Topological signatures of globular polymers.

Simulations in which a globular ring polymer with delocalized knots is separated in two interacting loops by a slipping link, or in two noninteracting globuli by a wall with a hole, show how the minimal crossing number of the knots controls the equilibrium statistics. With slipping link the ring length is divided between the loops according to a simple law, but with unexpectedly large fluctuations. These are suppressed only for unknotted loops, whose length distribution always shows a fast power-law decay. We also discover and explain a topological effect interfering with that of surface tension in the globule translocation through a membrane nanopore.

Knot localization in adsorbing polymer rings.

We study by Monte Carlo simulations a model of a knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent phi, and the metric exponent nu are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring, we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a continuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.

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-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) approximately (p-p(c))(-zeta) with zeta approximately 4. This power law behavior and that of other quantities are conjectured on the basis of scaling arguments and numerical evidence.

Size of knots in ring polymers.

We give two different, statistically consistent definitions of the length l of a prime knot tied into a polymer ring. In the good solvent regime the polymer is modeled by a self avoiding polygon of N steps on cubic lattice and l is the number of steps over which the knot "spreads" in a given configuration. An analysis of extensive Monte Carlo data in equilibrium shows that the probability distribution of l as a function of N obeys a scaling of the form p(l,N) approximately l(-c)f(l/N(D)) , with c approximately equal to 1.25 and D approximately equal to 1. Both D and c could be independent of knot type. As a consequence, the knot is weakly localized, i.e., approximately N(t) , with t=2-c approximately equal to 0.75 . For a ring with fixed knot type, weak localization implies the existence of a peculiar characteristic length l(nu) approximately N(tnu) . In the scaling approximately N(nu) (nu approximately equal to 0.58) of the radius of gyration of the whole ring, this length determines a leading power law correction which is much stronger than that found in the case of unrestricted topology. The existence of this correction is confirmed by an analysis of extensive Monte Carlo data for the radius of gyration. The collapsed regime is studied by introducing in the model sufficiently strong attractive interactions for nearest neighbor sites visited by the self-avoiding polygon. In this regime knot length determinations can be based on the entropic competition between two knotted loops separated by a slip link. These measurements enable us to conclude that each knot is delocalized (t approximately equal to 1) .

Point mutation of estrogen receptor (ER) in the ligand-binding domain changes the pharmacology of antiestrogens in ER-negative breast cancer cells stably expressing complementary DNAs for ER.

The antiestrogen tamoxifen is used in the treatment of hormone-responsive breast cancer. However, therapeutic failure has frequently been observed in both patients and animal models after long term treatment. We have studied the effect of a point mutation that leads to the substitution of Val for Gly at codon 400 in the ligand-binding domain of the estrogen receptor (ER) on estrogenic and antiestrogenic activities of 4-hydroxytamoxifen (4-OHT) and its derivatives. Stable ER transfectants derived from MDA-MB-231 CL10A, an ER-negative breast cancer cell line, have been used in these studies. 4-OHT and its fixed ring derivatives showed more estrogen-like activity in ER transfectants than in MCF-7, an ER-positive breast cancer cell line. In this study, 4-OHT was a partial agonist of cell growth in the transfectant S30 cells, which express the wild-type ER. However, it was a full agonist in the mutant ER transfectant ML alpha 2H, which expressed ER with Val at codon 400. The increased estrogenic activity of 4-OHT in ML alpha 2H cells was not due to the preferential isomerization of trans 4-OHT to cis 4-OHT, since the nonisomerizable fixed ring trans 4-OHT was a partial agonist for cell growth in S30 cells and was a full agonist in ML alpha 2H cells. Transient transfection using a reporter plasmid containing an estrogen response element demonstrated that fixed ring trans 4-OHT had estrogenic activity in ML alpha 2H cells.(ABSTRACT TRUNCATED AT 250 WORDS)

Scale-free network hidden in a collapsing polymer.

