Chichia Chiu

Depression and Plasma Amyloid β Peptides in the Elderly With and Without the Apolipoprotein E4 Allele

Depression associated with low plasma amyloid-β peptide 42 (Aβ42) leading to a high ratio of Aβ40/Aβ42, a biomarker of Alzheimer disease (AD), may represent a unique depression subtype. The relationship between low plasma Aβ42 in depression and the major risk factor of AD, apolipoprotein E4 (ApoE4), is unknown. With the goal of clarifying this relationship, we analyzed 1060 homebound elders with ApoE characterization and depression status in a cross-sectional study. Plasma Aβ40 and Aβ42 were measured, and cognition were evaluated. In the absence of the ApoE4 allele, depressed subjects had lower plasma Aβ42 [median (Q1, Q3): 17.1 (11.6, 27.8) vs. 20.2 (12.9, 32.9) pg/mL, P=0.006], a higher Aβ40/Aβ42 ratio [median (Q1, Q3): 7.1 (4.6, 11.3) vs. 6.9 (3.4, 9.7), P=0.03], and lower cognitive function (mean±SD of Mini-Mental State Examination: 24.5±3.1 vs. 25.5±3.3, P<0.0001) than those without depression. In contrast, these relationships were not observed in the presence of ApoE4. Instead, regardless the depression status ApoE4 carriers had lower plasma Aβ42 and a higher Aβ40/Aβ42 ratio than non-ApoE4 carriers. Using multivariate logistic regression, it was found that depression was not associated with ApoE4 allele, but with the interaction between plasma Aβ42 and ApoE4 (odds ratio=3.94, 95% confidence interval=1.50, 10.33, P=0.005), denoting low plasma Aβ42 in the absence of ApoE4. Both ApoE4 carriers and non-ApoE4 carriers with depression had lower Aβ42 and a higher Aβ40/Aβ42 ratio in plasma compared with non-ApoE4 carriers without depression in the homebound elderly. As a combination of low plasma Aβ42 and high plasma Aβ40 has been shown to increase the risk of AD in 2 large cohort studies, amyloid-associated depression shown in this study may suggest a risk factor of AD in the absence of ApoE4.

Error estimates of the Markov finite approximation of the Frobenius-Perron operator

IN THE practical application of the modern ergodic theory, one of the main problems is related to the computation of the absolutely continuous invariant measures for nonsingular transformations on measure spaces (see Lasota and Mackey [l]). A simple example is constructed in Li [2] to show that the round-off error can completely dominate the calculation if one is to compute the invariant measure directly using a sequence of Cesaro sums. An alternative is to compute the invariant density function for the Frobenius-Perron operator P,: L’(0, 1) + L’(0, 1) associated with the nonsingular measurable transformations S: [0, 11 + [0, 11. The Frobenius-Perron operator P, is defined by

Modeling microbial chemotaxis in a diffusion gradient chamber

The diffusion gradient chamber (DGC) has proven to be a useful experimental tool for studying population-level microbial growth and chemotaxis. A mathematical model capable of reproducing the population-level patterns formed as a result of cellular growth and chemotaxis in the DGC has been developed. The model consists of coupled partial differential balance equations for cells, chemoattractants, and a nutrient, which are solved simultaneously by the alternating direction implicit method. Modeling simulation results were compared with population-level migration patterns of Escherichia coli growing on glycerol and responding to a gradient of the chemoattractant aspartate for two different initial conditions. To accurately reproduce the experimental results, a second chemoattractant equation was necessary. The second chemoattractant has been identified as oxygen by directly measuring oxygen gradients in the DGC. Important trends observed experimentally and reproduced by the model include the formation of a chemotactic wave, a reduction in the wave velocity as it encounters higher chemoattractant concentrations, and chemotaxis in response to two different chemoattractants simultaneously. The model was also used to study the relative magnitude of cell fluxes due to random motility and chemotaxis, and the suppression of chemotaxis due to receptor saturation.

