22 research outputs found
Mesoscopic models for DNA stretching under force: new results and comparison to experiments
Single molecule experiments on B-DNA stretching have revealed one or two
structural transitions, when increasing the external force. They are
characterized by a sudden increase of DNA contour length and a decrease of the
bending rigidity. It has been proposed that the first transition, at forces of
60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA,
while the second one, at stronger forces, is a strand peeling resulting in
single stranded DNAs (ssDNA), similar to thermal denaturation. But due to
experimental conditions these two transitions can overlap, for instance for
poly(dA-dT). We derive analytical formula using a coupled discrete worm like
chain-Ising model. Our model takes into account bending rigidity, discreteness
of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit
of zero force, this model simplifies into a coupled model already developed by
us for studying thermal DNA melting, establishing a connexion with previous
fitting parameter values for denaturation profiles. We find that: (i) ssDNA is
fitted, using an analytical formula, over a nanoNewton range with only three
free parameters, the contour length, the bending modulus and the monomer size;
(ii) a surprisingly good fit on this force range is possible only by choosing a
monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase
length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss)
transitions; (iv) an analytical formula for fitting B to S transitions is
derived in the strong force approximation and for long DNAs, which is in
excellent agreement with exact transfer matrix calculations; (v) this formula
fits perfectly well poly(dG-dC) and -DNA force-extension curves with
consistent parameter values; (vi) a coherent picture, where S to ssDNA
transitions are much more sensitive to base-pair sequence than the B to S one,
emerges.Comment: 14 pages, 9 figure
Strategic games with security and potential level players
This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. Copyright Springer Science+Business Media, LLC 2007Allais paradoxes, equilibrium in beliefs, Nash equilibrium, non-expected utility theories, rationalizability, C72, D81,