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Mathematical tree models for cytogenetic development in solid tumors.

We present a new approach for modeling the occurrence of genetic changes in human tumors over time. In solid tumors, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumor development and progression is assumed to follow a probabilistic tree model. We use maximum likelihood estimation to reconstruct a tree model for the genetic evolution of a given tumor type. The use of the proposed method is illustrated by an application to cytogenetic data from 173 cases of clear cell renal cell carcinoma, which results in a model for the karyotypic evolution of this tumor.

Carcinoma, Renal Cell↗

Cost-utility model of rasagiline in the treatment of advanced Parkinson's disease in Finland.

BACKGROUND: The economic burden of Parkinson's disease (PD) is high, especially in patients experiencing motor fluctuations. Rasagiline has demonstrated efficacy against symptoms of PD in early and advanced stages of the disease. OBJECTIVE: To assess the cost-utility of rasagiline and entacapone as adjunctive therapies to levodopa versus standard levodopa care in PD patients with motor fluctuations in Finland. METHODS: A 2 year probabilistic Markov model with 3 health states: "25% or less off-time/day," "greater than 25% off-time/day," and "dead" was used. Off-time represents time awake with poor or absent motor function. Model inputs included transition probabilities from randomized clinical trials, utilities from a preference measurement study, and costs and resources from a Finnish cost-of-illness study. Effectiveness measures were quality-adjusted life years (QALYs) and number of months spent with 25% or less off-time/day. Uncertainty around parameters was taken into account by Monte Carlo simulations. RESULTS: Over 2 years from a societal perspective, rasagiline or entacapone as adjunctive therapies to levodopa showed greater effectiveness than levodopa alone at no additional costs. Benefits after 2 years were 0.13 (95% CI 0.08 to 0.17) additional QALYs and 5.2 (3.6 to 6.7) additional months for rasagiline and 0.12 (0.08 to 0.17) QALYs and 5.1 (3.5 to 6.6) months for entacapone, both in adjunct to levodopa compared with levodopa alone. CONCLUSIONS: The results of this study support the use of rasagiline and entacapone as adjunctive cost-effective alternatives to levodopa alone in PD patients with motor fluctuations in Finland. With a different mode of action, rasagiline is a valuable therapeutic alternative to entacapone at no additional charge to society.

Antiparkinson Agents↗

Growth, structure and dynamics of real neurons: model studies and experimental results.

One of the most striking features of vertebrate neurons is the immense diversity of their dendritic branching patterns, bearing witness to the range of operations subserved by dendritic membranes. The paper deals with three questions which naturally arise in this context: 1) What kind of growth process leads to a particular branching pattern? 2) How can we quantify such patterns? 3) Is it possible to derive a functional characterization related to the dendritic pattern so quantified? Probabilistic growth models were tested against morphological data derived from experiments with mammalian sensory-motor neurons, and their fractal dimensions were determined. The functionality of the dendritic neuron types was evaluated by electrotonic modelling of the synaptic transfer properties. The results support the hypothesis that a close relationship between dendritic pattern and neuron function might exist. The nonlinear properties of neuronal membranes represent the other determinant of neuron function. Using the Hodgkin-Huxley model for description, the functional role of the repolarizing ionic currents in the periodic activity of nerve membranes was analyzed. New models have been developed which allow the analytical treatment of both passive membrane voltage changes in neurons with branching dendrites and nerve impulse propagation in non-uniform axons.

Animals↗

Probabilistic code for DNA recognition by proteins of the EGR family.

A recognition code for protein-DNA interactions would allow for the prediction of binding sites based on protein sequence, and the identification of binding proteins for specific DNA targets. Crystallographic studies of protein-DNA complexes showed that a simple, deterministic recognition code does not exist. Here, we present a probabilistic recognition code (P-code) that assigns energies to all possible base-pair-amino acid interactions for the early growth response factor (EGR) family of zinc-finger transcription factors. The specific energy values are determined by a maximum likelihood method using examples from in vitro randomisation experiments (namely, SELEX and phage display) reported in the literature. The accuracy of the model is tested in several ways, including the ability to predict in vivo binding sites of EGR proteins and other non-EGR zinc-finger proteins, and the correlation between predicted and measured binding affinities of various EGR proteins to several different DNA sites. We also show that this model improves significantly upon the prediction capabilities of previous qualitative and quantitative models. The probabilistic code we develop uses information about the interacting positions between the protein and DNA, but we show that such information is not necessary, although it reduces the number of parameters to be determined. We also employ the assumption that the total binding energy is the sum of the energies of the individual contacts, but we describe how that assumption can be relaxed at the cost of additional parameters.

