A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

A loop-loop "kissing" complex is the essential part of the dimer linkage of genomic HIV-1 RNA.

RNA-RNA interactions govern a number of biological processes. Several RNAs, including natural sense and antisense RNAs, interact by means of a two-step mechanism: recognition is mediated by a loop-loop complex, which is then stabilized by formation of an extended intermolecular duplex. It was proposed that the same mechanism holds for dimerization of the genomic RNA of human immunodeficiency virus type 1 (HIV-1), an event thought to control crucial steps of HIV-1 replication. However, whereas interaction between the partially self-complementary loop of the dimerization initiation site (DIS) of each monomer is well established, formation of the extended duplex remained speculative. Here we first show that in vitro dimerization of HIV-1 RNA is a specific process, not resulting from simple annealing of denatured molecules. Next we used mutants of the DIS to test the formation of the extended duplex. Four pairs of transcomplementary mutants were designed in such a way that all pairs can form the loop-loop "kissing" complex, but only two of them can potentially form the extended duplex. All pairs of mutants form heterodimers whose thermal stability, dissociation constant, and dynamics were analyzed. Taken together, our results indicate that, in contrast with the interactions between natural sense and antisense RNAs, no extended duplex is formed during dimerization of HIV-1 RNA. We also showed that 55-mer sense RNAs containing the DIS are able to interfere with the preformed HIV-1 RNA dimer.

Scaling in geology: landforms and earthquakes.

Landforms and earthquakes appear to be extremely complex; yet, there is order in the complexity. Both satisfy fractal statistics in a variety of ways. A basic question is whether the fractal behavior is due to scale invariance or is the signature of a broadly applicable class of physical processes. Both landscape evolution and regional seismicity appear to be examples of self-organized critical phenomena. A variety of statistical models have been proposed to model landforms, including diffusion-limited aggregation, self-avoiding percolation, and cellular automata. Many authors have studied the behavior of multiple slider-block models, both in terms of the rupture of a fault to generate an earthquake and in terms of the interactions between faults associated with regional seismicity. The slider-block models exhibit a remarkably rich spectrum of behavior; two slider blocks can exhibit low-order chaotic behavior. Large numbers of slider blocks clearly exhibit self-organized critical behavior.