Bayesian Modeling of ChIP‐chip Data Through a High‐Order Ising Model

Summary ChIP‐chip experiments are procedures that combine chromatin immunoprecipitation (ChIP) and DNA microarray (chip) technology to study a variety of biological problems, including protein–DNA interaction, histone modification, and DNA methylation. The most important feature of ChIP‐chip data is that the intensity measurements of probes are spatially correlated because the DNA fragments are hybridized to neighboring probes in the experiments. We propose a simple, but powerful Bayesian hierarchical approach to ChIP‐chip data through an Ising model with high‐order interactions. The proposed method naturally takes into account the intrinsic spatial structure of the data and can be used to analyze data from multiple platforms with different genomic resolutions. The model parameters are estimated using the Gibbs sampler. The proposed method is illustrated using two publicly available data sets from Affymetrix and Agilent platforms, and compared with three alternative Bayesian methods, namely, Bayesian hierarchical model, hierarchical gamma mixture model, and Tilemap hidden Markov model. The numerical results indicate that the proposed method performs as well as the other three methods for the data from Affymetrix tiling arrays, but significantly outperforms the other three methods for the data from Agilent promoter arrays. In addition, we find that the proposed method has better operating characteristics in terms of sensitivities and false discovery rates under various scenarios.     

A model for dispersion experiments

Summary A new model is proposed for the dispersion of animals and other organisms and its use is discussed for the analysis of the data from experiments on dispersion. The model is a generalisation of the random walk model, but because of its flexibility it should be much more widely applicable than the random walk model.The new model has been found to fit the results of many dispersion experiments and examples are given of its use with data for millipedes and Drosophila.     

A Joint Matrix Completion and Filtering Model for Influenza Serological Data Integration

Antigenic characterization based on serological data, such as Hemagglutination Inhibition (HI) assay, is one of the routine procedures for influenza vaccine strain selection. In many cases, it would be impossible to measure all pairwise antigenic correlations between testing antigens and reference antisera in each individual experiment. Thus, we have to combine and integrate the HI tables from a number of individual experiments. Measurements from different experiments may be inconsistent due to different experimental conditions. Consequently we will observe a matrix with missing data and possibly inconsistent measurements. In this paper, we develop a new mathematical model, which we refer to as Joint Matrix Completion and Filtering, for HI data integration. In this approach, we simultaneously handle the incompleteness and uncertainty of observations by assuming that the underlying merged HI data matrix has low rank, as well as carefully modeling different levels of noises in each individual table. An efficient blockwise coordinate descent procedure is developed for optimization. The performance of our approach is validated on synthetic and real influenza datasets. The proposed joint matrix completion and filtering model can be adapted as a general model for biological data integration, targeting data noises and missing values within and across experiments.     

Estimation of coefficients in a model of radiation-induced myelopoiesis from mortality data for mice following X-ray exposure

The rate coefficients in the model of cell kinetics and mortality introduced by Jones et al. (Radiat. Res. 128, 258-266 (1991)) are estimated using mortality data from several mouse experiments. The evaluated model fits data from a large variety of prompt, protracted, and fractionated irradiations with 250-k Vp X rays with good fidelity. Although the maximum-likelihood estimates are not unique, all estimates lead to greater cell survival than that observed in in vitro experiments on nonterminally differentiated reproducing cells from the marrow.     

Role of the Hall flute instability in the interaction of laser and space plasmas with a magnetic field

The interaction of an expanding laser plasma with a uniform external magnetic field is studied over a wide range of experimental parameters (for a plasma energy of up to 300 J and a magnetic induction of up to 8 kG). By analyzing the data from these and other experiments, as well as the results of simulations with the use of a two-fluid Hall plasma model, it was found for the first time that the flute instability of the plasma boundary plays a decisive role in the process of the plasma cloud expansion. It is shown that, when the ion Larmor radius is sufficiently large, this instability can significantly affect the maximum radius of the diamagnetic cavity of the plasma cloud and the deceleration of its front by the magnetic field. A physical model based on the Hall effect is proposed to explain such influence. The model adequately describes data from one-dimensional simulations, as well as from experiments with quasi-spherical laser plasma clouds. The results obtained can be helpful in interpreting the data from active magnetospheric experiments with barium plasma clouds (such as AMPTE) and analyzing the plasma dynamics in future ICF reactors and propulsion systems with a magnetic field for direct conversion of fusion energy into electric energy.     