Soluble Electron Shuttles Can Mediate Energy Taxis toward Insoluble Electron Acceptors

Shewanella species grow in widely disparate environments and play key roles in elemental cycling, especially in environments with varied redox conditions. To obtain a system-level understanding of Shewanellas robustness and versatility, the complex interplay of cellular growth, metabolism, and transport under conditions of limiting carbon sources, energy sources, and electron acceptors must be elucidated. In this paper, population-level taxis of Shewanella oneidensis MR-1 cells in the presence of a rate-limiting, insoluble electron acceptor was investigated. A novel mechanism, mediated energy taxis, is proposed by which Shewanella use riboflavin as both an electron shuttle and an attractant to direct cell movement toward local sources of insoluble electron acceptors. The cells secrete reduced riboflavin, which diffuses to a nearby particle containing an insoluble electron acceptor and is oxidized. The oxidized riboflavin then diffuses away from the particle, establishing a spatial gradient that draws cells toward the particle. Experimental and modeling results are presented to support this mechanism. S. oneidensis MR-1 cells inoculated into a uniform dispersion of MnO(2) particles in dilute agar exhibited taxis outward, creating a clear zone within which riboflavin was detected by mass spectrometry. Cells inoculated into dilute agar containing oxidized riboflavin similarly exhibited taxis, rapidly forming an expanding zone of reduced riboflavin. A mathematical model based on the proposed mechanism was able to predict experimental trends, including how concentrations of riboflavin and insoluble electron acceptors (e.g., MnO(2)) affected tactic cell migration.

Image Processing and Analysis for Quantifying Gene Expression from Early Drosophila Embryos

Correlation of quantities of transcriptional activators and repressors with the mRNA output of target genes is a central issue for modeling gene regulation. In multicellular organisms, both spatial and temporal differences in gene expression must be taken into account; this can be achieved by use of in situ hybridization followed by confocal laser scanning microscopy (CLSM). Here we present a method to correlate the protein levels of the short-range repressor Giant with lacZ mRNA produced by reporter genes using images of Drosophila blastoderm embryos taken by CLSM. The image stacks from CLSM are processed using a semiautomatic algorithm to produce correlations between the repressor levels and lacZ mRNA reporter genes. We show that signals derived from CLSM are proportional to actual mRNA levels. Our analysis reveals that a suggested parabolic form of the background fluorescence in confocal images of early Drosophila embryos is evident most prominently in flattened specimens, with intact embryos exhibiting a more linear background. The data extraction described in this paper is primarily conceived for analysis of synthetic reporter genes that are designed to decipher cis-regulatory grammar, but the techniques are generalizable for quantitative analysis of other engineered or endogenous genes in embryos.

TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS

High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a Drosophila gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the models simulated data. Where protein and cis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.

An ADI Method for Hysteretic Reaction-Diffusion Systems

In this paper we consider a mathematical model motivated by patterned growth of bacterial cells. The model is a system of differential equations that consists of two subsystems. One is a system of ordinary differential equations and the other is a reaction-diffusion system. An alternating-direction implicit (ADI) method is derived for numerically solving the system. The ADI method given here is different from the usual ADI schemes for parabolic equations due to the special treatment of nonlinear reaction terms in the system. Stability and convergence of the ADI method are proved. We apply these results to the numerical solution of a problem in microbiology.

Analysis and computer simulation of accretion patterns in bacterial cultures

Patterned growth of bacteria created by interactions between the cells and moving gradients of nutrients and chemical buffers is observed frequently in laboratory experiments on agar pour plates. This has been investigated by several microbiologists and mathematicians usually focusing on some hysteretic mechanism, such as dependence of cell uptake kinetics on pH. We show here that a simpler mechanism, one based on cell torpor, can explain patterned growth. In particular, we suppose that the cell population comprises two subpopulations —one actively growing and the other inactive. Cells can switch between the two populations depending on the quality of their environment (nutrient availability, pH, etc.) We formulate here a model of this system, derive and analyze numerical schemes for solving it, and present several computer simulations of the system that illustrate various patterns formed. These compare favorably with observed experiments.

Nonlinear age-dependent models for prediction of population growth

In this paper, some new algorithms are proposed to estimate parameter functions in nonlinear age-dependent population models by practical data. These algorithms together with a numerical method are applied to compute the human population using the data provided by the United Nations Demographic Yearbook.

Optimal one-stage and two-stage schemes for steady state solutions of hyperbolic equations

Abstract Chiu, C., Optimal one-stage and two-stage schemes for steady state solutions of hyperbolic equations, Applied Numerical Mathematics 11 (1993) 475–496. In this paper, we consider finding steady state approximations to hyperbolic equations by solving the related ODE systems using spatial discretization. An optimal one-stage scheme is derived based on the particular distribution pattern of eigenvalues of the spatial discretization matrix. An optimal two-stage method is then designed based on a geometric closure of the eigenvalues and the results from the one-stage method. The applications of these methods include but are not limited to solving nonsymmetric linear systems.