Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

Modulation analysis of forced non-linear oscillators for biological modelling.

The synchronization of self-sustained oscillations by a forcing oscillation is of interest in a number of biological models. It has been considered for circadian rhythm modelling, heart-rate variability studies and forced breathing experiments. Outside the range of synchronization, conditions of almost-entrainment occur in which changes in amplitude and/or frequency are apparent. It is shown in this paper that such conditions can be analysed as modulation phenomena using the analytical method of harmonic balance. The degree of non-linearity in the self-sustained oscillation affects the nature of modulation, in that increasing distortion gives a trend towards frequency rather than amplitude modulation. The analytical results compare favourably with spectral analysis of simulated oscillators.     

Simultaneous analysis of neuroendocrine tumor markers by HPLC-electrochemical detection

A validated, high pressure liquid chromatographic (HPLC) method for simultaneous quantitation of urinary catecholic acids 4-hydroxy-3-methoxymandelic acid (HMMA) (vanylmandelic acid) (VMA), 4-hydroxy-3-methoxyphenylacetic acid (HVA) and 5-hydroxyindole-3-acetic acid (5-HIAA) was developed. Sample preparation involved liquid–liquid extraction of acidified urine, containing iso-HMMA (IS) as internal standard, with ether, evaporation of the organic extract, followed by reconstitution of the residue in phosphate buffer at pH 3.3. After reversed-phase HPLC at 35 °C and separation on a Licrospher 125 mm × 4 mm C₁₈ column (5 μm particle size) with phosphate buffer (pH 3.5)–acetone (950:50, v/v) as eluent, quantitation is achieved by electrochemical detection using coulometric detection at a potential of +350 mV. The method was successfully applied to routine diagnosis of neuroblastoma, carcinoid syndrome and pheochromocytoma.     

Exploiting quantitative information in the analysis of dominant markers

Dominant genetic markers such as AFLPs and RAPDs are usually analyzed based on the presence or absence of a band on an electrophoretic gel. This type of analysis does not allow a distinction among dominant homozygotes and heterozygotes. Such a distinction is possible based on the quantitative measurement of band intensities. In the present paper, we consider the problem of analyzing dominant markers based on band-intensity data. The basic step for mapping a marker is to assess its recombination frequency with other markers. Ordering markers on a map can then be done using a number of standard procedures. For this reason estimation of the recombination frequency is the main focus of the present paper. The method is demonstrated for the case of an F₂ population. By simulation we investigate its accuracy and compare it to the standard estimation based on dominant scoring for band presence/absence. There are a number of potential applications. For example, the map may be used to locate quantitative trait loci (QTLs), applying standard procedures modified to account for uncertainty of the marker genotype. Moreover, map information can be used to determine the most likely genotype at a marker, given its band intensity and the band intensities at flanking markers. Received: 2 May 2000 / Accepted: 6 December 2000     

Comparative analysis of certain metals and tumor markers in bronchopulmonary cancer and colorectal cancers. Metals and tumor markers in the neoplastic process

Carcinogenic metal levels in serum and tissue samples were measured in patients with bronchopulmonary or colorectal cancer. The cadmium and nickel tissue levels in the patients with lung cancer were significantly higher than in the controls. A statistical correlation was found between chromium and cadmium, as well as between cadmium and nickel in patients with colorectal cancer. In addition, prior to the operation, the tumor markers alpha-fetoprotein (AFP), carcinoembryonic antigen (CEA), carbohydrate antigen (Ca 19-9), polypeptide histidio antigen (TPA) and ferritin were analyzed. Their average concentrations were correlated with the existing concentrations of the metals. This was done for both types of cancer. Tumor marker detection showed an increase of CEA and TPA in patients with colorectal cancer. A statistical correlation was observed between AFP and zinc tumor tissue.     

