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Chaire d'Analyse Appliquée
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Overview of DNA Research
General Research Description
The group's work in modelling DNA involves the application of techniques
of continuum mechanics, particularly of the theory of elastic rods, to
the development of computational codes and analytical techniques for describing
the basic mechanical
properties of DNA. The objective of the modelling is to produce quantitative
predictions that can be compared with experimental data. To this end we
collaborate with various experimental groups--both biochemists in Jason
Kahn's lab, Maryland, and electron microscopists in Jacques Dubochet's
group at University of Lausanne LAU.
The motif of DNA mini-circles, i.e. closed loops of a few hundred base
pairs (check some cryo-em
stereo pairs of micrographs), is currently the centre of our attention.
The codes being developed include energy minimization, or statics, and
various dynamic models.
Statics
Our current research in statics is focussed on two areas:
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the development of improved ``constitutive relations'' for elastic rods
as models of DNA, i.e. rules for associating a potential energy with a
given deformation of the DNA. The input for this work are various experimental
and computational data (e.g. molecular
dynamics computations). The mathematical techniques involve various
forms of
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models of self-contact or plectonemes, where the DNA wraps around itself.
Here the major issues are appropriate models of the self-contact forces,
and efficient numerical methods for the rather ill-conditioned integral-differential
equations that arise in some models.
More detailed descriptions of completed research focused on rod
mechanics per se and applications
to DNA are available.
Dynamics
For dynamics
the research on constitutive relations is just as important as for statics,
but for dynamics the computational methods required are considerably more
intensive, and the mathematical models are less well-developed. DNA dynamics
involves motion that is both damped and stochastically driven by the solvent,
so the primary question is to understand the properties of the long-time
equilibrium distribution (if there is one) of the dynamics of the stochastic
partial differential equations arising in the models. Research areas of
interest include the investigation and comparison to cryo-EM experimental
data of equilibrium distributions computed via models involving Monte Carlo,
Langevin and Brownian approximations, the development of statistical mechanics
theories appropriate for continuum rod models, and the development of appropriate
continuum level approximations for damping and driving effects of the solvent.
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