Schedule for Miniworkshop on DNA Topology, December 9, 1994

bquigley at bquigley at
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

Alexander Vologodskii
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

Tamar Schlick
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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