Going from microscopic to macroscopic on nonuniform growing domains

Throughout development, chemical cues are employed to guide the functional specification of underlying tissues while the spatiotemporal distributions of such chemicals can be influenced by the growth of the tissue itself. These chemicals, termed morphogens, are often modeled using partial differential equations (PDEs). The connection between discrete stochastic and deterministic continuum models of particle migration on growing domains was elucidated by Baker, Yates, and Erban [ Bull. Math. Biol. 72 719 (2010)] in which the migration of individual particles was modeled as an on-lattice position-jump process. We build on this work by incorporating a more physically reasonable description of domain growth. Instead of allowing underlying lattice elements to instantaneously double in size and divide, we allow incremental element growth and splitting upon reaching a predefined threshold size. Such a description of domain growth necessitates a nonuniform partition of the domain. We first demonstrate that an individual-based stochastic model for particle diffusion on such a nonuniform domain partition is equivalent to a PDE model of the same phenomenon on a nongrowing domain, providing the transition rates (which we derive) are chosen correctly and we partition the domain in the correct manner. We extend this analysis to the case where the domain is allowed to change in size, altering the transition rates as necessary. Through application of the master equation formalism we derive a PDE for particle density on this growing domain and corroborate our findings with numerical simulations

Identification of novel chondroitin proteoglycans in Caenorhabditis elegans: embryonic cell division depends on CPG-1 and CPG-2.

Vertebrates produce multiple chondroitin sulfate proteoglycans that play important roles in development and tissue mechanics. In the nematode Caenorhabditis elegans, the chondroitin chains lack sulfate but nevertheless play essential roles in embryonic development and vulval morphogenesis. However, assignment of these functions to specific proteoglycans has been limited by the lack of identified core proteins. We used a combination of biochemical purification, Western blotting, and mass spectrometry to identify nine C. elegans chondroitin proteoglycan core proteins, none of which have homologues in vertebrates or other invertebrates such as Drosophila melanogaster or Hydra vulgaris. CPG-1/CEJ-1 and CPG-2 are expressed during embryonic development and bind chitin, suggesting a structural role in the egg. RNA interference (RNAi) depletion of individual CPGs had no effect on embryonic viability, but simultaneous depletion of CPG-1/CEJ-1 and CPG-2 resulted in multinucleated single-cell embryos. This embryonic lethality phenocopies RNAi depletion of the SQV-5 chondroitin synthase, suggesting that chondroitin chains on these two proteoglycans are required for cytokinesis

Sequential primed kinases create a damage-responsive phosphodegron on Eco1.

Sister-chromatid cohesion is established during S phase when Eco1 acetylates cohesin. In budding yeast, Eco1 activity falls after S phase due to Cdk1-dependent phosphorylation, which triggers ubiquitination by SCF(Cdc4). We show here that Eco1 degradation requires the sequential actions of Cdk1 and two additional kinases, Cdc7-Dbf4 and the GSK-3 homolog Mck1. These kinases recognize motifs primed by previous phosphorylation, resulting in an ordered sequence of three phosphorylation events on Eco1. Only the latter two phosphorylation sites are spaced correctly to bind Cdc4, resulting in strict discrimination between phosphates added by Cdk1 and by Cdc7. Inhibition of Cdc7 by the DNA damage response prevents Eco1 destruction, allowing establishment of cohesion after S phase. This elaborate regulatory system, involving three independent kinases and stringent substrate selection by a ubiquitin ligase, enables robust control of cohesion establishment during normal growth and after stress

Analysis of nuclear waste disposal in space, phase 3. Volume 1: Executive summary of technical report

The objectives, approach, assumptions, and limitations of a study of nuclear waste disposal in space are discussed with emphasis on the following: (1) payload characterization; (2) safety assessment; (3) health effects assessment; (4) long-term risk assessment; and (5) program planning support to NASA and DOE. Conclusions are presented for each task

Analysis of nuclear waste disposal in space, phase 3. Volume 2: Technical report

The options, reference definitions and/or requirements currently envisioned for the total nuclear waste disposal in space mission are summarized. The waste form evaluation and selection process is documented along with the physical characteristics of the iron nickel-base cermet matrix chosen for disposal of commercial and defense wastes. Safety aspects of radioisotope thermal generators, the general purpose heat source, and the Lewis Research Center concept for space disposal are assessed as well as the on-pad catastrophic accident environments for the uprated space shuttle and the heavy lift launch vehicle. The radionuclides that contribute most to long-term risk of terrestrial disposal were determined and the effects of resuspension of fallout particles from an accidental release of waste material were studied. Health effects are considered. Payload breakup and rescue technology are discussed as well as expected requirements for licensing, supporting research and technology, and safety testing

Transformation Kinetics and Mechanism of the Sulfonylurea Herbicides Pyrazosulfuron Ethyl and Halosulfuron Methyl in Aqueous Solutions

Little is known about how popular herbicides react and degrade in soil or aquatic environments. Two of these herbicides include Pyrazosulfuron Ethyl (PE) and Halosulfuron Methyl (HM), which are part of the sulfonylurea herbicide category. Both are post-emergence herbicides and are so highly effective that they need to be applied only at rates of grams per hector. Because these herbicides inhibit the key enzyme that participates in protein synthesis in plants, they can have a major effect on sensitive agricultural areas such as legumes or pastures for grazing. Typically these types of herbicides only degrade because of microbial influences or chemical hydrolysis. To understand the pathway and conditions for chemical hydrolysis degradation, ISTC’s Wei Zheng collaborated with researchers at the U.S. Department of Agriculture to conduct several laboratory experiments. Full results reported in Zheng, Wei et al (2008). "Transformation Kinetics and Mechanism of the Sulfonylurea Herbicides Pyrazosulfuron Ethyl and Halosulfuron Methyl in Aqueous Solutions." Journal of Agricultural and Food Chemistry 56(16), 7367-7372. https://doi.org/10.1021/jf800899eOpe

Fast Searching in Packed Strings

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let $m \leq n$ be the lengths $P$ and $Q$, respectively, and let $\sigma$ denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time O\left(\frac{n}{\log_\sigma n} + m + \occ\right). Here \occ is the number of occurrences of $P$ in $Q$. For $m = o(n)$ this improves the $O(n)$ bound of the Knuth-Morris-Pratt algorithm. Furthermore, if $m = O(n/\log_\sigma n)$ our algorithm is optimal since any algorithm must spend at least \Omega(\frac{(n+m)\log \sigma}{\log n} + \occ) = \Omega(\frac{n}{\log_\sigma n} + \occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.Comment: To appear in Journal of Discrete Algorithms. Special Issue on CPM 200