Topics to be Covered Introduction to Protein Folding - PowerPoint Presentation

Slide1

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

Slide2

Many Facets of Folding

Structure Prediction

Protein & Enzyme Design

Folding Kinetics & Mechanisms

Crowding

& confinement Effects

Relation to aggregation

Molecular

Chaperones

Unfolded protein response (UPR)

Folding

and clearance mechanisms are at

the center stage

Slide3

A Big Protein Folding Problem

Read the Genetic Code; Transcription; Produce

Proteins, Function, Degradation

Length ≈ 220 nm ≈ 700 water

Size ≈ 22nm

A very large protein in water – complex

problem indeed! (about 100,000 waters)

Slide4

Pictures, Models, Approximations & Reality

A bit Philosophy

Rich 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…)

Slide5

Folding Kinetics

Experiments

Theory

Prot Engg (TSE)

SAXS/NMR (DSE)

FAST Folding (T jump;

P JUMP; Rapid Mixing)

SM FRET (Folding/

unfolding)

LOT/AFM (Force Ramp

Force Quench)

Statistical Mechanics

(Energy Landscape)

Minimal Models

(Lattice/Off-Lattice)

MD Simulations

Bioinformatics

(Evolutionary Imprint)

Slide6

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

Slide7

Many facets of Protein Folding

How does a chain (necklace with different shape pearls) fold up and how fast?

Can things go wrong and then what?

As structure

gets organized

Energy gets lowered

Minimum Free Energy

(water ions

cosolvents

)

Anfinsen over 50 years

ago; Nobel Prize 1972

Computational approaches to Biological problems: 2013 Nobel Chemistry

Slide8

RNA and some Proteins



F



S

ΔF

i



NBA

/ΔF

i



j

>> 1

I: Gradient to NBA

dominates: Most

likely event under

folding conditions

All other transitions

less likely.

Page 881 of Textbook Chapter 18

Slide9

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

Slide10

Thermodynamics of src-SH3 folding

Green = Urea

Red= MTM predictions

Black = Experiments (Baker)

ΔG

NU

[C] = ΔG

NU

[0] + m[C]

m = (1.3 – 1.5) kcal/mol.M

Exp. m = 1.5kcal/mol.M

Excellent Agreement!

Z. Liu, G. Reddy, E. O’Brien and dt

PNAS 2011

Slide11

Characteristic Temperatures in Proteins

HIGH T

or [C]

Random

Coil (Flory)

T

 T



Or [C



]

T

 T

F

[C

F

]

Compact

Native State

R

g

≈ a

D

N

0.6

R

g

≈ a

N

N

0.33

Foldable:

 = (T



- T

F

)/T



small

Slide12

Estimating Protein Size as a Function of N

High denaturant concentration (

GdmCl

or Urea)

Good solvent for polypeptide chain – may be!

Flory Theory:

F(R

g

) ≈ (R

g2

/N

2

) + v(N

2

/R

g

d)

(see de

Gennes

book)

R

g

≈

aN

ν

ν

= 3/(d + 2)

Slide13

Folded States Globular Proteins

Maximally compact

Largely Spherical

R

g

≈

aN N(1/3)

So size of proteins follow polymer laws – surprising!

Slide14

Protein Collapse : R

g

follows Flory law

R

gU

= 2N

0.6

R

g

= 3N

1/3

Dima & dt JPCB (04)

Kohn PNAS (05)

“Unfolded”

Folded

Slide15

Tetrahymena

ribozyme

(...difficult)

RNA Folding:

Tetrahymena

ribozyme

RNA – Branched polymer

Ion valence size shape

Slide16

Rg

Scaling works for RNA too including

the ribosome!

Slide17

Size Dependence of RNA

R

g

≈ 5.5N

(1/3)

Fairly decent

(due to

Hyeon

)

Exponent may

Be

larger..analogy

To branched polymers

Ben

Shaul

,

Gelbart

,

Knobler

Slide18

Illustrating Key ideas using Lattice models

Seems like an Absurd Idea!

Role of non-native

attractions

Multiple Folding Nuclei

Fast and slow tracks

K. A. Dill Protein Science (1995)

Slide19

Blues Like Each other.

