Cell Biology: Simple Structures

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Cell Biology Simple Structures
M. Olvera de la Cruz
R. Bruinsma, A. Grosberg, M. Kardar, A. Liu, D.
Nelson, R. Phillips (F. J. Solis, E.Liujter,
R.Netz, E.Raspaud, A.Dobrynin, S. Stupp) M.
Schick, A. Tkachenko, F. MacKinstosh
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What can we learn? What have we learned? How can
we use it?
Cationic-Anionic Biological Complexes Electrostati
cs Viral assembly, DNA packing Viral Capsid
Structure Icosahedral symmetry DNA Unzipping, DNA
Transcription, Pore Translocation One
dimensional diffusion and disorder effects Gels
Imprinted gels, Actin, Collagen and Peptide
Amphiphile fibers self assembly
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Viral Self-Assembly from solution of capsid
protein RNA molecules Tabaco Mosaic Virus
Virus Life Cycle (Polio)
ASSEMBLY
RNA
Capsid
VIRAL PROTEINS
VIRAL RNA
TMV one RNA of 6,300 base 2,000 identical
capsid proteins. RNA is a TEMPLATE
(Fraenkel-Conrat, 55)
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2. Add ssTMV RNA (assembly infective virus)
Electrostatic attraction stabilizes viral
assembly.
1. Solution of TMV Capsid Proteins
Electrostatic repulsion inhibits protein
protein aggregation.
Salt (M)
ZRNA -1/mer
3. Sphere-like (icosahedral) RNA virus (Tsuruta
et al)
Acidity
4. Capsid Hole (density RNA crystal)
self-assembles from capsid protein viral RNA
solution
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Design model virus What is the maximum genome
mass that can be packaged ? Can capsids only
assemble with cargo ? Bruinsma et al 04
Self-assembly of capsid



monomers

?


RNA inside capsid
Equilibrium K
Empty capsid free energy
capsid
Non-Specfic Electrostatics Interactions1)
Protein-protein repulsion 2) Genome
self-repulsion 3) Protein-genome attraction. Mean
field free energy to determine degree of
encapsidation
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• Maximum packing density N/V 1/v is not
  achievable for
• the toy genome due to competitions.
• Packing density diminishes with virus size as
  1/R1/2

Temperature
g(T) ? T
FILLEDEMPTY CAPSIDS
Bruisnma, Gelbart, Rudnick van der Schoot
N gt Nmin
FILLED CAPSIDS
NNmin
MONOMERS
Salt
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Remove capsid proteins except for charged amino
acids
Geneo does not expands electrostatic virus
(A. McPherson)
Anionic and Cationic Complexes
DNA protein (Netz, 04)
DNA cationic (4) solutions
(Raspaud et al 98,99)
Low C
unwrapped (low/high salt)
wrapped (intermediate salt)
Intermediate C
High C
Correlation (strong electrostatic coupling in
ionic structures) Counterion Release
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Polyelelctrolyte (PE) Chains in multivalent ions
(Gonzalez-Mozuelos et al 95Solis et al 00, 01
Lee Thirumalai 01 Liu Muthukumar, 02)
E. Luijten 04
?m ? 2.5Å water at 298K lB ? 7.1Å ? lB / ?m
? 3 Cm 0.008?m3 1M
Scaling description RgN?
PE(N32) 8(41)salt
? 1/3 sphere ? 0.5 ideal chain ?
0.588 coil ? 1 rigid rod
Charged rods (DD DNA) the precipitation is into
bundles
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Charge inversion in charged spheres multivalent
salts
Charge inversion IS observed (Grosberg et al 02)
It depends on multivalent ion to co-ions sizes.
This explains the redissolution mechanism of DNA
as C increases (Solis 02, Luijter 04) and other
electrostatic complexes
The amount of inverted charge is restricted by
condensation of co-ions
Messina, Holm, Kremer, 2000 M.Tanaka, AG, 2001
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Effective charge
dpositive eNeutral, fnegative
Polyelectrolytes collapse beyond
neutralization, re-expansion occurs. Counterion
size has crucial role. In rod-like PE see also
Nguyen et al 00 Borukhov et al 02, and
simulations by C. Holm group
In biology stability of complexes to segregation
or to dissolution In physics
electrostatics In materials adsorption of PE,
design structures using electrsotatics biology
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Physics in the Bacteriophage Life Cycle

• The life cycle infection of host cell (i.e.
  injection of its DNA), exploitation of host cell
  machinery to make the relevant proteins and DNA,
  self-assembly and destruction of the host cell.
• physical processes
• infection, replication, assembly, packing, etc.
• Model systems for quantitative analysis.

Rate of packing 100bp/sec
Self-assembly
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Viral Packing Model Free Energy of Confinement
DNA is charged
DNA has elasticity
Hoop model of packed DNA
The idea set up a free energy function that
reflects the competition between these two
effects (Riemer et al.,Odijk, Gelbart et al.).
R. Phillips
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A gallery of virusesT.S. Baker et. al.,
Microbiol. Mol. Biol. Rev. 63, 862 (1999)
? The small viruses are round and large ones are
facetted
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Theory of Virus Shapes

• ?Shape depends only on the
• von-Karman number vK YR2/?
• ? bending rigidity of shell
• Y Youngs modulus of shell
• R mean virus radius
• ?(vK)c 154 in flat space.

