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A probabilistic modeling approach in thermal inactivation: estimation of postprocess Bacillus cereus spore prevalence and concentration.

The survival of spore-forming bacteria is linked to the safety and stability of refrigerated processed foods of extended durability (REPFEDs). A probabilistic modeling approach was used to assess the prevalence and concentration of Bacillus cereus spores surviving heat treatment for a semiliquid chilled food product. This product received heat treatment to inactivate nonproteolytic Clostridium botulinum during manufacture and was designed to be kept at refrigerator temperature postmanufacture. As key inputs for the modeling, the assessment took into consideration the following factors: (i) contamination frequency (prevalence) and level (concentration) of both psychrotrophic and mesophilic strains of B. cereus, (ii) heat resistance of both types (expressed as decimal reduction times at 90 degrees C), and (iii) intrapouch variability of thermal kinetics during heat processing (expressed as the time spent at 90 degrees C). These three inputs were established as statistical distributions using expert opinion, literature data, and specific modeling, respectively. They were analyzed in a probabilistic model in which the outputs, expressed as distributions as well, were the proportion of the contaminated pouches (the likely prevalence) and the number of spores in the contaminated pouches (the likely concentration). The prevalence after thermal processing was estimated to be 11 and 49% for psychrotrophic and mesophilic strains, respectively. In the positive pouches, the bacterial concentration (considering psychrotrophic and mesophilic strains combined) was estimated to be 30 CFU/g (95th percentile). Such a probabilistic approach seems promising to help in (i) optimizing heat processes, (ii) identifying which key factor(s) to control, and (iii) providing information for subsequent assessment of B. cereus resuscitation and growth.

Bacillus cereus↗

Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities. We compare the predictions of the probabilistic model with those of a deterministic model, and show how a deterministic approach can yield some inaccurate results; e.g., it cannot account for temporally continuous cell attach mentor detachment, it can underestimate the time needed for cell attachment, it can overestimate the time required for cell detachment for a given level of force, and it can overestimate the force necessary for cell detachment.

Biophysical Phenomena↗

The international normalized ratio and uncertainty. Validation of a probabilistic model.

The motivation behind the creation of the International Normalized Ratio (INR) was to improve interlaboratory comparison for patients on anticoagulation therapy. In principle, a laboratory that reports the prothrombin time (PT) as an INR can standardize its PT measurements to an international reference thromboplastin. Using probability theory, the authors derived the equation for the probability distribution of the INR based on the PT, the International Sensitivity Index (ISI), and the geometric mean PT of the reference population. With Monte Carlo and numeric integration techniques, the model is validated on data from three different laboratories. The model allows computation of confidence intervals for the INR as a function of PT, ISI, and reference mean. The probabilistic model illustrates that confidence in INR measurements degrades for higher INR values. This occurs primarily as a result of amplification of between-run measurement errors in the PT, which is inherent in the mathematical transformation from the PT to the INR. The probabilistic model can be used by any laboratory to study the reliability of its own INR for any measured PT. This framework provides better insight into the problems of monitoring oral anticoagulation.

Evaluation Studies as Topic↗

A probabilistic model of gaze imitation and shared attention.

An important component of language acquisition and cognitive learning is gaze imitation. Infants as young as one year of age can follow the gaze of an adult to determine the object the adult is focusing on. The ability to follow gaze is a precursor to shared attention, wherein two or more agents simultaneously focus their attention on a single object in the environment. Shared attention is a necessary skill for many complex, natural forms of learning, including learning based on imitation. This paper presents a probabilistic model of gaze imitation and shared attention that is inspired by Meltzoff and Moore's AIM model for imitation in infants. Our model combines a probabilistic algorithm for estimating gaze vectors with bottom-up saliency maps of visual scenes to produce maximum a posteriori (MAP) estimates of objects being looked at by an observed instructor. We test our model using a robotic system involving a pan-tilt camera head and show that combining saliency maps with gaze estimates leads to greater accuracy than using gaze alone. We additionally show that the system can learn instructor-specific probability distributions over objects, leading to increasing gaze accuracy over successive interactions with the instructor. Our results provide further support for probabilistic models of imitation and suggest new ways of implementing robotic systems that can interact with humans over an extended period of time.

Attention↗

[Probabilistic models to analyze psychiatric contacts].

OBJECTIVE: To present three probabilistic models (Poisson, negative binomial, Waring) to analyze the distribution of the number of contacts of patients followed using a psychiatric case register. DESIGN: Longitudinal to obtain the distribution of the number of contacts (during 91 days following that of the first contact) observed on patients followed using the South-Verona Psychiatric Case Register during the period 1/1/79-31/12/91. RESULTS: There were a total number of 6913 contacts on 3454 subjects. The chi-square test for the goodness of fit yields a significant result both for the Poisson distribution (3580 with 6 degrees of freedom, p < 0.001) and for the negative binomial distribution (65.47 with 18 degrees of freedom, p < 0.001); on the other hand a non significant result was obtained for the Waring distribution (25.31 with 19 degrees of freedom, p = 0.151). CONCLUSIONS: The Poisson distribution gave a very poor fit for the distribution of contacts. The negative binomial distribution could be employed to analyze the pattern of contacts when the right tail of the distribution is not important. The Waring distribution is the best of the three presented. Moreover, the variance of the Waring distribution can be decomposed in three components: a random component, a component which accounts for endogenous factors and another component which accounts for esogenous factors. Therefore the Waring distribution is useful when one wants to make comparisons between psychiatric case registers of the same country or of different countries.

