Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Development and Application of Covalent-Labeling Strategies for the Large-Scale Thermodynamic Analysis of Protein Folding and Ligand Binding

Thermodynamic stability measurements on proteins and protein-ligand complexes can offer insights not only into the fundamental properties of protein folding reactions and protein functions, but also into the development of protein-directed therapeutic agents to combat disease. Conventional calorimetric or spectroscopic approaches for measuring protein stability typically require large amounts of purified protein. This requirement has precluded their use in proteomic applications. Stability of Proteins from Rates of Oxidation (SPROX) is a recently developed mass spectrometry-based approach for proteome-wide thermodynamic stability analysis. Since the proteomic coverage of SPROX is fundamentally limited by the detection of methionine-containing peptides, the use of tryptophan-containing peptides was investigated in this dissertation. A new SPROX-like protocol was developed that measured protein folding free energies using the denaturant dependence of the rate at which globally protected tryptophan and methionine residues are modified with dimethyl (2-hydroxyl-5-nitrobenzyl) sulfonium bromide and hydrogen peroxide, respectively. This so-called Hybrid protocol was applied to proteins in yeast and MCF-7 cell lysates and achieved a ~50% increase in proteomic coverage compared to probing only methionine-containing peptides. Subsequently, the Hybrid protocol was successfully utilized to identify and quantify both known and novel protein-ligand interactions in cell lysates. The ligands under study included the well-known Hsp90 inhibitor geldanamycin and the less well-understood omeprazole sulfide that inhibits liver-stage malaria. In addition to protein-small molecule interactions, protein-protein interactions involving Puf6 were investigated using the SPROX technique in comparative thermodynamic analyses performed on wild-type and Puf6-deletion yeast strains. A total of 39 proteins were detected as Puf6 targets and 36 of these targets were previously unknown to interact with Puf6. Finally, to facilitate the SPROX/Hybrid data analysis process and minimize human errors, a Bayesian algorithm was developed for transition midpoint assignment. In summary, the work in this dissertation expanded the scope of SPROX and evaluated the use of SPROX/Hybrid protocols for characterizing protein-ligand interactions in complex biological mixtures.

Thermodynamic analysis of ligand-induced changes in protein thermal unfolding applied to high-throughput determination of ligand affinities with extrinsic fluorescent dyes.

The quantification of protein-ligand interactions is essential for systems biology, drug discovery, and bioengineering. Ligand-induced changes in protein thermal stability provide a general, quantifiable signature of binding and may be monitored with dyes such as Sypro Orange (SO), which increase their fluorescence emission intensities upon interaction with the unfolded protein. This method is an experimentally straightforward, economical, and high-throughput approach for observing thermal melts using commonly available real-time polymerase chain reaction instrumentation. However, quantitative analysis requires careful consideration of the dye-mediated reporting mechanism and the underlying thermodynamic model. We determine affinity constants by analysis of ligand-mediated shifts in melting-temperature midpoint values. Ligand affinity is determined in a ligand titration series from shifts in free energies of stability at a common reference temperature. Thermodynamic parameters are obtained by fitting the inverse first derivative of the experimental signal reporting on thermal denaturation with equations that incorporate linear or nonlinear baseline models. We apply these methods to fit protein melts monitored with SO that exhibit prominent nonlinear post-transition baselines. SO can perturb the equilibria on which it is reporting. We analyze cases in which the ligand binds to both the native and denatured state or to the native state only and cases in which protein:ligand stoichiometry needs to treated explicitly.

The Emergence of Access Controls in Small-Scale Fishing Commons: A Comparative Analysis of Individual Licenses and Common Property-Rights in Two Mexican Communities

Addressing global fisheries overexploitation requires better understanding of how small-scale fishing communities in developing countries limit access to fishing grounds. We analyze the performance of a system based on individual licenses and a common property-rights regime in their ability to generate incentives for self-governance and conservation of fishery resources. Using a qualitative before-after-control-impact approach, we compare two neighbouring fishing communities in the Gulf of California, Mexico. Both were initially governed by the same permit system, are situated in the same ecosystem, use similar harvesting technology, and have overharvested similar species. One community changed to a common property-right regime, enabling the emergence of access controls and avoiding overexploitation of benthic resources, while the other community, still relies on the permit system. We discuss the roles played by power, institutions, socio-historic, and biophysical factors to develop access controls. © 2012 The Author(s).

Integrated pathway and epistasis analysis reveals interactive effect of genetic variants at TERF1 and AFAP1L2 loci on melanoma risk.

Genome-wide association studies (GWASs) have characterized 13 loci associated with melanoma, which only account for a small part of melanoma risk. To identify new genes with too small an effect to be detected individually but which collectively influence melanoma risk and/or show interactive effects, we used a two-step analysis strategy including pathway analysis of genome-wide SNP data, in a first step, and epistasis analysis within significant pathways, in a second step. Pathway analysis, using the gene-set enrichment analysis (GSEA) approach and the gene ontology (GO) database, was applied to the outcomes of MELARISK (3,976 subjects) and MDACC (2,827 subjects) GWASs. Cross-gene SNP-SNP interaction analysis within melanoma-associated GOs was performed using the INTERSNP software. Five GO categories were significantly enriched in genes associated with melanoma (false discovery rate ≤ 5% in both studies): response to light stimulus, regulation of mitotic cell cycle, induction of programmed cell death, cytokine activity and oxidative phosphorylation. Epistasis analysis, within each of the five significant GOs, showed significant evidence for interaction for one SNP pair at TERF1 and AFAP1L2 loci (pmeta-int  = 2.0 × 10(-7) , which met both the pathway and overall multiple-testing corrected thresholds that are equal to 9.8 × 10(-7) and 2.0 × 10(-7) , respectively) and suggestive evidence for another pair involving correlated SNPs at the same loci (pmeta-int  = 3.6 × 10(-6) ). This interaction has important biological relevance given the key role of TERF1 in telomere biology and the reported physical interaction between TERF1 and AFAP1L2 proteins. This finding brings a novel piece of evidence for the emerging role of telomere dysfunction into melanoma development.