Numerical methods for strong solutions of stochastic differential equations: an overview

This paper gives a review of recent progress in the design of numerical methods for computing the trajectories (sample paths) of solutions to stochastic differential equations. We give a brief survey of the area focusing on a number of application areas where approximations to strong solutions are important, with a particular focus on computational biology applications, and give the necessary analytical tools for understanding some of the important concepts associated with stochastic processes. We present the stochastic Taylor series expansion as the fundamental mechanism for constructing effective numerical methods, give general results that relate local and global order of convergence and mention the Magnus expansion as a mechanism for designing methods that preserve the underlying structure of the problem. We also present various classes of explicit and implicit methods for strong solutions, based on the underlying structure of the problem. Finally, we discuss implementation issues relating to maintaining the Brownian path, efficient simulation of stochastic integrals and variable-step-size implementations based on various types of control.

Microstructure and application of mesoporous nanosize zirconia

The mesoporous nanoscale zircoina zeolite was firstly synthesized via solid state - Structure directing method without addition of any stabilizer. The sample bears lamellar or worm pore structures, relatively high surface area compared with that reported. The mesoporous nanosize structure can also resist higher calcination temperature. The introduction of above zirconia to the catalyst of methanol synthesis dedicates the nanosize particle size to the catalyst, which significantly changes the physical structure and electronic effect of the catalyst. The catalyst shows higher catalytic activity and selectivity to methanol. The active sites for methanol synthesis are demonstrated over various catalysts in this paper.

Role of LBPA and Alix in multivesicular liposome formation and endosome organization

What are the components that control the assembly of subcellular organelles in eukaryotic cells? Although membranes can clearly be distorted by cytosolic factors, very little is known about the intrinsic mechanisms that control the biogenesis, shape, and organization of organellar membranes. Here, we found that the unconventional phospholipid lysobisphosphatidic acid (LBPA) could induce the formation of multivesicular liposomes that resembled the multivesicular endosomes that exist where this lipid is found in vivo. This process depended on the same pH gradient that exists across endosome membranes in vivo and was selectively controlled by Alix. In turn, Alix regulated the organization of LBPA-containing endosomes in vivo.

Archaeology and age of a new hominin from Flores in eastern Indonesia

Excavations at Liang Bua, a large limestone cave on the island of Flores in eastern Indonesia, have yielded evidence for a population of tiny hominins, sufficiently distinct anatomically to be assigned to a new species, Homo floresiensis(1). The finds comprise the cranial and some post-cranial remains of one individual, as well as a premolar from another individual in older deposits. Here we describe their context, implications and the remaining archaeological uncertainties. Dating by radiocarbon (C-14), luminescence, uranium-series and electron spin resonance (ESR) methods indicates that H. floresiensis existed from before 38,000 years ago (kyr) until at least 18 kyr. Associated deposits contain stone artefacts and animal remains, including Komodo dragon and an endemic, dwarfed species of Stegodon. H. floresiensis originated from an early dispersal of Homo erectus ( including specimens referred to as Homo ergaster and Homo georgicus)(1) that reached Flores, and then survived on this island refuge until relatively recently. It overlapped significantly in time with Homo sapiens in the region(2,3), but we do not know if or how the two species interacted.

Sea surface temperature variations recorded on coralline Sr/Ca ratios during Mid-Late Holocene in Leizhou Peninsula

High-resolution Sr/Ca ratios of two Porites corals from Leizhou Peninsula were measured using inductively coupled plasma atomic spectrometry (ICP-AES). TIMS U-Th dating reveals that the life-spans of the two corals are 489500 AD and 539-530 BC, respectively. Monthly sea surface temperatures (SSTs) during these two periods can be reconstructed from their skeletal Sr/Ca ratios. The results reveal that SSTs during 539-530 BC were roughly the same as those during 1990-2000 AD in this area, indicating a relative warm climate period. However, the period of 489-500 AD was significantly cooler, with annual mean SST, the 10-a average of minimum monthly winter SSTs and the 10-a average of maximum monthly summer SSTs being about 2, 2.9 and 1degreesC lower than that in the 1990s, respectively. Such climate patterns agree well with the phenological results recorded in the historic documents in other areas of China.

Crystal structures of the DsbG disulfide isomerase reveal an unstable disulfide

Dsb proteins control the formation and rearrangement of disulfide bonds during the folding of secreted and membrane proteins in bacteria. DsbG, a member of this family, has disulfide bond isomerase and chaperone activity. Here, we present two crystal structures of DsbG at 1.7- and 2.0-Angstrom resolution that are meant to represent the reduced and oxidized forms, respectively. The oxidized structure, however, reveals a mixture of both redox forms, suggesting that oxidized DsbG is less stable than the reduced form. This trait would contribute to DsbG isomerase activity, which requires that the active-site Cys residues are kept reduced, regardless of the highly oxidative environment of the periplasm. We propose that a Thr residue that is conserved in the cis-Pro loop of DsbG and DsbC but not found in other Dsb proteins could play a role in this process. Also, the structure of DsbG reveals an unanticipated and surprising feature that may help define its specific role in oxidative protein folding. Thus, the dimensions and surface features of DsbG show a very large and charged binding surface that is consistent with interaction with globular protein substrates having charged surfaces. This finding suggests that, rather than catalyzing disulfide rearrangement in unfolded substrates, DsbG may preferentially act later in the folding process to catalyze disulfide rearrangement in folded or partially folded proteins.

