Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Dual-process action of exercise on appetite control : increase in orexigenic drive but improvement in meal-induced satiety

Background: Exercise could contribute to weight loss by altering the sensitivity of the appetite regulatory system. Objective: The aim of this study was to assess the effects of 12 wk of mandatory exercise on appetite control. Design: Fifty-eight overweight and obese men and women [mean (±SD) body mass index (in kg/m2) = 31.8 ± 4.5, age = 39.6 ± 9.8 y, and maximal oxygen intake = 29.1 ± 5.7 mL · kg–1 · min–1] completed 12 wk of supervised exercise in the laboratory. The exercise sessions were designed to expend 2500 kcal/wk. Subjective appetite sensations and the satiating efficiency of a fixed breakfast were compared at baseline (week 0) and at week 12. An Electronic Appetite Rating System was used to measure subjective appetite sensations immediately before and after the fixed breakfast in the immediate postprandial period and across the whole day. The satiety quotient of the breakfast was determined by calculating the change in appetite scores relative to the breakfast's energy content. Results: Despite large variability, there was a significant reduction in mean body weight (3.2 ± 3.6 kg), fat mass (3.2 ± 2.2 kg), and waist circumference (5.0 ± 3.2 cm) after 12 wk. The analysis showed that a reduction in body weight and body composition was accompanied by an increase in fasting hunger and in average hunger across the day (P < 0.0001). Paradoxically, the immediate and delayed satiety quotient of the breakfast also increased significantly (P < 0.05). Conclusions: These data show that the effect of exercise on appetite regulation involves at least 2 processes: an increase in the overall (orexigenic) drive to eat and a concomitant increase in the satiating efficiency of a fixed meal.

The Revised Transactional Model (RTM) of occupational stress and coping : an improved process approach

Despite more than three decades of research, there is a limited understanding of the transactional processes of appraisal, stress and coping. This has led to calls for more focused research on the entire process that underlies these variables. To date, there remains a paucity of such research. The present study examined Lazarus and Folkman’s (1984) transactional model of stress and coping. One hundred and twenty nine Australian participants with full time employment (i.e. nurses and administration employees) were recruited. There were 49 male (age mean = 34, SD = 10.51) and 80 female (age mean = 36, SD = 10.31) participants. The analysis of three path models indicated that in addition to the original paths, which were found in Lazarus and Folkman’s transactional model (primary appraisal-->secondary appraisal-->stress-->coping), there were also direct links between primary appraisal and stress level time one and between stress level time one to stress level time two. This study has provided additional insights into the transactional process which will extend our understanding of how individuals appraise, cope and experience occupational stress.

Recovery-based practice: do we know what we mean or mean what we know?

The concept of recovery is now widely promoted as the guiding principle for the provision of mental health services in Australia and overseas. While there is increasing pressure on service providers to ensure that services are recovery oriented, the way in which recovery-based practice is operationalized at the coalface presents a number of challenges. These are discussed in the context of five key questions that address (i) the appropriateness of recovery as a focus for service delivery, (ii) the distinction between recovery as a process and an outcome, (iii) the assessment of recovery initiatives, (iv) the alignment of recovery with current service delivery models, and (v) the risks associated with recovery-based practice. It is argued that these questions provide a framework for a debate that must extend beyond patients and providers of mental health services to the broader public, whose attitudes will ultimately determine the possibilities and limits of recovery-oriented practice.

Mean-field descriptions of collective migration with strong adhesion

Random walk models based on an exclusion process with contact effects are often used to represent collective migration where individual agents are affected by agent-to-agent adhesion. Traditional mean field representations of these processes take the form of a nonlinear diffusion equation which, for strong adhesion, does not predict the averaged discrete behavior. We propose an alternative suite of mean-field representations, showing that collective migration with strong adhesion can be accurately represented using a moment closure approach.

Estimating the effects of environmental exposures using a weighted mean of monitoring stations

The health effects of environmental hazards are often examined using time series of the association between a daily response variable (e.g., death) and a daily level of exposure (e.g., temperature). Exposures are usually the average from a network of stations. This gives each station equal importance, and negates the opportunity for some stations to be better measures of exposure. We used a Bayesian hierarchical model that weighted stations using random variables between zero and one. We compared the weighted estimates to the standard model using data on health outcomes (deaths and hospital admissions) and exposures (air pollution and temperature) in Brisbane, Australia. The improvements in model fit were relatively small, and the estimated health effects of pollution were similar using either the standard or weighted estimates. Spatial weighted exposures would be probably more worthwhile when there is either greater spatial detail in the health outcome, or a greater spatial variation in exposure.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Incorporating spatial correlations into multispecies mean-field models

