Unbiased estimation of Langevin dynamics from time series with application to hippocampal field potentials in vitro.

The last decade showed an increased interest in Langevin equations for modeling time series recorded from complex dynamical systems. These equations allow to discriminate between deterministic (drift) and stochastic (diffusion) components of the recorded time series. In practice, the estimation of drift and diffusion is often based on approximations of the models' dynamics that are valid only for high sampling frequencies. Also, model assessment is not or only indirectly performed, potentially leading to false claims. In this study we compare the performance of an asymptotically unbiased estimation method with a generally used approximate method, demonstrating the necessity of using (asymptotically) unbiased estimators. Furthermore, we describe how confidence intervals for the unknown parameters can be constructed and how model assessment can be carried out. We apply the methodology to local field potentials recorded in vitro from mouse hippocampus from eight genetically different strains. The recorded field potentials turn out to be well described by linearly damped Langevin equations with parabolic diffusion. The modeling enables a dynamical interpretation of the spectral power of the field potentials. It reveals that observed spectral power differences in the field potentials across hippocampal regions are associated with differences in the deterministic component of the system, and it reveals transiently active current dipoles, which are not detectable by conventional methods. Also, all estimated parameters have significant heritabilities, which suggests that the Langevin equations capture biological relevant aspects of electrical hippocampal activity.

Inbred mouse strains differ in multiple hippocampal activity traits.

A major challenge in neuroscience is to identify genes that influence specific behaviors and to understand the intermediary neuronal mechanisms. One approach is to identify so-called endophenotypes at different levels of neuronal organization from synapse to brain activity. An endophenotype is a quantitative trait that is closer to the gene action than behavior, and potentially a marker of neuronal mechanisms underlying behavior. Hippocampal activity and, in particular, hippocampal oscillations have been suggested to underlie various cognitive and motor functions. To identify quantitative traits that are potentially useful for identifying genes influencing hippocampal activity, we measured gamma oscillations and spontaneous activity in acute hippocampal slices from eight inbred mouse strains under three experimental conditions. We estimated the heritability of more than 200 quantitative traits derived from this activity. We observed significant differences between the different mouse strains, particularly in the amplitude of the activity and the correlation between activities in different hippocampal subregions. Interestingly, these traits had a low genetic correlation between the three experimental conditions, which suggests that different genetic components influence the activity in different conditions. Our findings show that several traits of hippocampal gamma oscillations and spontaneous activity are heritable and could thus be potentially useful in gene-finding strategies based on endophenotypes.

Model selection and parameter estimation for ion channel recordings with an application to the K+ outward-rectifier in barley leaf.

We present a statistical method, and its accompanying algorithms, for the selection of a mathematical model of the gating mechanism of an ion channel and for the estimation of the parameters of this model. The method assumes a hidden Markov model that incorporates filtering, colored noise and state-dependent white excess noise for the recorded data. The model selection and parameter estimation are performed via a Bayesian approach using Markov chain Monte Carlo. The method is illustrated by its application to single-channel recordings of the K(+) outward-rectifier in barley leaf.

[Growth charts for height, weight and body-mass index of twins during infancy]. / Groeidiagrammen voor lengte, gewicht en 'body mass index' van tweelingen in de peutertijd.

OBJECTIVE: To determine the magnitude of the growth retardation in Dutch monozygotic and dizygotic twins during infancy in comparison with the Dutch reference growth charts for general population infants from 1997 and to construct reference growth charts for twins. DESIGN: Descriptive. METHOD: The growth of twins was studied using longitudinal data on over 4000 Dutch twin pairs from birth until 2.5 years of age. The LMS method was used to obtain growth charts for height, weight and body-mass index (BMI) for twin pairs during infancy. Centiles were estimated by the Box-Cox power curve (L), the median curve (M) and the coefficient of variation curve (S). RESULTS: From birth until the age of half a year, the average height and weight of twin pairs were at about the 10th percentile of the Dutch reference population. One year later this difference had decreased to about the 25th percentile, and when the twin pairs were between 1.5 and 2.5 years of age the difference was further decreased to the 35th percentile. The BMI deviated less from that of the reference population: during the first half a year the BMI of twin pairs was at about the 25th percentile. Subsequently, the BMI improved, but remained slightly below the median of the reference population at the age of about two years. Approximately half (50% for height, 58% for weight) of the growth retardation from birth until 1.5 years was attributable to gestational age. Between 1.5 years and 2.5 years of age, this difference was reduced to one third: 33% for both height and weight. Thus, a substantial part of the growth difference could not be explained by gestational age. CONCLUSION: Correcting for gestational age alone is not sufficient to make possible a comparison of the growth of twin pairs with the growth of general population infants. The development of twins can, however, be followed by means of the reference growth charts designed by the authors.