Mathematical development of a physical model of some visco-elastic properties of the aorta

Visco-elastic properties of blood vessels, the aorta in particular, may be approximated by a suitable arrangement of two elastic rods and one viscous rod. This simple model is readily derived from models already proposed for individual components of the aortic wall: elastin, collagen, and smooth muscle. The model is even consistent with various results ofin vitro experimental data which have previously appeared uncorrelated, or even contradictory. What is more, when elastic and viscous coefficients of the model were calculated from these data, the density of each of the three histological components could be predicted for some specimens. The mathematical development of the model and the agreement with varied experiments justify use of the model for analysis ofin vivo aortic pressure curves in subsequent papers. The development also indicates the need for additional data from some simplein vitro experiments suggested by this analysis. Data from the suggested experiments may support the present model or require some modification of it.     

Bayesian analysis of non-linear differential equation models with application to a gut microbial ecosystem

Process models specified by non-linear dynamic differential equations contain many parameters, which often must be inferred from a limited amount of data. We discuss a hierarchical Bayesian approach combining data from multiple related experiments in a meaningful way, which permits more powerful inference than treating each experiment as independent. The approach is illustrated with a simulation study and example data from experiments replicating the aspects of the human gut microbial ecosystem. A predictive model is obtained that contains prediction uncertainty caused by uncertainty in the parameters, and we extend the model to capture situations of interest that cannot easily be studied experimentally.     

A mathematical model of the nutrient dynamics of phytoplankton in a nitrate-limited environment

Insofar as saturation kinetics are applicable to the growth of phytoplankton in laboratory experiments and to growth in nature, the computer modeling of intracellular nutrient partitioning in populations of cells can lead to better understanding of the dynamics of natural populations. A three-compartment mathematical model was developed to represent a phytoplankton population having the capability to store nitrogen in a nitrate-limited environment. Parameters were estimated by fitting the model to data from two chemostat experiments reported by Caperon (1968). The model was used to simulate growth dynamics observed in chemostat and batch experiments. The model demonstrated the changes which may occur in the nitrogenous constituents of a phytoplankton population with time and environmental conditions. The model also demonstrates three phenomena which have been observed in field and laboratory experiments but which are not represented by the customary Monod model: (1) uptake rates may significantly exceed not growth rates, (2) high growth rates may be encountered at very low environmental nitrate concentrations, and (3) the ratio of internal nitrogen to population size may change significantly during a study period. It is suggested that the amount of nitorgen in storage may be used as an indicator of the physiological state of a monospecific population. Parameters for the one-compartment Monod model were estimated by customary methods form data generated by the three-compartment model. It was shown that difficulties encountered in estimating the yield coefficient and the decay coefficient may be attributed to the intracellular storage phenomenon. It was also demonstrated that the one-compartment Monod model was inadequate to accurately represent population growth in chemostat experiments when intracellular storage is a significant factor.     

Experimental-neuromodeling framework for understanding auditory object processing: integrating data across multiple scales.

