Orientational exchange approach to fluorescence anisotropy decay.

Fluorescence depolarization is a powerful technique in resolving dynamics of molecular systems. Data obtained in fluorescence depolarization experiments are highly complex. Mathematical models for analyzing data from depolarization due to rotational motion have been largely based on the rotational diffusion equation. These results have been verified by Monte Carlo simulations. It has been implicitly stated that a 90 degrees jump model between predefined orientations such as presented by G. Weber (1971. J. Chem. Phys. 55:2399-2411) should, for the specific case of fluorescence depolarization, give the same answer as the diffusion equation. Since the highly symmetric cases considered by G. Weber gave the same result as the diffusion equation, it has been desirable to use this method in cases where depolarization arises from both discrete processes and rotational diffusion. We have derived, in a compartmental formalism, the general result for excitation and emission dipoles not necessarily coincident with any of the principal rotational axes of the fluorophore from this exchange model, and have found it to be different from that of the diffusion equation approach. We have also verified this difference with a Monte Carlo simulation of our exchange model. This derivation allows us to define the limits of validity of the 90 degrees exchanges to model rotational diffusion. Also, for systems where movements may be jumps between a few preferred orientations, the actual physical mechanism of depolarization may not be accurately represented by continuous diffusion. The compartmental formalism developed here can be used to easily combine rotational motions with discrete position jumps or other level kinetics.(ABSTRACT TRUNCATED AT 250 WORDS)     

Single-particle tracking: the distribution of diffusion coefficients.

In single-particle tracking experiments, the diffusion coefficient D may be measured from the trajectory of an individual particle in the cell membrane. The statistical distribution of single-trajectory diffusion coefficients is examined by Monte Carlo calculations. The width of this distribution may be useful as a measure of the heterogeneity of the membrane and as a test of models of hindered diffusion in the membrane. For some models, the distribution of the short-range diffusion coefficient is much narrower than the observed distribution for proteins diffusing in cell membranes. To aid in the analysis of single-particle tracking measurements, the distribution of D is examined for various definitions of D and for various trajectory lengths.     

Stochastic models for cell motion and taxis

Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. Directional cell motion in response to a stimulus, termed taxis, has previously been modeled at a phenomenological level using the Keller-Segel diffusion equation. The Keller-Segel model cannot distinguish certain modes of taxis, and this motivates the introduction of a richer class of models which is nevertheless still amenable to statistical analysis. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation via maximum likelihood for a range of applicable models. One particular experimental situation, involving the effect of an electric field on cell behavior, is considered in detail. In this case, an Ornstein- Uhlenbeck model for cell velocity is found to compare favorably with a nonlinear diffusion model.     

A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.     

Semiparametric Transformation Models with Time‐Varying Coefficients for Recurrent and Terminal Events

Summary In this article, we propose a family of semiparametric transformation models with time‐varying coefficients for recurrent event data in the presence of a terminal event such as death. The new model offers great flexibility in formulating the effects of covariates on the mean functions of the recurrent events among survivors at a given time. For the inference on the proposed models, a class of estimating equations is developed and asymptotic properties of the resulting estimators are established. In addition, a lack‐of‐fit test is provided for assessing the adequacy of the model, and some tests are presented for investigating whether or not covariate effects vary with time. The finite‐sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is also illustrated.     

Checking semiparametric transformation models with censored data

Semiparametric transformation models provide a very general framework for studying the effects of (possibly time-dependent) covariates on survival time and recurrent event times. Assessing the adequacy of these models is an important task because model misspecification affects the validity of inference and the accuracy of prediction. In this paper, we introduce appropriate time-dependent residuals for these models and consider the cumulative sums of the residuals. Under the assumed model, the cumulative sum processes converge weakly to zero-mean Gaussian processes whose distributions can be approximated through Monte Carlo simulation. These results enable one to assess, both graphically and numerically, how unusual the observed residual patterns are in reference to their null distributions. The residual patterns can also be used to determine the nature of model misspecification. Extensive simulation studies demonstrate that the proposed methods perform well in practical situations. Three medical studies are provided for illustrations.     

An evolutionary Monte Carlo algorithm for predicting DNA hybridization

Many DNA-based technologies, such as DNA computing, DNA nanoassembly and DNA biochips, rely on DNA hybridization reactions. Previous hybridization models have focused on macroscopic reactions between two DNA strands at the sequence level. Here, we propose a novel population-based Monte Carlo algorithm that simulates a microscopic model of reacting DNA molecules. The algorithm uses two essential thermodynamic quantities of DNA molecules: the binding energy of bound DNA strands and the entropy of unbound strands. Using this evolutionary Monte Carlo method, we obtain a minimum free energy configuration in the equilibrium state. We applied this method to a logical reasoning problem and compared the simulation results with the experimental results of the wet-lab DNA experiments performed subsequently. Our simulation predicted the experimental results quantitatively.     

