Schedule for Miniworkshop on DNA Topology, December 9, 1994
bquigley at dimacs.rutgers.edu
bquigley at dimacs.rutgers.edu
Tue Nov 15 14:26:09 EST 1994
DIMACS Workshop on DNA Topology
Friday, December 9, 1994
Schedule of Talks
8:00 - 8:30 Registration and refreshments
8:30 - 8:45 Introduction
8:45 - 9:35 DeWitt Sumners
9:35 - 10:25 Craig Benham
10:25 - 10:55 Coffee Break
10:55 - 11:45 John Maddocks
11:45 - 1:15 Lunch
1:15 - 2:05 William Bauer
2:05 - 2:55 Tamar Schlick
2:55 - 3:25 Break
3:25 - 4:15 Alex Vologodskii
4:15 - 5:05 Ned Seeman
Computation of the Free Energy of DNA Supercoiling
Department of Chemistry, New York University
An evaluation of supercoiling free energy is of critical importance for
understanding the structure and physiological role of supercoiling.
We have studied the question by Monte Carlo simulation of the
equilibrium distribution of supercoiled DNA conformations. Our
computational approach is based on the umbrella method, which
allows one to study the probability distribution of DNA writhe for very
wide ranges of values. We calculate the free energy as a function
of superhelix density for different ionic conditions. The computed
free energy, corresponding to 0.2 M monovalent salt concentration, agrees
with the commonly accepted dependence which is based on topoisomer
distributions. We found that the free energy for solutions with low
concentrations of monovalent ions is essentially higher and should
depend strongly on ion concentration. The partitioning of
supercoiling free energy into enthalpic and entropic contributions
will be discussed.
Computational Analysis of Stressed DNA Structures and Energetics
Craig J. Benham
Department of Biomathematical Sciences, Mount Sinai School of Medicine
DNA in living organisms is stressed by enzymes in a precisely regulated
manner. All the important physiological functions of DNA are regulated by
modulations of these molecular stresses. These stresses can induce local
separations of the strands of the DNA. This effect is biologically important
because strand separation is an obligate first step in gene expression and DNA
replication. So strict control must be maintained on the times and places
where strand separations occur.
This talk will describe the computational method by which stress-induced
strand separations are analyzed in molecules of biological interest.
Applications of this approach to several problems in biology and DNA physical
chemistry of DNA will be developed. Analysis of genomic DNAs indicate that
sites predicted to experience stress-induced strand separation occur at
specific regulatory regions in the DNA. In several cases this observation
suggests possible mechanisms for their regulatory activities. The analysis of
experimental results measuring the extent and locations of separated regions
in the pBR322 DNA molecule allows the determination of the free energy,
enthalpy and entropy associated to superhelical deformations of DNA.
Contemporary Rod Theories, Hamiltonian Systems and Simple Models for
the Supercoiling of DNA
John H. Maddocks
Institute for Physical Science and Technology and Department of Mathematics
University of Maryland, College Park, MD 20742.
There have been a number of recent articles that adopt a simple
elastic rod as a rudimentary model for the supercoiling of DNA
or other long chain molecules. The typical reference cited for
the elasticity theory is Love's 1927 treatise. However the theories
of both the statics and dynamics of rods is an active and contemporary
research area within the field of mechanics with many comparatively
recent advances. In this lecture I shall survey parts of this modern
theory, and in particular will describe a formulation of the equilibrium
conditions for rods in terms of a boundary value problem for a seven
degree of freedom Hamiltonian system. In addition to being an effective
description of the ``classic" case, the model encompasses non-uniform
and non-isotropic rods that are curved in their natural state.
Phase-transitions and self-contact can also be modelled. The Hamiltonian
formulation provides a natural setting for efficient numerical computation,
and also casts the DNA problem in a form where well-developed Hamiltonian
theories of perturbation and averaging can be applied.
Control of DNA Structure and Topology
Nadrian C. Seeman
Department of Chemistry, New York University, New York, NY 10003, USA
The control of structure on the nanometer scale relies
on intermolecular interactions whose specificity and
geometry can be treated on a predictive basis. With this
criterion in mind, DNA is an extremely useful construction
medium: The sticky-ended association of DNA molecules
has high specificity and selectivity. Furthermore, it results
in the formation of double helical DNA, whose structure is
well known. The combination of sticky-ended pairing with
stable branched DNA molecules permits the assembly of
stick-figures. Several years ago, we used this strategy to
construct a covalently closed catenated DNA molecule whose
helix axes have the connectivity of a cube. Each edge of the
cube contains two turns of double helical DNA, so each face
of the cube corresponds to an individual cyclic strand of
DNA; hence, the cube is a complex hexacatenane of DNA, in
which each strand is doubly linked to each of its four nearest
neighbors. Recently, we have developed and used a solid-
support-based methodology to construct a molecule whose
helix axes have the connectivity of a truncated octahedron.
