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PubMed2004

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis.

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.

Apoptosis↗

PubMedDate not supplied

Threshold analysis using diagnostic tests with multiple results.

Clinical problems represented by decision trees can be analyzed in terms of the probability threshold model, which provides management recommendations based on the prior probability of disease, the test threshold, and the test-treatment threshold. As originally proposed, the threshold model assumes that diagnostic tests provide information about a single event that is relevant to the decision. For some problems, however, a diagnostic test may provide information about more than one such event (e.g., a computed tomography [CT] scan gives information about both mediastinal and hilar metastases in lung cancer). The authors extend the probability threshold model to cases in which a single test provides information about two events that are relevant to the decision. They derive four thresholds that determine the best strategy for any combination of test results. The approach is illustrated for the decision to use a CT scan to stage lung cancer. The analysis reveals that: 1) the range of prior probabilities for which testing is optimal increases; 2) for some prior probabilities only test results about one event are important; 3) for some prior probabilities test results about both events are important; and 4) failure to account fully for information provided by a test can lead to erroneous test and treatment recommendations.

Bayes Theorem↗

PubMed1990

A dose-response analysis of ethylnitrosourea-induced recessive specific-locus mutations in treated spermatogonia of the mouse.

A dose-response analysis was carried out with 2 independent data sets available for ethylnitrosourea-induced specific-locus mutations in spermatogonia of the mouse. It was assumed that the occurrence of mutation is binomially distributed and maximum-likelihood procedures were employed to determine the appropriateness of 4 alternative models, Linear, Linear-Quadratic, Power, and Threshold, in describing the dependence of the binomial parameter on dose. For both data sets, the Threshold model yielded a far superior fit and the threshold dose was estimated to be between 34 and 39 mg/kg. These results are supported by the relatively inefficient response of ethylnitrosourea at lower doses in inducing DNA adducts. Relevant specific-locus mutation results in the mouse for low-dose fractionated treatment as well as the recovery of mutation mosaics indicate the threshold model to be an oversimplification. Rather than a threshold dose below which 100% of the induced DNA adducts are repaired, we propose that some DNA adducts which may eventually be fixed as a mutation persist through a number of repair-competent cell divisions and do not interfere with normal cell function nor do they induce a repair response before being eventually fixed as a mutation. We interpret the thresholded response for ethylnitrosourea-induced specific-locus mutations to be due to a saturable repair process which at lower doses results in ethylnitrosourea being less efficient in inducing mutation. Once this repair process is saturated, a clear dose-related increase in the mutation rate is observed.

Animals↗

PubMed2003

Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue.

Neuronal adaptation as well as interdischarge interval correlations have been shown to be functionally important properties of physiological neurons. We explore the dynamics of a modified leaky integrate-and-fire (LIF) neuron, referred to as the LIF with threshold fatigue, and show that it reproduces these properties. In this model, the postdischarge threshold reset depends on the preceding sequence of discharge times. We show that in response to various classes of stimuli, namely, constant currents, step currents, white gaussian noise, and sinusoidal currents, the model exhibits new behavior compared with the standard LIF neuron. More precisely, (1) step currents lead to adaptation, that is, a progressive decrease of the discharge rate following the stimulus onset, while in the standard LIF, no such patterns are possible; (2) a saturation in the firing rate occurs in certain regimes, a behavior not seen in the LIF neuron; (3) interspike intervals of the noise-driven modified LIF under constant current are correlated in a way reminiscent of experimental observations, while those of the standard LIF are independent of one another; (4) the magnitude of the correlation coefficients decreases as a function of noise intensity; and (5) the dynamics of the sinusoidally forced modified LIF are described by iterates of an annulus map, an extension to the circle map dynamics displayed by the LIF model. Under certain conditions, this map can give rise to sensitivity to initial conditions and thus chaotic behavior.

Action Potentials↗

PubMedDate not supplied

Relation of daily mortality to air pollution: an analysis of 14 London winters, 1958/59-1971/72.

The relationship between daily deaths and daily concentrations of Smoke and SO2 in London, England for 14 winters during the years 1958-1959 through 1971-1972 has been explored. Three types of analyses were used: (1) year-by-year multiple regression; (2) stratification using nested quartiles of one pollutant within quartiles of the other; and (3) multiple regression of a special subset of high pollution days. An association was found with Smoke, but not with SO2. Whether a linear model with zero threshold or a threshold model best fits could not be determined unambiguously because of a statistical artifact. Reasons for preferring a threshold-type quadratic model are given.