They gain one unit of energy

Toy model:

Explains protein

folding

Even simpler

Folded lower in energy by

one unit

Multiple paths!

Slide20

A simple minded approach

4 types of monomers

(H, P, +, -)

Monomer has 8 beads

# of sequences = 4

8

(amylome)

# of conformations on

cubic lattice = 1,841

http://dillgroup.org/#/code

HPSandbox

Slide21

Order parameter description

Macroscopic System

Ferromagnetism M

Nematic Phases S = P

2

(cos

)

Smectic Phases S,tilt angle

Spin Glasses: M; q

EAParamagnet M = 0. qEA

= 0

Spin Glass M = 0; q

EA

 0

Ferromanet M  0; q

EA

 0

Physics dictates OP

Proteins a lot of choices

OP is in the eye of the

beholder

= N/R

g

3

;  (overlap)

“unfolded” (Small,big)

Compact non-native

(O(1), big)

Native

(O(1), small)

Other Choices

Helix/sheet content;

Distribution of contacts

………

Slide22

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

Order Parameter Description

 = N/R

g

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”)

Slide23

Developing a “nucleation” picture

Free Energy of Creating a Droplet

G(R) ≈ -R

3

+ R

2

Driving force + Opposing

What are these forces in proteins?

Driving force: Hydrophobic Collapse

Burying H bonds

Opposing: “Droplet with nonconstant

”

Entropy loss due to looping

Slide24

Tentative Models + Slight refinement

Cost of creating

a region with N

R

ordered residues

out of N?

Rugged Landscape with Many possibilities

Slide25

Some phenomenological Models

G

BW

(N

R

)  -f(T)N

R

+ a

2N

R2/3

N

R

*

 (8a

2

/3 f(T))

3

N

R

*

too large for typical  and f(T) values

G

GT

(N

R

)  

h

(

h

- 1)N

R

2

+ a

2

N

R

2/3

N

R

*

 (8a

2

/

h

)

3/4

N

R

*

 15 or so…

Using experimental parameters

N

R

*

 27 or so..

Slide26

Folding trajectories to MFN to transition state ensemble (TSE)

Structures near Barrier top or TSE

Simulations

Moving from one scenario to another – pressure jump…

Slide27

Refinement (Hiding Ignorance)

G(N

R

)  -

1

N

R



+ NR

 + S (loop)





small barrier (downhill folding)

Surface tension cannot be a constant

Multiple Folding Nuclei (Structural

Plasticity

)

Multi-domain proteins involve interfaces between globular parts..

Slide28

Finite Size Effects on Folding

Order parameters matter

Slide29

Scaling of 

C

with N (number of aa)

Two points:

1) T

F

= max in

 (suceptibility)

 = T(d<>/dh; h = ordering field (analogy to mag system)

 is dimensionless  h ~ T (in proteins or [C])

2) Efficient folding T

F

 T



(collapse Temp; Camacho & dt

PNAS (1993)) 

C

controlled by protein DSE at T  T

F

 T



R

g

~ (T/T

F

)

-

~ N



(DSE a SAW & manget analogy)

T/T

F

~ 1/N (Result I)

Slide30

Finite-size effects on TF

T/T

F

~ 1/N

Experiments

Lattice models

Side Chains

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

Slide31

Scaling of 

c

with N

Magnet-Polymer analogy



c

= (T

F

/T) [T

F(d<>/dT)]

“disp in T

F

” X “suspectibility”



C

 N



;  = 1 +  (Universal);   1.2

Result II

T

 T

F

 T



  N



Slide32

Universality in Cooperativity

Li,

Klimov

,

dt

PRL (04)



c

~ N



Experiments

Slide33

Residue-dependent melting Tm

-

Holtzer

Effect

Consequences of finite size

f

m

(T

mi

) = 0.5

Lattice Models

Side Chains

Klimov & dt J. Comp. Chemistry (2002)

Slide34

Is the melting temperature Unique?

Finite-size effects!

BBL

Holtzer

Leucine

Zipper

Biophys J

1997

-hairpin

PNAS 2000

Klimov & dt

T large

Munoz

Nature

2006

Udgaonkar

Barstar Monnelin

Slide35

Residue dependent ordering Protein L

O’Brien, Brooks & dt Biochemistry (2009)

Spread decreases as

N decreases….finite-size

effects

Slide36

Summary So Far – Really with little work on a

complex 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

Slide37

Part II: Protein Folding Kinetics

Organization of structure

Fluctuations due to finite-size

effects

Changes in distributions at

various stages of folding

[C]

Or

T

Slide38

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

Slide39

Illustrating Key ideas using Lattice models

Seems like an Absurd Idea!

Role of non-native

attractions

Multiple Folding Nuclei

Fast and slow tracks

K. A. Dill Protein Science (1995)

Slide40

Stages in folding

Random

Coil

“Specific

Collapse”

Native State



C



F



F

/

C

 (100 - 1000)



F



C

Camacho and dt, PNAS (1993)

dt J. de. Physique (1995)

Slide41

Need for Quantitative Models

Using mechanical

force to trigger

folding

smFRET trajectories

Fernandez, Rief..

Hyeon, Morrison, dt

Eaton, Schuler, Haran…

Slide42

Non-native interactions

early (time scales of collapse) in folding;

Subsequently native interactions

dominate

Camacho & dt Proteins

22,

27-40 (1995);

Cardenas-Elber (all atom simulations)

Dill type HP model

Beads on a lattice

Native Centric (or Go)

models appropriate!

Slide43

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

Proteins: Structure, Function, and Bioinformatics

Volume 43, Issue 4,

pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058

http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig5

LMSC Exact

Enumeration

MC simulations;

600 folding

Trajectories;

Folding time:

A/AGO ≈ 3

Klimov and dt (2001)

Slide44

Transition State Ensemble: Neural Net

Go

Klimov and

dt Proteins

2001

ES NSB 2000

Equivalent

to p

fold

Slide45

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

Proteins: Structure, Function, and Bioinformatics

Volume 43, Issue 4,

pages 465-475, 17 APR 2001 DOI: 10.1002/prot.1058

http://onlinelibrary.wiley.com/doi/10.1002/prot.1058/full#fig9

Multiple Channels Carry

Flux to the NBA

Multiple Transition States

Connecting these Channels

Bottom line:

To get semi-quantitative

results Go-type models

May be enough…

Slide46

Folding Rate versus N

k

F

≈ k

0

exp(-N

β

) with

β = 0.5

Barriers scale

sublinearly

with N

Proteins: Hydrophobic residues buried

In interior (chain compact); Polar and

charged residues want solvent exposure

(extended states). Frustration between

Conflicting requirements.

P(ΔG

♯

) ≈ exp( -

(ΔG

♯

)

2

/2N)

<ΔG

♯

>

≈

N

0.5

(Analogy to glasses)

Slide47

Fit to Experiments (80 Proteins Dill, PNAS 2012)

Reasonable given

data from so many different

laboratories

Slide48

Even better for RNA (Hyeon

, 2012)

Slide49

At high [C] is DSE a Flory Coil?

It appears that high [C] is a

Θ

-solvent

!

P(x) ~ x



exp(-x

1/(1-)

)

Protein

collapse



CT

=(C



- C

m

)/C



 = 2 + (

γ

-1)/

ν

O’Brien

PNAS 2008

Slide50

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 = 4

8

(amylome)

# of conformations on

cubic lattice = 1,841

Slide51

Structure of “protofilament” + “fibril”

Single and double layer

Slide52

Interplay of E+-

and E

HH

a: Monomers parallel

b: Monomer alternate

c: Double layer

d: No fibril compact

Optimal growth temp



fib

= (10

4

- 10

n

)

F

Largest n about 9

Seeding speeds up fibril

rate formation

Slide53

Growth rate depends on N*

population P

N

*

Depends on sequence

Sequence + N

*

ensemble

fibril kinetics  monomer

landscape encodes

structure + growth rate

Slide54

Lifshitz-Slyazov Growth Law

Supersaturated solution

J. Phys. Chem. Solids (1961)



G

 

0

M

1/3

Large clusters

incorporate

small oligomers

M

 M

n

* [ PF Fibrils]