This molecule also contains two turns of double helical DNA
in each edge, so it is a catenane of fourteen molecules.
Proof of synthesis relies on digesting the target polyhedron
with restriction endonucleases, to generate target catenanes
of characteristic electrophoretic mobilities.
The Holliday junction is an intermediate in the
process of genetic recombination. We have used double
crossover DNA molecules to establish the topology of the
Holliday junction crossover point. Closing the ends of each
arm to form hairpins converts these molecules into
catenanes, whose linking number is sensitive to the sign of
the crossover. By comparing these catenanes with standards
formed by topological protection techniques, we have shown
that the crossover is unbraided.
We have developed a general method for the design
of any knot or catenane. We do this by equating a half-turn
of DNA with a node in the target molecule. Nodes of
negative sign are produced by conventional right-handed B-
DNA, but positive nodes can be derived from left-handed Z-
DNA. We have constructed several target knots from single-
stranded DNA molecules. These include an amphicheiral
figure-8 knot, and trefoil knots of both signs; they can be
made from the same strand of DNA, by changing the
conditions of the solution in which ligation occurs.
The control of topology is strong in this system, but
the control of 3-D structure remains elusive. Our key aim is
the formation of prespecified 2-D and 3-D periodic structures
with defined structures, as well as linking and branching
topologies. In addition to specificity and predictable
structure, periodic construction requires high structural
integrity in the components; the flexibility of the building
blocks of the array can result in cyclization instead of
extension, thereby poisoning the growth of the crystal.
Applications envisioned include nanomechanical devices,
scaffolding for the assembly of molecular electronic devices,
and the assembly of macromolecular-scale zeolites that orient
macromolecules for diffraction studies.
This research has been supported by grants from
ONR and NIH.
DNA Recombination Topology
De Witt Sumners
Mathematics Department, Florida State University
Enzyme-mediated DNA recombination is an important mechanism in cellular
metabolism, being involved in the life cycle of viruses, gene regulation
and the generation of antibody diversity. In site-specific recombination,
duplex DNA sites are juxtaposed in the presence of the enzyme, the sites
are broken apart and reconnected to different ends. When both
recombination sites are present on the same circular DNA substrate
molecule, intramolecular recombination occurs and recombination produces an
enzymatic signature in the form of DNA knots and catenanes. This talk will
describe the tangle model for site-specific recombination, which provides a
rigorous mathematical description and computation for the active enzyme-DNA
complex and its changes when performing recombination.
Molecular Dynamics of Supercoiled DNA
Courant Institute, New York University
Recent work on molecular dynamics simulations of supercoiled DNA
will be presented. Interesting studies include the influence
of salt and solvent on the structure and dynamics of supercoiled DNA.
The simulations, based on an elastic and electrostatic potential
energy and implicit integration of the Langevin equations of motion,
reveal the profound effects of salt and solvent, such as
the entropic lowering of the writhe and enhanced mobility
at critical conditions. Significantly, dynamical behavior
is nonlinear as a function of salt concentration and solvent
density: both qualitative and quantitative differences
emerge as concentrations and densities are varied. These
findings suggest a critical regulatory role for
salt and solvent on biological processes involving supercoiled DNA.
Finite Element ASnalysis of DNA Supercoiling
William R. Bauer,
Microbiology Department, SUNY Stony Brook
We have applied the finite element method of solid mechanics to the
calculation of the three-dimensional structure of closed circular DNA,
modeled as an elastic rod subject to large motions. The results
predict the minimum elastic energy conformation of a closed loop of DNA as
a function of relaxed equilibrium configuration and linking number $Lk$.
We have examined several different initial configurations including a
straight rod, various rods containing between one and eighteen in-plane
bends, a semicircular rod, and a circular O-ring. The results,
calculated at low superhelix density, show the change in writhe ($Wr$)
and in twist ($Tw$) as $Lk$ is progressively reduced. The presence of
even a single intrinsic bend reduces significantly the linking number
change at which $Wr$ first becomes significant, compared to an initially
straight, bend-free rod. The presence of two in-phase bends situated at
opposite ends of a diameter leads to the formation of at least two
regions of different but relatively uniform $Tw$ increment. The behavior
of rods containing greater numbers of bends depends in detail on the number
and distribution of the bends. The O-ring begins to writhe immediately
upon reduction of $Lk$, and the $Tw$ increment distribution is sinusoidal
along the rod. We also show that these results are independent of the
length of the rod.
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