Air Pollutants↗

PubMed2004

Genetic evaluation of calving to first insemination using natural and artificial insemination mating data.

Mating and calving records for 51,084 first-parity heifers in Australian Angus herds were used to examine the relationship between probability of calving to first insemination (CFI) in artificial insemination and natural service (NS) mating data. Calving to first insemination was defined as a binary trait for both sources of data. Two Bayesian models were employed: 1) a bivariate threshold model with CFI in AI data regarded as a trait separate from CFI in NS data and 2) a univariate threshold model with CFI regarded as the same trait for both sources of data. Posterior means (SD) of additive variance in the bivariate analysis were similar: 0.049 (0.013) and 0.075 (0.021) for CFI in AI and NS data, respectively, indicating lack of heterogeneity for this parameter. A similar trend was observed for heritability in the bivariate analysis, with posterior means (SD) of 0.025 (0.007) and 0.048 (0.012) for AI and NS data, respectively. The posterior means (SD) of the additive covariance and corresponding genetic correlation between the traits were 0.048 (0.006) and 0.821 (0.138), respectively. Differences were observed between posterior means for herd-year variance: 0.843 vs. 0.280 for AI and NS data, respectively, which may reflect the higher incidence of 100% conception rates within a herd-year class (extreme category problem) in AI data. Parameter estimates under the univariate model were close to the weighted average of the corresponding parameters under the bivariate model. Posterior means (SD) for additive, herd-year, and service sire variance and heritability under the univariate model were 0.063 (0.007), 0.56 (0.029), 0.131 (0.013), and 0.036 (0.007), respectively. These results indicate that, genetically, cows with a higher probability of CFI when mated using AI also have a high probability of CFI when mated via NS. The high correlation between the two traits, along with the lack of heterogeneity for the additive variance, implies that a common additive variance could be used for AI and NS data. A single-trait analysis of CFI with heterogeneous variances for herd-year and service sire could be implemented. The low estimates of heritability indicate that response to selection for probability of calving to first insemination would be expected to be low.

Animals↗

PubMed2006

Characterization of Holstein heifer fertility in the United States.

The overall object of this research was to characterize US Holstein (virgin) heifer fertility. This included investigation of factors influencing heifer fertility and estimation of heritability, as well as correlations with cow fertility and first-lactation milk yield. A secondary objective was to compare linear and logistic model estimates of fixed effects and linear and threshold model estimates of heritability. Data consisted of Holstein heifers, which were artificially inseminated, with their first breeding between March 2003 and August 2005. Herds were required to have at least 60 breedings across the 3 yr of data and an overall mean conception rate (CR) between 20 and 80%. After edits there were 537,938 breedings of 362,512 heifers in 2,668 herds from 41 states used for analysis. After edits, the overall mean CR for US Holstein heifers was 57%. Linear and logistic model estimates for all factors were nearly identical. Year of breeding accounted for the most variation in heifer CR, with heifer age and month of breeding being the next most important factors. Conception rate in heifers is maximal at an intermediate age of 15 to 16 mo. Heifers at 26 mo of age and older have roughly a 10% lower CR than heifers bred at younger ages. Although month of breeding affected heifer CR, effects are less than for cows. In contrast to cow fertility, heifer CR is nearly as good in the hotter summer months as in cooler months. Approximately 88% of US herds had a 40 to 70% heifer CR. Heritability estimates of heifer CR on first service were 0.5% from the linear model and 1.0% from the threshold model. Genetic correlation estimates of heifer CR on first service with cow CR on first service and with first-lactation milk yield were 0.39 and -0.19, respectively. Results indicated that selection on either the currently available US daughter pregnancy rate evaluations for cow fertility or on cow CR will also improve heifer fertility. Furthermore, heritability of heifer CR is lower than for cow CR and reporting of heifer breedings is currently less complete than for cow breedings. Thus, there are currently no immediate plans to implement a US genetic evaluation for heifer CR.

Animals↗

PubMed1998

Genetic analysis of clinical lameness in dairy cattle.