Exploring the Dynamics of Cell Processes through Simulations of Fluorescence Microscopy Experiments

Fluorescence correlation spectroscopy (FCS) methods are powerful tools for unveiling the dynamical organization of cells. For simple cases, such as molecules passively moving in a homogeneous media, FCS analysis yields analytical functions that can be fitted to the experimental data to recover the phenomenological rate parameters. Unfortunately, many dynamical processes in cells do not follow these simple models, and in many instances it is not possible to obtain an analytical function through a theoretical analysis of a more complex model. In such cases, experimental analysis can be combined with Monte Carlo simulations to aid in interpretation of the data. In response to this need, we developed a method called FERNET (Fluorescence Emission Recipes and Numerical routines Toolkit) based on Monte Carlo simulations and the MCell-Blender platform, which was designed to treat the reaction-diffusion problem under realistic scenarios. This method enables us to set complex geometries of the simulation space, distribute molecules among different compartments, and define interspecies reactions with selected kinetic constants, diffusion coefficients, and species brightness. We apply this method to simulate single- and multiple-point FCS, photon-counting histogram analysis, raster image correlation spectroscopy, and two-color fluorescence cross-correlation spectroscopy. We believe that this new program could be very useful for predicting and understanding the output of fluorescence microscopy experiments.     

Hemoglobin affinity for 2,3-bisphosphoglycerate in solutions and intact erythrocytes: studies using pulsed-field gradient nuclear magnetic resonance and Monte Carlo simulations.

The diffusion coefficient (D) of 2,3-bisphosphoglycerate (DPG) was measured using pulsed-field gradient (PFG)-31P nuclear magnetic resonance spectroscopy in solutions containing 2.7-5.0 mM hemoglobin (Hb) and a range of DPG concentrations. The dependence of the measured values of D on the fraction of the total DPG in the sample that is bound to Hb enabled the estimation of the dissociation constants (Kd) of complexes of DPG with carbonmonoxygenated, oxygenated, and deoxygenated Hb; the values of Kd (mM), measured at 25 degrees C, pH 6.9 and in 100 mM bis Tris/50 mM KCl, were 1.98 +/- 0.26, 1.8 +/- 0.5 and 0.39 +/- 0.26, respectively. In intact erythrocytes the apparent diffusion coefficient, Dapp, of DPG was larger in oxygenated and carbonmonoxygenated cells (6.17 +/- 0.20 x 10(-11) m2s-1) than in deoxygenated cells (4.10 +/- 0.23 x 10(-11) m2s-1). Changes in intracellular DPG concentration (5-55 mM) in erythrocytes, brought about by incubation in a medium containing inosine and pyruvate, did not result in significant changes in the value of Dapp; this result supports the hypothesis that DPG binds to other sites in the erythrocyte. Monte Carlo simulations of diffusion in biconcave discs were used to test the adequacy of the values of Kd estimated in solution to describe the binding of DPG to Hb in oxygenated and deoxygenated erythrocytes. The results of the simulations implied that the value of Kd estimated for deoxygenated Hb-DPG was greater than expected from the experiments involving intact erythrocytes. This difference is surmised to be at least partly due to the difficulty of measuring D at low-ligand concentrations. Notwithstanding this shortcoming, the PFG method appears to be suitable for probing interactions between macromolecules and ligands when the Kd is in the millimolar range. It is one of the few techniques available in which these interactions can be studied in intact cells. In addition, the Monte Carlo simulations of the diffusion experiments highlighted important differences between theory and experiment relating to the nature of molecular motion inside the cells.     

Stochastic effects in intercellular calcium spiking in hepatocytes

We carry out a Monte Carlo simulation of stochastic effects for two models of intercellular calcium wave propagation in rat hepatocytes. Both models involve gap junction diffusion by a second messenger. We find that, in general, the stochastic effects improve agreement with experiment, for a reasonable choice of model parameters. Both stochastic models exhibit baseline fluctuations and variations in the peak heights of Ca(2+). In addition, we find for one model that there is a distribution of latency times, rather than a single latency time, with a distribution width which is comparable to the experimental observation of spike widths. We also find for the other model with low gap junction diffusion that it is possible for cell multiplets to oscillate independently initially, but to subsequently become synchronized.     

