Population fluctuation in the system of host-parasite interaction

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Contributions from the Entomological Laboratory, Kyoto University, No. 226.     

Validation of a single-compartment approach to the calculation of secretion rates of ACTH.

A single-compartment model used in this laboratory for continuously calculating ACTH secretion rates from measured plasma ACTH concentrations has been tested for its ability to follow changing rates of ACTH entry (rapid departure from steady state). ACTH was infused at known moderately high but physiological rates into anaesthetized dogs (Nembutal). Under such conditions endogenous secretion is initially less than 5% of infused rates. Orthogonal polynomials (ACTHt) were fitted to plasma ACTH vs. time data. Then secretion ratet = (ACTHt X MCR) + (dACTHt/dt X V) where it was previously shown that the metabolic clearance rate of ACTH (MCR) lacked significant inter-animal or concentration-dependent variation, and its distribution volume (V) was also constant. The calculated ACTH entry rate curves (a) followed a 10-fold increase in infusion rate over 4 min and subsequent rapid decline with a lag of only about 1 min and, despite some blurring, gave an integrated response equal to 94 +/- 5.5% of the known signal, and (b) followed a sinusoidal change in infusion rate (amplitude, 1.7 X base rate; period, 40 min) with a few percent error and negligible lag. These signals imitate (a) an abrupt stress response, and (b) other rapid departures from steady state.     

An indirect approach to the extensive calculation of relationship coefficients

A method was described for calculating population statistics on relationship coefficients without using corresponding individual data. It relied on the structure of the inverse of the numerator relationship matrix between individuals under investigation and ancestors. Computation times were observed on simulated populations and were compared to those incurred with a conventional direct approach. The indirect approach turned out to be very efficient for multiplying the relationship matrix corresponding to planned matings (full design) by any vector. Efficiency was generally still good or very good for calculating statistics on these simulated populations. An extreme implementation of the method is the calculation of inbreeding coefficients themselves. Relative performances of the indirect method were good except when many full-sibs during many generations existed in the population.     

A matrix approach to the theory of biotopological mapping

A method is introduced for using matrices to represent the organism-graphs of Rashevsky's theory of biotopological mapping. The representation is made in such a way as to reveal the structure of these graphs. Using insight gained from the consideration of the matrix representations, a theorem is proved concerning the primordial origins of organisms and counterexamples are displayed to show the necessity of the hypotheses of this theorem.     

Fatigue estimation using a novel multi-fractal detrended fluctuation analysis-based approach

This paper presents a novel multi-fractal detrended fluctuation analysis-based approach for fatigue estimation. This approach exploits the statistical self-similarity and long-range correlation of surface electromyography signals at different time scales in which the myoelectric manifestation of fatigue is more significant compared to the influence of varying force, muscle length (joint angle), and innervation zone. This approach provides a fatigue index which outperforms the conventional median frequency during cyclic and random contractions. This type of analysis is promising an efficient framework for analysis of surface electromyography signals with several potential applications.     

Protein-level fluctuation correlation at the microcolony level and its application to the Vibrio harveyi quorum-sensing circuit

Gene expression is stochastic, and noise that arises from the stochastic nature of biochemical reactions propagates through active regulatory links. Thus, correlations in gene-expression noise can provide information about regulatory links. We present what to our knowledge is a new approach to measure and interpret such correlated fluctuations at the level of single microcolonies, which derive from single cells. We demonstrated this approach mathematically using stochastic modeling, and applied it to experimental time-lapse fluorescence microscopy data. Specifically, we investigated the relationships among LuxO, LuxR, and the small regulatory RNA qrr4 in the model quorum-sensing bacterium Vibrio harveyi. Our results show that LuxR positively regulates the qrr4 promoter. Under our conditions, we find that qrr regulation weakly depends on total LuxO levels and that LuxO autorepression is saturated. We also find evidence that the fluctuations in LuxO levels are dominated by intrinsic noise. We furthermore propose LuxO and LuxR interact at all autoinducer levels via an unknown mechanism. Of importance, our new method of evaluating correlations at the microcolony level is unaffected by partition noise at cell division. Moreover, the method is first-order accurate and requires less effort for data analysis than single-cell-based approaches. This new correlation approach can be applied to other systems to aid analysis of gene regulatory circuits.     

Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix

Correlated multiple testing is widely performed in genetic research, particularly in multilocus analyses of complex diseases. Failure to control appropriately for the effect of multiple testing will either result in a flood of false-positive claims or in true hits being overlooked. Cheverud proposed the idea of adjusting correlated tests as if they were independent, according to an 'effective number' (M(eff)) of independent tests. However, our experience has indicated that Cheverud's estimate of the Meff is overly large and will lead to excessively conservative results. We propose a more accurate estimate of the M(eff), and design M(eff)-based procedures to control the experiment-wise significant level and the false discovery rate. In an evaluation, based on both real and simulated data, the M(eff)-based procedures were able to control the error rate accurately and consequently resulted in a power increase, especially in multilocus analyses. The results confirm that the M(eff) is a useful concept in the error-rate control of correlated tests. With its efficiency and accuracy, the M(eff) method provides an alternative to computationally intensive methods such as the permutation test.     