Cannibalistic feeding of larval Trichogramma carverae parasitoids in moth eggs

Wasps of the genus Trichogramma parasitise the eggs of Lepidoptera. They may deposit one or many eggs in each host. Survival is high at low density but reaches a plateau as density increases. To reveal the mechanism by which excess larvae die we chose a lepidopteran host that has flattened, transparent eggs and used video microscopy to record novel feeding behaviours and interactions of larval Trichogramma carverae (Oatman and Pinto) at different densities. Single larvae show a rapid food ingestion phase, followed by a period of extensive saliva release. Ultimately the host egg is completely consumed. The larva then extracts excess moisture from the egg, providing a dry environment for pupation. When multiple larvae are present, the initial scramble for food results in the larvae consuming all of the egg contents early in development. All larvae survive if there is sufficient food for all to reach a threshold developmental stage. If not, physical proximity results in attack and consumption of others, continuing until the surviving larvae reach the threshold stage beyond which attacks seem to be no longer effective. The number of larvae remaining at the end of rapid ingestion dictates how many will survive to emerge as adults.

Engineering stable peptide toxins by means of backbone cyclization: Stabilization of the alpha-conotoxin MII

Conotoxins (CTXs), with their exquisite specificity and potency, have recently created much excitement as drug leads. However, like most peptides, their beneficial activities may potentially be undermined by susceptibility to proteolysis in vivo. By cyclizing the alpha-CTX MII by using a range of linkers, we have engineered peptides that preserve their full activity but have greatly improved resistance to proteolytic degradation. The cyclic MII analogue containing a seven-residue linker joining the N and C termini was as active and selective as the native peptide for native and recombinant neuronal nicotinic acetylcholine receptor subtypes present in bovine chromaffin cells and expressed in Xerl oocytes, respectively. Furthermore, its resistance to proteolysis against a specific protease and in human plasma was significantly improved. More generally, to our knowledge, this report is the first on the cyclization of disulfide-rich toxins. Cyclization strategies represent an approach for stabilizing bioactive peptides while keeping their full potencies and should boost applications of peptide-based drugs in human medicine.

A falsification of the thermal specialization paradigm: compensation for elevated temperatures in Antarctic fishes

Specialization to a particular environment is one of the main factors used to explain species distributions. Antarctic fishes are often cited as a classic example to illustrate the specialization process and are regarded as the archetypal stenotherms. Here we show that the Antarctic fish Pagothenia borchgrevinki has retained the capacity to compensate for chronic temperature change. By displaying astounding plasticity in cardiovascular response and metabolic control, the fishes maintained locomotory performance at elevated temperatures. Our falsification of the specialization paradigm indicates that the effect of climate change on species distribution and extinction may be overestimated by current models of global warming.

H-ras, K-ras, and inner plasma membrane raft proteins operate in nanoclusters with differential dependence on the actin cytoskeleton

Plasma membrane compartmentalization imposes lateral segregation on membrane proteins that is important for regulating signal transduction. We use computational modeling of immunogold spatial point patterns on intact plasma membrane sheets to test different models of inner plasma membrane organization. We find compartmentalization at the nanoscale level but show that a classical raft model of preexisting stable domains into which lipid raft proteins partition is incompatible with the spatial point patterns generated by the immunogold labeling of a palmitoylated raft marker protein. Rather, approximate to 30% of the raft protein exists in cholesterol-dependent nanoclusters, with approximate to 70% distributed as monomers. The cluster/monomer ratio (number of proteins in clusters/number of proteins outside clusters) is independent of expression level. H-rasG12V and K-rasG12V proteins also operate in nanoclusters with fixed cluster/monomer ratios that are independent of expression level. Detailed calibration of the immunogold imaging protocol suggests that radii of raft and RasG12V protein nanoclusters may be as small as 11 and 6 nm, respectively, and shows that the nanoclusters contain small numbers (6.0-7.7) of proteins. Raft nanoclusters do not form if the actin cytoskeleton is disassembled. The formation of K-rasG12V but not H-rasG12V nanoclusters also is actin-dependent. K-rasG12V but not H-rasG12V signaling is abrogated by actin cytoskeleton disassembly, which shows that nanoclustering is critical for Ras function. These findings argue against stable preexisting domains on the inner plasma membrane in favor of dynamic actively regulated nanoclusters similar to those proposed for the outer plasma membrane. RasG12V nanoclusters may facilitate the assembly of essential signal transduction complexes.

The chemistry and biology of human relaxin-3

A novel member of the human relaxin subclass of the insulin superfamily was recently discovered during a genomics database search and named relaxin-3. Like human relaxin-1 and relaxin-2, relaxin-3 is predicted to consist of a two-chain structure and three disulfide bonds in a disposition identical to that of insulin. To undertake detailed biophysical and biological characterization of the peptide, its chemical synthesis was undertaken. In contrast to human relaxin-1 and relaxin-2, however, relaxin-3 could not be successfully prepared by simple combination of the individual chains, thus necessitating recourse to the use of a regioselective disulfide bond formation strategy. Solid phase synthesis of the separate, selectively S-protected A and B chains followed by their purification and the subsequent stepwise formation of each of the three disulfides led to the successful acquisition of human relaxin-3. Comprehensive chemical characterization confirmed both the correct chain orientation and the integrity of the synthetic product. Relaxin-3 was found to bind to and activate native relaxin receptors in vitro and stimulate water drinking through central relaxin receptors in vivo. Recent studies have demonstrated that relaxin-3 will bind to and activate human LGR7, but not LGR8, in vitro. Secondary structural analysis showed it to adopt a less ordered confirmation than either relaxin-1 or relaxin-2, reflecting the presence in the former of a greater percentage of nonhelical forming amino acids. NMR spectroscopy and simulated annealing calculations were used to determine the three-dimensional structure of relaxin-3 and to identify key structural differences between the human relaxins.