Algorithms↗

Birthweight by gestational age in preterm babies according to a Gaussian mixture model.

OBJECTIVE: To provide a statistically sound criterion for identifying implausibly large birthweights for gestational age. DESIGN: Review of ISTAT 1990-1994 national newborn records. SETTING: Italy POPULATION: Forty-two thousand and twenty-nine single first and second liveborn preterm babies. METHODS: Two-component Gaussian mixture models are used to describe the birthweight distributions stratified by gestational age. Implausibly large babies are identified through model-based probabilistic clustering. MAIN OUTCOME MEASURES: Gestational age misclassification and weight-for-gestational age centile curves RESULTS: Gestational age appears under-estimated by about six weeks in 12.3% of the cases. Large babies are equally present in males and females, but are more frequent in second-borns than in first-borns, even when parity-specific models are fitted. CONCLUSIONS: The approach allows for a quantification of the gestational age under-estimate error and for data correction through model-based clustering. Correct birthweight distributions and growth curves are also provided.

Birth Weight↗

Overlapping events with application to image sequences.

Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising results. The model was applied on biological image sequences of in-vivo cells in order to estimate new parameters such as the mean number and duration distribution of endocytic events. Our results show that the proposed temporal Boolean model is effective for obtaining information about dynamic processes which exhibit short-lived, but spatially and temporally overlapping events.

Algorithms↗

Modeling aggressive driver behavior at unsignalized intersections.

The processing of vehicles at unsignalized intersections is a complex and highly interactive process, whereby each driver makes individual decisions about when, where, and how to complete the required maneuver, subject to his perceptions of distances, velocities, and own car's performance. Typically, the performance of priority-unsignalized intersections has been modeled with probabilistic approaches that consider the distribution of gaps in the major-traffic stream and their acceptance by the drivers of minor street vehicles based on the driver's "critical gap". This paper investigates the aggressive behavior of minor street vehicles at intersections that are priority-unsignalized but operate with little respect of control measures. The objective is to formulate a behavioral model that predicts the probability that a driver performs an aggressive maneuver as a function of a set of driver and traffic attributes. Parameters that were tested and modeled include driver characteristics (gender and age), car characteristics (performance and model year), and traffic attributes (number of rejected gaps, total waiting time at head of queue, and major-traffic speed). Binary probit models are developed and tested, based on a collected data set from an unsignalized intersection in the city of Beirut, to determine which of the studied variables are statistically significant in determining the aggressiveness of a specific driver. Primary conclusions reveal that age, car performance, and average speed on the major road are the major determinants of aggressive behavior. Another striking conclusion is that the total waiting time of the driver while waiting for an acceptable gap is of little significance in incurring the "forcing" behavior. The obtained model is incorporated in a simple simulation framework that reflects driver behavior and traffic stream interactions in estimating delay and conflict measures at unsignalized intersections. The simulation results were then compared against real world observations, representing an important step in validating the model of aggressive driver behavior at unsignalized intersections.

Age Factors↗

Normally occurring environmental and behavioral influences on gene activity: from central dogma to probabilistic epigenesis.

The central dogma of molecular biology holds that "information" flows from the genes to the structure of the proteins that the genes bring about through the formula DNA-->RNA-->Protein. In this view, a set of master genes activates the DNA necessary to produce the appropriate proteins that the organism needs during development. In contrast to this view, probabilistic epigenesis holds that necessarily there are signals from the internal and external environment that activate DNA to produce the appropriate proteins. To support this view, a substantial body of evidence is reviewed showing that external environmental influences on gene activation are normally occurring events in a large variety of organisms, including humans. This demonstrates how genes and environments work together to produce functional organisms, thus extending the author's model of probabilistic epigenesis.

Behavior↗

A macroscopic analytical model of collaboration in distributed robotic systems.

In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased.

