A hybrid agent-based approach for modeling microbiological systems

Models for systems biology commonly adopt Differential Equations or Agent-Based modeling approaches for simulating the processes as a whole. Models based on differential equations presuppose phenomenological intracellular behavioral mechanisms, while models based on Multi-Agent approach often use directly translated, and quantitatively less precise if-then logical rule constructs. We propose an extendible systems model based on a hybrid agent-based approach where biological cells are modeled as individuals (agents) while molecules are represented by quantities. This hybridization in entity representation entails a combined modeling strategy with agent-based behavioral rules and differential equations, thereby balancing the requirements of extendible model granularity with computational tractability. We demonstrate the efficacy of this approach with models of chemotaxis involving an assay of 10³ cells and 1.2×10⁶ molecules. The model produces cell migration patterns that are comparable to laboratory observations.     

Bayesian Local Influence in Growth Curve Model with Unstructured Covariance

From the Bayesian point of view, a local influence approach is developed to diagnose the adequacy of the growth curve model with an unstructured covariance. Based on the Kullback-Leibler divergence, the Bayesian Hessian matrices of the parameters in the model are studied under an abstract perturbation scheme and the eigenvector associated with the largest eigenvalue of the Hessian matrix is used to identify influential observations. For illustration, the covariance-weighted perturbation, a commonly encountered perturbation, is considered particularly and used to analyze a practical data set. Comparisons with the likelihood-based local influence are also made.     

Model fitting and model testing in the method of joint mapping of quantitative trait loci

A previous paper proposed a new method of QTL mapping called joint mapping (JM). Some problems have been found in model fitting and model testing due to the neglect of the correlations among different observations of the dependent variable in this model. The present paper reports a method of solving the problems. The coefficient of correlation between two observations of the dependent variable is derived. A generalized least square (GLS) approach is developed for model fitting and a strategy and procedure of model testing based on a chi-square test is suggested. A simulated example is given. The example shows that the JM method is quite efficient in mapping multiple linked QTLs.     

Stem cell therapy for ischemic heart disease

Recent experimental and clinical observations have suggested that cell transplantation could be of therapeutic value for the treatment of heart disease. This approach was based on the idea that transplanted donor cardiomyocytes would integrate with the host myocardium and thereby directly contribute to cardiac function. Surprisingly, the observation that non-cardiomyogenic cells could also improve cardiac function indicates that functional integration of donor cells might not be required to achieve a beneficial effect. More recently, several observations have suggested the presence of a greater than anticipated developmental repertoire in adult-derived stem cells, which, if further validated, would offer unprecedented opportunities for the restoration of cardiac function in diseased hearts. Here, we discuss current issues regarding the potential use of stem cell transplantation for the treatment of ischemic heart disease.     

Parameter estimation and sensitivity analysis for batch fermentation of recombinant cells

Summary An interactive scheme for estimating parameters in an unstructured model of a recombinant fermentation process is presented. Sensitivity analysis is simultaneously evaluated in this approach so that the instantaneous influence of parameters on state variables can be inspected. The predicted profiles of fermentation by both the model and the sensitivity analysis based on ±50% variations of the initial concentration of glucose fit the experimental observations.     

A semiparametric mixture cure survival model for left‐truncated and right‐censored data

In follow‐up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left‐truncated and right‐censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum‐likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput‐wall distance event for patients with ankylosing spondylitis.     

Use of zoospore concentrations and life cycle parameters in determining the population of anaerobic fungi in the rumen ecosystem

An indirect approach to quantification of the fibrolytic anaerobic fungi in the rumen is described. A mathematical model of the life cycle of anaerobic fungi, based upon observations of the life histories and growth kinetics of these organisms in vitro and in vivo, is constructed and solved in the steady-state to determine the population of particle-attached (substrate-associated) fungal thalli from the concentration of free-swimming zoospores in rumen liquid. The values obtained are broadly consistent with ruminal observations and with observations on faecal populations, which assume that a significant proportion of fungi leaving the rumen (as cysts or spores) can ultimately be accounted for in the faeces.     