Variance-based sensitivity analysis of biological uncertainties in carbon ion therapy

PurposeBiological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2) are needed for treatment planning and plan evaluation in carbon ion therapy. We present a model-independent, Monte Carlo based sensitivity analysis (SA) approach to quantify the impact of different uncertainties on the biological models.Methods and materialsThe Monte Carlo based SA is used for the evaluation of variations in biological parameters. The key property of this SA is the high number of simulation runs, each with randomized input parameters, allowing for a statistical variance-based ranking of the input variations. The potential of this SA is shown in a simplified one-dimensional treatment plan optimization. Physical properties of carbon ion beams (e.g. fragmentation) are simulated using the Monte Carlo code FLUKA. To estimate biological effects of ion beams compared to X-rays, we use the Local Effect Model (LEM) in the framework of the linear-quadratic (LQ) model. Currently, only uncertainties in the output of the biological models are taken into account.Results/conclusionsThe presented SA is suitable for evaluation of the impact of variations in biological parameters. Major advantages are the possibility to access and display the sensitivity of the evaluated quantity on several parameter variations at the same time. Main challenges for later use in three-dimensional treatment plan evaluation are computational time and memory usage. The presented SA can be performed with any analytical or numerical function and hence be applied to any biological model used in carbon ion therapy.     

Non-exponential tolerance to infection in epidemic systems--modeling, inference, and assessment

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.     

A General Monte Carlo Method for Mapping Multiple Quantitative Trait Loci

In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm for fitting multiple-QTL models to such data. Implementation of this algorithm is straightforward in standard statistical software, but computation may take much time. The method may be generalized to cope with more complex models for animal and human pedigrees. A practical example is presented, where a three-QTL model is adopted in an outbreeding situation with dominant markers. The example is concerned with the linkage between randomly amplified polymorphic DNA (RAPD) markers and QTLs for partial resistance to Fusarium oxysporum in lily.     

Parallel Markov chain Monte Carlo - bridging the gap to high-performance Bayesian computation in animal breeding and genetics

Background

Most Bayesian models for the analysis of complex traits are not analytically tractable and inferences are based on computationally intensive techniques. This is true of Bayesian models for genome-enabled selection, which uses whole-genome molecular data to predict the genetic merit of candidate animals for breeding purposes. In this regard, parallel computing can overcome the bottlenecks that can arise from series computing. Hence, a major goal of the present study is to bridge the gap to high-performance Bayesian computation in the context of animal breeding and genetics.

Results

Parallel Monte Carlo Markov chain algorithms and strategies are described in the context of animal breeding and genetics. Parallel Monte Carlo algorithms are introduced as a starting point including their applications to computing single-parameter and certain multiple-parameter models. Then, two basic approaches for parallel Markov chain Monte Carlo are described: one aims at parallelization within a single chain; the other is based on running multiple chains, yet some variants are discussed as well. Features and strategies of the parallel Markov chain Monte Carlo are illustrated using real data, including a large beef cattle dataset with 50K SNP genotypes.

Conclusions

Parallel Markov chain Monte Carlo algorithms are useful for computing complex Bayesian models, which does not only lead to a dramatic speedup in computing but can also be used to optimize model parameters in complex Bayesian models. Hence, we anticipate that use of parallel Markov chain Monte Carlo will have a profound impact on revolutionizing the computational tools for genomic selection programs.     

A Monte Carlo method for combined segregation and linkage analysis.

We introduce a Monte Carlo approach to combined segregation and linkage analysis of a quantitative trait observed in an extended pedigree. In conjunction with the Monte Carlo method of likelihood-ratio evaluation proposed by Thompson and Guo, the method provides for estimation and hypothesis testing. The greatest attraction of this approach is its ability to handle complex genetic models and large pedigrees. Two examples illustrate the practicality of the method. One is of simulated data on a large pedigree; the other is a reanalysis of published data previously analyzed by other methods.     

Analysis of Yield-Density Models for Intercropping Experiments

Yield density models are used to describe the relationship between the yield of one or more crops and densities of planting. In this paper, we propose a correlated error structure for a linear yield-density model for intercopping and competition experiments. Four possible estimators of the parameters of the error structure are evaluated using a Monte Carlo study. The estimators are compared on the basis of gain in efficiency as measured by the generalized variance. An example is provided.     

Growth of yeast on n-alkanes. II. Batch experiments

In this paper the results of the Monte Carlo simulations as described in an earlier paper are compared with those of batch experiments. A number of batch experiments were carried out at a low inoculation rate so that only a fraction of the oil drops were inoculated. Under these conditions the effect of the segregation of the oil phase is more clearly demonstrated. Special attention is paid to the preparation of actively growing yeast cells with which the cultures is inoculated. Also a method is developed to estimate the amount of actively growing cells with which the culture is inoculated. The other parameters necessary for the Monte Carlo simulation are measured in separate experiments: the maximum growth rate of the cells, oil drop size, and the drop parameters. Finally the growth curves (measured in the batch experiments) are compared with those calculated with the Monte Carlo procedure. A good agreement is found.     

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

Summary We propose a Bayesian chi‐squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi‐squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222–230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.