Numerical Integration of the Master Equation in Some Models of Stochastic Epidemiology

The processes by which disease spreads in a population of individuals are inherently stochastic. The master equation has proven to be a useful tool for modeling such processes. Unfortunately, solving the master equation analytically is possible only in limited cases (e.g., when the model is linear), and thus numerical procedures or approximation methods must be employed. Available approximation methods, such as the system size expansion method of van Kampen, may fail to provide reliable solutions, whereas current numerical approaches can induce appreciable computational cost. In this paper, we propose a new numerical technique for solving the master equation. Our method is based on a more informative stochastic process than the population process commonly used in the literature. By exploiting the structure of the master equation governing this process, we develop a novel technique for calculating the exact solution of the master equation – up to a desired precision – in certain models of stochastic epidemiology. We demonstrate the potential of our method by solving the master equation associated with the stochastic SIR epidemic model. MATLAB software that implements the methods discussed in this paper is freely available as Supporting Information S1

Bioavailable iron in the Southern Ocean: the significance of the iceberg conveyor belt

Productivity in the Southern Oceans is iron-limited, and the supply of iron dissolved from aeolian dust is believed to be the main source from outside the marine reservoir. Glacial sediment sources of iron have rarely been considered, as the iron has been assumed to be inert and non-bioavailable. This study demonstrates the presence of potentially bioavailable Fe as ferrihydrite and goethite in nanoparticulate clusters, in sediments collected from icebergs in the Southern Ocean and glaciers on the Antarctic landmass. Nanoparticles in ice can be transported by icebergs away from coastal regions in the Southern Ocean, enabling melting to release bioavailable Fe to the open ocean. The abundance of nanoparticulate iron has been measured by an ascorbate extraction. This data indicates that the fluxes of bioavailable iron supplied to the Southern Ocean from aeolian dust (0.01–0.13 Tg yr-1) and icebergs (0.06–0.12 Tg yr-1) are comparable. Increases in iceberg production thus have the capacity to increase productivity and this newly identified negative feedback may help to mitigate fossil fuel emissions

Energetic Selection of Topology in Ferredoxins

Models of early protein evolution posit the existence of short peptides that bound metals and ions and served as transporters, membranes or catalysts. The Cys-X-X-Cys-X-X-Cys heptapeptide located within bacterial ferredoxins, enclosing an Fe4S4 metal center, is an attractive candidate for such an early peptide. Ferredoxins are ancient proteins and the simple α+β fold is found alone or as a domain in larger proteins throughout all three kingdoms of life. Previous analyses of the heptapeptide conformation in experimentally determined ferredoxin structures revealed a pervasive right-handed topology, despite the fact that the Fe4S4 cluster is achiral. Conformational enumeration of a model CGGCGGC heptapeptide bound to a cubane iron-sulfur cluster indicates both left-handed and right-handed folds could exist and have comparable stabilities. However, only the natural ferredoxin topology provides a significant network of backbone-to-cluster hydrogen bonds that would stabilize the metal-peptide complex. The optimal peptide configuration (alternating αL,αR) is that of an α-sheet, providing an additional mechanism where oligomerization could stabilize the peptide and facilitate iron-sulfur cluster binding

Ligand-Induced Modulation of the Free-Energy Landscape of G Protein-Coupled Receptors Explored by Adaptive Biasing Techniques

Extensive experimental information supports the formation of ligand-specific conformations of G protein-coupled receptors (GPCRs) as a possible molecular basis for their functional selectivity for signaling pathways. Taking advantage of the recently published inactive and active crystal structures of GPCRs, we have implemented an all-atom computational strategy that combines different adaptive biasing techniques to identify ligand-specific conformations along pre-determined activation pathways. Using the prototypic GPCR β2-adrenergic receptor as a suitable test case for validation, we show that ligands with different efficacies (either inverse agonists, neutral antagonists, or agonists) modulate the free-energy landscape of the receptor by shifting the conformational equilibrium towards active or inactive conformations depending on their elicited physiological response. Notably, we provide for the first time a quantitative description of the thermodynamics of the receptor in an explicit atomistic environment, which accounts for the receptor basal activity and the stabilization of different active-like states by differently potent agonists. Structural inspection of these metastable states reveals unique conformations of the receptor that may have been difficult to retrieve experimentally

Treatment of advanced, recurrent, resistant to previous treatments basal and squamous cell skin carcinomas with a synergistic formulation of interferons. Open, prospective study