We show that the collapsed globular phase of a polymer accommodates a scale-free incompatibility graph of its contacts. The degree distribution of this network is found to decay with the exponent gamma=1/(2-c) up to a cutoff degree dc proportional to L(2-c), where is the loop exponent for dense polymers (c=11/8 in two dimensions) and is the length of the polymer. Our results exemplify how a scale-free network can emerge from standard criticality.

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 pseudoknot number (Npk) at different temperature regimes in two and three dimensions. We find that, although the total number of pseudoknots is extensive at all temperatures, the number of those forming between the two halves of the chain diverges logarithmically at (both dimensions) and below (two dimensions only) the theta temperature. We later introduce a simple model that emphasizes the role of pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched, and collapsed homopolymer phases with transitions between each pair.

Polymer theta-point as a knot delocalization transition.

We study numerically the tightness of prime flat knots in a model of self-attracting polymers with excluded volume. We find that these knots are localized in the high temperature swollen regime, but become delocalized in the low temperature globular phase. Precisely at the collapse transition, the knots are weakly localized. Some of our results can be interpreted in terms of the theory of polymer networks, which allows one to conjecture exact exponents for the knot length probability distributions.

Zipping and collapse of diblock copolymers.

Using exact enumeration methods and Monte Carlo simulations, we study the phase diagram relative to the conformational transitions of a diblock copolymer in two dimensions. The polymer is made of two homogeneous strands of monomers of different species which are joined to each other at one end. We find that, depending on the values of the energy parameters in the model, there is either a first order collapse from a swollen phase to a compact phase of spiral type, or a continuous transition to an intermediate zipped phase followed by a first order collapse at lower temperatures. Critical exponents of the zipping transition are computed, and their exact values are conjectured on the basis of a mapping onto percolation geometry, thanks to recent results on path-crossing probabilities.

Interstrand distance distribution of DNA near melting.

The distance distribution between complementary base pairs of the two strands of a DNA molecule is studied near the melting transition. Scaling arguments are presented for a generalized Poland-Scheraga-type model that includes self-avoiding interactions. At the transition temperature and for a large distance r, the distribution decays as 1/r(kappa) with kappa=1+(c-2)/nu. Here nu is the self-avoiding walk correlation length exponent and c is the exponent associated with the entropy of an open loop in the chain. Results for the distribution function just below the melting point are also presented. Numerical simulations that fully take into account the self-avoiding interactions are in good agreement with the scaling approach.

Ranking knots of random, globular polymer rings.

An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and suggests that the total number of different knots realized grows exponentially with the chain length. Relative frequencies of specific knots converge to definite values because the free energy per monomer, and its leading finite size corrections, do not depend on the ring topology, while a subleading correction only depends on the crossing number of the knots.

Precise toppling balance, quenched disorder, and universality for sandpiles.

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling Bak-Tang-Wiesenfeld universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.

Peculiar scaling of self-avoiding walk contacts.

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N-->infinity they are strictly finite in number but their radius of gyration R(c) is power law distributed proportional to R(-tau)(c), where tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging length scales is associated with the R(c) distribution. A possibly superuniversal tau = 2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.

Directed polymers with tilted columnar disorder and Burgers-like turbulence.

The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario is analogous to that of structure functions in bifractal Burgers turbulence. Some scaling properties are predicted from extreme value statistics. The multiscaling disappears for zero tilt.

RNA denaturation: excluded volume, pseudoknots, and transition scenarios.

A lattice model of RNA denaturation which fully accounts for the excluded volume effects among nucleotides is proposed. A numerical study shows that interactions forming pseudoknots must be included in order to get a sharp continuous transition. Otherwise a smooth crossover occurs from the swollen linear polymer behavior to highly ramified, almost compact conformations with secondary structures. In the latter scenario, which is appropriate when these structures are much more stable than pseudoknot links, probability distributions for the lengths of both loops and main branches obey scaling with nonclassical exponents.