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PubMed1999

Probabilistic modeling of shear-induced formation and breakage of doublets cross-linked by receptor-ligand bonds.

A model was constructed to describe previously published experiments of shear-induced formation and breakage of doublets of red cells and of latexes cross-linked by receptor-ligand bonds (. Biophys. J. 65:1318-1334; Tees and Goldsmith. 1996. Biophys. J. 71:1102-1114;. Biophys. J. 71:1115-1122). The model, based on McQuarrie's master equations (1963. J. Phys. Chem. 38:433-436), provides unifying treatments for three distinctive time periods in the experiments of particles in a Couette flow in which a doublet undergoes 1) formation upon two-body collision between singlets; 2) evolution of bonds at low shear rate; and 3) break-up at high shear rate. Neglecting the applied force at low shear rate, the probability of forming a doublet per collision as well as the evolution of probability distribution of bonds in a preformed doublet were solved analytically and found to be in quite good agreement with measurements. At high shear rate with significant force acting to accelerate bond dissociation, the predictions for break-up of doublets were obtained numerically and compared well with data in both individual and population studies. These comparisons enabled bond kinetic parameters for three types of particles cross-linked by two receptor-ligand systems to be calculated, which agreed well with those computed from Monte Carlo simulations. This work can be extended to analyze kinetics of receptor-ligand binding in cell aggregates, such as those of neutrophils and platelets in the circulation.

Cell Aggregation↗
PubMed2001

[Probabilistic models of mortality for patients hospitalized in conventional units].

BACKGROUND: We have developed a tool to measure disease severity of patients hospitalized in conventional units in order to evaluate and compare the effectiveness and quality of health care in our setting. PATIENTS AND METHOD: A total of 2,274 adult patients admitted consecutively to inpatient units from the Medicine, Surgery and Orthopaedic Surgery, and Trauma Departments of the Corporació Sanitària Parc Taulí of Sabadell, Spain, between November 1, 1997 and September 30, 1998 were included. The following variables were collected: demographic data, previous health state, substance abuse, comorbidity prior to admission, characteristics of the admission, clinical parameters within the first 24 hours of admission, laboratory results and data from the Basic Minimum Data Set of hospital discharges. Multiple logistic regression analysis was used to develop mortality probability models during the hospital stay. RESULTS: The mortality probability model at admission (MPMHOS-0) contained 7 variables associated with mortality during hospital stay: age, urgent admission, chronic cardiac insufficiency, chronic respiratory insufficiency, chronic liver disease, neoplasm, and dementia syndrome. The mortality probability model at 24-48 hours from admission (MPMHOS-24) contained 9 variables: those included in the MPMHOS-0 plus two statistically significant laboratory variables: hemoglobin and creatinine. CONCLUSIONS: Severity measures, in particular those presented in this study, can be helpful for the interpretation of hospital mortality rates and can guide mortality or quality committees at the time of investigating health care-related problems.

Female↗
PubMed1977

Micrometastases formation: a probabilistic model.

A mathematical model of the process of metastases is formulated in which the hematogenous metastatic process from a solid tumor is considered to consist of a series of stages. A mathematical expression is obtained for the probability that no metastases will have been established by a characteristic time interval after tumor initiation. The murine T241 fibrosarcoma that rapidly and reproduceably produces pulmonary metastases was studied. Estimates of parameters required for the expression of probability of metastases formation were derived experimentally. The probability remains close to one for a characteristic time at which point it drops to zero. This indicates that at least in this experimental system there is a predictable critical time period beyond which micrometastases are virtually certain to have been formed.

Animals↗
PubMed1995

Probabilistic models for sequential taste effects in triadic choice.

Sequential effects and positional response bias are accounted for in new models for triadic choice. These models were applied to data on distilled water and dilute NaCl solutions by use of the triangular and 3-alternative forced-choice methods with 4 participants. The concept of a "conditional stimulus" is introduced to describe stimuli that are created partially by prior oral environmental effects. The effects of 1 or 2 prior stimuli on triadic choice was evaluated. The triad models used were based on a Thurstonian variant of M. W. Richardson's (1938) method of triads and a Thurstonian model for first choice among 3 possibly different stimuli. Maximum likelihood estimates of the scale values for conditional stimuli and bias parameters showed that it was necessary only to consider 1 prior stimulus. It was also shown that salt concentration differences are not the physical analog of the mental representations for the conditional stimuli. The results strongly suggest a water taste to salt taste continuum.

Adult↗
PubMed2001

SCOPE: a probabilistic model for scoring tandem mass spectra against a peptide database.