Computer Communication Networks↗

An analysis of Berkson's bias in case-control studies.

The bias described by Berkson arises as a mathematical phenomenon, caused by the probabilistic union of different rates of hospitalization for people with different medical phenomena. When the concept is extended to case-control studies, these rates will occur as hd for people with the target disease, he for people with the control condition, and hc for the separate effect of exposure to the suspected etiologic agent. An algebraic analysis of patterns of hospitalization and case-control selection demonstrates that Berkson's bias will be avoided if both cases and controls are chosen from the community or if he = 0. When the cases are chosen from hospitalized patients, the odds ratio will be biased if, as in the usual clinical situation, he not equal to 0. The odds ratio will be falsely elevated if the control groups are chosen from a community population rather than from hospitalized patients, and falsely lowered if the controls are hospitalized patients who do not have the target disease. If the control groups are chosen from patients hospitalized with specific comparison conditions, the odds ratio will be falsely elevated or lowered, depending on the relative magnitudes of hd and hc. In Berkson's mathematical model, the probabilistic calculations depend on the assumption that each of the exposed or diseased clinical conditions has an independent additive effect on hospitalization rates. In reality, however, the concurrence of two or more conditions of disease and exposure may synergistically affect the examining physician's nosocomial decisions and may thereby substantially change the hospitalization rates from what is expected mathematically. In creating hospitalization bias in case-control studies, these selective clinical decisions about referral to hospital may be more cogent than the probabilistic distinctions described by Berkson.

Biometry↗

A fully Bayesian model to cluster gene-expression profiles.

MOTIVATION: With cDNA or oligonucleotide chips, gene-expression levels of essentially all genes in a genome can be simultaneously monitored over a time-course or under different experimental conditions. After proper normalization of the data, genes are often classified into co-expressed classes (clusters) to identify subgroups of genes that share common regulatory elements, a common function or a common cellular origin. With most methods, e.g. k-means, the number of clusters needs to be specified in advance; results depend strongly on this choice. Even with likelihood-based methods, estimation of this number is difficult. Furthermore, missing values often cause problems and lead to the loss of data. RESULTS: We propose a fully probabilistic Bayesian model to cluster gene-expression profiles. The number of classes does not need to be specified in advance; instead it is adjusted dynamically using a Reversible Jump Markov Chain Monte Carlo sampler. Imputation of missing values is integrated into the model. With simulations, we determined the speed of convergence of the sampler as well as the accuracy of the inferred variables. Results were compared with the widely used k-means algorithm. With our method, biologically related co-expressed genes could be identified in a yeast transcriptome dataset, even when some values were missing. AVAILABILITY: The code is available at http://genome.tugraz.at/BayesianClustering/

Algorithms↗

A procedure for incorporating spatial variability in ecological risk assessment of Dutch river floodplains.

Floodplain soils along the river Rhine in the Netherlands show a large spatial variability in pollutant concentrations. For an accurate ecological risk characterization of the river floodplains, this heterogeneity has to be included into the ecological risk assessment. In this paper a procedure is presented that incorporates spatial components of exposure into the risk assessment by linking geographical information systems (GIS) with models that estimate exposure for the most sensitive species of a floodplain. The procedure uses readily available site-specific data and is applicable to a wide range of locations and floodplain management scenarios. The procedure is applied to estimate exposure risks to metals for a typical foodweb in the Afferdensche and Deestsche Waarden floodplain along the river Waal, the main branch of the Rhine in the Netherands. Spatial variability of pollutants is quantified by overlaying appropriate topographic and soil maps resulting in the definition of homogeneous pollution units. Next to that, GIS is used to include foraging behavior of the exposed terrestrial organisms. Risk estimates from a probabilistic exposure model were used to construct site-specific risk maps for the floodplain. Based on these maps, recommendations for future management of the floodplain can be made that aim at both ecological rehabilitation and an optimal flood defense.

Animals↗

A joint model of regulatory and metabolic networks.

