Consider a Spherical Mad Cow: Physical modeling of amyloid diseases

1
Consider a Spherical Mad Cow Physical modeling
of amyloid diseases

• D.L. Cox, Physics, UC Davis
• R.R.P. Singh, Physics, UC Davis
• K.Kunes, S. Dai, J. Romnes, N.R. Hayre, C.
  Trevisan, Physics, UC Davis
• A. Slepoy, Sandia Labs
• R. Kulkarni, Physics, Virginia Polytechnic
  University
• D. Mobley, Pharmaceutical Chemistry, UCSF
• F. Pazmandi, Sidney Austin LLP (Patent Law,
  Intellectual Property)
• S. Yang, U. Chicago Med z
• S. Clark, Oregon State
• E. Olson, Central College Iowa
• H. Levine, J. Onuchic, Center for Theoretial
  Biological Physics, UCSD
• Support NIH (Seed award from regional
  Alzheimers center), NSF (NEAT IGERT, CTBP,
  ICAM), US Army CDMRC

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Outline

• What is amyloid matter?
• Biophysics vs. Biological Physics
• The Central Dogma and Protein Folding
• Amyloids where physics can clearly make inroads
• -Precision biology in Huntingtons and prion
  diseases
• Prions Why they are interesting
• Prions Intrinsically slow?
• Prions Molecular models
• Recent developments p53 (Cancer gene) and AIDS

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What we are talking about is novel materials..
Plaques this is your mind on amyloid
Model cross section
Alzheimers
Parkinsons
Ab42 Fibrils (H. Lashuel) Diameter 10
nm Fibrils have been used to template
nanowires!
Huntingtons
Kuru (prion)
Fatality is correlated with plaques. Plaques are
bundles of fibrils (Pictures Feaney lab,
Harvard)
Fibrils Protein Nanotubes/nanofibers!
(Model H. Saibil see also Perutz)
4
Amyloid diseases 20 known Not
knownmechanism for cell death, toxicity BUT, in
at least two cases, precision biology

• Most proteins involved
• are of unknown function
• Incidence rates for
• Huntingtons and Prion
• diseases are quite
• reproducible, in a way
• I will define more later
• Alone among these
• diseases, prion diseases
• can be infectious.

5
Recent developments amyloid in cancer, AIDS?

• CANCER
• Two separate regions of the p53 protein, for
  which mutations play a
• role in 50 of known cancers undergo amyloid
  aggregation
• In aggregate form, the p53 cannot carry out
  programmed cell death or cell
• cycle reset functions to arrest tumors.
• AIDS
• Naturally forming fragments of the HPAP
  protein found in semen bind
• strongly to the HIV virus.
• Evidence suggests that this enhances
  infectivity of the virus by 10x or
• more in lab animal studies.
• May explain greater susceptibility of women
  to infection by men

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Biophysics vs. Biological Physics

• Tradition biophysics importation of
  techniques from physical sciences to study of
  biological problems frequently a one way flow
  of both ideas and people.
• Example first physicist in UC Davis Biophysics
  Grad Group (in existence since 1961) me!

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Biological Physics

• Ask not what physics can do for biology, but
  what biology can do for physics S. Ulam via
  Hans Frauenfelder
• Study biological problems as interesting problems
  of the physical world, and ask interesting
  questions.
• Practical two way flow of ideas

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Caveats

• Just because you can throw a dog off of a roof
  to measure g does NOT mean you are doing
  biological physics L. Pelliti
• Just as physicists can study materials with
  physics ideas and methods, physicists can study
  biological systems with physics ideas and methods
  
• Prerequisites humility courage. We have some
  unique techniques and styles of inquiry, but we
  are not the only smart people in the world. BUT
  dont be cowed by jargon or expertise
• Martin Perl, Nobel Laureate and t-lepton
  discoverer When you enter a new field, dont
  know too much, and watch out for fast talkers!

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What can biological physics ask and say about
amyloid diseases,
OR, Consider a spherical mad cow

• Are these diseases of aging, or just slow?
  (Spontaneous prion disease thermodynamically
  unlucky). Namely, can we physically model the
  onset distributions of disease
• What are the organizing principles of the
  relevant protein structures (fibrils,
  oligomers..) and how can we constrain these from
  data and make falsifiable predictions?
• Do the structures suggest/correlate with toxicity
  mechanisms? (time permitting)
• Can the structures be modified by interacting
  with other atoms/molecules? (time permitting.)
• For experiment frontier nanosciencehow to
  reliably probe biological matter at the nanoscale
  in complex environments????

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First, a brief tour of the central dogma and
proteins

• Or, Biological Physics, the early years

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A reminder In some ways, biological phyiscs is
not new!