Humans↗

A probabilistic model for detecting coding regions in DNA sequences.

A probabilistic model is presented to predict whether or not an anonymous sequence of DNA contains exons. The method is shown to be at least as reliable as Grail, a well-known neural network solution to the problem, and to be significantly more amenable to customization for specific prediction problems.

Base Sequence↗

An example to illustrate the potential use of probabilistic modelling to estimate operator exposure to pesticides.

To illustrate the potential for probabilistic simulation modelling of operator exposure a probabilistic model was constructed using the draft EUROPOEM II database. The model also incorporated actual pesticide use data. Although the EUROPOEM II database is not complete, and the resulting simulation has to be regarded as only provisional, the data were sufficient to illustrate some of the principles involved. The model was constructed using non-parametric empirical input distributions. Associations were observed in the input exposure data and were reflected in the model. The exposure and usage data were all variable and showed highly negatively skewed distributions and the technique avoided concerns about having to define single representative values for point estimates. Increasing the number of iterations improved the stability of the output, but as expected, resulted in higher exposures being predicted due to a combination of rare events. Analysis of the inputs for individual iterations giving high results indicated that, in this example, these were due to unrepresentatively high input values for inhalation exposure. Simulations that excluded these values were more stable and showed lower exposures, illustrating the need to ensure the validity of the input distributions.

Databases, Factual↗

Validation of a probabilistic model of dietary exposure to selected pesticides in Dutch infants.

A probabilistic model for dietary exposure to pesticides was validated. For this, we evaluated the agreement of dietary exposure to six pesticides as estimated with the model with exposures measured in duplicate diet samples (='real intake') and those calculated with the point estimate. To calculate the exposure with the model and point estimate, consumption data of the duplicate diet survey and pesticide residue measurements from Dutch monitoring programmes in 2000 and 2001 were used. The model was considered validated when the outcome was both higher than the real intake and lower than the point estimate. Results showed that exposures estimated with the model were closer to the real intake than those of the point estimate, and that the model outcome was lower than the point estimate. Furthermore, it was shown that the probabilistic approach can address the exposure to a pesticide via the consumption of different food products, while the point estimate only estimates the exposure through the consumption of one product. The model validated is a valuable asset when estimating the dietary exposure to pesticides in both the authorization of new pesticides and the evaluation of exposures using monitoring data.

Diet↗

An integrated probabilistic model for functional prediction of proteins.

We develop an integrated probabilistic model to combine protein physical interactions, genetic interactions, highly correlated gene expression networks, protein complex data, and domain structures of individual proteins to predict protein functions. The model is an extension of our previous model for protein function prediction based on Markovian random field theory. The model is flexible in that other protein pairwise relationship information and features of individual proteins can be easily incorporated. Two features distinguish the integrated approach from other available methods for protein function prediction. One is that the integrated approach uses all available sources of information with different weights for different sources of data. It is a global approach that takes the whole network into consideration. The second feature is that the posterior probability that a protein has the function of interest is assigned. The posterior probability indicates how confident we are about assigning the function to the protein. We apply our integrated approach to predict functions of yeast proteins based upon MIPS protein function classifications and upon the interaction networks based on MIPS physical and genetic interactions, gene expression profiles, tandem affinity purification (TAP) protein complex data, and protein domain information. We study the recall and precision of the integrated approach using different sources of information by the leave-one-out approach. In contrast to using MIPS physical interactions only, the integrated approach combining all of the information increases the recall from 57% to 87% when the precision is set at 57%-an increase of 30%.

Computational Biology↗

Probabilistic models of the role of oxygen in human decompression sickness.

Probabilistic models of human decompression sickness (DCS) have been successful in describing DCS risk observed across a wide variety of N2-O2 dives but have failed to account for the observed DCS incidence in dives with high PO2 during decompression. Our most successful previous model, calibrated with 3,322 N2-O2 dives, predicts only 40% of the observed incidence in dives with 100% O2 breathing during decompression. We added 1,013 O2 decompression dives to the calibration data. Fitting the prior model to this expanded data set resulted in only a modest improvement in DCS prediction of O2 data. Therefore, two O2-specific modifications were proposed: PO2-based alteration of inert gas kinetics (model 1) and PO2 contribution to total inert gas (model 2). Both modifications statistically significantly improved the fit, and each predicts 90% of the observed DCS incidence in O2 dives. The success of models 1 and 2 in improving prediction of DCS occurrence suggests that elevated PO2 levels contribute to DCS risk, although less than the equivalent amount of N2. Both models allow rational optimization of O2 use in accelerating decompression procedures.

Air Pressure↗

Probabilistic models of cognition: conceptual foundations.

Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, 'sophisticated' probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of the approach, explore how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today.

