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Topics to be Covered Introduction to Protein Folding Mechanism of folding and misfolding GroEL – biological machine (chaperones folding) Molecular motors: Polymer physics and Myosin V motility

Topics to be Covered

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Introduction to Protein Folding Mechanism of folding and misfolding GroEL – biological machine (chaperones folding) Molecular motors: Polymer physics and Myosin V motility. Topics to be Covered. Structure Prediction Protein & Enzyme Design Folding Kinetics & Mechanisms - PowerPoint PPT Presentation

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Page 1: Topics to be Covered

Topics to be Covered

Introduction to Protein Folding

Mechanism of folding and misfolding

GroEL – biological machine (chaperones folding)

Molecular motors: Polymer physics and Myosin V motility

Page 2: Topics to be Covered

Many Facets of Folding

1. Structure Prediction

2. Protein & Enzyme Design

3. Folding Kinetics & Mechanisms

4. Crowding & confinement Effects

5. Relation to aggregation

6. Molecular Chaperones

7. Unfolded protein response (UPR)

Folding and clearance mechanisms are at the center stage

Page 3: Topics to be Covered

A Big Protein Folding Problem

Read the Genetic Code; Transcription; ProduceProteins, Function, Degradation

Length ≈ 220 nm ≈ 700 water

Size ≈ 22nmA very large protein in water – complexproblem indeed! (about 100,000 waters)

Page 4: Topics to be Covered

Pictures, Models, Approximations & Reality

A bit PhilosophyRich History in Condensed Matter physics & Soft Matter (Analytic Theory)

• Ising model for magnetic systems (Ni/also biology; 1920)

• Spin glasses – Edwards-Anderson model (CuMn alloy; 1975)

• Polymer statistics (Flory; 1948)

• Liquid Crystals (TMV) (Onsager 1949)

• BCS Theory (1956…)

Page 5: Topics to be Covered

Folding Kinetics

Experiments Theory

o Prot Engg (TSE)

o SAXS/NMR (DSE)

o FAST Folding (T jump; P JUMP; Rapid Mixing)

o SM FRET (Folding/ unfolding)

o LOT/AFM (Force Ramp Force Quench)

Statistical Mechanics (Energy Landscape)

Minimal Models (Lattice/Off-Lattice)

MD Simulations

Bioinformatics (Evolutionary Imprint)

Page 6: Topics to be Covered

Outline

How far can we go using polymer physics? (no force)

Toy models and generic lessons

Finite size effects: Universal relations

Bringing “specificity” back: Phenomenological Models

Page 7: Topics to be Covered

Many facets of Protein FoldingHow does a chain (necklace with different shape pearls) fold up and

how fast?Can things go wrong and then what?

As structuregets organizedEnergy gets lowered

Minimum Free Energy(water ions cosolvents)

Anfinsen over 50 yearsago; Nobel Prize 1972

Computational approaches to Biological problems: 2013 Nobel Chemistry

Page 8: Topics to be Covered

RNA and some Proteins

F

S

ΔFiNBA/ΔFij >> 1

I: Gradient to NBAdominates: Most likely event underfolding conditions

All other transitionsless likely.

Page 881 of Textbook Chapter 18

Page 9: Topics to be Covered

Approximation to Reality!

Another Nobel Protein! (GFP)

Not all molecules take the same route:Folding is stochastic! At least 4 classes of folding trajectories (Reddy)

Complicated Energy Function

Page 10: Topics to be Covered

Thermodynamics of src-SH3 folding

Green = UreaRed= MTM predictionsBlack = Experiments (Baker)

ΔGNU[C] = ΔGNU[0] + m[C]

m = (1.3 – 1.5) kcal/mol.M

Exp. m = 1.5kcal/mol.MExcellent Agreement!

Z. Liu, G. Reddy, E. O’Brien and dt PNAS 2011

Page 11: Topics to be Covered

Characteristic Temperatures in Proteins

HIGH Tor [C]

RandomCoil (Flory)

T T

Or [C]

T TF

[CF]

Compact

Native State

Rg ≈ aDN0.6

Rg ≈ aN N0.33

Foldable: = (T - TF)/T

small

Page 12: Topics to be Covered

Estimating Protein Size as a Function of N

High denaturant concentration (GdmCl or Urea)

Good solvent for polypeptide chain – may be!

Flory Theory: F(Rg) ≈ (Rg2/N2) + v(N2/Rg

d)

(see de Gennes book)

Rg ≈ aNν ν = 3/(d + 2)

Page 13: Topics to be Covered

Folded States Globular Proteins

• Maximally compact

• Largely Spherical

• Rg ≈ aN N(1/3)

• So size of proteins follow polymer laws – surprising!

Page 14: Topics to be Covered

Protein Collapse : Rg follows Flory law

RgU = 2N0.6

Rg = 3N1/3

Dima & dt JPCB (04)

Kohn PNAS (05)

“Unfolded”

Folded

Page 15: Topics to be Covered

Tetrahymena ribozyme(...difficult)

RNA Folding: Tetrahymena ribozymeRNA – Branched polymer

Ion valence size shape

Page 16: Topics to be Covered

Rg Scaling works for RNA too includingthe ribosome!