• 1940s Erwin Schroedinger wrote What is Life? In
  which he looked at the major problems of biology
  from the perspective of a physicist. Among other
  things-he predicted that DNA would turn out to be
  an aperiodic crystal as it did-
• The non-physicist cannot be expected to grasp -
  let alone to appreciate the relevance of - the
  difference in statistical structure' stated in
  terms so abstract I have just used. To give the
  statement life and colour, let me anticipate
  that.. the most essential part of a living
  cell - the chromosome fibre - may suitably be
  called an aperiodic crystal. In physics we have
  dealt hitherto only with periodic crystals.
• Lots of physicists were inspired at this time to
  dive into biological problems (Perutz, Crick,
  Delbruck, Monod)

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Central Dogma of Molecular Biology I
(Schroedinger to Watson to Crick to)
Who ordered That? Each Biological amino Acid
comes from Triplets of the four Base
nucleotides G,A,T,C for DNA G,A,U,C for RNA
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Central Dogma II Elements of Protein Structure
Proteins are polymers formed from The 20 amino
acidsRESIDUES, coded for from DNA/RNA. They
can, depending upon the side chain, be polar
(but uncharged), charged, or hydrophobic
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Most common secondary structures
a-Helices Amide? carbonyl Hydrogen bonds every
3-4 residues

• ? b-structurecan be parallel or
• or antiparallel
• ?Lends to aggregation on edges
• No constraint on where bonding
• arises along the sequence

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Paradox Typical ensembles of random
heteropolymers ? act like a glassy system--

• Typical random heteropolymers DONT fold into
  compact shapesFrustration unsatisfiable
  competing interactions arise from i) putting
  hydrophobic residues out
• How on earth do we get well folded useful
  biological proteins in reasonable time scales
  (milliseconds to seconds)?
• Levinthal Paradox (c.f. Wikipedia) In 1969
  Cyrus Levinthal noted that, because of the very
  large number of degrees of freedom in an unfolded
  polypeptide chain, the molecule has an
  astronomical number of possible conformations.
  (The estimate 10300 appears in the original
  article). If the protein is to attain its
  corrected folded configuration by sequentially
  sampling all the possible conformations, it would
  require a time longer than the age of universe to
  arrive at its correct native conformation. This
  is true even if conformations are sampled at
  rapid (nanosecond or picosecond) rates.
• The protein folding problem!!!

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Organizing Principle Minimal Frustration
(Wolynes, Onuchic Shakhnovich, Dill)

• Evolution selects for minimal frustration of
  sequence, which in model simulations leads to a
  funneled landscape
• Formation of partially folded molten globule
  largely erases Levinthal paradox (to within a few
  orders of magnitude)
• Correlations of nearbye states on landscape
  erases the rest
• Sufficient stabilization of minimum with respect
  to mean of glassy continuum ? fast folding and
  well folded proteins

Frustration
Onuchic and Wolynes
Designed Stability
Bryngelson and Wolynes, PNAS 1987
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So what about amyloid proteins?

• Most have large stretches of random structure or
  are completely random!
• Stabilization of structure apparently comes with
  aggregation.
• Whether in fibril or oligomer form, there is
  cross-beta structure

Fibril axis ? ? b-sheets
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Cross ?-Structure - Evidence from Experiment

• 8 different amyloid diseases, x-ray diffraction
  off of fibers of fibrils
• fiber axis vertical - peak at /- 2?/C, C
  4.8-5 angstroms
• Cross ??structure (Pauling, 1951)
• Also see ??in circular dichroism, FTIR
• (From M. Sunde et al., Journal of Molecular
  Biology
• Volume 273, Issue 3, 31 October 1997, Pages
  729-739)

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Why is ?-sheet prone to aggregation?
unstructured
Unsatisfied H-bonds - Allows Aggregation
Critical nucleus
elongation
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Amyloids can be GOOD!

• Curli amyloids present in bacteria (E. Coli image
  from Chapman lab, U. Mich.) - can participate in
  stationary phase survival mechanism (Bad-may play
  a role in infection)
• Spider silk manufacture has been argued to be pH
  switched alpha -gt beta amyloid self assembly
• Amyloids appear to be part of some insect eggs
  (silk fibroin)
• Controlled reversible amyloid scaffolds useful in
  tissue engineering (e.g., J. Schneider, U.
  Delaware)
• Prions in yeast/fungus convey useful,
  heritable traits (outside the genome!!!)

