Conformally invariant fractals and potential theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a Q-state Potts cluster, is solved in two dimensions. The dimension &fcirc;(straight theta) of the boundary set with local wedge angle straight theta is &fcirc;(straight theta) = pi / straight theta-25-c / 12 (pi-straight theta)(2) / straight theta(2pi-straight theta), with c the central charge of the model. As a corollary, the dimensions D(EP) of the external perimeter and D(H) of the hull of a Potts cluster obey the duality equation (D(EP)-1) (D(H)-1) = 1 / 4. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.

DNA crossovers and type II DNA topoisomerases: A thermodynamical study

We present a theoretical study of the interaction of tight DNA crossovers with eukaryotic type II DNA topoisomerases. A quantitative analysis of the role of the enzyme during anaphase first shows that a tight DNA crossover should be an intermediate of the strand-passage reaction. We then focus on the initial steps of the strand-passage reaction in vitro which lead to the formation of a ternary complex ES1S2 between the enzyme and a tight DNA crossover (where E is the enzyme, S1 (respectively S2) is the first (respectively the second) DNA segment bound by the enzyme, and S1S2 is a tight crossover). This formation can be described by three equilibrium association constants: KS1 (for the reaction E+S1left arrow over right arrow ES1), KS2 (for ES1+S2left arrow over right arrow ES1S2), and KS (for E+S1S2left arrow over right arrow ES1S2) Using published experimental data obtained on the Drosophila enzyme, we derive rough estimates for the intrinsic equilibrium constants KS1 ( approximately 2.5x10(6) M-1) and KS2 ( approximately 10(4) M-1) and for Ks. The huge value found for Ks, about 5x10(16) M-1, suggests that the ternary complex bears a close resemblance with a transition state complex, and is consistent with the notion of a capture of the crossover by a protein clamp. We give a theoretical description of analogues of tight DNA crossovers which consist of two DNA segments stabilized by a covalent crosslinking. Such analogues are predicted to bind the enzyme with a high affinity and should be useful tools for the study of the enzyme.

Symmetry and chirality in topoisomerase II-DNA crossover recognition

Several experimental data support the notion that the recognition of DNA crossovers play an important role in the multiple functions of topoisomerase II. Here, a theoretical analysis of the possible modes of assembly of yeast topoisomerase II with right and left-handed tight DNA crossovers is performed, using the crystal coordinates of the docking partners. The DNA crossovers are assumed to be clamped into the central hole of the enzyme. Taking into account the rules for building symmetric ternary complexes and the structural constraints imposed by DNA-DNA and protein-DNA interactions, this analysis shows that two geometric solutions could exist, depending on the chirality of the DNA crossovers. In the first one, the two DNA segments are symmetrically recognized by the enzyme while each single double helix binds asymmetrically the protein dimer. In the second one, each double helix is symmetrically recognized by the protein around its dyad axis, while the two DNA segments have their own binding modes. The finding of potential DNA-binding domains which could interact with the crossovers provides structural supports for each model. The structural similarity of a loop containing a cluster of conserved basic residues pointing into the central hole of topoisomerase II and the second DNA-binding site of histone H5 which binds DNA crossover is of particular interest. Each solution, which is consistent with different sets of experimental data found in the literature, could either correspond to different functions of the enzyme or different steps of the reaction. This work provides structural insights for better understanding the role of chirality and symmetry in topoisomerase II-DNA crossover recognition, suggests testable experiments to further elucidate the structure of ternary complexes, and raises new questions about the relationships between the mechanism of strand-passage and strand-exchange catalyzed by the enzyme.

Forces on chromosomal DNA during anaphase

In the course of anaphase, the chromosomal DNA is submitted to the traction of the spindle. Several physical problems are associated with this action. In particular, the sister chromatids are generally topologically intertwined at the onset of anaphase, and the removal of the intertwinings results from a coupling between the enzymatic action of type II DNA topoisomerases and the force exerted by the spindle. We propose a physical analysis of some of these problems: 1) We compare the maximum force the spindle can produce with the force required to break a DNA molecule, and define the conditions compatible with biological safety during anaphase. 2) We show that the behavior of the sister chromatids in the absence of type II DNA topoisomerases can be described by two distinct models: a chain pullout model accounts for the experimental observations made in the budding yeast, and a model of the mechanical rupture of rubbers accounts for the nondisjunction in standard cases. 3) Using the fluctuation-dissipation theorem, we introduce an effective protein friction associated with the strand-passing activity of type II DNA topoisomerases. We show that this friction can be used to describe the situation in which one chromosome passes entirely through another one. Possible experiments that could test these theoretical analyses are discussed.

Anaphase chromatid motion: involvement of type II DNA topoisomerases

Sister chromatids are topologically intertwined at the onset of anaphase: their segregation during anaphase is known to require strand-passing activity by type II DNA topoisomerase. We propose that the removal of the intertwinings involves at the same time the traction of the mitotic spindle and the activity of topoisomerases. This implies that the velocity of the chromatids is compatible with the kinetic constraints imposed by the enzymatic reaction. We show that the greatest observed velocities (about 0.1 microns s-1) are close to the theoretical upper bound compatible with both the diffusion rate (calculated here within a probabilistic model) and the measured reaction rate of the enzyme.