Les Houches Lectures (October 2000): William M. Gelbart
A primary aim of these lectures is to introduce two structural
motifs in biology that have provided the motivation for many recent
studies of electrostatic effects in solutions of macro-ions. The first
motif involves condensates of DNA that are induced by the presence
of polyvalent counterions, and corresponds to the packaging of DNA
in viruses. The second involves complexes of DNA with oppositelycharged colloidal particles, and corresponds to nucleosome core
particles and the basic fiber of chromatin. In this spirit, we devote
considerable time to gaining some feeling for the biological systems
themselves, even though we will almost always be concerned with
their study under highly-controlled -- i.e., in vitro -- conditions.
LECTURE #1:
SEMIFLEXIBLE CHAIN CONDENSATION AND VIRAL INFECTION
I.
brief introduction to bacterial viruses (“phages”) and their infection of
cells
A. a typical bacterial virus -- lambda
B. a typical bacterial cell -- E. coli
C. the in vivo infection process
D. the in vitro virus synthesis (not “synthetic viruses”)
(Natural presence of polyamines -- polyvalent cations -- implies DNA is
condensed.)
REFERENCES: any of the standard molecular biology textbooks, e.g.,
Molecular Biology of the Cell, 3rd edition, B. Alberts, D. Bray, J. Lewis,
M. Raff, K. Roberts and J. D. Watson (Garland Publishing, New York,
1994).
II. classical DNA condensation experiments
Addition of polyvalent cations (or low MW polymer, or alcohol, …) to
highly dilute solution of DNA leads to toroidal condensates of limited
size, largely independent of DNA length and origin (sequence!),
condensing agent, and monovalent salt concentration
(Is limited size due to kinetics or thermodynamics?)
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REFERENCE: V. A. Bloomfield, “Condensation of DNA by Multivalent
Cations: Considerations on Mechanism”, Biopolymers 31, 1471-81
(1991).
III. barriers to larger toroids
A. thermodynamic: “competing interactions”
short-range attractions plus long-range repulsions, analogous to:
*passivated metal nanocrystals on the surface of water [see R. P. Sear,
S.-W. Chung, G. Markovich, W. M. Gelbart and J. R. Heath,
“Spontaneious Patterning of Quantum Dots at the Air-Water
Interface”, Phys. Rev. E59, R6255-8 (1999)];
*charged latex spheres on the surface of water [see J. Ruiz-Garcia, R.
Gamez-Corrales and B. I. Ivlev, “Formation of Two-Dimensional
Colloidal Voids, Soap Froths, and Clusters”, Phys. Rev. E58, 660-3
(1998)];
*instability of charged liquid drop and of polyelectrolytes in bad
solvents [see A. V. Dobrynin, M. S. Rubinstein and S. P. Obukhov,
“Cascade of Transitions of Polyelectrolytes in Poor Solvents”,
Macromolecules 29, 2974-9 (1996)]
B. thermodynamic: topological defects
[see S. Y. Park, D. Harries and W. M. Gelbart, “Topological Defects
and the Optimum Size of DNA Condensates”, Biophys. J. 75, 714-20
(1998)]
C. kinetic: barrier to alignment
long-range repulsion favors perpendicular alignment, whereas shortrange attractions favor parallel, implying barrier to re-orientation
whose height grows with size of condensate
[see B.-Y. Ha and A. J. Liu, “Kinetics of Bundle Growth in DNA
Condensation”, Europhys. Lett. 46, 624-30 (1999)]
IV. non-classical condensation experiments
Bacterial viruses (in the presence of polyvalent cations) can be used to
prepare DNA toroids of arbitrary size. [O. Lambert, L. Letellier, W. M.
Gelbart and J.-L. Rigaud, “DNA Delivery by Phage as a Strategy for
Encapsulating Toroidal Condensates of Arbitrary Size into Liposomes”,
Proc. Natl. Acad. Sci. (USA) 97, 7248-53 (2000)]
V.
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the viral “loading problem”
How does a long, semi-flexible chain get packaged into a small volume?
Current phenomenological and simulation approaches to this problem are
outlined.
LECTURE #2:
CHAIN-BALL COMPLEXATION AND NUCLEOSOMES/CHROMATIN
I.
brief introduction to the structure of nucleosomes and chromatin
A. hieirarchy of organization in chromosomes, from microns down to
Angstroms
B. basic “beads-on-a-necklace” motif -- the “10nm fiber”
C. the nucleosome core particle -- high-resolution X-ray crystallography
II. effects of salt on chromatin structures
A. first step in folding/condensing of the “necklace” (the 10nm fiber) [see J.
Widom, “Physicochemical Studies of the Folding of the 100A
Nucleosome Filament into the 300A Filament”, J. Mol. Biol. 190, 411-24
(1986)]
B. unbinding of beads from the necklace [see T. D. Yager, C. T. McMurray
and K. E. van Holde, “Salt-Induced Release of DNA from Nucleosome
Core Particles”, Biochemistry 28, 2271-81 (1989)]
C. common, polyvalent-cation-induced, behavior of “naked” DNA and of the
nucleosome core particles [see E. Raspaud, I. Chaperon, A. Leforestier
and F. Livolant, “Spermine-Induced Aggregation of DNA, Nucleosomes,
and Chromatin”, Biophys. J. 77, 1547-55 (1999)]
III. geometric aspects of chromatin folding
Intrinsic structure of nucleosomes -- in particular, the entry-exit angle for
wrapped DNA and the angle between superhelical axes of neighboring
nucleosomes -- determines the structural states of the 10nm/30nm fiber [see
poster by H. Schiessel]
IV. the chain-ball “wrapping problem”, with and without explicit treatment of
the electrostatics
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A. Marking-Manning [N. L. Marky and G. S. Manning, “A Theory of DNA
Dissociation from the Nucleosome”, J. Mol. Biol. 254, 50-61 (1995)]
B. Wallin-Linse [T. Wallin and P. Linse, “Monte Carlo Simulations of
Polyelectrolytes at Charged Micelles. 1. Effects of Chain Flexibility”,
Langmuir 12, 305-14 (1996)]
C. Park et al. [S. Y. Park, R. F. Bruinsma and W. M. Gelbart, “Spontaneous
Overcharging of Macro-ion Complexes”, Europhys. Lett. 46, 454-60
(1999)]
D. Mateescu et al. [E. M. Mateescu, C. Jeppesen and P. Pincus,
“Overcharging of a Spherical Macroion by an Oppositely Charged
Polyelectrolyte”, Europhys. Lett. 46, 493-8 (1999)]
E. Netz-Joanny [R. R. Netz and J.-F. Joanny, “Complexation between a
Semiflexible Polyelectrolyte and an Oppositely Charged Sphere”,
Macromolecules 32, 9026-40 (1999)]
F. Kunze-Netz [K.-K. Kunze and R. R. Netz, “Salt-Induced DNA-Histone
Complexation”, preprint -- see poster by K.-K. Kunze]
V. nucleosome repositioning (iff time permits)
How does a ball that is wrapped several times by a chain move to a new
position along the chain while remaining bound to it?
A. review of relevant experiments
[see: G. Meersseman, S. Pennings and E. M. Bradbury, “Mobile
Nucleosomes -- A General Behavior”, EMBO J. 11, 2951-9 (1992); and
K. J. Polach and J. Widom, “Mechanism of Protein Access to Specific
DNA Sequences in Chromatin: A Dynamic Equilibrium Model for Gene
Regulation”, J. Mol. Biol. 254, 130-49 (1995)]
B. theory of motion by loop diffusion (stored length reptation)
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