Non-parametric exploratory analysis of the covariance structure for genetic analysis of repeated measures and other function-value traits

In the analysis of longitudinal data, before assuming a parametric model, an idea of the shape of the variance and correlation functions for both the genetic and environmental parts should be known. When a small number of observations is available for each subject at a fixed set of times, it is possible to estimate unstructured covariance matrices, but not when the number of observations over time is large and when individuals are not measured at all times. The non-parametric approach, based on the variogram, presented by Diggle & Verbyla (1998), is specially adapted for exploratory analysis of such data. This paper presents a generalization of their approach to genetic analyses. The methodology is applied to daily records for milk production in dairy cattle and data on age-specific fertility in Drosophila.     

Cytotoxicity of superoxide dismutase 1 in cultured cells is linked to Zn2+ chelation

Neurodegeneration in protein-misfolding disease is generally assigned to toxic function of small, soluble protein aggregates. Largely, these assignments are based on observations of cultured neural cells where the suspect protein material is titrated directly into the growth medium. In the present study, we use this approach to shed light on the cytotoxic action of the metalloenzyme Cu/Zn superoxide dismutase 1 (SOD1), associated with misfolding and aggregation in amyotrophic lateral sclerosis (ALS). The results show, somewhat unexpectedly, that the toxic species of SOD1 in this type of experimental setting is not an aggregate, as typically observed for proteins implicated in other neuro-degenerative diseases, but the folded and fully soluble apo protein. Moreover, we demonstrate that the toxic action of apoSOD1 relies on the protein's ability to chelate Zn(2+) ions from the growth medium. The decreased cell viability that accompanies this extraction is presumably based on disturbed Zn(2+) homeostasis. Consistently, mutations that cause global unfolding of the apoSOD1 molecule or otherwise reduce its Zn(2+) affinity abolish completely the cytotoxic response. So does the addition of surplus Zn(2+). Taken together, these observations point at a case where the toxic response of cultured cells might not be related to human pathology but stems from the intrinsic limitations of a simplified cell model. There are several ways proteins can kill cultured neural cells but all of these need not to be relevant for neurodegenerative disease.     

Application of Multiple Imputation for Missing Values in Three-Way Three-Mode Multi-Environment Trial Data

It is a common occurrence in plant breeding programs to observe missing values in three-way three-mode multi-environment trial (MET) data. We proposed modifications of models for estimating missing observations for these data arrays, and developed a novel approach in terms of hierarchical clustering. Multiple imputation (MI) was used in four ways, multiple agglomerative hierarchical clustering, normal distribution model, normal regression model, and predictive mean match. The later three models used both Bayesian analysis and non-Bayesian analysis, while the first approach used a clustering procedure with randomly selected attributes and assigned real values from the nearest neighbour to the one with missing observations. Different proportions of data entries in six complete datasets were randomly selected to be missing and the MI methods were compared based on the efficiency and accuracy of estimating those values. The results indicated that the models using Bayesian analysis had slightly higher accuracy of estimation performance than those using non-Bayesian analysis but they were more time-consuming. However, the novel approach of multiple agglomerative hierarchical clustering demonstrated the overall best performances.     

Hormone gradients and cartilage cell kinetics

We present a model of growth control in mammalian cartilage growth plates by hormones. The model is based on the distribution of insulin-like growth factors I and II (IGF-I and IGF-II) and their receptors, and assumes that a hormone-receptor complex of IGF controls cells proliferation. A system of differential equations is derived and solved with simplifications in extreme cases, for the one-dimensional time independent case. Even if opposite extremes, such as proliferation control by factors extrinsic to the cell versus intrinsic to the cell, are assumed, similar distributions of hormones and proliferating cells are produced. Hence, choice between alternative models of growth control must be based on empirical observations. On the positive side, similarities between our model for cartilage growth and other models for differentiation and proliferation are evident and might be exploited for unifying these systems on an abstract level.     

Implicit Estimation of Ecological Model Parameters

We introduce an implicit method for state and parameter estimation and apply it to a stochastic ecological model. The method uses an ensemble of particles to approximate the distribution of model solutions and parameters conditioned on noisy observations of the state. For each particle, it first determines likely values based on the observations, then samples around those values. This approach has a strong theoretical foundation, applies to nonlinear models and non-Gaussian distributions, and can estimate any number of model parameters, initial conditions, and model error covariances. The method is called implicit because it updates the particles without forming a predictive distribution of forward model integrations. As a point of comparison for different assimilation techniques, we consider examples in which one or more bifurcations separate the true parameter from its initial approximation. The implicit estimator is asymptotically unbiased, has a root-mean-squared error comparable to or less than the other methods, and is accurate even with small ensemble sizes.     

