Pseudoknots in a Homopolymer

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.Comment: submitted to PR

Supercoil formation in DNA denaturation

We generalize the Poland-Scheraga (PS) model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent single-molecule experiments on DNA strands, we assume that the torsional stress induced by denaturation enforces formation of supercoils whose writhe absorbs the linking number expelled by the loops. Our model predicts that, when the entropy parameter of a loop satisfies $c \le 2$, denaturation transition does not take place. On the other hand for $c>2$ a first-order denaturation transition is consistent with our model and may take place in the actual system, as in the case with no supercoils. These results are in contrast with other treatments of circular DNA melting where denaturation is assumed to be accompanied by an increase in twist rather than writhe on the bound segments.Comment: 4 pages, 3 figures, accepted for publication in PRE Rapid Com

Percolation transition in a dynamically clustered network

We consider a percolationlike phenomenon on a generalization of the Barabasi-Albert model, where a modification of the growth dynamics directly allows formation of disconnected clusters. The transition is located with high precision by an original numerical technique based on the comparison of the largest and second largest clusters. A careful investigation focusing on finite size scaling allows us to highlight properties which would hardly be accessible by an analytical solution of cluster growth equations in the stationary limit. Our analysis shows that some critical features of the percolation transition are different from those observed in the case of dilution in fully grown networks. At variance with other models of percolation on growing networks we also find evidence that the order parameter approaches zero as a power of the field p-p(c) driving the transition, rather than as a stretched exponential.This behavior does not agree with the Berezinskii-Kosterlitz-Thouless scenario found in other similar models. For describing the phase in which a giant cluster develops, a key role is played by the crossover number of nodes N-x similar to(p-p(c))(-zeta) with zeta similar or equal to 4. This power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence

Percolation transition in a dynamically clustered network

We consider a percolationlike phenomenon on a generalization of the Barabási-Albert model, where a modification of the growth dynamics directly allows formation of disconnected clusters. The transition is located with high precision by an original numerical technique based on the comparison of the largest and second largest clusters. A careful investigation focusing on finite size scaling allows us to highlight properties which would hardly be accessible by an analytical solution of cluster growth equations in the stationary limit. Our analysis shows that some critical features of the percolation transition are different from those observed in the case of dilution in fully grown networks. At variance with other models of percolation on growing networks we also find evidence that the order parameter approaches zero as a power of the field p- pc driving the transition, rather than as a stretched exponential. This behavior does not agree with the Berezinskii-Kosterlitz- Thouless scenario found in other similar models. For describing the phase in which a giant cluster develops, a key role is played by the crossover number of nodes Nx ∼ (p- pc) -ζ with ζ 4. This power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence. © 2007 The American Physical Society

New results on the melting thermodynamics of a circular DNA chain

We investigate the impact of supercoil period and nonzero supercoil formation energy on the thermal denaturation of a circular DNA. Our analysis is based on a recently proposed generalization of the Poland Scheraga model that allows the DNA melting to be studied for plasmids with circular topology, where denaturation is accompanied by formation of supercoils. We find that the previously obtained first-order melting transition persists under the generalization discussed. The dependence of the size of the order-parameter jump at the transition point and the associated melting temperature are obtained analytically

Function changing mutations in glucocorticoid receptor evolution correlate with their relevance to mode coupling

Nonlinear effects in protein dynamics are expected to play role in function, particularly of allosteric nature, by facilitating energy transfer between vibrational modes. A recently proposed method focusing on the non-Gaussian shape of the population near equilibrium projects this information onto real space in order to identify the aminoacids relevant to function. We here apply this method to three ancestral proteins in glucocorticoid receptor (GR) family and show that the mutations that restrict functional activity during GR evolution correlate significantly with locations that are highlighted by the nonlinear contribution to the near-native configurational distribution. Our findings demonstrate that nonlinear effects are not only indispensible for understanding functionality in proteins, but they can also be harnessed into a predictive tool for functional site determination.Comment: 8 pages, 6 figure