Assessing individual metabolic responsiveness to a lipid challenge using a targeted metabolomic approach

The development of assessment techniques with immediate clinical applicability is a priority for resolving the growing epidemic in metabolic disease. Many imbalances in diet-dependent metabolism are not detectable in the fasted state. Resolving the high inter-individual variability in response to diet requires the development of techniques that can detect metabolic dysfunction at the level of the individual. The intra- and inter-individual variation in lipid metabolism in response to a standardized test meal was determined. Following an overnight fast on three different days, three healthy subjects consumed a test meal containing 40% of their daily calories. Plasma samples were collected at fasting, and 1, 3, 6, and 8 h after the test meal. Plasma fatty acid (FA) concentrations within separated lipid classes and lipoprotein fractions were measured at each time point. The intra-individual variation within each subject across three days was lower than the inter-individual differences among the three subjects for over 50% of metabolites in the triacylglycerol (TG), FA, and phosphatidylcholine (PC) lipid classes at 6 h, and for 25–50% of metabolites across lipid classes at 0, 1, 3, and 8 h. The consistency of response within individuals was visualized by principal component analysis (PCA) and confirmed by ANOVA. Three representative metabolites that discriminated among the three individuals in the apolipoprotein B (ApoB) fraction, TG16:1n7, TG18:2n6, and PC18:3n3, are discussed in detail. The postprandial responses of individuals were unique within metabolites that were individual discriminators (ID) of metabolic phenotype. This study shows that the targeted metabolomic measurement of individual metabolic phenotype in response to a specially formulated lipid challenge is possible even without lead-in periods, dietary and lifestyle control, or intervention over a 3-month period in healthy free-living individuals.     

Comparison between a phenomenological approach and a morphoelasticity approach regarding the displacement of extracellular matrix

Biomechanics and Modeling in Mechanobiology - Plastic (permanent) deformations were earlier, modeled by a phenomenological model in Peng and Vermolen (Biomech Model Mechanobiol...     

A sparse matrix approach to the solubilization of overexpressed proteins

Many biophysical experiments depend on large amounts of pure, soluble protein. Indeed, the revolution in structural biology has depended on molecular biology's potential to make experiments possible by allowing the overexpression of normally rare proteins in a heterologous host. All too often, however, overexpressed proteins are poorly soluble in buffers that attempt to mimic physiological conditions. Often in such cases the overexpressed protein is assumed to be present in inclusion bodies and hopes of obtaining the desired sample from the overexpression vector are abandoned. We have developed a sparse matrix approach to the solubilization of such proteins that is often successful. This approach relies on well accepted theories of protein solubility and folding to build a sparse matrix that samples 'solubility space' effectively. The buffers of the sparse matrix are used to make crude extracts that are rapidly assayed for soluble protein using gel electrophoresis. We describe our approach and give examples of its application.     

RCMAT: a regularized covariance matrix approach to testing gene sets

Background  

Gene sets are widely used to interpret genome-scale data. Analysis techniques that make better use of the correlation structure of microarray data while addressing practical "n<p" concerns could provide a real increase in power. However correlation structure is hard to estimate with typical genomics sample sizes. In this paper we present an extension of a classical multivariate procedure that confronts this challenge by the use of a regularized covariance matrix.     

A collocation approach to the numerical calculation of simple gradients in reaction-diffusion systems

Reaction diffusion equations are frequently used to model pattern formation problems in biology, but numerical experiments in two or three space dimensions can be expensive in computing time. We show that the spectral method with collocation is a particularly efficient method for the numerical study of the evolution of simple patterns in such models. In many cases of interest, the scheme is sufficiently simple and efficient for calculations to be carried out on a micro-computer.     

The effect of field fluctuation on a macromolecular system.

The Brownian motion of small ions in a solution produces fluctuating electric potential and field. If a molecule put in the solution can assume two states, of which the free energy depends on the field, the state of the molecule fluctuates according to the fluctuating field. The problem is formulated as a reversible reaction in the fluctuating environment. The effect of fluctuation on the rate constants and the average probability of the molecule in each state is estimated. The coupling between fluctuations of the field and the molecule is analysed, taking into consideration the space and time correlation of those fluctuations. Apparent correlation appears between the states of independent molecules in the solution due to the correlating fluctuation of the field around those molecules. The theoretical result is available for estimation of the probability of spontaneous response of the cell membrane without specific input. Special importance of such a field fluctuation is expected in the biological system because of its capacity to amplify and digitalize the effect of fluctuation.     

Determination of metabolic fluxes in a non-steady-state system

Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to calculate fluxes from both mass isotopomer and positional isotopomer labelling information and thus has general applicability to data generated from common spectrometry- or NMR-based analytical platforms. The approach is applied to a GC-MS time-series dataset of (13)C-labelling of metabolites in a heterotrophic Arabidopsis cell suspension culture. Threonine biosynthesis is used to demonstrate that non-steady-state fluxes can be successfully estimated from such data while organic acid metabolism is used to highlight some common issues that can complicate flux estimation. These include multiple pools of the same metabolite that label at different rates and carbon skeleton rearrangements.     

Consistency analysis of metabolic correlation networks

Background  

Metabolic correlation networks are derived from the covariance of metabolites in replicates of metabolomics experiments. They constitute an interesting intermediate between topology (i.e. the system's architecture defined by the set of reactions between metabolites) and dynamics (i.e. the metabolic concentrations observed as fluctuations around steady-state values in the metabolic network).     

Stochastic fractal behavior in concentration fluctuation and fluorescence correlation spectroscopy.

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in two dimensions, but non-singular in three dimensions. This discovery provides one simple physical mechanism for possible long-memory fractal behavior, and its implications to various biological processes are discussed.