Biological applications
of elasticity theory
18.354 - L11
dunkel@mit.edu
Polymers
DNA = biopolymer pair
~ 3m per cell
!
~ 10^14 cells/human
!
> max. distance between
Earth and Pluto
(~50 AU = 7.5 x 10^12 m)
dunkel@math.mit.edu
DNA packaging
Virus Phi-29
http://www.mit.edu/~kardar/teaching/projects/dna_packing_website/
dunkel@math.mit.edu
DNA packaging in eukaryotes
dunkel@math.mit.edu
Nucleosomes
dunkel@math.mit.edu
DNA packaging in eukaryotes
dunkel@math.mit.edu
the nuclear periphery (14).
n on individual chromoher there are chromosomtially associate with each
ce proximity strongly inlity, we defined a normal-
correlations (P ≤ 0.05).
The plaid pattern suggests that each chromosome can be decomposed into two sets of loci
(arbitrarily labeled A and B) such that contacts
within each set are enriched and contacts between
sets are depleted. We partitioned each chromosome
DNA packaging in humans
C
Lieberman-Aiden et al.
(2011) Science
D
Vol. 326 | No. 5950 | Pages 189–324
B
www.sciencemag.org
1009Cover.indd 189
9 October 2009 | $10
ed from www.sciencemag.org on October 9, 2009
A
9 October 2009
-C. (A)
h formovalent
djacent
A frague, red;
ate such
n light
atin is
on entriction
ne; see
g sticky
nucleis bioigation
remely
ate chiHindIII
site is
urified
d juncstrepfied by
B) Hi-C
de conshown
rachrohromo-
large blocks of enriched and depleted interactions,
generating a plaid pattern (Fig. 3B). If two loci
(here 1-Mb regions) are nearby in space, we
reasoned that they will share neighbors and have
correlated interaction profiles. We therefore defined a correlation matrix C in which cij is the
10/2/09 4:54:46 PM
dunkel@math.mit.edu
92
DNA packaging in humans
9 OCTOBER 2009
VOL 326
SCIENCE
D
Downloaded from www.sciencemag.org o
gion) with a slope of –1.08 (fit
shown in cyan). (B) Simulation
results for contact probability as
a function of distance (1 monomer ~ 6 nucleosomes ~ 1200
base pairs) (10) for equilibrium
(red) and fractal (blue) globules.
The slope for a fractal globule is
very nearly –1 (cyan), confirming our prediction (10). The slope C
for an equilibrium globule is –3/2,
matching prior theoretical expectations. The slope for the fractal
globule closely resembles the slope
we observed in the genome. (C)
(Top) An unfolded polymer chain,
4000 monomers (4.8 Mb) long.
Coloration corresponds to distance
from one endpoint, ranging from
blue to cyan, green, yellow, orange, and red. (Middle) An equilibrium globule. The structure is
highly entangled; loci that are
nearby along the contour (similar color) need not be nearby in
3D. (Bottom) A fractal globule.
Nearby loci along the contour
tend to be nearby in 3D, leading
to monochromatic blocks both
on the surface and in cross section. The structure lacks knots.
(D) Genome architecture at three
scales. (Top) Two compartments,
corresponding to open and closed
chromatin, spatially partition the
genome. Chromosomes (blue, cyan,
green) occupy distinct territories.
(Middle) Individual chromosomes
weave back and forth between
the open and closed chromatin
compartments. (Bottom) At the
scale of single megabases, the chromosome consists of a series of fractal globules.
www.sciencemag.org
Lieberman-Aiden et al. (2011) Science
dunkel@math.mit.edu
Cyto-skeleton
Nucleus
!
Actin
!
Microtubuli
mechanical properties,
network topology, ...
