Power spectra methods for a stochastic description of diffusion on deterministically growing domains

A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state

Stochastic reaction & diffusion on growing domains: understanding the breakdown of robust pattern formation

Many biological patterns, from population densities to animal coat markings, can be thought of as heterogeneous spatiotemporal distributions of mobile agents. Many mathematical models have been proposed to account for the emergence of this complexity, but, in general, they have consisted of deterministic systems of differential equations, which do not take into account the stochastic nature of population interactions. One particular, pertinent criticism of these deterministic systems is that the exhibited patterns can often be highly sensitive to changes in initial conditions, domain geometry, parameter values, etc. Due to this sensitivity, we seek to understand the effects of stochasticity and growth on paradigm biological patterning models. In this paper, we extend spatial Fourier analysis and growing domain mapping techniques to encompass stochastic Turing systems. Through this we find that the stochastic systems are able to realize much richer dynamics than their deterministic counterparts, in that patterns are able to exist outside the standard Turing parameter range. Further, it is seen that the inherent stochasticity in the reactions appears to be more important than the noise generated by growth, when considering which wave modes are excited. Finally, although growth is able to generate robust pattern sequences in the deterministic case, we see that stochastic effects destroy this mechanism for conferring robustness. However, through Fourier analysis we are able to suggest a reason behind this lack of robustness and identify possible mechanisms by which to reclaim it

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases

Splenic Injury and ERCP: A Possible Risk for Patients with Advanced Chronic Pancreatitis

Splenic injury is a rare but potentially life-threatening complication of endoscopy, with very few cases of endoscopic retrograde cholangiopancreatography (ERCP)-induced injury reported in the literature. Here we report a patient with chronic alcoholic pancreatitis who was diagnosed with a sub-capsular splenic laceration nearly 6 days after an ERCP. Clinicians should be alerted to the potential post-procedure complications associated with ERCP, particularly as this procedure is being utilized more frequently for the management of patients with complex hepatobiliary and pancreatic conditions

The pH-dependence of lipid-mediated antimicrobial peptide resistance in a model Staphylococcal plasma membrane: a two-for-one mechanism of epithelial defence circumvention.

The mechanisms of membrane defence by lysylphosphatidylglycerol (LPG), were investigated using synthetic biomimetic mono- and bilayer models of methicillin resistant S. aureus ST239 TW, based on its lipid composition in both pH 7.4 (28% LPG) and pH 5.5 (51% LPG) cultures. These models incorporated a stable synthetic analogue of LPG (3adLPG) to facilitate long-duration biophysical studies, which were previously limited by the lability native LPG. Both increased 3adLPG content and full headgroup ionization at pH 5.5, increased bilayer order and dampened overall charge, via the formation of neutral ion pairs with anionic lipids. Ion pair formation in air/liquid interface lipid monolayers elicited a significant condensing effect, which correlated with the inhibition of subphase-injected magainin 2 F5W partitioning. In fluid phase lipid vesicles, increasing the proportion of 3adLPG from 28 to 51 mol% completely inhibited the adoption of the membrane-active ?-helical conformation of the peptide, without the need for full headgroup ionization. Neutron reflectivity measurements performed on biomimetic PG/3adLPG fluid floating bilayers, showed a significant ordering effect of mild acidity on a bilayer containing 30 mol% 3adLPG, whilst peptide binding/partitioning was only fully inhibited in a bilayer with 55 mol% 3adLPG at pH 5.5. These findings are discussed with respect to the roles of LPG in resistance to human epithelial defences in S. aureus and the continued evolution of this opportunistic pathogen’s virulence

Soot reduction in diesel engines by catalytic effects

Recent tests at Brookhaven National Laboratory indicate that both small additions of alcohols to the fuel and the presence of platinum surfaces in the combustion chamber can reduce soot emissions in a diesel engine. These tests were conducted over a limited range of operation in a single cylinder CFR engine. Most of the testing was done using pure cetane as a fuel at constant speed and load. Possible major features of the reaction mechanisms for both fuel additives and surface catalyst effectiveness are presented

Variation in the upstream region of P-Selectin (SELP) is a risk factor for SLE

Systemic lupus erythematosus (SLE) is a complex autoimmune disease. Genome-wide linkage studies implicated a region containing the adhesion molecule P-Selectin. This family-based study revealed two regions of association within P-Selectin. The strongest signal, from a 21.4-kb risk haplotype, stretched from the promoter into the first two consensus repeat (CR) regions (P=8 × 10−4), with a second association from a 14.6-kb protective haplotype covering CR 2–9 (P=0.0198). The risk haplotype is tagged by the rare C allele of rs3753306, which disrupts the binding site of the trans-activating transcription factor HNF-1. One other variant (rs3917687) on the risk haplotype was significant after permutation (P10000<1 × 10−5), replicated in independent pseudo case-control analysis and was significant by meta-analysis (P=4.37 × 10−6). A third associated variant on the risk haplotype (rs3917657) replicated in 306 US SLE families and was significant in a joint UK-SLE data set after permutation. The protective haplotype is tagged by rs6133 (a non-synonymous variant in CR8 (P=9.00 × 10−4), which also shows association in the pseudo case-control analysis (P=1.09 × 10−3) and may contribute to another signal in P-Selectin. We propose that polymorphism in the upstream region may reduce expression of P-Selectin, the mechanism by which this promotes autoimmunity is unknown, although it may reduce the production of regulatory T cells

Laplaciens de graphes infinis I Graphes m\'etriquement complets

We introduce the weighted graph Laplacian and the notion of Schr\"odinger operator on a locally finite weighted graph . Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant weight. The main result in this work states that on any metrically complete weighted graph with bounded degree, the Laplacian is essentially self-adjoint and the same holds for the Schr\"odinger operator provided the associated quadratic form is bounded from below. We construct for the proof a strictly positive and harmonic function which allows us to write any Schr\"odinger operator as a weighted graph Laplacian modulo a unitary transform

Determination of the QCD color factor ratio CA/CF from the scale dependence of multiplicity in three jet events

I examine the determination of the QCD color factor ratio CA/CF from the scale evolution of particle multiplicity in e+e- three jet events. I fit an analytic expression for the multiplicity in three jet events to event samples generated with QCD multihadronic event generators. I demonstrate that a one parameter fit of CA/CF yields the expected result CA/CF=2.25 in the limit of asymptotically large energies if energy conservation is included in the calculation. In contrast, a two parameter fit of CA/CF and a constant offset to the gluon jet multiplicity, proposed in a recent study, does not yield CA/CF=2.25 in this limit. I apply the one parameter fit method to recently published data of the DELPHI experiment at LEP and determine the effective value of CA/CF from this technique, at the finite energy of the Z0 boson, to be 1.74+-0.03+-0.10, where the first uncertainty is statistical and the second is systematic.Comment: 20 pages including 6 figures Version 2 corrects typographical error in equation (2

Study of bound states in 12Be through low-energy 11Be(d,p)-transfer reactions

The bound states of 12Be have been studied through a 11Be(d,p)12Be transfer reaction experiment in inverse kinematics. A 2.8 MeV/u beam of 11Be was produced using the REX-ISOLDE facility at CERN. The outgoing protons were detected with the T-REX silicon detector array. The MINIBALL germanium array was used to detect gamma rays from the excited states in 12Be. The gamma-ray detection enabled a clear identification of the four known bound states in 12Be, and each of the states has been studied individually. Differential cross sections over a large angular range have been extracted. Spectroscopic factors for each of the states have been determined from DWBA calculations and have been compared to previous experimental and theoretical results