BACKGROUND: Gene regulation and metabolic reactions are two primary activities of life. Although many works have been dedicated to study each system, the coupling between them is less well understood. To bridge this gap, we propose a joint model of gene regulation and metabolic reactions. RESULTS: We integrate regulatory and metabolic networks by adding links specifying the feedback control from the substrates of metabolic reactions to enzyme gene expressions. We adopt two alternative approaches to build those links: inferring the links between metabolites and transcription factors to fit the data or explicitly encoding the general hypotheses of feedback control as links between metabolites and enzyme expressions. A perturbation data is explained by paths in the joint network if the predicted response along the paths is consistent with the observed response. The consistency requirement for explaining the perturbation data imposes constraints on the attributes in the network such as the functions of links and the activities of paths. We build a probabilistic graphical model over the attributes to specify these constraints, and apply an inference algorithm to identify the attribute values which optimally explain the data. The inferred models allow us to 1) identify the feedback links between metabolites and regulators and their functions, 2) identify the active paths responsible for relaying perturbation effects, 3) computationally test the general hypotheses pertaining to the feedback control of enzyme expressions, 4) evaluate the advantage of an integrated model over separate systems. CONCLUSION: The modeling results provide insight about the mechanisms of the coupling between the two systems and possible "design rules" pertaining to enzyme gene regulation. The model can be used to investigate the less well-probed systems and generate consistent hypotheses and predictions for further validation.

Cell Physiological Phenomena↗

Sensitive pattern discovery with 'fuzzy' alignments of distantly related proteins.

MOTIVATION: Evolutionary comparison leads to efficient functional characterisation of hypothetical proteins. Here, our goal is to map specific sequence patterns to putative functional classes. The evolutionary signal stands out most clearly in a maximally diverse set of homologues. This diversity, however, leads to a number of technical difficulties. The targeted patterns-as gleaned from structure comparisons-are too sparse for statistically significant signals of sequence similarity and accurate multiple sequence alignment. RESULTS: We address this problem by a fuzzy alignment model, which probabilistically assigns residues to structurally equivalent positions (attributes) of the proteins. We then apply multivariate analysis to the 'attributes x proteins' matrix. The dimensionality of the space is reduced using non-negative matrix factorization. The method is general, fully automatic and works without assumptions about pattern density, minimum support, explicit multiple alignments, phylogenetic trees, etc. We demonstrate the discovery of biologically meaningful patterns in an extremely diverse superfamily related to urease.

Algorithms↗

Nuclear architecture of human pachytene spermatocytes: quantitative analysis of associations between nucleolar and XY bivalents.

Nucleolar association and heterochromatin coalescence have both been invoked as mechanisms involved in the origin of chromosomal associations between nucleolar bivalents themselves, as well as between these bivalents and the XY pair, during meiotic prophase in human spermatocytes. However, these mechanisms do not satisfactorily explain how associating bivalents meet each other within the nuclear space. To elucidate this problem, we have characterized different types of nucleolar-nucleolar and nucleolar-XY bivalent associations, and their frequencies, in light and electron microscope serial sections of spermatocyte nuclei. In the pachytene nucleus, nucleolar bivalent associations were found to involve only one nucleolar sphere of RNP granules connected through a fibrillar center to a chromatin mass composed of two, or more, nucleolar-bivalent short arms. Structural relationships between these elements were examined using 3D computer models of various nucleolar associations. XY and nucleolar bivalents were usually located towards the nuclear periphery associated with the inner face of the nuclear envelope. Some nucleolar bivalents, whether single or associated appeared beside or over XY chromatin. When nucleolar-bivalent short arms (BK) were found over nucleolar or over XY chromatin, their telomeres were unattached to the nuclear envelope and the corresponding synaptonemal complexes were not observed. Ninety nucleoli were found in sixty pachytene nuclei. Thirty six percent of these nucleoli were bound to associated BKs and the remaining 64% to single BKs. Over 40% of individual spermatocytes showed at least one cluster of associated BKs and about 20% presented single or multiple BKs associated with the XY pair. The frequencies of random BK associations, over the total or restricted areas of the nuclear envelope, were calculated according to a probabilistic nuclear model. A correspondence was found in comparing the observed frequencies of associated BKs with those calculated on the basis of bouquet formation. Such an analysis strongly suggests that the occurrence of associations between nucleolar bivalents may arise at random within the bouquet. Thus, the architecture of the meiocyte nucleus, particularly the organization of the bouquet, may be the primary mechanism by which nucleolar bivalents meet each other and, consequently, become associated either through common nucleolus formation or by heterochromatin coalescence.