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VIRAL SELF-ASSEMBLY AS A THERMODYNAMIC PROCESS
Bruisnma et al. 03 Viral self-assembly by
disklike capsomers model shows that icosahedral
symmetry is not a generic consequence of
minimization of the free energy, but requires (at
least) two internal configurations for the capsid
subunits (switching), corresponding to pentamer
and hexamer capsomers (the units are
not equivalent).
Hamiltonian path by the icosahedrally-ordered
RNA. (Rudnick Bruisnma, 03). Certain viruses
package a portion of their genome in a manner
that mirrors the icosahedral symmetry of the
capsid. A quasi-icosahedral genome structures
model discusses the connection between genomic
structure and viral assembly.
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One dimensional processesDNA ejection from
Bacteriophage T5
M. de Frutos, L. Letellier, and E. Raspaud,
Orsay, France
F(t) fraction of ejected DNA mass by light
scattering
120 000 base pairs
Permeable capsid

T 23C Activation energy 70 kBT
Complex kinetics, interpreted using a multi-step
process per capsid (scattering gives an average).
Addition of natural multivalent ions partial
inhibition of the DNA ejection
E. Coli Membrane receptor
Pore translocation theory Muthukumar 01
Slutski et al , 03 Zandi et al 03 Kafri et a.
03
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Single Molecule DNA Unzipping Transitions
Bockelmann et. al., Biophys. J. 82, 1537 (2002)
D. K. Lubensky and D. R. Nelson

• Unzipping for F lt Fc(T) dominated by pauses and
  jumps determined by the base pair sequence
• Precise predictions available even for single
  molecule experiments
• Anomalous dynamics of the DNA unzipping fork
  for F gt Fc(T) barriers scale as square root of
  genome size!

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Unzipping of heterogeneous DNA (D Lubensky and
DR Nelson)
sequence information!
For most coding DNA
average along sequence
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Dynamics of the unzipping fork for F gt Fc(T)
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Transcription factors / nucleosomes sliding
along DNA
random walk in a correlated random potential
(Slutsky, Kardar Mirny, PRE 04)
MFPT averaging over all potential profile
configurations yields a normal diffusion law
with a renormalized diffusion coefficient D(?)
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MFPT Fluctuations
Diffusion in a gaussian profile is characterized
by strong sample-dependence and lack of
self-averaging even in the absence of long-range
correlations
Other biological systems of 1D Random Walk in
Random Potential are discussed by T. Hwa et al 03
and Tom Chou

• Typical MFPT very different from mean MFPT up to
  a certain Nc. Below Nc, typical MFPT is
  influenced mainly by the extrema of the landacape

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Bacteria Mobility Model of Molecular Nozzle
Growing Polymer Chain Inside Nozzle (Dobrynin et
al, 04)

• Listeria motility by Andrea Liu is another
  example

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Phase diagram of designed copolymer
Sequence design (conformation dependent
preparation) Strong or weak design (Grosberg)
solvent quality
Coil
q
Random Globule
Folded Globule
Glass
1/design strength
Smart Gels by sequence design (Tanaka)
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Cycle of ligand binding/dissociation
Dreaming of an artificial molecular size
nano-machine
AL Borovinskiy A. Grosberg JCP, 03
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Polymorphism of the Cytoskeleton gels or bundles
? ACTIN (Liu et al. 04)

• What are the different possible phases for
  charged rigid rods with linkers?
• Bundle dominates
• or
• Gel dominates
• Only in a very small range they co-exist

J. Hartwig
or
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Possible Connection to Cytoskeleton

• Jump from bundle-dominated to network-dominated
  diagram in lt 1 kBT
• VASP changes binding energy by phosphorylation
• Actin polymerization and depolymerization can
  take system around kinetic barriers

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Semiflexible Polymer Models of Cytoskeletal
Networks Cell Mechanics
Gardel, Shin, MacKintosh,
Mahadevan, Matsudaira, Weitz,Science, in press
(2004)
Tunable materials with stiffness strongly
dependent on crosslinking at fixed concentration
A
Quantitative test of semiflexible polymer based
model of shear modulus
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Collagen Fibril Architecture
Peptide Amphiphiles (Stupp et al. 01, 02) Cells
read surfaces (Stupp, 03)
11nm
a nanoscale cylinder with highly ordered surface
to deliver biological information--peptides
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Peptide Amphiphiles (PA) nanofibers are formed
from acidic PAs like IKVAV-PA by dropping the pH
below 4.5. Basic PAs could behave analogously,
self-assembling above pH 9 (middle). Combining
acidic and basic PAs at neutral pH also causes
self-assembly. Only form cylinders. (S. Stupp
lab)
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Multi-component micelles? (Solis, de la Cruz,
Stupp 04)
Use oppositely charge units to built stable
nano-aggregates with surface structure if units
are otherwise immiscible.

?
Flat surface pattern due to the competition of
surface tension ? and charge density ? domain
of size L A1/2 is L(?/?2)1/2 The fraction of
area f of one unit in the cell of are A
determines the pattern structure.
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The phase diagram in 2D looks like this
Homogeneous
Lamella
g
Hexagonal
Hexagonal
fc0.35, 0.65
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Pure Coulomb F L Screened F L, Llt1/? or
F 1/?, Lgt1/?
Macrophase segregation
Homogeneous
T
g
Hexagonal
Hexagonal
f
Full segregation
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Electrostatics generate multicomponent micelles
and vesicles with surface patterns
With screening the domain size jumps from finite
to macroscopic segregation
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Statistical Mechanics Molecular Biology New
Opportunities
1) Dynamics of Chromosomes. 2) The Polyglutamine
Problem. 3) Protein Computers Transcription
Complex Assembly. 4) Protein Computers Ribosomal
Proofreading. 5) Protein Machines Mechanical,
Optical, Chemical 6) Self-Assembly and
Pre-Existing Information 7) Artificial Membranes
and Cells 8) Cell motion and Artificial Motors 9)
Artificial Specialized Membranes