Group Members:

- Giuseppe Gaeta (Università di Milano)
- Mariano Cadoni (Università di Cagliari)
- Roberto De Leo (Università di Cagliari)
- Sergio Demelio (Università di Cagliari)

- Gianne Derks (University of Surrey)
- Todor Gramchev (Università di Cagliari)
- Giuseppe Saccomandi (Università di Perugia)
- Sebastian Walcher (RWTH Aachen)

- L. Venier (former M.Sc. student, Università di Milano)

We aim at providing sound mathematical
modeling
of DNA dynamics,

in particular for what concerns the *transcription*
process.

This subject is linked, since the
pioneering
work by Englander et al.,

with the theory of *solitons*
travelling
along the DNA double chain.

Recently, we provided a new model
overcoming
the main obstacle the

theory is confronted to, i.e.
exhibiting
a mechanism which allows

solitary waves in the presence of
disorder
(the latter being a result

of the base sequence along the helix).

The work on this model uncovered some
general
mechanisms for

multi-component nonlinear wave
equations,
valid outside the realm

of DNA or Biology.

Our work, prompted by advances
directly related
to DNA modeling

by Saccomandi and Sgura, also considers
the existence of solitary wave

solutions with strictly compact support
(*compactons*) for certain classes

of nonlinear wave equations.

Research on Mathematical Modelling of
DNA
Dynamics was fostered by a grant

from the Italian Ministery for
University
and Research in the framework of the

PRIN (National Interest Reasearch
Programs)
covering the years 2005 & 2006.

The Research Unit based in Milano
(actually
including also a substantial group

from Cagliari) was part of a national
project
coordinated by prof. Giuseppe

Saccomandi from Lecce (he now moved to
Perugia).

Two meetings were held in the
framework of
this Project. Here you can access

information about these meetings.

Meeting
on
DNA Dynamics
Lecce, may 2005 |
Meeting
on
DNA Dynamics
Cagliari, september 2006 |

Here is a description of the (old, to a large extent realized) research program for the Milano unit, in italian and english

Papers
by
G. Gaeta |
Papers
by
M. Cadoni |
Papers
by
R. De Leo |
Papers
by
S. Demelio |

G. Derks and G. Gaeta:

``A minimal model of DNA dynamics in interaction with
RNA-Polymerase'',

Physica D 240 (2011), 1805-1817

G. Gaeta:

``Biology, Physics and Nonlinear Science''

(preface to the Special Issue of JNMP devoted to Nonlinear

Mathematical Biophysics),

*J.
Nonlin.
Math. Phys.* 18-S2
(2011), v-xii

M. Cadoni, R. De Leo, S. Demelio and G. Gaeta,

``Propagation of twist
solitons in real DNA chains'',

*J.
Nonlin.
Math. Phys.* 17
(2010), 557-569

M. Cadoni, R. De Leo, S. Demelio and G. Gaeta, *Nonlinear*

*torsional dynamics of macromolecules: from DNA to polyethylene*,

International Journal of Non-Linear Mechanics **43 **(2008),
1094-1107

Roberto De Leo, Sergio Demelio, *Numerical analysis of
solitons*

*profiles in a composite model for DNA torsion dynamics,*

International Journal of Non-Linear Mechanics **43** (2008),
1029--1039

G. Gaeta and L. Venier, *Solitary waves in twist-opening
models*

*of DNA dynamics*,

Physical Review E **78**
(2008),
011901 (9pp)

G. Gaeta and L. Venier, *Solitary waves in helicoidal models
of*

*DNA dynamics*,

Journal
of Nonlinear Mathematical Physics **15** (2008), 186-204

M. Cadoni, R. De Leo and G. Gaeta, *Sine-Gordon solitons,*

*auxiliary fields, and singular limit of a double pendulums
chain*,

Journal of Physics
A
**40** (2007), 12917-12929

M. Cadoni, R. De Leo and G. Gaeta, *A symmetry breaking*

*mechanism for selecting the speed of relativistic solitons*,

Journal of Physics
A
**40** (2007), 8517-8534

M. Cadoni, R. De Leo and G. Gaeta, *A composite model*

*for DNA torsion dynamics*,

Physical Review E **75 **(2007),
021919

M. Cadoni, R. De Leo and G. Gaeta, *Solitons in a double*

*pendulums chain model, and DNA roto-torsional dynamics*,

Journal
of Nonlinear Mathematical Physics **14 **(2007),
128-146

G. Gaeta, *Solitons in Yakushevich-like models of DNA*

*dynamics with improved intrapair potential*,

Journal
of Nonlinear Mathematical Physics **14** **
**(2007),
57-81

G. Gaeta, *Compact travelling waves and non-smooth*

*potentials*,

EuroPhysics Letters
**79** (2007), 20003 (6 pp)

M. Destrade. G. Gaeta and G. Saccomandi,

*Weierstrass's criterion and compact solitary waves*,

Physical Review E **75**
(2007),
047601 (4 pp)

G. Gaeta, T. Gramchev and S. Walcher, *Compact solitary waves*

*in linearly elastic chains with non-smooth on-site potential*,

Journal of Physics
A
**40** (2007), 4493-4509

G. Gaeta, *Solitons in the Yakushevich model of DNA*

*beyond the contact approximation*,

Physical Review E **74 **(2006),
021921

Proceedings Royal Society A,

R.W. Ogden, G. Saccomandi and I. Sgura,

*Computational aspects of Worm-Like-Chain interpolation formulas*,

Computers
and
Mathematics with Applications **53** (2007), 276-286

G. Saccomandi and I. Sgura,

*The Relevance of nonlinear stacking interactions*

*in simple models of double-stranded DNA*,

Journal
of
Royal Society Interface **3** (2006), 655–667

F. Maggioni and R.L. Ricca, *Writhing and coiling*

*of closed filaments*,

Proceedings
Royal
Society A, **462 **(2006), 3151–3166

F. Maggioni and R.L. Ricca, *Multiple folding and*

*packing in DNA modelling*,

Computers
and
Mathematics with Applications in press

Introduction to DNA structure

Nucleic acids nomenclature and structure

Atomic structure and bonding

Hydrogen bonding

Chemical bonding

Science

Physics of Life Reviews

Physical Biology

Journal of Biological Physics

Journal of Mathematical Biology

Bulletin of Mathematical Biology

Physics Letters A

Nonlinearity

Journal of Physics A

Physical Review E

Physical Review Letters

Simona Cocco

Thierry Dauxois

Gianne Derks

Laura Finzi

Giuseppe Gaeta

Marc Joyeux

Annick Lesne

Luca Peliti

Michel Peyrard

Giuseppe Saccomandi

Anxo Sanchez

Ivonne Sgura