In this article, we review a combined experimental-neuromodeling framework for understanding brain function with a specific application to auditory object processing. Within this framework, a model is constructed using the best available experimental data and is used to make predictions. The predictions are verified by conducting specific or directed experiments and the resulting data are matched with the simulated data. The model is refined or tested on new data and generates new predictions. The predictions in turn lead to better-focused experiments. The auditory object processing model was constructed using available neurophysiological and neuroanatomical data from mammalian studies of auditory object processing in the cortex. Auditory objects are brief sounds such as syllables, words, melodic fragments, etc. The model can simultaneously simulate neuronal activity at a columnar level and neuroimaging activity at a systems level while processing frequency-modulated tones in a delayed-match-to-sample task. The simulated neuroimaging activity was quantitatively matched with neuroimaging data obtained from experiments; both the simulations and the experiments used similar tasks, sounds, and other experimental parameters. We then used the model to investigate the neural bases of the auditory continuity illusion, a type of perceptual grouping phenomenon, without changing any of its parameters. Perceptual grouping enables the auditory system to integrate brief, disparate sounds into cohesive perceptual units. The neural mechanisms underlying auditory continuity illusion have not been studied extensively with conventional neuroimaging or electrophysiological techniques. Our modeling results agree with behavioral studies in humans and an electrophysiological study in cats. The results predict a particular set of bottom-up cortical processing mechanisms that implement perceptual grouping, and also attest to the robustness of our model.     

A geometric approach to determine association and coherence of the activation times of cell-cycling genes under differing experimental conditions

Differing arresting agents and protocols can be used to synchronize cells in cultures to specific phases of the cell when studying cell-cycle gene expressions. Often, data derived from individual experiments are analyzed separately, since no appropriate statistical methodology is available at the moment to analyze the data from all such experiments simultaneously. The focus of this paper is to determine the association and coherence of the relative activation times of cell-cycling genes under different experimental conditions. Using a circular-circular regression model, we define two parameters, a rotation parameter for the angular difference between cells' arresting times (phases) in two cell-cycle experiments, and an association parameter to describe the correspondence between the cycle times of maximal expression (phase angles) for a set of genes studied in two experiments. Further, we propose a procedure to assess coherence across multiple experiments, i.e. to what extent the circular ordering of the phase angles of genes is maintained across multiple experiments. Coherence of genes across experiments suggests that functionally these genes tend to respond in a stereotypically sequenced way under different experimental conditions. Our proposed methodology is illustrated by applying it to a HeLa cell-cycle gene-expression data.     

A model for avian lung ventilation, and the effect of accelerating stimulation in Japanese quail embryos

A simple stages model is proposed for the interval between the start of lung ventilation and the start of clicking in Japanese quail embryos. The model is extended to describe the effect of accelerating stimuli and is fitted to data sets from three different experiments. We see that the model provides a useful synthesis of the variety of results, and furnishes a framework for the analysis of further experiments.     

Modeling Facilitative Sugar Transporters: Transitions Between Single and Double Ligand Occupancy of Multiconformational Channel Models Explain Anomalous Kinetics

The four-state simple carrier model (SCM) is employed to describe ligand translocation by diverse passive membrane transporters. However, its application to systems like facilitative sugar transporters (GLUTs) is controversial: unidirectional fluxes under zero-trans and equilibrium-exchange experimental conditions fit a SCM, but flux data from infinite-cis and infinite-trans experiments appear not to fit the same SCM. More complex kinetic models have been proposed to explain this ``anomalous' behavior of GLUTs, but none of them accounts for all the experimental findings. We propose an alternative model in which GLUTs are channels subject to conformational transitions, and further assume that the results from zero-trans and equilibrium-exchange experiments as well as trans-effects corresponds to a single-occupancy channel regime, whereas the results from the infinite-cis and infinite-trans experiments correspond to a regime including higher channel occupancies. We test the plausibility of this hypothesis by studying a kinetic model of a two-site channel with two conformational states. In each state, the channel can bind the ligand from only one of the compartments. Under single-occupancy, for conditions corresponding to zero-trans and equilibrium-exchange experiments, the model behaves as a SCM capable of exhibiting trans-stimulations. For a regime including higher degrees of occupancy and infinite-cis and infinite-trans conditions, the same channel model can exhibit a behavior qualitatively similar to a SCM, albeit with kinetic parameters different from those for the single-occupancy regime. Numerical results obtained with our model are consistent with available experimental data on facilitative glucose transport across erythrocyte membranes. Hence, if GLUTs are multiconformational channels, their particular kinetic properties can result from transitions between single and double channel occupancies. Received: 12 April 1995/Revised: 28 August 1995     