<p>Abstract</p> <p>Background</p> <p>Aggressive non-melanoma skin cancer (deeply infiltrating, recurrent, and morphea form lesions) are therapeutically challenging because they require considerable tissue loss and may demand radical disfiguring surgery. Interferons (IFN) may provide a non-surgical approach to the management of these tumors. The aim of this work was to evaluate the effect of a formulation containing IFNs-α and -γ in synergistic proportions on patients with recurrent, advanced basal cell (BCC) or squamous cell skin carcinomas (SCSC).</p> <p>Methods</p> <p>Patients with extensive, recurrent, resistant to other procedures BCC or SCSC received the IFN formulation peri- and intralesionally, three times per week for 3 weeks. They had been previously treated with surgery and/or radiotherapy or chemotherapy. Thirteen weeks after the end of treatment, the original lesion sites were examined for histological evidence of remaining tumor.</p> <p>Results</p> <p>Sixteen elder (median 70 years-old) patients were included. They beared 12 BCC and 4 SCSC ranging from 1.5 to 12.5 cm in the longest dimension. At the end of treatment 47% CR (complete tumor elimination), 40% PR (>30% tumor reduction), and 13% stable disease were obtained. None of the patients relapsed during the treatment period. The median duration of the response was 38 months. Only one patient with complete response had relapsed until today. Principal adverse reactions were influenza-like symptoms well known to occur with interferon therapy, which were well tolerated.</p> <p>Conclusion</p> <p>The peri- and intralesional combination of IFNs-α and -γ was safe and showed effect for the treatment of advanced, recurrent and resistant to previous treatments of BCC and SCSC in elder patients. This is the first report of such treatment in patients with advance non-melanoma skin cancer. The encouraging result justifies further confirmatory trials.</p> <p>Trial registration</p> <p>Current Controlled Trials RPCEC00000052.</p

The Contribution of Occult Precipitation to Nutrient Deposition on the West Coast of South Africa

The Strandveld mediterranean-ecosystem of the west coast of South Africa supports floristically diverse vegetation growing on mostly nutrient-poor aeolian sands and extending from the Atlantic Ocean tens of kilometers inland. The cold Benguela current upwelling interacts with warm onshore southerly winds in summer causing coastal fogs in this region. We hypothesized that fog and other forms of occult precipitation contribute moisture and nutrients to the vegetation. We measured occult precipitation over one year along a transect running inland in the direction of the prevailing wind and compared the nutrient concentrations with those in rainwater. Occult deposition rates of P, N, K, Mg, Ca, Na, Al and Fe all decreased with distance from the ocean. Furthermore, ratios of cations to Na were similar to those of seawater, suggesting a marine origin for these. In contrast, N and P ratios in occult precipitation were higher than in seawater. We speculate that this is due to marine foam contributing to occult precipitation. Nutrient loss in leaf litter from dominant shrub species was measured to indicate nutrient demand. We estimated that occult precipitation could meet the demand of the dominant shrubby species for annual N, P, K and Ca. Of these species, those with small leaves intercepted more moisture and nutrients than those with larger leaves and could take up foliar deposits of glycine, NO3-, NH4 + and Li (as tracer for K) through leaf surfaces. We conclude that occult deposition together with rainfall deposition are potentially important nutrient and moisture sources for the Strandveld vegetation that contribute to this vegetation being floristically distinct from neighbouring nutrient-poor Fynbos vegetation

Inactivation of a Single Copy of Crebbp Selectively Alters Pre-mRNA Processing in Mouse Hematopoietic Stem Cells

Global expression analysis of fetal liver hematopoietic stem cells (FL HSCs) revealed the presence of unspliced pre-mRNA for a number of genes in normal FL HSCs. In a subset of these genes, Crebbp+/− FL HSCs had less unprocessed pre-mRNA without a corresponding reduction in total mRNA levels. Among the genes thus identified were the key regulators of HSC function Itga4, Msi2 and Tcf4. A similar but much weaker effect was apparent in Ep300+/− FL HSCs, indicating that, in this context as in others, the two paralogs are not interchangeable. As a group, the down-regulated intronic probe sets could discriminate adult HSCs from more mature cell types, suggesting that the underlying mechanism is regulated with differentiation stage and is active in both fetal and adult hematopoiesis. Consistent with increased myelopoiesis in Crebbp hemizygous mice, targeted reduction of CREBBP abundance by shRNA in the multipotent EML cell line triggered spontaneous myeloid differentiation in the absence of the normally required inductive signals. In addition, differences in protein levels between phenotypically distinct EML subpopulations were better predicted by taking into account not only the total mRNA signal but also the amount of unspliced message present. CREBBP thus appears to selectively influence the timing and degree of pre-mRNA processing of genes essential for HSC regulation and thereby has the potential to alter subsequent cell fate decisions in HSCs

Single-Molecule Force Spectroscopy: Experiments, Analysis, and Simulations

International audienceThe mechanical properties of cells and of subcellular components are important to obtain a mechanistic molecular understanding of biological processes. The quantification of mechanical resistance of cells and biomolecules using biophysical methods matured thanks to the development of nanotechnologies such as optical and magnetic tweezers, the biomembrane force probe and atomic force microscopy (AFM). The quantitative nature of force spectroscopy measurements has converted AFM into a valuable tool in biophysics. Force spectroscopy allows the determination of the forces required to unfold protein domains and to disrupt individual receptor/ligand bonds. Molecular simulation as a computational microscope allows investigation of similar biological processes with an atomistic detail. In this chapter, we first provide a step-by-step protocol of force spectroscopy including sample preparation, measurement and analysis of force spectroscopy using AFM and its interpretation in terms of available theories. Next, we present the background for molecular dynamics (MD) simulations focusing on steered molecular dynamics (SMD) and the importance of bridging of computational tools with experimental technique