Scores for clinical lameness from two separate studies were combined, and genetic parameters were estimated based on linear and threshold models. Cows were from 24 herds in Minnesota, Wisconsin, and Virginia. To evaluate clinical lameness, cows were observed walking and were assigned a score between 0 and 4 (where 0 = no observable problems to 4 = inability to walk). Data included 1624 records on 1342 cows. The models included fixed effects of herd visit, parity, and stage of lactation. Random effects were additive genetics, permanent environment to account for repeated records, and residual. Estimates of heritability were 0.10 and 0.22 from the linear and threshold models, respectively. The correlation between ETA from linear and threshold models based on all animals was 0.974. Deregressed ETA of sires and REML were used to estimate genetic correlations between clinical lameness and conformation traits. Among the type traits, foot angle, rear legs (rear view), and rump width had strongest associations with clinical lameness; absolute values for genetic correlations between these traits and clinical lameness were approximately 0.65. Low foot angle, hocking in, and wide rumps were associated with increased clinical lameness. Correlations with strength and body depth ranged from 0.20 to 0.43, indicating that heavier cows were more prone to clinical lameness.

Animals↗

PubMed2006

Relationships between host viremia and vector susceptibility for arboviruses.

Using a threshold model where a minimum level of host viremia is necessary to infect vectors affects our assessment of the relative importance of different host species in the transmission and spread of these pathogens. Other models may be more accurate descriptions of the relationship between host viremia and vector infection. Under the threshold model, the intensity and duration of the viremia above the threshold level is critical in determining the potential numbers of infected mosquitoes. A probabilistic model relating host viremia to the probability distribution of virions in the mosquito bloodmeal shows that the threshold model will underestimate the significance of hosts with low viremias. A probabilistic model that includes avian mortality shows that the maximum number of mosquitoes is infected by feeding on hosts whose viremia peaks just below the lethal level. The relationship between host viremia and vector infection is complex, and there is little experimental information to determine the most accurate model for different arthropod-vector-host systems. Until there is more information, the ability to distinguish the relative importance of different hosts in infecting vectors will remain problematic. Relying on assumptions with little support may result in erroneous conclusions about the importance of different hosts.

Animals↗

PubMed2004

Mapping multiple quantitative trait Loci for ordinal traits.

Many complex traits in humans and other organisms show ordinal phenotypic variation but do not follow a simple Mendelian pattern of inheritance. These ordinal traits are presumably determined by many factors, including genetic and environmental components. Several statistical approaches to mapping quantitative trait loci (QTL) for such traits have been developed based on a single-QTL model. However, statistical methods for mapping multiple QTL are not well studied as continuous traits. In this paper, we propose a Bayesian method implemented via the Markov chain Monte Carlo (MCMC) algorithm to map multiple QTL for ordinal traits in experimental crosses. We model the ordinal traits under the multiple threshold model, which assumes a latent continuous variable underlying the ordinal phenotypes. The ordinal phenotype and the latent continuous variable are linked through some fixed but unknown thresholds. We adopt a standardized threshold model, which has several attractive features. An efficient sampling scheme is developed to jointly generate the threshold values and the values of latent variable. With the simulated latent variable, the posterior distributions of other unknowns, for example, the number, locations, genetic effects, and genotypes of QTL, can be computed using existing algorithms for normally distributed traits. To this end, we provide a unified approach to mapping multiple QTL for continuous, binary, and ordinal traits. Utility and flexibility of the method are demonstrated using simulated data.

Algorithms↗

PubMed2005

Paradigm lost, paradigm found: the re-emergence of hormesis as a fundamental dose response model in the toxicological sciences.

This paper provides an assessment of the toxicological basis of the hormetic dose-response relationship including issues relating to its reproducibility, frequency, and generalizability across biological models, endpoints measured and chemical class/physical stressors and implications for risk assessment. The quantitative features of the hormetic dose response are described and placed within toxicological context that considers study design, temporal assessment, mechanism, and experimental model/population heterogeneity. Particular emphasis is placed on an historical evaluation of why the field of toxicology rejected hormesis in favor of dose response models such as the threshold model for assessing non-carcinogens and linear no threshold (LNT) models for assessing carcinogens. The paper argues that such decisions were principally based on complex historical factors that emerged from the intense and protracted conflict between what is now called traditional medicine and homeopathy and the overly dominating influence of regulatory agencies on the toxicological intellectual agenda. Such regulatory agency influence emphasized hazard/risk assessment goals such as the derivation of no observed adverse effect levels (NOAELs) and the lowest observed adverse effect levels (LOAELs) which were derived principally from high dose studies using few doses, a feature which restricted perceptions and distorted judgments of several generations of toxicologists concerning the nature of the dose-response continuum. Such historical and technical blind spots lead the field of toxicology to not only reject an established dose-response model (hormesis), but also the model that was more common and fundamental than those that the field accepted.