eukaryotic cells (source: wiki)
dunkel@math.mit.edu
Cyto-skeleton
http://library.thinkquest.org/C004535/cytoskeleton.html
dunkel@math.mit.edu
Amoeba
Actin bundles
http://www-ssrl.slac.stanford.edu/research/highlights_archive/actinin.html
dunkel@math.mit.edu
i
y
Cyto-skeleton
1
x
0
x
1
I
y
H
-0.5
0.5
photo:
Philipp Khuc- Trong
0
-0.6 -0.4 -0.2
1
0
x
0.5
0
0
Microtubuli network in Drosophila embryo
0.2 0.4 0.6 0.8
r
FIG. 1. PAR-1 polarity organizes the localdunkel@math.mit.edu
net direction
Polymers & filaments
Dogic Lab, Brandeis
Drosophila oocyte
Physical parameters
(e.g. bending rigidity) from fluctuation
analysis
Goldstein lab, PNAS 2012
dunkel@math.mit.edu
Actin in 2D
F-Actin
helical filament
Dogic Lab (Brandeis)
dunkel@math.mit.edu
Actin in 2D
F-Actin
helical filament
Dogic Lab (Brandeis)
dunkel@math.mit.edu
Actin in 2D
F-Actin
helical filament
with attractive solvent
Dogic Lab (Brandeis)
dunkel@math.mit.edu
Actin in flow
PRL 108, 038103 (2012)
week ending
20 JANUARY 2012
PHYSICAL REVIEW LETTERS
FIG. 1 (color online). Experimental setup. (a) Microfluidic cross-flow geometry controlled by a pressure difference $P between inlet
and outlet branches. (b) Close-up of the velocity field near the stagnation point, showing a typical actin filament. (c) Raw contour (red)
of an actin filament and definition of geometric quantities used in the analysis.
were stored at !80 " C. Polymerization to form filamentous
actin (F-actin) was achieved by addition of 1=10th volume
of 10 # ABþ , then stabilized by the addition of an equimolar amount (to G-actin monomers) of Alexa Fluor 488
phalloidin (Invitrogen), dissolved to a final concentration
of %10 !M of G-actin, and then stored in the dark at 4 " C
for up to 3 months. For an experiment, an aliquot of
10 # AB! stock was thawed and mixed with 9 parts of
of eigenfunctions W ðnÞ (and eigenvalues &n ) with boundary
conditions Wxx ð)L=2Þ ¼ Wxxx ð)L=2Þ ¼ 0 [3,21]. Under
the convenient rescaling ' ¼ $x=L, these obey
Kantsler & Goldstein (2012) PRL
ðnÞ
W4'
! !@' ½ð$2 =4 ! '2 ÞW'ðnÞ - ¼ "n W ðnÞ :
(3)
The eigenvalues "n ¼ L4 &n =$4 A are functions of [22]
dunkel@math.mit.edu
_ 4
2!%L
Actin in flow
PRL 108, 038103 (2012)
PHYSICAL REVIEW LETTERS
FIG. 1 (color online). Experimental setup. (a) Microfluidic cross-flow geometry controlled by a pressure differenc
and outlet branches. (b) Close-up of the velocity field near the stagnation point, showing a typical actin filament. (c
of an actin filament and definition of geometric quantities used in the analysis.
Kantsler & Goldstein (2012) PRL
were stored at !80 " C. Polymerization to form filamentous
actin (F-actin) was achieved by addition of 1=10th volume
of eigenfunctions W ðnÞ (and eigenvalues &
conditions Wxxdunkel@math.mit.edu
ð)L=2Þ ¼ Wxxx ð)L=2Þ ¼
8, 038103 (2012)
P Hflow
YSICAL
Actin in
REVIEW
Kantsler
&
Goldstein
(2012)
PRL
dunkel@math.mit.edu
olor online). The stretch-coil transition of single
actin filam
DNA Origami - principle
source: wiki
dunkel@math.mit.edu
DNA Origami - principle
Strong M: Protein Nanomachines. PLoS Biol 2/3/2004: e73!
dunkel@math.mit.edu
DNA Origami - 2D
http://www.nature.com/scitable/blog/bio2.0/dna_origami
dunkel@math.mit.edu
DNA Origami - 3D
http://www.nature.com/scitable/blog/bio2.0/dna_origami
dunkel@math.mit.edu
DNA polyhedra
edge ~ 10nm
A rigid tetrahedron formed by self-assembly from DNA,
figure from Goodman et al, Science 310 p1661 (2005)
dunkel@math.mit.edu
Artificial cilia
10 ㎛
~ 50 beats / sec
Goldstein et al (2011) PRL
10 ㎛
speed ~100 μm/s
dunkel@math.mit.edu
tracted into asterlike structures (16, 17); however,
a number of bundles remained attached to the
bulk of the contracting structures. Once separated,
these bundles exhibited uniform large-scale beat-
Artificial cilia
Dogic Lab (Brandeis)
in
im
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an
p
m
m
b
m
w
ac
an
ac
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dl
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dunkel@math.mit.edu to
Science 2011
Artificial cilia
Dogic Lab (Brandeis)
Science 2011
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