An efficient multivariate approach for estimating preference when individual observations are dependent

1. We discuss aspects of resource selection based on observing a given vector of resource variables for different individuals at discrete time steps. A new technique for estimating preference of habitat characteristics, applicable when there are multiple individual observations, is proposed. 2. We first show how to estimate preference on the population and individual level when only a single site- or resource component is observed. A variance component model based on normal scores in used to estimate mean preference for the population as well as the heterogeneity among individuals defined by the intra-class correlation. 3. Next, a general technique is proposed for time series of observations of a vector with several components, correcting for the effect of correlations between these. The preference of each single component is analyzed under the assumption of arbitrarily complex selection of the other components. This approach is based on the theory for conditional distributions in the multi-normal model. 4. The method is demonstrated using a data set of radio-tagged dispersing juvenile goshawks and their site characteristics, and can be used as a general tool in resource or habitat selection analysis.     

Sparse kernel methods for high-dimensional survival data

Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be 'kernelized'. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, depending only on a small fraction of the training data. We propose two methods. One is based on a geometric idea, where-akin to support vector classification-the margin between the failed observation and the observations currently at risk is maximised. The other approach is based on obtaining a sparse model by adding observations one after another akin to the Import Vector Machine (IVM). Data examples studied suggest that both methods can outperform competing approaches. AVAILABILITY: Software is available under the GNU Public License as an R package and can be obtained from the first author's website http://www.maths.bris.ac.uk/~maxle/software.html.     

Exact inference for growth curves with intraclass correlation structure

We consider repeated observations taken over time for each of several subjects. For example, one might consider the growth curve of a cohort of babies over time. We assume a simple linear growth curve model. Exact results based on sufficient statistics (exact tests of the null hypothesis that a coefficient is zero, or exact confidence intervals for coefficients) are not available to make inference on regression coefficients when an intraclass correlation structure is assumed. This paper will demonstrate that such exact inference is possible using generalized inference.     

Estimation and Prediction With HIV-Treatment Interruption Data

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.     

Sensitivity analysis for nonrandom dropout: a local influence approach

Diggle and Kenward (1994, Applied Statistics 43, 49-93) proposed a selection model for continuous longitudinal data subject to nonrandom dropout. It has provoked a large debate about the role for such models. The original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests. Since then, the view has emerged that these models should ideally be made part of a sensitivity analysis. This paper presents a formal and flexible approach to such a sensitivity assessment based on local influence (Cook, 1986, Journal of the Royal Statistical Society, Series B 48, 133-169). The influence of perturbing a missing-at-random dropout model in the direction of nonrandom dropout is explored. The method is applied to data from a randomized experiment on the inhibition of testosterone production in rats.     

Hierarchical analysis of wild Atlantic salmon (Salmo salar) fecundity in relation to body size and developmental traits

Using data from wild Atlantic salmon Salmo salar returning to spawn in seven Scottish rivers, we developed a model of fecundity based on individual body size and key developmental traits. We used a novel approach to model selection which maximises predictive accuracy for application to target river stocks to select the best from a suite of Bayesian hierarchical models. This approach aims to ensure the optimal model within the candidate set includes covariates that best predict out-of-sample data to estimate fecundity in areas where no direct observations are available. In addition to body size, the final model included the developmental characteristics of age at smolting and years spent at sea. Using two independent long-term monitoring datasets, the consequences of ignoring these characteristics was revealed by comparing predictions from the best model with models that omitted them.     

What is truth – in science and beyond

Truth is threatened in our societies and one might wish that scientists should stand up for truth, but in order to do so, one needs to know what is truth and how it can be recognized. The oldest and most widely accepted concept of truth is the Correspondence Theory requesting a fit of propositions and reality. In the Coherence Theory truth is a consistent property of a whole system of propositions. In the Pragmatic Theory truth works in practical terms. Scientists have defined criteria to verify true statements by experiments and by the simplicity of theories. Aristotle proposed parsimony claiming the superiority of theories which derive from fewer hypotheses. David Hume suggested probability arguments to assess the force of evidence. Nicolai Hartmann elaborated a model based on the congruence of a priori logical arguments with a posteriori empirical observations. Karl Popper introduced the falsification of testable theories as a way to better theories. The analysis shows that scientific and medical research uses classical philosophical criteria of truth in their daily work. Humanities use different, hermeneutic criteria of truth. Finally, societies need for their coherence a dialectic approach to truth based on honest discussion of opposing views.