Folding DNA and Proteins—WLC

When they have problems—Prion diseases

How proteins get help--Chaperones

Analysis: The Worm-Like Chain for elasticity

F= - kxHooke’s Law: You apply a force on something and it increases in length linearly. Proportional constant = k. Minus sign because it’s a restoring force.

Force related to fractional increase (x/L). What if force isn’t proportional to distance?

http://biocurious.com/2006/07/04/wormlike-chains

Need something more sophisticated: k is not a constant, independent of x;As x gets bigger k gets bigger: F = f(k)x.

Two Models of DNA (simple) Freely Jointed Chain (FJC)

& (more complicated) Worm-like Chain (WLC)

Idealized FJC:

Realistic Chain:

FJC: Head in one direction for length b, then turn in any direction for length b.

[b= Kuhn length = ½ P, where P= Persistence

Length]

WLC: Have a correlation length

FJC: Completely straight, unstretchable. No thermal fluctuations away from straight line are allowed

The polymer can only disorder at the joints between segments

FJC: Can think of DNA as a random walk in 3-D.

The Freely jointed Chain (FJC)The molecule as a chain of perfectly rigid subunits of length b joined

by perfectly flexible hinges. Segment-to-segment angle =

You can think of b as the length of the repeating subunits, and is called the Kuhn length (= 2 x Persistence length).Persistence length: you start out going in some direction: how long will you tend to keep going: for DNA—about 50 nm, or 150bp.

If the molecule is under an applied force f as above, the effective energy for the chain is given by

If there were no applied force, all configurations have equal energy (and therefore the system has large configurational entropy), and the chain orients itself in any which way—analogous to a random walk.

http://biocurious.com/2006/07/04/wormlike-chains

The Freely jointed Chain (FJC)

From Science, 1992, Vol 258, pg.1122,by SB Smith, L Finzi, C Bustamante

Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads.

The equation can be solved and yields

Force vs. Extension for DNA

At very low (< 100 fN) and at high forces (> 5 pN), the FJC does a good job.

In between it has a problem.

There you have to use WJC.

You measure the Persistence length

F=-kx works well at very low force; at higher force, DNA is extended (> 50%), need FJC or better is WLC

Strick, J. Stat. Physics,1998.

A new phenomenological parameter has entered the energy term, A, which is a measure of the persistence length of the chain, or how long a segment of the chain will have tangent vectors all pointing in nearly the same direction. Indeed, the tangent-tangent correlation function for the wormlike chain at zero stretching force is given by

or, the similarity in directionality for the chain decays as an exponential in the persistence length.

WLC: A slight extension of FJC

An analytic solution to WLC is not currently known, but the above equation has been solved numerically. At low force it again displays a Hookean linear relation, but as the extension nears the contour length of the molecule, it scales not as 1/f as predicted by freely jointed chains, but as 1/f1/2, in significantly better agreement with the data.

The Worm-Like Chain (WLC) for elasticity

Increase in end-to-end length (x) of polymer:Worm Like Chain (WLC) of entropic elasticity.

Force related to fractional increase (z/L)

where A = Lp: persistence length, a measure of the chains bending rigidity = 2x Kuhn Length L = contour length z = extension

Each unfolding event increases the contour length of the homopolymer by a constant value, ∆L.

WLC Fits very well at all stretches

Protein Mis-Folding & Chaperones

Protein Folding Summary(From previous Protein Folding Lectures)

• Proteins can fold and do say fairly fast (< second).

• Protein Funnel is a good model. Extending beyong nearest neighbor interaction: Molecular Dynamic Simulations sometimes do a better job (with a lot of $$).

• ΔG is almost always small: (5-10 kT—few H-bonds). E goes down; S goes down. They compensate.

• Kinetics – fast cause not huge barriers. (Detailed calculations necessary.)

• In most cases, don’t need help. In complicated cases (big proteins, very crowded conditions such as in a cell) proteins get help: proteins called chaperones.

Protein folding: the energy landscape theoryProtein folding: the energy landscape theory

Native state

IB

IA

Unfolded state

Intermediate states

EN

ER

GY

ENTROPY

Molten Globule

State

Unfolded Folded

Inactive Active

Lattice Model: only worry about nearest neighbor interactions. Hydrophilic and hydrophobic interactions

Molecular Dynamics: write F=ma for everything

Misfolding of Proteins

Most proteins can spontaneously refold: Primary sequence determines tertiary.

Some proteins do not: boil an egg, bring temp back down and won’t re-form. (Albumin goes from clear to milky white.)Commonly the hydrophobic residues get exposed. When concentration of protein is high, they can fold up with other proteins instead of with itself and remain unfolded and aggregated.

Wide variety of proteins; similar structure, bad outcomes!

Amyloid fibers & plaques: Mad Cow diseases, Alzheimer Disease, Parkinson Disease, maybe some forms of diabetes

Protein Folding in the Cell• Most proteins probably go through several stages on their way to a

stable structure. Some need help, particularly in crowded env of cell.• Chaperones are protein molecules that assist the proper folding of

other proteins. Often are heat shock proteins (HSP#) because they help cell with elevated temperature which tend to cause proteins to mis-fold. Also involved in newly synthesized proteins where a lot of hydrophobic groups haven’t yet folded up properly.

• Some chaperone systems (Chaperonins) work as foldases: they support the folding of proteins in an ATP-dependent manner (for example, the GroEL/GroES system). Other chaperones work as holdases: they bind folding intermediates to prevent their aggregation, no ATP required.

• Diseases such as Alzheimer’s, Parkinson’s, and mad cow disease are associated with misfolded proteins

• “Recent advances in single-molecule analysis have brought insights into structural heterogeneity of chaperones, folding intermediates and affinity of chaperones for unstructured and structured protein chains.” [Wikipedia]

NativeAggregate

Partially folded state

Ag

gre

gat

ion

fu

nn

elA

gg

reg

atio

n f

un

nel

Fo

ldin

g f

un

nel

Fo

ldin

g f

un

nel

Unfolded

EN

ER

GY

EN

ER

GY

Native contacts, %Native contacts, %

Stabilized by inter-chain interactions

Stabilized by intramolecular interactions

When intermolecular contacts are significant, need to modify energy funnel

Idealized case:

Assume that 50% of contacts are formed, then can either fold normally (i.e. in dilute conditions), or it can react with another partially unfolded protein and fall down the aggregation funnel.

Fibril

AggregationAggregationF

old

ing

fu

nn

elF

old

ing

fu

nn

el

EN

ER

GY

EN

ER

GY

+

Nucleation Polymerization

Slightly More Realistic Scenario(allow for formation of long fibrils)

Lysozyme fiberLysozyme fiberLysozymeLysozyme

T70NT70ND67HD67H

I56TI56T

W64RW64R

S-SS-S

S-SS-S

S-SS-S

S-SS-S

αα-d

om

ain

-do

mai

nββ

-do

mai

n-d

om

ain

CC

NN

Lysozyme is abundant in a number of secretions, such as tears, saliva, human milk, and mucus. Also in egg white. (Well studied.)Damage bacterial cell walls through catalyzing. Forms amyloid fibers.

form amyloid deposits in the gut

Lysozyme: Well Studied example of mis-folding

Simple, but excellent Videos about Prions

http://www.youtube.com/watch?v=pqhpVpafjmk

http://www.youtube.com/watch?v=tfv3xAw0XOE

Stanley Prusiner has added prions to the list of well known infectious agents including bacteria, viruses, fungi and parasites. Prions exist normally as innocuous cellular proteins, (generally called PrP). However, prions possess an innate capacity to convert their structures into highly stabile conformations that ultimately result in the formation of harmful particles, the causative agents of several deadly brain diseases of the dementia type in humans and animals. This is called PrPSC (where SC standards for scrapie, the original prion-disease where it was discovered in sheep). PrPSC is very stable, resistance to degradation by a number of proteases, heating chemical denaturants…). Prion diseases may be inherited, laterally transmitted, or occur spontaneously. Regions within diseased brains have a characteristic porous and spongy appearance, evidence of extensive nerve cell death, and affected individuals exhibit neurological symptoms including impaired muscle control, loss of mental acuity, memory loss and insomnia.

A prion in the Scrapie form (PrPSc) is an infectious agent composed of protein in a mis-folded form. This is the central idea of the Prion Hypothesis. This would be in contrast to all other known infectious agents, like viruses, bacteria, fungi, or parasites—all of which must contain nucleic acids (either DNA, RNA, or both). PrPsc can catalyze PrP to form amyloid fibrils.

