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.

Thermodynamic analysis of a molecular chaperone binding to unfolded protein substrates.

Molecular chaperones are a highly diverse group of proteins that recognize and bind unfolded proteins to facilitate protein folding and prevent nonspecific protein aggregation. The mechanisms by which chaperones bind their protein substrates have been studied for decades. However, there are few reports about the affinity of molecular chaperones for their unfolded protein substrates. Thus, little is known about the relative binding affinities of different chaperones and about the relative binding affinities of chaperones for different unfolded protein substrates. Here we describe the application of SUPREX (stability of unpurified proteins from rates of H-D exchange), an H-D exchange and MALDI-based technique, in studying the binding interaction between the molecular chaperone Hsp33 and four different unfolded protein substrates, including citrate synthase, lactate dehydrogenase, malate dehydrogenase, and aldolase. The results of our studies suggest that the cooperativity of the Hsp33 folding-unfolding reaction increases upon binding with denatured protein substrates. This is consistent with the burial of significant hydrophobic surface area in Hsp33 when it interacts with its substrate proteins. The SUPREX-derived K(d) values for Hsp33 complexes with four different substrates were all found to be within the range of 3-300 nM.

Frontal eye field neurons assess visual stability across saccades.

The image on the retina may move because the eyes move, or because something in the visual scene moves. The brain is not fooled by this ambiguity. Even as we make saccades, we are able to detect whether visual objects remain stable or move. Here we test whether this ability to assess visual stability across saccades is present at the single-neuron level in the frontal eye field (FEF), an area that receives both visual input and information about imminent saccades. Our hypothesis was that neurons in the FEF report whether a visual stimulus remains stable or moves as a saccade is made. Monkeys made saccades in the presence of a visual stimulus outside of the receptive field. In some trials, the stimulus remained stable, but in other trials, it moved during the saccade. In every trial, the stimulus occupied the center of the receptive field after the saccade, thus evoking a reafferent visual response. We found that many FEF neurons signaled, in the strength and timing of their reafferent response, whether the stimulus had remained stable or moved. Reafferent responses were tuned for the amount of stimulus translation, and, in accordance with human psychophysics, tuning was better (more prevalent, stronger, and quicker) for stimuli that moved perpendicular, rather than parallel, to the saccade. Tuning was sometimes present as well for nonspatial transaccadic changes (in color, size, or both). Our results indicate that FEF neurons evaluate visual stability during saccades and may be general purpose detectors of transaccadic visual change.

Component-wise gradient boosting and false discovery control in survival analysis with high-dimensional covariates.

MOTIVATION: Technological advances that allow routine identification of high-dimensional risk factors have led to high demand for statistical techniques that enable full utilization of these rich sources of information for genetics studies. Variable selection for censored outcome data as well as control of false discoveries (i.e. inclusion of irrelevant variables) in the presence of high-dimensional predictors present serious challenges. This article develops a computationally feasible method based on boosting and stability selection. Specifically, we modified the component-wise gradient boosting to improve the computational feasibility and introduced random permutation in stability selection for controlling false discoveries. RESULTS: We have proposed a high-dimensional variable selection method by incorporating stability selection to control false discovery. Comparisons between the proposed method and the commonly used univariate and Lasso approaches for variable selection reveal that the proposed method yields fewer false discoveries. The proposed method is applied to study the associations of 2339 common single-nucleotide polymorphisms (SNPs) with overall survival among cutaneous melanoma (CM) patients. The results have confirmed that BRCA2 pathway SNPs are likely to be associated with overall survival, as reported by previous literature. Moreover, we have identified several new Fanconi anemia (FA) pathway SNPs that are likely to modulate survival of CM patients. AVAILABILITY AND IMPLEMENTATION: The related source code and documents are freely available at https://sites.google.com/site/bestumich/issues. CONTACT: yili@umich.edu.