Proteomics, or the direct analysis of the expressed protein components of a cell, is critical to our understanding of cellular biological processes in normal and diseased tissue. A key requirement for its success is the ability to identify proteins in complex mixtures. Recent technological advances in tandem mass spectrometry has made it the method of choice for high-throughput identification of proteins. Unfortunately, the software for unambiguously identifying peptide sequences has not kept pace with the recent hardware improvements in mass spectrometry instruments. Critical for reliable high-throughput protein identification, scoring functions evaluate the quality of a match between experimental spectra and a database peptide. Current scoring function technology relies heavily on ad-hoc parameterization and manual curation by experienced mass spectrometrists. In this work, we propose a two-stage stochastic model for the observed MS/MS spectrum, given a peptide. Our model explicitly incorporates fragment ion probabilities, noisy spectra, and instrument measurement error. We describe how to compute this probability based score efficiently, using a dynamic programming technique. A prototype implementation demonstrates the effectiveness of the model.

Amino Acid Sequence↗
PubMed1984

A general probabilistic model of carcinogenesis: analysis of experimental urinary bladder cancer.

A theoretical model of two-stage carcinogenesis has been hypothesized. Variables that are modeled include the populations of normal, initiated, and transformed cells; mitotic rates of these cells; hyperplasia; and the probabilities of cell initiation and transformation during replication. The size of the cell populations can be estimated and mitotic rates determined directly from animal studies. Tumor occurrences at different time intervals following varying periods of N-[4-(5-nitro-2-furyl)-2-thiazolyl]formamide (FANFT) and sodium saccharin administration are known and are used in the indirect estimation of values for unobservable model variables. Model-based analyses suggest FANFT markedly increases the probability of cell initiation in addition to its experimentally verifiable effects on increasing the stem cell population and mitotic rates. Further, experimental results appear inconsistent with the hypothesis that FANFT increases the probability of cell transformation over background levels. Similarly, the effect of sodium saccharin was found to be attributable entirely to increases in stem cell populations and mitotic rates without influencing either the probability of initiation or the probability of transformation.

Animals↗
PubMed2004

A probabilistic model of 3' end formation in Caenorhabditis elegans.

The 3' ends of mRNAs terminate with a poly(A) tail. This post-transcriptional modification is directed by sequence features present in the 3'-untranslated region (3'-UTR). We have undertaken a computational analysis of 3' end formation in Caenorhabditis elegans. By aligning cDNAs that diverge from genomic sequence at the poly(A) tract, we accurately identified a large set of true cleavage sites. When there are many transcripts aligned to a particular locus, local variation of the cleavage site over a span of a few bases is frequently observed. We find that in addition to the well-known AAUAAA motif there are several regions with distinct nucleotide compositional biases. We propose a generalized hidden Markov model that describes sequence features in C.elegans 3'-UTRs. We find that a computer program employing this model accurately predicts experimentally observed 3' ends even when there are multiple AAUAAA motifs and multiple cleavage sites. We have made available a complete set of polyadenylation site predictions for the C.elegans genome, including a subset of 6570 supported by aligned transcripts.

3' Untranslated Regions↗
PubMed2001

Performance of a divergence time estimation method under a probabilistic model of rate evolution.

Rates of molecular evolution vary over time and, hence, among lineages. In contrast, widely used methods for estimating divergence times from molecular sequence data assume constancy of rates. Therefore, methods for estimation of divergence times that incorporate rate variation are attractive. Improvements on a previously proposed Bayesian technique for divergence time estimation are described. New parameterization more effectively captures the phylogenetic structure of rate evolution on a tree. Fossil information and other evidence can now be included in Bayesian analyses in the form of constraints on divergence times. Simulation results demonstrate that the accuracy of divergence time estimation is substantially enhanced when constraints are included.

Bayes Theorem↗
PubMed1998

A probabilistic model for the failure frequency of underground gas pipelines.

A model is constructed for the failure frequency of underground pipelines per kilometer year, as a function of pipe and environmental characteristics. The parameters in the model were quantified, with uncertainty, using historical data and structured expert judgment. Fifteen experts from institutes in The Netherlands, the United Kingdom, Italy, France, Germany, Belgium, Denmark, and Canada participated in the study.

Algorithms↗
PubMedDate not supplied

Numerical implementation of a backward probabilistic model of ground water contamination.

Backward location and travel time probabilities can be used to characterize known and unknown sources or prior positions of ground water contamination. Backward location probability describes the position of the observed contamination at some time in the past; backward travel time probability describes the amount of time prior to observation that the contamination was released from its source or was at a particular upgradient location. The governing equation for backward probabilities is the adjoint of the governing equation for contaminant transport, but with new load terms. Numerical codes that have been written to solve the forward equations of contaminant transport, e.g., the advection-dispersion equation, can also be used to solve the adjoint equation for location and travel time probabilities; however, the interpretation of the results is different and some new approximations must be made for the load terms. We present the governing equations for backward location and travel time probabilities, and provide appropriate numerical approximations for these load terms using the cell-centered finite difference method, one of the most popular numerical methods in ground water hydrology. We discuss some additional numerical considerations for the backward model including boundary conditions, reversal of the flow field, and interpretation of the results. We illustrate the implementation of the backward probability model using hypothetical examples in one- and two-dimensional domains. We also present a three-dimensional application of a pump-and-treat remediation capture zone delineation at the Massachusetts Military Reservation. The illustrations are performed using MODFLOW-96 for flow simulations and MT3DMS for transport simulations.