Page 17: Topics to be Covered

Size Dependence of RNA

Rg ≈ 5.5N(1/3)

Fairly decent (due to Hyeon)

Exponent mayBe larger..analogyTo branched polymers

Ben Shaul, Gelbart,Knobler

Page 18: Topics to be Covered

Illustrating Key ideas using Lattice models

Seems like an Absurd Idea! Role of non-nativeattractions

Multiple Folding Nuclei

Fast and slow tracks

K. A. Dill Protein Science (1995)

Page 19: Topics to be Covered

Blues Like Each other.They gain one unit of energy

Toy model:Explains proteinfolding

Even simpler Folded lower in energy byone unit

Multiple paths!

Page 20: Topics to be Covered

A simple minded approach

4 types of monomers(H, P, +, -)

Monomer has 8 beads

# of sequences = 48

(amylome)

# of conformations oncubic lattice = 1,841

http://dillgroup.org/#/code

HPSandbox

Page 21: Topics to be Covered

Order parameter description

Macroscopic System

Ferromagnetism MNematic Phases S = P2(cos)Smectic Phases S,tilt angle

Spin Glasses: M; qEAParamagnet M = 0. qEA = 0Spin Glass M = 0; qEA 0Ferromanet M 0; qEA 0

Physics dictates OP

Proteins a lot of choicesOP is in the eye of thebeholder= N/Rg

3 ; (overlap)“unfolded” (Small,big)

Compact non-native(O(1), big)

Native(O(1), small)

Other ChoicesHelix/sheet content;Distribution of contacts………

Page 22: Topics to be Covered

Folding reaction as a phase transition: A rationale N = number of amino acids

Order Parameter Description = N/Rg

3 ; = Overlap with NBA (0 for NBA)

Unfolded (U), Collapsed Globules (CG);Folded (NBA)U: (small), Large (“vapor”)

CG: ≈ O(1), Large (Dense no order “Liquid”)

NBA: ≈ O(1), Small (Dense order “Solid”)

Page 23: Topics to be Covered

Developing a “nucleation” pictureFree Energy of Creating a DropletG(R) ≈ -R3 + R2

Driving force + OpposingWhat are these forces in proteins?

Driving force: Hydrophobic Collapse Burying H bonds Opposing: “Droplet with nonconstant ” Entropy loss due to looping

Page 24: Topics to be Covered

Tentative Models + Slight refinement

Cost of creating a region with NRordered residuesout of N?

Rugged Landscape with Many possibilities

Page 25: Topics to be Covered

Some phenomenological ModelsGBW(NR) -f(T)NR + a2NR

2/3

NR

* (8a2/3 f(T))3 NR

* too large for typical and f(T) values

GGT(NR) h(h - 1)NR2 + a2NR

2/3

NR* (8a2/h)3/4

NR* 15 or so…

Using experimental parameters NR

* 27 or so..

Page 26: Topics to be Covered

Folding trajectories to MFN to transition state ensemble (TSE)

Structures near Barrier top or TSESimulations

Moving from one scenario to another – pressure jump…

Page 27: Topics to be Covered

Refinement (Hiding Ignorance)

G(NR) -1NR + NR

+ S (loop) small barrier (downhill folding)

Surface tension cannot be a constantMultiple Folding Nuclei (StructuralPlasticity)

Multi-domain proteins involve interfaces between globular parts..

Page 28: Topics to be Covered

Finite Size Effects on FoldingOrder parameters matter

Page 29: Topics to be Covered

Scaling of C with N (number of aa)Two points:

1) TF = max in (suceptibility)

= T(d<>/dh; h = ordering field (analogy to mag system) is dimensionless h ~ T (in proteins or [C])

2) Efficient folding TF T (collapse Temp; Camacho & dt PNAS (1993)) C controlled by protein DSE at T TF T

Rg ~ (T/TF)- ~ N (DSE a SAW & manget analogy)

T/TF ~ 1/N (Result I)

Page 30: Topics to be Covered

Finite-size effects on TF

T/TF ~ 1/N

Experiments

Lattice modelsSide Chains

Li, Klimov & DT Phys. Rev. Lett. (04)

Page 31: Topics to be Covered

Scaling of c with NMagnet-Polymer analogy

c= (TF/T) [TF(d<>/dT)] “disp in TF” X “suspectibility”

C N ; = 1 + (Universal); 1.2 Result II

T TF T

N

Page 32: Topics to be Covered

Universality in CooperativityLi, Klimov, dt PRL (04)

c ~ N

Experiments

Page 33: Topics to be Covered

Residue-dependent melting Tm-Holtzer Effect

Consequences of finite size

fm(Tmi) = 0.5

Lattice Models Side Chains

Klimov & dt J. Comp. Chemistry (2002)

Page 34: Topics to be Covered

Is the melting temperature Unique? Finite-size effects!