Quantitative analysis of tumor initiation in rat liver: role of cell replication and cell death (apoptosis).

The formation and development of initiated cells has been studied at the beginning of hepatocarcinogenesis. Rats received the genotoxic carcinogen N-nitrosomorpholine (NNM); placental glutathione S-transferase was used as a marker of initiated cells (G+ cells). Single G+ cells appeared within 24 h after NNM; their frequency increased steeply for approximately 2 weeks, then decreased and finally remained constant. G+ foci consisting of >/=2 G+ cells appeared successively after the single cells. Histological determination of DNA replication and apoptosis revealed that: the formation of single G+ cells may not depend on DNA replication of precursor cells; single G+ cells showed considerably lower DNA replication than G- normal hepatocytes; from the 2-cell stage onwards G+ foci displayed enhanced DNA replication and apoptosis. Data from histological sections were transformed into the third dimension by a new stereological method which considers the non-spherical shape of many G+ lesions. Rates of division and death of G+ cells and of formation and growth of G+ foci were estimated by a stochastic model: initially G+ clones appeared at a rate of 12 000 per day and liver until a maximal number of 176 000 (phase I) was reached; thereafter they declined to 134 000 (phase II); they then remained constant (phase III). Estimated division rates of G+ cells decreased from phase I to phase III, while the death rate increased in phase II, when every third G+ clone disappeared. As a result, at day 50 after NNM only 0.3% of G+ single cells had formed a clone containing >/=5 cells. In conclusion, experimental and computed parameters provide direct evidence that hepatocarcinogenesis evolves clonally and that initiated hepatocytes have a selective proliferation advantage, associated with an enhanced potential to undergo apoptosis. Thereby, depending on the conditions, initiated clones expand or become extinct. Extinction may lead to reversion of the biological effects of initiation.

A method for parametric estimation of the number and size distribution of cell clusters from observations in a section plane.

The problem of finding the number and size distribution of cell clusters that grow in an organ or tissue from observations of the number and sizes of transections of such cell clusters in a planar section is considered. This problem is closely related to the well-known corpuscle or Wicksell problem in stereology, which deals with transections of spherical objects. However, for most biological applications, it is unrealistic to assume that cell clusters have spherical shapes since they may grow in various ways. We therefore propose a method that allows for more general spatial configurations of the clusters. Under the assumption that a parametric growth model is available for the number and sizes of the cell clusters, expressions are obtained for the probability distributions of the number and sizes of transections of the clusters in a section plane for each point in time. These expressions contain coefficients that are independent of the parametric growth model and time but depend on which model is chosen for the configuration of the cell clusters in space. These results enable us to perform estimation of the parameters of the growth model by maximum likelihood directly on the data instead of having to deal with the inverse problem of estimation of three-dimensional quantities based on two-dimensional data. For realistic choices of the configuration model, it will not be possible to obtain the exact values of the coefficients, but they can easily be approximated by means of computer simulations of the spatial configuration. Monte Carlo simulations were performed to approximate the coefficients for two particular spatial configuration models. For these two configuration models, the proposed method is applied to data on preneoplastic minifoci in rat liver under the assumption of a two-event model of carcinogenesis as the parametric growth model.

Quantitative analysis of two-dimensional observations of premalignant clones in the presence or absence of malignant tumors.

Based on a two-mutation model for carcinogenesis the mathematical theory is developed which is needed for the quantitative analysis of premalignant clones induced by specific carcinogens. In particular, the article deals with the situation where additional knowledge about the presence or absence of malignant tumors in the tissue of interest is available. The main difficulty arises from the fact that the data on premalignant clones are as a rule obtained from observation of a two-dimensional plane section of the tissue, so that the model needs to be translated from three dimensions into two before it is applicable to the data.

Quantitative analysis of enzyme-altered foci in rat hepatocarcinogenesis experiments--I. Single agent regimen.

Considerable recent attention has focused on the quantitative analysis of enzyme-altered foci in rodent hepatocarcinogenesis experiments. These foci are believed to represent clones of premalignant cells. A method is presented for the quantitative analysis of these foci that takes into account both the total number of focal transections observed in each liver cross-section and the size distribution of these transections. The method, which has a natural interpretation within the framework of a two-mutation model for carcinogenesis, yields estimates of rates of initiation and of growth rates of enzyme-altered foci as functions of dose of the agent under consideration. Definitions of initiation and promotion potencies are proposed. The method is illustrated by application to an experiment in which rats were administered N-nitrosomorpholine at various concentrations in their drinking water.