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The Beautiful? Organizing principles for amyloid
matter
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Organizing Principle 1 Extend minimal
frustration in well ordered proteins by domain
swapping

• Link native contacts on one monomer to
  corresponding native contacts on another
  (champion-D. Eisenberg)
• Example - human cystatin at left (Janowski et
  al., Nat Struct Bio 2001)
• Theory extends minimal frustration concept to
  aggregates - Yang, Cho, Levy, Cheung, Levine,
  Onuchic, Wolynes, PNAS 2004

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Organizing Principle 2 Steric Zippers (D.
Eisenberg group, Nature 2007)

• Synthesized lots of fragments from amyloid-
  ogenic proteins
• Fibrils from combination of beta sheet stacking
  plus steric zipper (interlocking of well packed
  side chains)

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Organizing principle 3 Amyloid stucture from
monomeric motifs
PrPSc model
Overlay
1T3D
1T3D stacked in silico

• Appears in multiple bacterial enzymes and insect
  antifreeze proteins (11 on PDB)
• Who ordered that? Unlike a-helix which
  Pauling predicted prior to discovery
• and has local hydrogen bonding (residue j bonds
  to residue j3 or j4) b-helix is
• very nonlocal (residue j bonds to j18)
• b-helix structures easily bond into aggregate
  (edge-to-edge bonding of monomers)

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Example Huntingtons one of 10
neurodegenerative diseases associated with
genetically acquired added repeats of glutamine
(polyQ diseases)

• Model with elongation of equilib.
• nucleus
• Growth PQM2 t2 for simple
• elongation from critical nucleus of
• size M. Here M1!!!!

Intrinsically Slow!!! Extrapolate slow PolyQ lag
kinetics to physiological con- centrations
(Chen, Ferrone, Wetzel, PNAS 2002)
Zoghbi Orr, Ann Rev Neurosci 2000
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Theory as a probe of possible sub-observable
structure I

• All atom molecular dynamics (MD Newtons laws
  for approxmate force fields) used to probe
  stability of left handed b-helix for PolyQ
  (folding to helix not possible!) (CHARMM)
• drms mean square deviation of atoms from
  starting positions.
• Two layered b-helix not stable within several ns
  of simulation time
• Three layered b-helix is stable out to 10 ns

• PolyQ diseases have critical insert number of 36
• Aggregation studies of PolyQ suggest critical
  nucleus of 1 (!) monomer (Chen, Ferrone, Wetzel,
  PNAS 2002)
• This is the minimal stable left handed beta
  helical turn (18 residues per turn)
• Is the minimal stable PolyQ a left handed
  b-helix? (But Hear Rappu)

Stork et al, Biophysical Journal 2005
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From organizing principle to disease - one
possibility - oligomers

• Fibrils are not perfectly correlated with disease
  (many have plaques with no AD, some prion
  diseases have no plaques).
• Fibrils may be protective (collecting aggregate
  away from cells)
• Some oligomers can form pores which permeate
  membrane and let in excess calcium.

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a
Ab
SOD1
Ab
c
A4V
Arctic (E22G)
?-Synuclein
?-Synuclein
A30P
A53T
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What about prions?
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What is special about prions?

• Prion Proteinaceous infectious particle
  (Prusiner 1980s).
• Along among amyloid diseases infectious as well
  as sporadic, inherited possibilities (PrPSc)
• Numerous experiments (radiation damage,
  UV/temperature/protease/denaturant
  insensitivity.) -gt NO nucleic acids (not a virus
  or bacteria)
• Bolstered by test-tube synthesis of infectious
  protein only prions last year (Baskakov, Prusiner
  et al, Science 2004)
• Prusiner isolated the PrPc protein as key to the
  diseasemice with the gene for PrPc knocked out
  dont get sick on innoculation with infectious
  prion material (PrPSc and PrPC are identical
  after full denaturation-same primary sequence!)
• Examples Scrapies (sheep), Kuru (humans),
  Creutzfeldt-Jakob Disease (CJD) (humans), Mad
  Cow, Chronic Wasting Disease (deer and elk)

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Structure of normal PrPC (Wuethrich et al, PNAS
97, 8334 (2000) 97, 8340 2000)
Proposed structure of PrPSc in one case (Wille
et al, PNAS 99, 3993 (2002) Govaerts et al,
PNAS 101, 83422004)

• 90-95 homology in mammals
• Observed in all vertebrates
• Binds copper in divalent form
• sites in humans, mice, six in
• cattle

Trimer of left-handed beta helices gives best
model
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What is special about the prion diseases?

• Alone amongst ANY disease, prions can be
  spontaneous, heriditary AND infectious
• Prion diseases represent precision biology
  rates of incidence and dose incubation
  distributions are highly reproducible. (1 in
  106 in developed countries get sporadic CJD
  worldwide). Suggests a purely physico-chemical
  model might capture important features of the
  disease
• Simple models can test important questions about
  the disease from this perspective that protein
  conformation (and potentially aggregate
  structure) dictate disease dynamics and properties

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Two dimensional aggregation kinetics?

• Prions are membrane bound
• Can there be interesting differences in models
  with 2D aggregation?