In biology, we frequently observe different species existing within the same environment. For example, there are many cell types in a tumour, or different animal species may occupy a given habitat. In modelling interactions between such species, we often make use of the mean field approximation, whereby spatial correlations between the locations of individuals are neglected. Whilst this approximation holds in certain situations, this is not always the case, and care must be taken to ensure the mean field approximation is only used in appropriate settings. In circumstances where the mean field approximation is unsuitable we need to include information on the spatial distributions of individuals, which is not a simple task. In this paper we provide a method that overcomes many of the failures of the mean field approximation for an on-lattice volume-excluding birth-death-movement process with multiple species. We explicitly take into account spatial information on the distribution of individuals by including partial differential equation descriptions of lattice site occupancy correlations. We demonstrate how to derive these equations for the multi-species case, and show results specific to a two-species problem. We compare averaged discrete results to both the mean field approximation and our improved method which incorporates spatial correlations. We note that the mean field approximation fails dramatically in some cases, predicting very different behaviour from that seen upon averaging multiple realisations of the discrete system. In contrast, our improved method provides excellent agreement with the averaged discrete behaviour in all cases, thus providing a more reliable modelling framework. Furthermore, our method is tractable as the resulting partial differential equations can be solved efficiently using standard numerical techniques.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Low-phosporous nickel-coated carbon microcoils : Controlling microstructure through an electroless plating process

Carbon microcoils (CMCs) have been coated with a nickel-phosphorus (Ni-P) film using an electroless plating process, with sodium hypophosphite as a reducing agent in an alkaline bath. CMC composites have potential applications as microwave absorption materials. The morphology, elemental composition and phases in the coating layer of the CMCs and Ni-coated CMCs were investigated by scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD), respectively. The effects of process parameters such as pH, temperature and coating time of the plating bath on the phosphorus content and deposition rate of the electroless Ni-P coating were studied. The results revealed that a continuous, uniform and low-phosphorous nickel coating was deposited on the surface of the CMCs for 20 min at pH 9.0, plating bath temperature 70 °C. The as-deposited coatings with approximately 4.5 wt.% phosphorus were found to consist of a mix of nano- and microcrystalline phases. The mean particle size of Ni-P nanoparticles on the outer surface of the CMCs was around 11.9 nm. The deposition rate was found to moderately increase with increasing pH, whereas, the phosphorous content of the deposit exhibited a significant decrease. Moreover, the material of the coating underwent a phase transition between an amorphous and a crystalline structure. The thickness of the deposit and the deposition rate may be controlled through careful variation of the coating time and plating bath temperature.

Process considerations related to the microencapsulation of plasmid DNA via ultrasonic atomization

An effective means of facilitating DNA vaccine delivery to antigen presenting cells is through biodegradable microspheres. Microspheres offer distinct advantages over other delivery technologies by providing release of DNA vaccine in its bioactive form in a controlled fashion. In this study, biodegradable poly(D,L-lactide-coglycolide) (PLGA) microspheres containing polyethylenimine (PEI) condensed plasmid DNA (pDNA) were prepared using a 40 kHz ultrasonic atomization system. Process synthesis parameters, which are important to the scale-up of microspheres that are suitable for nasal delivery (i.e., less than 20 μm), were studied. These parameters include polymer concentration; feed flowrate; volumetric ratio of polymer and pDNA-PEI (plasmid DNA-polyethylenimine) complexes; and nitrogen to phosphorous (N/P) ratio. PDNA encapsulation efficiencies were predominantly in the range 82-96%, and the mean sizes of the particle were between 6 and 15 μm. The ultrasonic synthesis method was shown to have excellent reproducibility. PEI affected morphology of the microspheres, as it induced the formation of porous particles that accelerate the release rate of pDNA. The PLGA microspheres displayed an in vitro release of pDNA of 95-99% within 30 days and demonstrated zero order release kinetics without an initial spike of pDNA. Agarose electrophoresis confirmed conservation of the supercoiled form of pDNA throughout the synthesis and in vitro release stages. It was concluded that ultrasonic atomization is an efficient technique to overcome the key obstacles in scaling-up the manufacture of encapsulated vaccine for clinical trials and ultimately, commercial applications.

The effect of using different regions of interest on local and mean skin temperature

The dynamic nature of tissue temperature and the subcutaneous properties, such as blood flow, fatness, and metabolic rate, leads to variation in local skin temperature. Therefore, we investigated the effects of using multiple regions of interest when calculating weighted mean skin temperature from four local sites. Twenty-six healthy males completed a single trial in a thermonetural laboratory (mean ± SD): 24.0 (1.2) °C; 56 (8%) relative humidity; < 0.1 m/s air speed). Mean skin temperature was calculated from four local sites (neck, scapula, hand and shin) in accordance with International Standards using digital infrared thermography. A 50 x 50 mm square, defined by strips of aluminium tape, created six unique regions of interest, top left quadrant, top right quadrant, bottom left quadrant, bottom right quadrant, centre quadrant and the entire region of interest, at each of the local sites. The largest potential error in weighted mean skin temperature was calculated using a combination of a) the coolest and b) the warmest regions of interest at each of the local sites. Significant differences between the six regions interest were observed at the neck (P < 0.01), scapula (P < 0.001) and shin (P < 0.05); but not at the hand (P = 0.482). The largest difference (± SEM) at each site was as follows: neck 0.2 (0.1) °C; scapula 0.2 (0.0) °C; shin 0.1 (0.0) °C and hand 0.1 (0.1) °C. The largest potential error (mean ± SD) in weighted mean skin temperature was 0.4 (0.1) °C (P < 0.001) and the associated 95% limits of agreement for these differences was 0.2 to 0.5 °C. Although we observed differences in local and mean skin temperature based on the region of interest employed, these differences were minimal and are not considered physiologically meaningful.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations