A "partitioned leaping" approach for multiscale modeling of chemical reaction dynamics

We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic framework. The technique correctly accounts for stochastic noise at significantly reduced computational cost, requires the definition of only three model-independent parameters and is particularly well-suited for simulating systems containing widely disparate species populations. We present the theoretical foundations of partitioned leaping, discuss various options for its practical implementation and demonstrate the utility of the method via illustrative examples.Comment: v4: 12 pages, 5 figures, final accepted version. Error found and fixed in Appendi

Enhancement of the stability of genetic switches by overlapping upstream regulatory domains

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.Comment: 4 pages, 5 figures, RevTeX

Simple Wriggling is Hard unless You Are a Fat Hippo

We prove that it is NP-hard to decide whether two points in a polygonal domain with holes can be connected by a wire. This implies that finding any approximation to the shortest path for a long snake amidst polygonal obstacles is NP-hard. On the positive side, we show that snake's problem is "length-tractable": if the snake is "fat", i.e., its length/width ratio is small, the shortest path can be computed in polynomial time.Comment: A shorter version is to be presented at FUN 201

Analytical study of an exclusive genetic switch

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be repressed. The model may be thought of as a minimal model of the power struggle between two competing parties. Exact solutions are given for the limits of vanishing binding/unbinding rates and infinite binding/unbinding rates. A mean field theory is introduced which is exact in the limit of vanishing binding/unbinding rates. The mean field theory and numerical simulations reveal that generically bistability occurs and the system is in a symmetry broken state. An exact perturbative solution which in principle allows the nonequilibrium stationary state to be computed is also developed and computed to first and second order.Comment: 28 pages, 6 figure

Novel cruzain inhibitors for the treatment of Chagas' disease.

The protozoan parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, affects millions of individuals and continues to be an important global health concern. The poor efficacy and unfavorable side effects of current treatments necessitate novel therapeutics. Cruzain, the major cysteine protease of T. cruzi, is one potential novel target. Recent advances in a class of vinyl sulfone inhibitors are encouraging; however, as most potential therapeutics fail in clinical trials and both disease progression and resistance call for combination therapy with several drugs, the identification of additional classes of inhibitory molecules is essential. Using an exhaustive virtual-screening and experimental validation approach, we identify several additional small-molecule cruzain inhibitors. Further optimization of these chemical scaffolds could lead to the development of novel drugs useful in the treatment of Chagas' disease

Maximizing Maximal Angles for Plane Straight-Line Graphs

Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The incident angles of a vertex $p \in S$ of $G$ are the angles between any two edges of $G$ that appear consecutively in the circular order of the edges incident to $p$. A plane straight-line graph is called $\phi$-open if each vertex has an incident angle of size at least $\phi$. In this paper we study the following type of question: What is the maximum angle $\phi$ such that for any finite set $S\subset\R^2$ of points in general position we can find a graph from a certain class of graphs on $S$ that is $\phi$-open? In particular, we consider the classes of triangulations, spanning trees, and paths on $S$ and give tight bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that were omitted in the previous version are now include

Draft Genome Sequence for Desulfovibrio africanus Strain PCS.

Desulfovibrio africanus strain PCS is an anaerobic sulfate-reducing bacterium (SRB) isolated from sediment from Paleta Creek, San Diego, CA. Strain PCS is capable of reducing metals such as Fe(III) and Cr(VI), has a cell cycle, and is predicted to produce methylmercury. We present the D. africanus PCS genome sequence

Complete Genome Sequence of Pelosinus fermentans JBW45, a Member of a Remarkably Competitive Group of Negativicutes in the Firmicutes Phylum.

The genome of Pelosinus fermentans JBW45, isolated from a chromium-contaminated site in Hanford, Washington, USA, has been completed with PacBio sequencing. Nine copies of the rRNA gene operon and multiple transposase genes with identical sequences resulted in breaks in the original draft genome and may suggest genomic instability of JBW45

When Can You Fold a Map?

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by +-180 degrees. We first consider the analogous questions in one dimension lower -- bending a segment into a flat object -- which lead to interesting problems on strings. We develop efficient algorithms for the recognition of simply foldable 1D crease patterns, and reconstruction of a sequence of simple folds. Indeed, we prove that a 1D crease pattern is flat-foldable by any means precisely if it is by a sequence of one-layer simple folds. Next we explore simple foldability in two dimensions, and find a surprising contrast: ``map'' folding and variants are polynomial, but slight generalizations are NP-complete. Specifically, we develop a linear-time algorithm for deciding foldability of an orthogonal crease pattern on a rectangular piece of paper, and prove that it is (weakly) NP-complete to decide foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper, (2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a square piece of paper, and (3) crease patterns without a mountain/valley assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks to referees, including formal definitions of simple folds, more figures, table summarizing results, new open problems, and additional reference