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Model prions in action
Seed introduced slow initial conversion and
aggregation
Wait a while conversion and aggregation
accelerates
35
More precision biology? prion incubation (Slepoy
et al., Phys Rev Lett, 2001 Mobley et al.,
Biophys. J. 2003)
Seed Aggregate Fission
Fission adds (short) doubling and translates-gt
(BSE best fit)
Distribution of aggregation times
Time to aggregate to critical size N over peak
time
36
Role of membrane in toxicity and exponential
growth (fission)

• Cheseboro et al, Science, 2005 Engineer
  transgenic (Tg) mice with GPI anchor deleted.
• Evidence is that expressed PrPC transport to
  membrane but are sent off between cells.
• Innoculate mice with a particular lethal dose of
  PrPSc for which wild type (WT) mice get symptoms
  at 150 days.
• Tg mice dont die or get symptoms out to 600
  days, but accumulate infectious prion material in
  between cells!

WT
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Exponential growth also requires the membrane!
(Cox, Singh, Yang)

• Short time elongation kinetics without fission or
  autocatalysis gives t2agrees remarkably well
  with Cheseboro et al!
• We estimate PrPCTg 28 X PrPCWT

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Proposed b-helical trimer model for minimal
infectious prion particle (UCSF, Govaerts et al.
PNAS 2004)
Loop
1THJ
Raw EM image of infectious prion aggregatenote
faceting!
Signal averaged density (difference) mapnote
3 Fold symmetry
Proposed prion trimer has same size as known
bacterial trimer (1THJ)

• What holds the UCSF model together? Known
  bacterial trimers are held together by
  intermonomer Zn bonding (1THJ) or massive
  hydrogen bond networks (1T3D)

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Stabilize Prion Trimer by Domain Swapping (S.
Yang, H. Levine, J. Onuchic, D.L.C. FASEB J, Nov.
2005)
Domain swapped Prion Trimer (DSTP) model
UCSF or BPT model (beta helical Prion trimer)

• All atom MD Amber 8 on trial
• structure energy minimized in loop region
• Domain swap Grab part of one monomer and bind it
  to anotheralternative approach to generating
  amyloid (Eisenberg et al 1995)
• Domain swapping relaxes stress in loop Elastic
  energy relaxed by 2 kBT
• Domain swapping adds hydrogen bonds now
  structure plausibly held together sufficient to
  run MD to 1-2 ns for H-bonds
• Alternative domain swap being explored by S.
  Cho, Y. Levy, P. Wolynes

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The plot thickens test tube grown fibrils
(Saibil et al, JMB 06)
Kunes, Clark, Cox, Singh, to appear in Prion
For this model, M129 Contacts D178!!!
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C terminal stability good

• Molecular dynamics simulation out to 10 ns of
  root mean square deviation of atoms from starting
  positions (subtracting center of mass motion) -
  black, red known stable beta helices, blue green
  our models.

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Templating - possible connection to kinetics

• Roughly, extra H bond to link M129 to H177, N178
  in FFI
• Hard to link R177 for dogs to this
• For mice the suspicion is that the S143N change
  relative to humans leads to a different preferred
  thread

For this model, M129 Contacts D178!!!
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Conclusions

• Amyloid diseases emergent and generic COLLECTIVE
  stabilization of structure
• Can be INTRINSICALLY SLOW (Huntingtons,
  prions..)
• Simple areal aggregation model with little
  biology accounts for much within the protein only
  model for proins!
• Membrane mediates toxicity (Chesboro et al,
  Science 2005) AND exponential growth via fission
  or oligomeric autocatalysis (Cox, Singh, Yang)
• Domain swapping of the b-helices in the proposed
  prion trimer may stabilize the structure Also
  suggests a model for strains of prions, possible
  understanding of GSS mutations
• More complex domain swapping and C-terminal beta
  helix formation can possibly explain fibrils and
  more!!!
• Amyloid formation is possibly playing a role in
  other surprising places (p53 cancer gene,
  protein in semen which increases infectivity of
  AIDS virus)

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Some essential issues to explore in modeling

• Autocatalysis vs. Autocatalytic Aggregation
  (cooperative conversion) Strong arguments (Eigen)
  and data legislate against autocatalysis at the
  monomer level conversion upon aggregation is
  more sensible (and supported by our work).
• What aggregate structures and sizes best
  correspond to experiment?
• Fission is critical to explain exponential
  runaway (Masel, 2000). Do aggregate shapes and
  sizes influence this?
• Can infectious and sporadic time scales be
  reconciled in the models?

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More precision biology? prion incubation (Slepoy
et al., Phys Rev Lett, 2001 Mobley et al.,
Biophys. J. 2003)
Seed Aggregate Fission
Soft Oligomer/Micelle
Hard/Oligomer
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Dependence upon coordination environment
?----------------gt
12 years --------------?1000 years(!) (Kuru?)
(CJD?)

----gt
----gt
qc 3 Seeded
Sporadic
qc1 Seeded Sporadic
qc2 Seeded Sporadic