Prions– infectious agents that can be transferredwhich are devoid of Nucleic Acids

http://en.wikipedia.org/wiki/Prion

Prions– Alzheimers and more (Nobel Prize 1992)

The figure schematically illustrates how variants of disease causing prions affect different parts of the brain. In Bovine Spongiform Encephalitis (cattle), the brain stem is affected; in Fatal Familial Insomnia (humans, a different mutation of the PrP protein) the thalamus region; in Creutzfeldt-Jakob Disease (humans), the cerebral cortex; in KURU (cannibalistic humans in Papa New Guinea) and Gerstmann-Sträussler-Scheinker (humans, inherited form) disease the cerebellum is damaged.

http://www.nobelprize.org/nobel_prizes/medicine/laureates/1997/press.html

Prions are not considered living organisms but are misfolded protein molecules which may propagate by transmitting a misfolded protein state. If a prion enters a healthy organism, it induces existing, properly folded proteins to convert into the disease-associated, misfolded prion form; the prion acts as a template to guide the misfolding of more proteins into prion form. These newly formed prions can then go on to convert more proteins themselves; this triggers a chain reaction that produces large amounts of the prion form. All known prions induce the formation of an amyloid fold, in which the protein polymerises into an aggregate consisting of tightly packed beta sheets.

Amyloid Fibers…involved in Alzheimers

Protein amyloid aggregation has been recognized as a major cause of several important diseases, including Alzheimer’s disease (the fourth most common cause of death in the Western world), Parkinson’s disease, type II or noninsulin-dependent diabetes, and the transmissible spongiform encephalopathies. About 17 different proteins have been found to form amyloid in vivo. Amyloid fibrils formed from those proteins share some common morphological features, but these proteins do not have a conserved sequence or native structural motif

Cao A, Hu D, Lai L. Formation of amyloid fibrils from fully reduced hen egg white lysozyme. Protein Sci. 2004

There is a lower energy state which is fibers—e.g. ameloid fibers– multiple states!

Amyloid Fibers…involved in AlzheimersProtein amyloid fibers are often found to have a β-sheet structure regardless of their sequence, leading some to believe that it is the molecule's misfolding that leads to aggregation.

http://www.informaworld.com/smpp/content~content=a779685983~db=medi~order=page

Enzymes act on the APP (Amyloid precursor protein) and cut it into fragments of protein, one of which is called beta-amyloid and its crucial in the formation of senile plaques in Alzheimer

Chaperones—how proteins get help in folding

Figure 5.23

The cap attaches, causingthe cylinder to changeshape in such a way thatit creates a hydrophilicenvironment for thefolding of the polypeptide.

Cap: GroESPolypeptide

Correctlyfoldedprotein

Chaperonin(fully assembled)

Steps of ChaperoninAction:

An unfolded poly-peptide enters thecylinder fromone end.

HollowcylinderGroEL

The cap comesoff, and theproperly foldedprotein isreleased.

1

2 3

ChaperonesGroES/GroEL—(Class I) bacterial, mitochondrial,

1MD(Other class, Class II, not nearly as well characterized)

In general, poorly understood how works. Whether it is active in terms of interactions between chaperonins, or inert, where chaperonines simply make a environment conducive to folding, is not known. It is however, required for the proper folding of many proteins.

In eukaryotes the proteins Hsp60 and Hsp10 are structurally and functionally nearly identical to GroEL and GroES, respectively.

GroEL

GroES

135Å

45Å

145Å 18

4Å

binding

Misfolded protein in kinetic trap

Correctly folded protein

ATP-dependent folding along a smooth energy landscape

ADP x 7ADP x 7

ATP x 7ATP x 7

20º

10º

ATP x 7ATP x 7 ATP x 7ATP x 7

120º

60º

ATP x 7ATP x 710s10s

Chaperones (Bacterial GroES-GroEL)With ATP, environmental conditions suitable for proper folding

Binding of a 7 ATP molecules to the GroEL ring triggers conformational change that results in slight twist and tilt in the subunits and in exposure of hydrophobic patches that interact with and help to unfold misfolded protein.

GroEL

GroES

[Don’t worry about details but know via ATP hydrolysis, that can get over the bumpsAnd slide down “easily”]

Class evaluation

1. What was the most interesting thing you learned in class today?

2. What are you confused about?

3. Related to today’s subject, what would you like to know more about?

4. Any helpful comments.

Answer, and turn in at the end of class.