In silico model as a tool for interpretation of intestinal infection studies

In nutrition research the number of human in vivo experiments is limited because of the many restrictions and the high costs of testing in humans. Up to now predictive computer models aiming to enhance research have been rare or too complex, with many nonmeasurable adjustable parameters. This study aimed to develop a basic physicochemical computer model for a first quantitative interpretation of results obtained from in vivo intestinal experiments with bacteria. This new modeling approach is validated with results obtained from gut infection studies in vivo. The design of the model is described, and its ability to reproduce experimental data is evaluated. The model predictions are compared with new experimental data. The phenomena that take place in the gastrointestinal tract are summarized by model constants for growth, adherence, and release of bacteria. Although the model is far from describing all details and many processes in the intestine are combined, the model calculation results lead to reasonable conclusions and interesting hypotheses. One of these hypotheses concluded from the model outcomes is that Escherichia coli bacteria have a much lower intestinal growth rate in humans than in rats. Extra laboratory validation experiments proved the reliability of this hypothesis predicted by the model. In addition, the known protective effect of dietary calcium and detrimental effect of clindamycin on the growth and adherence of Salmonella bacteria could be quantified. From these results it is clear that the model enhances the interpretation of in vivo gastrointestinal experiments and will facilitate research trajectories towards new functional foods that improve resistance to pathogenic bacteria in humans.     

Simultaneous modeling of pharmacokinetics and pharmacodynamics: an improved algorithm

An algorithm and computer program is presented that fits a largelynon-parametric model to pharmacokinetic (PK) and pharmacodynamic(PD) data; it is an extension of a recently proposed approach.A PK model relates dose to plasma concentrations (Cp), a linkmodel relates plasma concentrations to the concentration inthe effect site (C_e), a PD model relates Ce to the effect. Boththe PK and the PD model are non-parametric, but the link modelis parametric. The extension presented here allows modelingof PK/PD data arising from non-steady-state experiments afterarbitrary dosage. In addition, several data sets from the sameindividual (or from different individuals) can now be analyzedsimultaneously, assuming the same link model for all, but allowingeither all the PD models to be the same, or all to be different. Received on March 15, 1987; accepted on July 27, 1987     

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. Current FE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model for brain tissue and implemented it in an explicit FE code. To obtain sufficient numerical accuracy for modeling the nearly incompressible brain tissue, deviatoric and volumetric stress contributions are separated. Deviatoric stress is modeled in a non-linear viscoelastic differential form. Volumetric behavior is assumed linearly elastic. Linear viscoelastic material parameters were derived from published data on oscillatory experiments, and from ultrasonic experiments. Additionally, non-linear parameters were derived from stress relaxation (SR) experiments at shear strains up to 20%. The model was tested by simulating the transient phase in the SR experiments not used in parameter determination (strains up to 20%, strain rates up to 8s(-1)). Both time- and strain-dependent behavior were predicted accurately (R2>0.96) for strain and strain rates applied. However, the stress was overestimated systematically by approximately 31% independent of strain(rate) applied. This is probably caused by limitations of the experimental data at hand.     

