Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations

When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.     

Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems

Lack of unique structural identifiability for parameters of dynamic system models is a very common situation with practical experimental schemes, particularly when studying biological systems. However, for well-structured (e.g., multicompartmental) models, it is often possible to localize unidentifiable parameters between finite limits (“interval identifiability”), using the same data base, and under certain conditions these limits nearly coincide. Two new results in this area are presented: (1) The smallest ranges on all unidentifiable rate constants and pool sizes of the most general n-compartment mammillary system are derived, in an easy-to-program algorithmic form, for the common case of input forcing and output measurements in the central pool only. From these results we see why elimination rate constants (“leaks”) are difficult to distinguish from zero, whereas exchange rate constants between pools, and pool sizes, may be bounded very tightly in certain circumstances. (2) The notion of quasiidentifiability, or sufficient identifiability for practical purposes, is introduced to quantify these circumstances. Each of the rate constants between central and peripheral pools, and all pool sizes, are quasiidentifiable if the magnitude of the ratio of the coefficient to the eigenvalue of the slowest mode is very much greater than the largest coefficient in the sum-of-exponentials response function. Also quasiidentifiability is a necessary condition for applicability of noncompartmental analysis to estimate pool sizes and residence times of mammillary systems with “leaky” noncentral pools.     

An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the ‘simplest’ globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.     

Subset Selection Procedures for Randomized Designs

Starting from the principle that there exists a randomization procedure that assigns treatments to experimental units, four subset selection rules for the problem of selecting the best treatment from a set of different treatments are proposed. Two of these are extensions of already existing subset selection procedures, which were defined for unbalanced designs, and need a separate selection constant for each individual treatment. The other two rules proposed are new and need only one selection constant for all treatments. The various procedures are compared, and illustrated by application to a plant breeding variety trial.     

Ingestion of latex beads by filopodia of adherent mouse peritoneal macrophages. A scanning electron microscopical and reflection contrast microscopical study

Scanning electron microscopy (SEM) of mouse peritoneal macrophages attached to glass shows that these cells have filopodia, i.e., cord-like extensions arising from the cell surface. To confirm that these extensions are not the result of the preparative procedure required for SEM or cell-surface material left behind by cells moving on the substrate surface, the cells were studied with a reflection contrast microscope prior to the preparative procedure. The results indicate that reflection-contrast microscopy and SEM both show the same filopodia for a given cell. The filopodia appear to be functional components of the cytoplasm, as shown by their ability to ingest latex beads.     

Testing for ordered group effects in binary and continuous outcomes

A likelihood ratio test is proposed for the detection of an ordered group effect on bivariate responses where one response is binary and the other is continuous. The procedure is based on a conditional logistic model for the binary response given the continuous outcome. We also develop a likelihood ratio test for simultaneously determining the goodness of fit of the ordering assumption on both responses. Our approach is motivated by a particular toxicity study application involving laboratory animals that focused on the effect of a food color additive on the development of reticuloendothelial (RE) tumors. A brief discussion on extensions to the methodology introduced here is also given, along with a comparison of the approach with a marginal strategy where the presence of an ordered group effect is assessed independently for each of the two responses.     

Abstract representations of biological systems in supercategories

An abstract representation of biological systems from the standpoint of the theory of supercategories is presented. The relevance of such representations forG-relational biologies is suggested. In section A the basic concepts of our representation, that is class, system, supercategory and measure are introduced. Section B is concerned with the mathematical representation starting with some axioms and principles which are natural extensions of the current abstract representations in biology. Likewise, some extensions of the principle of adequate design are introduced in section C. Two theorems which present the connection between categories and supercategories are proved. Two other theorems concerning the dynamical behavior of biological and biophysical systems are derived on the basis of the previous considerations. Section D is devoted to a general study of oscillatory behavior in enzymic systems, some general quantitative relations being derived from our representation. Finally, the relevance of these results for a quantum theoretic approach to biology is discussed.     

Modeling and simulation of molecular biology systems using petri nets: modeling goals of various approaches

Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.     

Dynamic causal models of neural system dynamics: current state and future extensions

Complex processes resulting from interaction of multiple elements can rarely be understood by analytical scientific approaches alone; additional, mathematical models of system dynamics are required. This insight, which disciplines like physics have embraced for a long time already, is gradually gaining importance in the study of cognitive processes by functional neuroimaging. In this field, causal mechanisms in neural systems are described in terms of effective connectivity. Recently, dynamic causal modelling (DCM) was introduced as a generic method to estimate effective connectivity from neuroimaging data in a Bayesian fashion. One of the key advantages of DCM over previous methods is that it distinguishes between neural state equations and modality-specific forward models that translate neural activity into a measured signal. Another strength is its natural relation to Bayesian model selection (BMS) procedures. In this article, we review the conceptual and mathematical basis of DCM and its implementation for functional magnetic resonance imaging data and event-related potentials. After introducing the application of BMS in the context of DCM, we conclude with an outlook to future extensions of DCM. These extensions are guided by the long-term goal of using dynamic system models for pharmacological and clinical applications, particularly with regard to synaptic plasticity.     

REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm

Nonlinear mixed effects models are now widely used in biometrical studies, especially in pharmacokinetic research or for the analysis of growth traits for agricultural and laboratory species. Most of these studies, however, are often based on ML estimation procedures, which are known to be biased downwards. A few REML extensions have been proposed, but only for approximated methods. The aim of this paper is to present a REML implementation for nonlinear mixed effects models within an exact estimation scheme, based on an integration of the fixed effects and a stochastic estimation procedure. This method was implemented via a stochastic EM, namely the SAEM algorithm. The simulation study showed that the proposed REML estimation procedure considerably reduced the bias observed with the ML estimation, as well as the residual mean squared error of the variance parameter estimations, especially in the unbalanced cases. ML and REML based estimators of fixed effects were also compared via simulation. Although the two kinds of estimates were very close in terms of bias and mean square error, predictions of individual profiles were clearly improved when using REML vs. ML. An application of this estimation procedure is presented for the modelling of growth in lines of chicken.     

Quantitative film detection of 3H and 14C in polyacrylamide gels by fluorography.

Methods which use the scintillator PPO to record film images of 3H in chromatograms and polyacrylamide gels (fluorography) have been described elsewhere. This paper demonstrates that pre-exposure of the film to a brief flash of light greatly increases the sensitivity of fluorography. Pre-exposure also permits quantitative interpretation of the film image, because it corrects the non-linear relationship between radioactivity of the sample and absorbance of the film image. Therefore the distribution of radioactivity in the sample is accurately represented by microdensitometry of the image obtained on pre-exposed film. Using pre-exposed film 300 dis. 3H/min or 30 dis. 14C/min can be detected in a band in a gel in a 24-h exposure. The Appendix describes revisions and extensions of existing fluorographic procedures, including application to agarose gels and a rapid procedure for recovering PPO for re-use.     

应用贝叶斯理论推断DNA分子标记基因型

引入贝叶斯理论用以从DNA分子标记的表现型（电泳谱带）推断其基因型（DNA来源）。结果表明,根据标记座位独立贫富而确定的遗传信息不完全标记的基因型概率,与根据邻近的遗传信息完全标记的基因型和有关重组率算得的相应贝叶斯概率,通常都有很大的差异,所以在进行数量性状基因定位和标记辅助选择等工作前前,应当计算每一个体基因组上所有遗传信息不完全座位的有关基因型的贝叶斯概率,文中列出计算未知基因型的贝叶斯概率的详细过程,也讨论了贝叶斯概率的若干推广应用。     

Evaluation of a technique designed to correct nasolabial folds.

This is a long-term follow-up of correction of nasolabial folds in conjunction with face lift that was first published in 1987. In the last 200 face lifts, nasolabial lipectomy has been carried out in 90 percent. Refinements and extensions of the procedure are also described with case illustrations.     

Dual immunostaining procedure demonstrating neurotransmitter and neuropeptide codistribution in the same brain section

A method for sequential immunostaining of two antigens in the same section and the application to neuronal elements in the CNS is described. This method employs the peroxidase-antiperoxidase (PAP) technique as a first sequence, followed by glucose oxidase-antiglucose oxidase (GAG) complex as the second sequence, yielding rich brown and vibrant blue reaction products, respectively. Application of the PAP/GAG immunoreagents as dual markers for various neuropeptide and neurotransmitter systems is described in detail and the procedure is outlined. Comparisons with other dual staining methods are discussed and the application to other systems is presented.     

Subcellular Localization of 5''-Nucleotidase in Rat Brain

The subcellular distribution of the ectoenzyme, 5'-nucleotidase, in cerebral cortex and cerebellum of the rat was studied both biochemically and cytochemically. The fractions were characterized biochemically by marker enzymes. The localization of 5'-nucleotidase activity was also investigated cytochemically in the myelin, synaptosomal, mitochondrial, and microsomal fractions. Biochemically 5'-nucleotidase was found to be enriched in the membrane-containing fractions, i.e., myelin, synaptosomal, and microsomal fractions. Cytochemistry showed the reaction product in the myelin fraction to be associated with myelin profiles. In the synaptosomal fraction reaction product could occasionally be seen at synaptosomal membranes, although it could not be attributed unequivocally to the synaptosome itself, since in positions with reaction product unidentifiable membrane structures could always be seen attached. Mitochondria were virtually without any reaction product. In the microsomal fraction 5'-nucleotidase activity was associated with unidentifiable membrane structures. It is concluded that 5'-nucleotidase is associated with myelin profiles and that the high activity found in the synaptosomal fraction is probably not associated with nerve ending plasma membranes.     

