Mathematical Models of DNA Dynamics

 

 

Group Members:

We also collaborate on these or related themes with: In the recent past, we also worked with:

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





 

Publications

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


See also

R.W. Ogden, G. Saccomandi and I. Sgura,
On Worm-Like Chain model within the three-dimensional continuum mechanics framework,
Proceedings Royal Society A462 (2006), 749-768

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 A462 (2006), 3151–3166

F. Maggioni and R.L. Ricca, Multiple folding and
packing in DNA modelling,
Computers and Mathematics with Applications  in press
 



 

Useful links / Links utili

General

Generalities about DNA
Introduction to DNA structure
Nucleic acids nomenclature and structure
Atomic structure and bonding
Hydrogen bonding
Chemical bonding

Journals

Nature
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

Persons

Maria Barbi
Simona Cocco
Thierry Dauxois
Gianne Derks
Laura Finzi
Giuseppe Gaeta
Marc Joyeux
Annick Lesne
Luca Peliti
Michel Peyrard
Giuseppe Saccomandi
Anxo Sanchez
Ivonne Sgura



g.gaeta 1/12/2011