In Silico Model as a Tool for Interpretation of Intestinal Infection Studies

In nutrition research the number of human in vivo experiments is limited because of the many restrictions and the high costs of testing in humans. Up to now predictive computer models aiming to enhance research have been rare or too complex, with many nonmeasurable adjustable parameters. This study aimed to develop a basic physicochemical computer model for a first quantitative interpretation of results obtained from in vivo intestinal experiments with bacteria. This new modeling approach is validated with results obtained from gut infection studies in vivo. The design of the model is described, and its ability to reproduce experimental data is evaluated. The model predictions are compared with new experimental data. The phenomena that take place in the gastrointestinal tract are summarized by model constants for growth, adherence, and release of bacteria. Although the model is far from describing all details and many processes in the intestine are combined, the model calculation results lead to reasonable conclusions and interesting hypotheses. One of these hypotheses concluded from the model outcomes is that Escherichia coli bacteria have a much lower intestinal growth rate in humans than in rats. Extra laboratory validation experiments proved the reliability of this hypothesis predicted by the model. In addition, the known protective effect of dietary calcium and detrimental effect of clindamycin on the growth and adherence of Salmonella bacteria could be quantified. From these results it is clear that the model enhances the interpretation of in vivo gastrointestinal experiments and will facilitate research trajectories towards new functional foods that improve resistance to pathogenic bacteria in humans.     

A diverse view of protein dynamics from NMR studies of HIV-1 protease flaps

Internal motion in proteins fulfills a multitude of roles in biological processes. NMR spectroscopy has been applied to elucidate protein dynamics at the atomic level, albeit at a low resolution, and is often complemented by molecular dynamics simulation. However, it is critical to justify the consistency between simulation results and conclusions often drawn from multiple experiments in which uncertainties arising from assumed motional models may not be explicitly evaluated. To understand the role of the flaps of HIV-1 protease dimer in substrate recognition and protease function, many molecular dynamics simulations have been performed. The simulations have resulted in various proposed models of the flap dynamics, some of which are more consistent than others with our working model previously derived from experiments. However, using the working model to discriminate among the simulation results is not straightforward because the working model was derived from a combination of NMR experiments and crystal structure data. In this study, we use the NMR chemical shifts and relaxation data of the protease "monomer" rather than structural data to narrow down the possible conformations of the flaps of the "dimer". For the first time, we show that the tips of the flaps in the unliganded protease dimer interact with each other in solution. Accordingly, we discuss the consistency of the simulations with the model derived from all experimental data.     

Phenomenological model of fungal biofilters for the abatement of hydrophobic VOCs

This work describes the growth of filamentous fungi in biofilters for the degradation of hydrophobic VOCs. The study system was n-hexane and Fusarium solani B1. The system is mathematically described and the main physical, kinetic data and morphological parameters were obtained by independent experiments and validated with data from laboratory experiments. The model describes the increase in the transport area by the growth of the filamentous cylindrical mycelia and its relation with n-hexane elimination in quasi-stationary state in a biofilter. The model describing fungal growth includes Monod-Haldane kinetic and hyphal elongation and ramification. A specific surface area of transport (SSAT) of 1.91 x 10(5) m(2) m(-3) and a maximum elimination capacity (EC) of 248 g m(-3) h(-1) were obtained by the mathematical model simulation, with a 10% of error with respect to the experimental EC.     

RNA folding with soft constraints: reconciliation of probing data and thermodynamic secondary structure prediction

Thermodynamic folding algorithms and structure probing experiments are commonly used to determine the secondary structure of RNAs. Here we propose a formal framework to reconcile information from both prediction algorithms and probing experiments. The thermodynamic energy parameters are adjusted using 'pseudo-energies' to minimize the discrepancy between prediction and experiment. Our framework differs from related approaches that used pseudo-energies in several key aspects. (i) The energy model is only changed when necessary and no adjustments are made if prediction and experiment are consistent. (ii) Pseudo-energies remain biophysically interpretable and hold positional information where experiment and model disagree. (iii) The whole thermodynamic ensemble of structures is considered thus allowing to reconstruct mixtures of suboptimal structures from seemingly contradicting data. (iv) The noise of the energy model and the experimental data is explicitly modeled leading to an intuitive weighting factor through which the problem can be seen as folding with 'soft' constraints of different strength. We present an efficient algorithm to iteratively calculate pseudo-energies within this framework and demonstrate how this approach can be used in combination with SHAPE chemical probing data to improve secondary structure prediction. We further demonstrate that the pseudo-energies correlate with biophysical effects that are known to affect RNA folding such as chemical nucleotide modifications and protein binding.