Animals↗

PubMed2003

Commentary on hormesis and public risk communication: is there a basis for public discussions?

Research on radiation exposure is now focusing on microbiology and the impact of low dose exposures on cells and cell components. Eventually, this research may provide evidence to support changes in the models used to regulate human and environmental exposures. Currently, three models using older research results are subjects of interest and comparison. The linear no-threshold model, the most restrictive on behalf of public health values, dominates regulatory decision making. Alternative models (i.e., the threshold model and the hormesis model) could reduce costs of radiation management, depending upon new research results and public acceptance. Enacting a new public exposure model is a daunting task for risk communication given existing public risk perceptions and the established public decision-making processes. Each of the three prominent models must answer the question, 'what social good requires the use of this model in contrast to the others?'

Animals↗

PubMed1987

Functional properties of models for direction selectivity in the retina.

Poggio and Reichardt (Kybernetik, 13:223-227, 1973) showed that if the average response of a visual system to a moving stimulus is directionally selective, then this sensitivity must be mediated by a nonlinear operation. In particular, it has been proposed that at the behavioral level, motion-sensitive biological systems are implemented by quadratic nonlinearities (Hassenstein and Reichardt: Z. Naturforsch., 11b:513-524, 1956; van Santen and Sperling: J. Opt. Soc. Am. [A] 1:451-473, 1984; Adelson and Bergen: J. Opt. Soc. Am. [A], 2:284-299, 1985). This paper analyzes theoretically two nonlinear neural mechanisms that possibly underlie retinal direction selectivity and explores the conditions under which they behave as a quadratic nonlinearity. The first mechanism is shunting inhibition (Torre and Poggio: Proc. R. Soc. Lond. [Biol.], 202:409-416, 1978), and the second consists of the linear combination of the outputs of a depolarizing and a hyperpolarizing synapse, followed by a threshold operation. It was found that although sometimes possible, it is in practice hard to approximate the Shunting Inhibition and the Threshold models for direction selectivity by quadratic systems. For instance, the level of the threshold on the Threshold model must be close to the steady-state level of the cell's combined synaptic input. Furthermore, for both the Shunting and the Threshold models, the approximation by a quadratic system is only possible for a small range of low contrast stimuli and for situations where the rectifications due to the ON-OFF mechanisms, and to the ganglion cells' action potentials, can be linearized. The main question that this paper leaves open is, how do we account for the apparent quadratic properties of motion perception given that the same properties seem so fragile at the single cell level? Finally, as a result of this study, some system analysis experiments were proposed that can distinguish between different instances of the models.

Animals↗

PubMed1999

An approach to estimating bone and joint loads and muscle strength in living subjects and skeletal remains.

Skeletal physiology that clarified after 1990 shows that bone modeling normally makes a bone strong enough to keep its loads from causing strains above a "modeling threshold". That arrangement adapts bone strength to the largest loads on a bone, which are usually brief and infrequent. Accordingly, in bone adapted chiefly to uniaxial compression loads, the modeling threshold's value and the cross-sectional amount of that bone could suggest the size of those loads. Bone loaded in that way does support the articular surfaces of synovial joints as their "supporting bone", so its amount could suggest the size of the loads it had adapted to, and therefore the loads on the joint that it supports. During growth a joint's size is proportional, directly but not linearly, to the size of its total loads, so that its size at skeletal maturity could be an index of those loads at that time. Joints cannot decrease in size. Yet throughout life their supporting bone can decrease or increase in strength and "mass" to adapt to changes in a joint's loads. Thus, an adult joint's size could suggest the size of the loads it adapted to by skeletal maturity, while the cross-sectional amount of its supporting bone at any later age could reveal the size of those loads at that later age, and thus suggest any change in those loads that might have occurred after skeletal maturity. Since the bone modeling threshold, and the relationships between bone strain, stress, and unit loads are now known, it is possible with this procedure to estimate the total loads on joints, and how body weight and muscle strength contribute to those loads in both living subjects and skeletal remains. To make a reliable technology of the idea involves some problems which this paper identifies and suggests how to resolve. Am. J. Hum. Biol. 11:437-455, 1999. Copyright 1999 Wiley-Liss, Inc.