Algorithms↗

Introduction to the Monte Carlo project and the approach to the validation of probabilistic models of dietary exposure to selected food chemicals.

The Monte Carlo project was established to allow an international collaborative effort to define conceptual models for food chemical and nutrient exposure, to define and validate the software code to govern these models, to provide new or reconstructed databases for validation studies, and to use the new software code to complete validation modelling. Models were considered valid when they provided exposure estimates (e(a)) that could be shown not to underestimate the true exposure (e(b)), but at the same time are more realistic than the currently used conservative estimates (e(c)). Thus, validation required e(b) </= e(a)<e(c). In the case of pesticides, validation involved the collection of duplicate diets from 500 infants for pesticide analysis. In the case of intense sweeteners, a new consumption dataset was created among prescreened high consumers of intense sweeteners by recording, at brand level, all foods and beverages ingested over 12 days. In the case of nutrients and additives, existing databases were modified to minimize uncertainty over the model parameters. In most instances, it was possible to generate probabilistic models that fulfilled the validation criteria.

Diet↗

Dynamic probabilistic model for determination of optimal timing of surveillance chest radiography in pediatric Hodgkin disease.

A dynamic probabilistic model based on hazard rate analysis, Monte Carlo modeling, and lead-time estimation techniques was developed to determine the optimal timing and frequency of chest radiography in the monitoring for relapse of children with treated Hodgkin disease. The analysis incorporates the performance characteristics of chest radiography, the natural history of the disease process, and therapeutic efficacy as a function of earliness of detection in the determination of optimal strategy. Examples of the model applied to the experiences of Stanford Medical Center and St. Jude Children's Research Hospital illustrate the utility of such a model in customizing an optimal monitoring strategy for a specific institution and clinical experience. The results suggest that monitoring protocols significantly overutilize chest radiography in the evaluation for recurrent Hodgkin disease in children.

Child↗

Probabilistic modeling of oxygen transport in brain tissue.

A three-dimensional model of a subregion of the microcirculation was developed. The model employed parallel probabilistic distributions of reaction and convection of oxygen. A Green's function solution to oxygen transport in this system was derived and applied in a series of dynamic solutions on a minicomputer. Results include the transient response of oxygen tension at grid points throughout the system and a correlation of the oxygen demand and surplus supply. Results clearly represent anticipated oxygen partial pressure behavior trends of a countercurrent flow system and in pertinent ways compared favorably with the results obtained by previous investigators. The technique is conservative and employs from 2,000 to 3,600 time steps to achieve precision of seven significant figures. Excellent stability was observed as well. The simulation provides a reliable means to represent the transient response of oxygen partial pressure in a three-dimensional system. Case studies show effects of changing arterial oxygen partial pressure as well as the importance in this system of the convection of dissolved oxygen. It is concluded that the system adequately simulates the anticipated broad profiles of a probabilistically distributed system and provides a rather original insight into neuronal viability through a correlation of oxygen supply and demand. Adaptation of such a complex, dynamic, three-dimensional stimulation to a minicomputer is a step toward simulation of more sophisticated geometries.

Animals↗

Experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems.

The paper deals with an experimental validation of a nonparametric probabilistic model of nonhomogeneous uncertainties for dynamical systems. The theory used, recently introduced, allows model uncertainties and data uncertainties to be simultaneously taken into account. An experiment devoted to this validation was specifically developed. The experimental model is constituted of two simple dural rectangular plates connected together with a complex joint. In the mean mechanical model, the complex joint, which is constituted of two additional plates attached with 40 screw-bolts, is modeled by a homogeneous orthotropic continuous plate with constant thickness, as usual. Consequently, the mean model introduces a region (the joint) which has a high level of uncertainties. The objective of the paper is to present the experiment and the comparisons of the theoretical prediction with the experiments.

Journal Article↗

A probabilistic model for the establishment of neuron polarity.

The main aim of this paper is to present a simple probabilistic model for the early stage of neuron growth: the specification on an axon out of several initially similar neurites. The model is a Markov process with competition between the growing neurites, wherein longer objects have more chances to grow, and parameter alpha determines the intensity of the competition. For alpha > 1 the model provides results which are qualitatively similar to the experimental ones, i.e. selection of one rapidly elongating axon out of several neurites while other less successful neurites stop growing at some random time. Rigorous mathematical proofs are given.

Cell Polarity↗

Analysis of glycosidase-catalyzed transglycosylation reaction using probabilistic model.

General mechanism of transglycosylation reaction by glycosidases contains branched paths to form and destroy the glycosylated intermediate. The probabilistic model was applied for the simulation and analysis of the transglycosylation mechanism. The model is composed of a single enzyme molecule and finite amounts of substrates and water molecules mimicking the possible smallest enzyme-catalyzed reaction system in a microcompartment. Using random numbers and probabilities, progress of distribution of reactants and products can be simulated and predicted with minimum adjustable parameters. Experimental data of beta-xylosidase and beta-glucosidase reactions were quantitatively analyzed with the simple scheme. Since the algorithm and simulation procedures are simple, the model is applicable to related complicated enzyme mechanisms containing many branched reaction paths.

Algorithms↗