BBL

HoltzerLeucineZipperBiophys J1997

-hairpinPNAS 2000Klimov & dt

T large

MunozNature2006

UdgaonkarBarstar Monnelin

Page 35: Topics to be Covered

Residue dependent ordering Protein LO’Brien, Brooks & dt Biochemistry (2009)

Spread decreases asN decreases….finite-sizeeffects

Page 36: Topics to be Covered

Summary So Far – Really with little work on acomplex problem

• Sizes of single domain proteins (folded and unfolded) roughly follow Flory’s expectation

• Same holds good for RNA folded structures

• Nucleation Picture of Folding

• Finite size effects – theory matches experiments

Page 37: Topics to be Covered

Part II: Protein Folding Kinetics

Organization of structure

Fluctuations due to finite-sizeeffects

Changes in distributions at various stages of folding [C]

Or T

Page 38: Topics to be Covered

A Few Questions

• Mechanisms of Structural organization

• Nature of the Folding Nuclei

• Interactions that guide folding (native vs non-native)

• Folding rates – dependence on N

Page 39: Topics to be Covered

Illustrating Key ideas using Lattice models

Seems like an Absurd Idea! Role of non-nativeattractions

Multiple Folding Nuclei

Fast and slow tracks

K. A. Dill Protein Science (1995)

Page 40: Topics to be Covered

Stages in folding

RandomCoil

“SpecificCollapse”

Native StateC F

F/C (100 - 1000)

F

C

Camacho and dt, PNAS (1993)

dt J. de. Physique (1995)

Page 41: Topics to be Covered

Need for Quantitative Models

Using mechanicalforce to triggerfolding

smFRET trajectories

Fernandez, Rief.. Hyeon, Morrison, dt

Eaton, Schuler, Haran…

Page 42: Topics to be Covered

Non-native interactions early (time scales of collapse) in folding;

Subsequently native interactionsdominate Camacho & dt Proteins22, 27-40 (1995);Cardenas-Elber (all atom simulations)

Dill type HP modelBeads on a lattice

Native Centric (or Go)models appropriate!

Page 43: Topics to be Covered

Multiple protein folding nuclei and the transition state ensemble in two state proteins‐

Proteins: Structure, Function, and BioinformaticsVolume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig5

LMSC ExactEnumeration

MC simulations;600 folding Trajectories;Folding time:

A/AGO ≈ 3

Klimov and dt (2001)

Page 44: Topics to be Covered

Transition State Ensemble: Neural Net

Go

Klimov anddt Proteins 2001

ES NSB 2000

Equivalentto pfold

Page 45: Topics to be Covered

Multiple protein folding nuclei and the transition state ensemble in two state proteins‐

Proteins: Structure, Function, and BioinformaticsVolume 43, Issue 4, pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig9

Multiple Channels CarryFlux to the NBA

Multiple Transition StatesConnecting these Channels Bottom line:

To get semi-quantitativeresults Go-type modelsMay be enough…

Page 46: Topics to be Covered

Folding Rate versus N

kF ≈ k0 exp(-Nβ) with β = 0.5

Barriers scale sublinearly with N

Proteins: Hydrophobic residues buriedIn interior (chain compact); Polar and charged residues want solvent exposure(extended states). Frustration betweenConflicting requirements.

P(ΔG♯) ≈ exp( - (ΔG♯)2/2N)

<ΔG♯> ≈ N0.5 (Analogy to glasses)

Page 47: Topics to be Covered

Fit to Experiments (80 Proteins Dill, PNAS 2012)

Reasonable givendata from so many differentlaboratories

Page 48: Topics to be Covered

Even better for RNA (Hyeon, 2012)

Page 49: Topics to be Covered

At high [C] is DSE a Flory Coil?It appears that high [C] is a Θ-solvent!

P(x) ~ xexp(-x1/(1-))

Proteincollapse

CT =(C - Cm)/C

= 2 + (γ-1)/ν

O’BrienPNAS 2008

Page 50: Topics to be Covered

Toy Model (Is the fibril structure encoded in monomer spectrum) Prot Sci 2002; JCP 2008

4 types of monomers(H, P, +, -)

Monomer has 8 beads

# of sequences = 48

(amylome)

# of conformations oncubic lattice = 1,841

Page 51: Topics to be Covered

Structure of “protofilament” + “fibril”Single and double layer

Page 52: Topics to be Covered

Interplay of E+- and EHH

a: Monomers parallelb: Monomer alternatec: Double layerd: No fibril compact

Optimal growth tempfib = (104 - 10n)F

Largest n about 9

Seeding speeds up fibrilrate formation

Page 53: Topics to be Covered

Growth rate depends on N* population PN*

Depends on sequence

Sequence + N* ensemblefibril kinetics monomerlandscape encodes structure + growth rate

Page 54: Topics to be Covered

Lifshitz-Slyazov Growth Law Supersaturated solution

J. Phys. Chem. Solids (1961)

G 0M1/3

Large clustersincorporate small oligomers

M Mn* [ PF Fibrils]