Zigzag stacks and m-regular linear stacks.

The contact map of a protein fold is a graph that represents the patterns of contacts in the fold. It is known that the contact map can be decomposed into stacks and queues. RNA secondary structures are special stacks in which the degree of each vertex is at most one and each arc has length of at least two. Waterman and Smith derived a formula for the number of RNA secondary structures of length n with exactly k arcs. Höner zu Siederdissen et al. developed a folding algorithm for extended RNA secondary structures in which each vertex has maximum degree two. An equation for the generating function of extended RNA secondary structures was obtained by Müller and Nebel by using a context-free grammar approach, which leads to an asymptotic formula. In this article, we consider m-regular linear stacks, where each arc has length at least m and the degree of each vertex is bounded by two. Extended RNA secondary structures are exactly 2-regular linear stacks. For any m ≥ 2, we obtain an equation for the generating function of the m-regular linear stacks. For given m, we deduce a recurrence relation and an asymptotic formula for the number of m-regular linear stacks on n vertices. To establish the equation, we use the reduction operation of Chen, Deng, and Du to transform an m-regular linear stack to an m-reduced zigzag (or alternating) stack. Then we find an equation for m-reduced zigzag stacks leading to an equation for m-regular linear stacks.

A low concentration of ethanol impairs learning but not motor and sensory behavior in Drosophila larvae.

Drosophila melanogaster has proven to be a useful model system for the genetic analysis of ethanol-associated behaviors. However, past studies have focused on the response of the adult fly to large, and often sedating, doses of ethanol. The pharmacological effects of low and moderate quantities of ethanol have remained understudied. In this study, we tested the acute effects of low doses of ethanol (∼7 mM internal concentration) on Drosophila larvae. While ethanol did not affect locomotion or the response to an odorant, we observed that ethanol impaired associative olfactory learning when the heat shock unconditioned stimulus (US) intensity was low but not when the heat shock US intensity was high. We determined that the reduction in learning at low US intensity was not a result of ethanol anesthesia since ethanol-treated larvae responded to the heat shock in the same manner as untreated animals. Instead, low doses of ethanol likely impair the neuronal plasticity that underlies olfactory associative learning. This impairment in learning was reversible indicating that exposure to low doses of ethanol does not leave any long lasting behavioral or physiological effects.

Olfactory conditioning in the third instar larvae of Drosophila melanogaster using heat shock reinforcement.

Adult Drosophila melanogaster has long been a popular model for learning and memory studies. Now the larval stage of the fruit fly is also being used in an increasing number of classical conditioning studies. In this study, we employed heat shock as a novel negative reinforcement for larvae and obtained high learning scores following just one training trial. We demonstrated heat-shock conditioning in both reciprocal and non-reciprocal paradigms and observed that the time window of association for the odor and heat shock reinforcement is on the order of a few minutes. This is slightly wider than the time window for electroshock conditioning reported in previous studies, possibly due to lingering effects of the high temperature. To test the utility of this simplified assay for the identification of new mutations that disrupt learning, we examined flies carrying mutations in the dnc gene. While the sensitivity to heat shock, as tested by writhing, was similar for wild type and dnc homozygotes, dnc mutations strongly diminished learning. We confirmed that the learning defect in dnc flies was indeed due to mutation in the dnc gene using non-complementation analysis. Given that heat shock has not been employed as a reinforcement for larvae in the past, we explored learning as a function of heat shock intensity and found that optimal learning occurred around 41 °C, with higher and lower temperatures both resulting in lower learning scores. In summary, we have developed a very simple, robust paradigm of learning in fruit fly larvae using heat shock reinforcement.

Random K-noncrossing RNA structures.

In this paper, we introduce a combinatorial framework that provides an interpretation of RNA pseudoknot structures as sampling paths of a Markov process. Our results facilitate a variety of applications ranging from the energy-based sampling of pseudoknot structures as well as the ab initio folding via hidden Markov models. Our main result is an algorithm that generates RNA pseudoknot structures with uniform probability. This algorithm serves as a steppingstone to sequence-specific as well as energy-based transition probabilities. The approach employs a correspondence between pseudoknot structures, parametrized in terms of the maximal number of mutually crossing arcs and certain tableau sequences. The latter can be viewed as lattice paths. The main idea of this paper is to view each such lattice path as a sampling path of a stochastic process and to make use of D-finiteness for the efficient computation of the corresponding transition probabilities.

Onset of tethered chain overcrowding.

We proposed an approach to precisely control the density of tethered chains on solid substrates using PEO-b-PS and PLLA-b-PS. As the crystallization temperature Tx increased, the PEO or PLLA lamellar crystal thickness d(L) increased as well as the reduced tethering density sigma; of the PS chains. The onset of tethered PS chains overcrowding in solution occurs at sigma(*) approximately 3.7-3.8 as evidenced by an abrupt change in the slope between (d(L))(-1) and Tx. This results from the extra surface free energy created by the tethered chain that starts to affect the growth barrier of the crystalline blocks.