Cell Nucleolus↗

Analysis of the myogenic lineage in chick embryos. III. Quantitative evidence for discrete compartments of precursor cells.

Probabilistic and programmed lineage models for the generation of terminally differentiated skeletal muscle cells were tested in a clonal culture assay. Myogenic cells from the breast muscles of 10-day chick embryos were plated at an initial density of 250-1000 cells per 60 mm dish. Well-isolated individual cells were marked with a ring on the underside of the dishes, and clones arising from only these cells were followed. The presence of post-mitotic myoblasts in clones was assayed by peroxidase-antiperoxidase (PAP) and fluorescence immunocytochemical staining for both M-type creatine kinase (MCK) and skeletal muscle myosin heavy chain (MHC). Clones were fixed at intervals up to 76 h and were scored for the number of cells per clone and the number of MCK + and MHC + cells per clone. Quantitative and kinetic data were obtained indicating that post-mitotic myoblasts occurred overwhelmingly in homogeneous clones (all cells MCK + and MHC +) which contained 2" cells (n = 0, 1, 2, 3, 4). This result does not support either probabilistic models of myogenesis or the existence of 'proliferative' mitoses at the end stages of differentiation. Rather, it indicates that myogenic precursor cells are a heterogeneous population, within which individual cells are predetermined to undergo a set number of symmetrical mitoses prior to yielding terminally differentiated progeny. These findings are strong evidence for a programmed, cell cycle-dependent lineage in the end stages of muscle differentiation.

Animals↗

Exposure to persistent organochlorines in Canadian breast milk: a probabilistic assessment.

Exposure to persistent organochlorines in breast milk was estimated probabilistically for Canadian infants. Noncancer health effects were evaluated by comparing the predicted exposure distributions to published guidance values. For chemicals identified as potential human carcinogens, cancer risks were evaluated using standard methodology typically applied in Canada, as well as an alternative method developed under the Canadian Environmental Protection Act. Potential health risks associated with exposure to persistent organochlorines were quantitatively and qualitatively weighed against the benefits of breast-feeding. Current levels of the majority of contaminants identified in Canadian breast milk do not pose unacceptable risks to infants. Benefits of breast-feeding are well documented and qualitatively appear to outweigh potential health concerns associated with organochlorine exposure. Furthermore, the risks of mortality from not breast-feeding estimated by Rogan and colleagues exceed the theoretical cancer risks estimated for infant exposure to potential carcinogens in Canadian breast milk. Although levels of persistent compounds have been declining in Canadian breast milk, potentially significant risks were estimated for exposure to polychlorinated biphenyls, dibenzo-p-dioxins, and dibenzofurans. Follow-up work is suggested that would involve the use of a physiologically based toxicokinetic model with probabilistic inputs to predict dioxin exposure to the infant. A more detailed risk analysis could be carried out by coupling the exposure estimates with a dose-response analysis that accounts for uncertainty.

Benzofurans↗

Localized PD-1 CAR T therapy reprograms neuroinflammation.

B cell-depleting therapies are effective in multiple sclerosis (MS), yet some patients relapse, underscoring the need for more precise interventions. To identify new therapeutic targets, we generated a single-cell RNA sequencing (scRNA-seq) atlas of cerebrospinal fluid (CSF), brain, and blood from non-inflammatory controls and patients with MS or other neuroinflammatory diseases. We found disease-associated enrichment of class-switched immunoglobulin G+ (IgG+) B cells and plasma cells in MS CSF. Unbiased analysis identified a rare disease-enriched subset of activated, T cell receptor (TCR)-restricted, PD-1+ T follicular helper-like cells with B cell-recruiting features. To target this population, we developed PD-1-directed chimeric antigen receptor (CAR) T cells that selectively depleted pathogenic PD-1+ CD4 T cells and locally released IL-10. This strategy attenuated central nervous system (CNS) inflammation, reprogrammed the local immune milieu, and improved clinical outcomes across murine neuroinflammation models. These findings define a CNS-localized adaptive immune circuit in MS and nominate programmable PD-1 CAR T cells as a strategy to disrupt it.

Animals↗