move along that mode for a small separation step

4. Otherwise, pick a random mode and move a small step

5. Repeat steps 1-5 until the two domains are separated or the iteration reaches its limit

Fitting to Achieve Transition (Separation)

Diphtheria toxin transition pathway

(1) the distance between the two domains

(2) the RMS distance to the final state

(3) the number of inter-domain contacts

(4) the mode selected at each step.

0 20 402

4

6

8

10Minimum Dist btw Domains

0 20 405

10

15

20Distance (RMSD) to Target

0 20 406

8

10

12

Step Index

Modes Selected

0 20 400

100

200

300

Step Index

Number of Contacts btw Domains

(1) (2)

(3) (4)

Transitions Usually Easy to Achieve

Mode contributions for XanthineDehydrogenase

10-5

0.0001

0.001

0.01

0.1

1 10 100 1000 104

xanthine dehydrogenase

NN/5N/20N/40

mode index

Log-log plot so only a small number of important modes

These important motionssimilar for differentlevels of coarse graining

Only a Few Modes Are Important

Superimposed TriosephosphateIsomerases

Residues 130-248 Show Large Changes – treated here as atoms

Triose phosphate isomerase – enzyme reaction

Deformations of loop

Coordinated Atom Motions at Reaction Site

Domain Motions Simultaneously Controlling the Loop and Active Site Atom Motions

Ratchet Motions of the RibosomeFirst 6 modes

Overall in Agreement with Electron Microscopy Images

What’s happening inside the ribosome?

Efficient conversion of rotational motion into translational motion

Correlations of motions between ribosome components

50S A-tRNA

P-tRNA

E-tRNA

mRNA

30S -0.987 -0.061 -0.099 -0.066 0.49850S -0.006 0.025 -0.010 -0.545A-

tRNA0.772 0.165 0.422

P-tRNA

0.313 0.386

E-tRNA

0.188

For 100 Slowest Modes

Local Motions of tRNA

Anti-codon rigid

Acceptor end rigid

Functional Parts Are Held Rigid ~ No Deformations

Ribosome Mechanism

Ratchet motion is dominant motiontRNAs at A, P and E sites have similar motionsmRNA is extremely constrained at decoding siteChannel rotates (twisting/release mechanism?)

A Complex Coordinated Machine

Abundant Evidence of the Control of Protein Motions

Pre-existing structures for bound statesUsually overlaps between directions of slowest normal modes and known transitionsEnzyme atomic motions controlled by domain motionsBinding loop opening/closing controlled by domain motionsRegulation of motions by binding partners

Control of Function through Domain Motions

Networks as unifying models Connecting Atomic to the Larger Scale

BiomechanicsGenomesProteomesMetabolomesStructuresIntegrating All CombinationsDifferent Levels of Abstraction – Spatial, Temporal

Networks’ Advantage - Easy to Connect

Elastic Network ModelsUseful for:

Motions of largest structural assemblages Functional mechanisms for processing proteins and enzymes Predicting pathways for transitions between two forms of a proteinInterpreting single molecule experimentsRefinement of structures and models

A Simplifying View of Protein Machine Motions

ConclusionsProtein structure (shape) probable motions Various levels of coarse-grained models, & mixed - OKUsually must have full assemblage – not partial structures!Large domain motions dominate – simpler, functional motions – not so many important onesAtoms & loops on surfaces can be controlled by domain motions – atoms pushed in directions of enzyme reactionsMotions depend strongly on binding partnersUseful for large conformational transitionsDetails of mechanisms and control - from modes of motion

Simple Models Can Tell Us Many Things

FutureInclude EnergiesInclude Disordered Parts of ProteinsIntroduce Forces (microscopic forces??)

Molecular Mechanisms, Including EnzymesHinge MotionsSingle Molecule ApplicationsSimulations from Static Images (Electron microscopy)Protein-Protein Network Analyses for RegulationEffects of Ligands on Motions

Ultimate Goal – Cell Structure Simulations

CollaboratorsO Kurkcuoglu, P Doruker (Bogazici Univ, Istanbul)Y Wang (Univ Memphis) G Culver (Univ Rochester)T Sen, A Kloczkowski, Y Feng (ISU)G Song, L Yang (ISU)D Dobbs, V Honavar (ISU)J Sulkowska, M Cieplak (Polish Acad Sci)A Kolinski, P Pokarowski (Warsaw University)

G Chirikjian (Johns Hopkins)I Bahar, NA Temiz (Univ Pittsburgh)AR Atilgan (Bogazici Univ, Istanbul)O Keskin (Koc Univ, Istanbul)DG Covell (NCI-Frederick)

NIH-NIGMS R01-GM081680, R01-GM072014, R01-GM073095, R33-GM066387

NSF 0234102, 0521568

ISU CIAG