%0 Book Section %1 statphys23_0367 %A Straeten, E. Van Der %A Naudts, J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K entropy folding protein residual statphys23 topic-10 %T Residual entropy in theoretical model for single molecule %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=367 %X The unfolding transition from compact globule to stretched coil in bio-polymers was already predicted 15 years ago $1$, based on heuristic arguments. Nowadays, the theoretical study of this transition is dominated by numerical simulations. The self-avoiding walk in two dimensions is often used to model the unfolding of polymers $2,3$. The benefit of self-avoiding walks is that local interactions like monomer-monomer attraction and the excluded volume effect are taken into account. The disadvantage is that one is limited to short walks due to the computational cost (up to chain length $55$ $2$). The present work uses random walks without self-avoiding constraints in an attempt to obtain analytical instead of numerical results. In $4$ we use a one-dimensional random walk with Markovian increments to compare two polymer stretching experiments. This model can also be used to calculate analytically a force-temperature state diagram. The obtained state diagram is similar to the diagrams of the numerical simulations. The most remarkable property of these diagrams, the re-entrance behavior due to residual entropy, is also observed in our calculations $5$. The disadvantages of the present model are that its application is restricted to flexible molecules in a poor solvent, and that the excluded volume effect is not taken into account. The benefit of this simplified model is, that it can be solved completely in closed form. It is also possible to generalize the model to higher dimensions (see $6$ for some general results about chains with Markovian increments).\\ 1) A. Halperin, E. B. Zhulina, On the Deformation Behaviour of Collapsed Polymers, Europhys. Lett. 15, 417 (1991). \\ 2) S. Kumar, I. Jensen, J. L. Jacobsen and A. J. Guttmann, Role of conformatinal entropy in force-induced bio-polymer unfolding, cond-mat/0702436 (Accepted in Phys. Rev. Lett.) \\ 3) D. Marenduzzo, A. Maritan, A. Rosa and F. Seno, Stretching of a Polymer below the $þeta$ Point, Phys. Rev. Lett. 90, 088301 (2003) \\ 4) E. Van der Straeten, J. Naudts, A one-dimensional model for theoretical analysis of single molecule experiments, J. Phys. A: Math. Gen. 39, 5715 (2006). \\ 5) E. Van der Straeten and J. Naudts, Residual entropy in theoretical model for single molecules, in preparation \\ 6) J. Naudts and E. Van der Straeten, Transition records of stationary Markov chains, Phys. Rev. E. 74, 040103 (2006).

@incollection{statphys23_0367, abstract = {The unfolding transition from compact globule to stretched coil in bio-polymers was already predicted 15 years ago $[1]$, based on heuristic arguments. Nowadays, the theoretical study of this transition is dominated by numerical simulations. The self-avoiding walk in two dimensions is often used to model the unfolding of polymers $[2,3]$. The benefit of self-avoiding walks is that local interactions like monomer-monomer attraction and the excluded volume effect are taken into account. The disadvantage is that one is limited to short walks due to the computational cost (up to chain length $55$ $[2]$). The present work uses random walks without self-avoiding constraints in an attempt to obtain analytical instead of numerical results. In $[4]$ we use a one-dimensional random walk with Markovian increments to compare two polymer stretching experiments. This model can also be used to calculate analytically a force-temperature state diagram. The obtained state diagram is similar to the diagrams of the numerical simulations. The most remarkable property of these diagrams, the re-entrance behavior due to residual entropy, is also observed in our calculations $[5]$. The disadvantages of the present model are that its application is restricted to flexible molecules in a poor solvent, and that the excluded volume effect is not taken into account. The benefit of this simplified model is, that it can be solved completely in closed form. It is also possible to generalize the model to higher dimensions (see $[6]$ for some general results about chains with Markovian increments).\\ 1) A. Halperin, E. B. Zhulina, {\sl On the Deformation Behaviour of Collapsed Polymers,} Europhys. Lett. {\bf 15}, 417 (1991). \\ 2) S. Kumar, I. Jensen, J. L. Jacobsen and A. J. Guttmann, {\sl Role of conformatinal entropy in force-induced bio-polymer unfolding,} cond-mat/0702436 (Accepted in Phys. Rev. Lett.) \\ 3) D. Marenduzzo, A. Maritan, A. Rosa and F. Seno, {\sl Stretching of a Polymer below the $\theta$ Point,} Phys. Rev. Lett. {\bf 90}, 088301 (2003) \\ 4) E. Van der Straeten, J. Naudts, {\sl A one-dimensional model for theoretical analysis of single molecule experiments,} J. Phys. A: Math. Gen. 39, 5715 (2006). \\ 5) E. Van der Straeten and J. Naudts, {\sl Residual entropy in theoretical model for single molecules,} in preparation \\ 6) J. Naudts and E. Van der Straeten, {\sl Transition records of stationary Markov chains,} Phys. Rev. E. {\bf 74}, 040103 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Straeten, E. Van Der and Naudts, J.}, biburl = {https://www.bibsonomy.org/bibtex/22a905023e188c6786eff3bdd256b433b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {ba8d1eba807d3fc27dfb5f74ddb50aa0}, intrahash = {2a905023e188c6786eff3bdd256b433b}, keywords = {entropy folding protein residual statphys23 topic-10}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Residual entropy in theoretical model for single molecule}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=367}, year = 2007 }