Calorimetric and computational study of enthalpy of formation of 3,6-dibutanoic-1,2,4,5-tetroxane

A thermochemical a rather simple experimental technique method, is used to determine the enthalpy of the formation of 3,6-dibutanoic-1,2,4,5-tetroxane. The study is complemented with suitable theoretical calculations at the semiempirical and ab initio levels. A particular satisfactory agreement between both ways is found for the ab initio calculation at the 6-311G basis set level. Some possible extensions of the present procedure are pointed out.     

A simple work flow for biologically inspired model reduction - application to early JAK-STAT signaling

Background  

Modeling of biological pathways is a key issue in systems biology. When constructing a model, it is tempting to incorporate all known interactions of pathway species, which results in models with a large number of unknown parameters. Fortunately, unknown parameters need not necessarily be measured directly, but some parameter values can be estimated indirectly by fitting the model to experimental data. However, parameter fitting, or, more precisely, maximum likelihood parameter estimation, only provides valid results, if the complexity of the model is in balance with the amount and quality of the experimental data. If this is the case the model is said to be identifiable for the given data. If a model turns out to be unidentifiable, two steps can be taken. Either additional experiments need to be conducted, or the model has to be simplified.     

Phylogenetic analysis of archaea in three fractions of cow rumen based on the 16S rDNA sequence

Phylogenetic analysis of archaea in the rumen ecosystem was analysed by PCR of 16S rDNA from the bovine rumen using archaea-specific primers. The libraries were constructed from rumen fluid (AF), rumen solid (AS), and rumen epithelium (AE) from a rumen-fistulated Korean cow (Hanwoo). The 45 AF clones could be divided into three groups and the largest group was affiliated with the Methanomicrobiaceae family (96% of clones). The AF clones contained a high proportion of unidentifiable clones (67%). The 39 AE clones could be divided into two groups and the largest group was also affiliated with the Methanomicrobiaceae family (95% of clones). The AE clones contained a low proportion of unidentifiable clones (5%). The 20 AS clones could be divided into two groups that were affiliated with either the Methanobacteriaceae family (55%) or the Methanomicrobiaceae family (45%). The AS clones contained a moderate proportion of unidentifiable clones (40%). The predominant family of whole rumen archaea was found to belong to the Methanomicrobiaceae (85%). Methanomicrobiaceae were predominant in the rumen epithelium and the rumen fluid while Methanobacteriaceae were predominant in the rumen solid. One clone from the rumen fluid and two clones from the rumen epithelium contained rDNA sequences of Non-Thermophilic-Crenarchaeota (NTC) and Thermophilic-Crenarchaeota (TC), respectively, which have not previously been described from the rumen.     

Further improvements to a method for analysing stage-frequency data

An iterative procedure for correcting stage-frequency data is described to allow for situations where the period during which a population is sampled begins after some individuals have entered stage 2 or ends before all individuals are dead. The reason for correcting data in this way is to enableKiritani andNakasuji's method for estimating stage-specific survival rates, with extensions proposed byManly (1976, 1977), to be used to analyse the data. The proposed procedure is illustrated on data obtained by sampling a population of the grasshopper Chorthippus brunneus passing through four instar stages to reach the adult stage.     

Statistische analyse eines nichtlinearen systems mit mehreren eingängen durch optimale linearisierung

As compared to linear systems for which well-proven standardised procedures exist, the analysis of nonlinear systems based on random signals cannot be handled in a similar manner because of the lack of a nonlinear systems theory. A number of different procedures has been published, the most popular of them based on the application of the Volterra series, but also procedures based on the optimal linearisation of a given nonlinearity. This paper applies the procedure of optimal linearisation to a system with several imputs and one output. It is possible to extend the procedure to systems having several outputs. As an example, the parameters of the coupling function of a one-stage nerve-network will be computed. The practicability of the procedure and associated errors will be investigated.

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Der Autor dankt Herrn Prof. Dr.-Ing. W. v. Seelen, Universität Mainz für wertvolle Diskussionen und die kritische durchsicht des Manuskripts