Journal Article↗

PubMed2006

Success at first insemination in Australian Angus cattle: analysis of uncertain binary responses.

Field data from Australian Angus herds were used to investigate 2 methods of analyzing uncertain binary responses for success or failure at first insemination. A linear mixed model that included herd, year, and month of mating as fixed effects; unrelated service sire, additive animal, and residual as random effects; and linear and quadratic effects of age at mating as covariates was used to analyze binary data. An average gestation length (GL) derived from artificial insemination data was used to assign an insemination date to females mated to natural service sires. Females that deviated from this average GL led to uncertain binary responses. Two analyses were carried out: 1) a threshold model fitted to uncertain binary data, ignoring uncertainty (M1); and 2) a threshold model fitted to uncertain binary data, accounting for uncertainty via fuzzy logic classification (M2). There was practically no difference between point estimates obtained from M1 and M2 for service sire and herd variance; however, when uncertain binary data were analyzed ignoring uncertainty (M1), additive variance and heritability estimates were greater than with M2. Pearson correlations indicated that no major reranking would be expected for service sire effects and animal breeding values using M1 and M2. Given the results of the current study, a threshold model contemplating uncertainty is suggested for noisy binary data to avoid bias when estimating genetic parameters.

Animals↗

PubMed1988

Pragmatics of measuring recognition memory: applications to dementia and amnesia.

This article has two purposes. The first is to describe four theoretical models of yes-no recognition memory and present their associated measures of discrimination and response bias. These models are then applied to a set of data from normal subjects to determine which pairs of discrimination and bias indices show independence between discrimination and bias. The following models demonstrated independence: a two-high-threshold model, a signal detection model with normal distributions using d' and C (rather than beta), and a signal detection model with logistic distributions and a bias measure analogous to C. C is defined as the distance of criterion from the intersection of the two underlying distributions. The second purpose is to use the indices from the acceptable models to characterize recognition memory deficits in dementia and amnesia. Young normal subjects, Alzheimer's disease patients, and parkinsonian dementia patients were tested with picture recognition tasks with repeated study-test trials. Huntington's disease patients, mixed etiology amnesics, and age-matched normals were tested by Butters, Wolfe, Martone, Granholm, and Cermak (1985) using the same paradigm with word stimuli. Demented and amnesic patients produced distinctly different patterns of abnormal memory performance. Both groups of demented patients showed poor discrimination and abnormally liberal response bias for words (Huntington's disease) and pictures (Alzheimer's disease and parkinsonian dementia), whereas the amnesic patients showed the worst discrimination but normal response bias for words. Although both signal detection theory and two-high-threshold discrimination parameters showed identical results, the bias measure from the two-high-threshold model was more sensitive to change than the bias measure (C) from signal detection theory. Three major points are emphasized. First, any index of recognition memory performance assumes an underlying model. Second, even acceptable models can lead to different conclusions about patterns of learning and forgetting. Third, efforts to characterize and ameliorate abnormal memory should address both discrimination and bias deficits.

Adult↗

PubMed2002

Evaluation of the effects of a smoking cessation intervention using the multilevel thresholds of change model.

The multilevel thresholds of change model is used to analyze the effect of a smoking cessation intervention on stage of readiness to quit across a 2-year follow-up period. The intervention, targeted to females with high school or less education, consisted of a televised component and a written manual. Any exposure to the intervention had a significant effect on stages that precede quitting but not on quitting; participation in the intervention had significant effects at all levels of change, including quitting. The written component had a stronger independent effect than the televised component. Intervention effects were strongest within women who were initially precontemplative.

Adult↗

PubMed2004

Economic implications of hormesis.

The implications of hormesis for decision making about control of environmental exposures are examined. From an economic perspective, environmental exposures should be controlled to a level that optimizes health effects and minimizes control costs. The possibility that substances are, or may be, hormetic poses no fundamental challenge for economic analysis. In contrast with the linear no-threshold model, optimal control may be either less or more stringent under the hormetic model, depending on the incremental control cost. When exposure levels or exposure-response functions differ across individuals or are uncertain, the optimal population-level control of exposure must balance possible benefits and harms to individuals against control costs. Economic-incentive-based regulatory instruments, such as tradable permits, are likely to offer less improvement relative to command-and-control regulations under a hormetic model than under a linear no-threshold model.

Cost-Benefit Analysis↗