Models, Statistical↗
PubMed1994

Probabilistic model of altitude decompression sickness based on mechanistic premises.

To develop a predictive equation and to test ideas about the mechanisms involved in hypobaric decompression sickness, we performed statistical analyses on published results of 7,023 exercising O2-breathing men subjected to one-step decompressions in altitude chambers. The dependent variable was signs or symptoms so severe that the person's trial was terminated (forced descent). The three independent variables were 1) duration of 100% O2 breathing at ground level (prebreathing), 2) atmospheric pressure after ascent, and 3) exposure duration. The best model, chosen from trial-and-error combinations of premises about bubble behavior, indicates that decompression sickness outcome depends on 1) prebreathing time, but with an unexpectedly long washout half time for N2; 2) time at altitude, as if bubbles grow; and 3) the estimated difference, raised to the fifth power, between the partial pressure of N2 in tissue before and that in bubbles after decompression, perhaps an index of the number of bubbles generated. We expect the model to provide accurate predictions for decompressions matching those of the bulk of the data; the mechanistic cues should be considered hypotheses for further investigation.

Altitude Sickness↗
PubMed2000

Probabilistic model for prediction of angiographically defined obstructive coronary artery disease using electron beam computed tomography calcium score strata.

BACKGROUND: Electron beam CT (EBCT) is an accurate, noninvasive method to detect and quantify coronary artery calcification, a marker of coronary artery disease (CAD). This investigation examined the accuracy of EBCT to detect obstructive CAD (> or =50% stenosis) and determined the optimal strata for quantity of coronary artery calcification to facilitate clinical decision-making. METHODS AND RESULTS: Clinical research patients (n=213) were examined with coronary angiography and EBCT (angiography group), and 765 research participants were examined with only EBCT (nonangiography group). Of the angiography group, 53% had obstructive CAD. After adjustment for verification bias, the estimated sensitivity and specificity for calcium score > or =1 were 97.0% and 72.4%, respectively. Likelihood ratios for strata of calcium score associated with obstructive CAD were calculated in each sex and 2 age groups. Among those > or =50 years old, the same 4 strata of EBCT calcium scores were identified in each sex; likelihood ratios ranged from 0.03 (calcium score 0) to 12.85 (calcium score > or =200). The same 3 strata EBCT calcium scores were identified in each sex among those <50 years old; likelihood ratios ranged from 0.13 (calcium score 0) to 190 (calcium score > or =100). CONCLUSIONS: A calcium score > or =200 among those > or =50 years old and calcium score > or =100 among those <50 years old provided strong evidence that patients of either sex had obstructive CAD. A calcium score of 0 provided strong evidence that patients > or =50 years old did not have obstructive CAD.

Adult↗
PubMed2004

A probabilistic model for the evolution of RNA structure.

BACKGROUND: For the purposes of finding and aligning noncoding RNA gene- and cis-regulatory elements in multiple-genome datasets, it is useful to be able to derive multi-sequence stochastic grammars (and hence multiple alignment algorithms) systematically, starting from hypotheses about the various kinds of random mutation event and their rates. RESULTS: Here, we consider a highly simplified evolutionary model for RNA, called "The TKF91 Structure Tree" (following Thorne, Kishino and Felsenstein's 1991 model of sequence evolution with indels), which we have implemented for pairwise alignment as proof of principle for such an approach. The model, its strengths and its weaknesses are discussed with reference to four examples of functional ncRNA sequences: a riboswitch (guanine), a zipcode (nanos), a splicing factor (U4) and a ribozyme (RNase P). As shown by our visualisations of posterior probability matrices, the selected examples illustrate three different signatures of natural selection that are highly characteristic of ncRNA: (i) co-ordinated basepair substitutions, (ii) co-ordinated basepair indels and (iii) whole-stem indels. CONCLUSIONS: Although all three types of mutation "event" are built into our model, events of type (i) and (ii) are found to be better modeled than events of type (iii). Nevertheless, we hypothesise from the model's performance on pairwise alignments that it would form an adequate basis for a prototype multiple alignment and genefinding tool.

Evolution, Molecular↗
PubMed2006

Probabilistic model of nonlinear penalties due to collision-induced timing jitter for calculation of the bit error ratio in wavelength-division-multiplexed return-to-zero systems.

We introduce a fully deterministic, computationally efficient method for characterizing the effect of nonlinearity in optical fiber transmission systems that utilize wavelength-division multiplexing and return-to-zero modulation. The method accurately accounts for bit-pattern-dependent nonlinear distortion due to collision-induced timing jitter and for amplifier noise. We apply this method to calculate the error probability as a function of channel spacing in a prototypical multichannel return-to-zero undersea system.

Journal Article↗