Critical analysis of musculoskeletal modelling complexity in multibody biomechanical models of the upper limb

The inverse dynamics technique applied to musculoskeletal models, and supported by optimisation techniques, is used extensively to estimate muscle and joint reaction forces. However, the solutions of the redundant muscle force sharing problem are sensitive to the detail and modelling assumptions of the models used. This study presents four alternative biomechanical models of the upper limb with different levels of discretisation of muscles by bundles and muscle paths, and their consequences on the estimation of the muscle and joint reaction forces. The muscle force sharing problem is solved for the motions of abduction and anterior flexion, acquired using video imaging, through the minimisation of an objective function describing muscle metabolic energy consumption. While looking for the optimal solution, not only the equations of motion are satisfied but also the stability of the glenohumeral and scapulothoracic joints is preserved. The results show that a lower level of muscle discretisation provides worse estimations regarding the muscle forces. Moreover, the poor discretisation of muscles relevant to the joint in analysis limits the applicability of the biomechanical model. In this study, the biomechanical model of the upper limb describing the infraspinatus by a single bundle could not solve the complete motion of anterior flexion. Despite the small differences in the magnitude of the forces predicted by the biomechanical models with more complex muscular systems, in general, there are no significant variations in the muscular activity of equivalent muscles.     

About emergent properties and complexity in biological theories.

Our aim is to present some ideas about the notion of scientific theory which includes the biological theories. We examine relationships among theories and examples of theoretical situations. In this context we propose definitions of emergent property and complexity. These definitions are exemplified by the development of some biological theories.     

Improving the analysis of designed studies by combining statistical modelling with study design information

Background  

In the fields of life sciences, so-called designed studies are used for studying complex biological systems. The data derived from these studies comply with a study design aimed at generating relevant information while diminishing unwanted variation (noise). Knowledge about the study design can be used to decompose the total data into data blocks that are associated with specific effects. Subsequent statistical analysis can be improved by this decomposition if these are applied on selected combinations of effects.     

Catastrophe modelling in the biological sciences

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional physical way, it could also be applied in a new metaphysical way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology.Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised.This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.     

Predicting the onset of filamentous bulking in biological wastewater treatment systems by exploiting image analysis information

The performance of the activated sludge process is limited by the ability of the sedimentation tank (1) to separate the activated sludge from the treated effluent and (2) to concentrate it. Apart from bad operating strategies or poorly designed clarifiers, settling failures can mainly be attributed to filamentous bulking. Image analysis is a promising technique that can be used for early detection of filamentous bulking. The aim of this paper is therefore twofold. Foremost, correlations are sought between image analysis information (i.e., the total filament length per image, the mean form factor, the mean equivalent floc diameter, the mean floc roundness and the mean floc reduced radius of gyration) and classical measurements (i.e., the Sludge Volume Index (SVI)). Secondly, this information is both explored and exploited in order to identify dynamic ARX and state space-type models. Their performance is compared based on two criteria.     

Flexible processing of sensory information induced by axo-axonic synapses on afferent fibers.

Recent experiments indicate that afferent information is processed in the intraspinal arborisation of mammalian group I fibres. During muscle contraction, Ib inputs arising from tendon organs are filtered out by presynaptic inhibition after their entry in the spinal cord. This paper reviews the mechanisms by which GABAergic axo-axonic synapses, i.e., the morphological substrate of presynaptic inhibition, exert this filtering effect. Using confocal microscopy, axo-axonic synapses were demonstrated on segmental Ib collaterals. Most synapses were located on short preterminal and terminal branches. Using a simple compartmental model of myelinated axon, the primary afferent depolarisation (PAD), generated by such synapses, was predicted to reduce the amplitude of incoming action potentials by inactivating the sodium current, and this prediction was experimentally verified. A further theoretical work, relying on cable theory, suggests that the electrotonic structure of collaterals and the distribution of axo-axonic synapses allow large PADs (about 10 mV) to develop on some distal branches, which is likely to result in a substantial presynaptic inhibition. In addition, the electrotonic structure of group I collaterals is likely to prevent PAD from spreading to the whole arborisation. Such a non-uniform diffusion of the PAD accounts for differential presynaptic inhibition in intraspinal branches of the same fibre. Altogether, our experimental and theoretical works suggest that axo-axonic synapses can control the selective funnelling of sensory information toward relevant targets specified according to the motor task.     

Data security in information systems by language analysis.

The paper describes how a language analyser (parser) is used as interface between a user and the functions of an information system. A specific user is at log-on forced into a sublanguage analyser, which only recognizes statements relevant to this specific user. Every attempt to use non-allowed functions is rejected, and the user is guided into his sublanguage. The language analyser is defined completely separately from the semantics of the information system, and it can be automatically generated outgoing from a definition of language functions.     

Intrinsic time scaling in survival analysis: Application to biological populations

A method of dimensionless time-scaling based on extrinsic expectation of life at birth but intrinsic to a system generating a survival distribution is introduced. Such scaling allows the survival fraction function and its associated mortality function to serve as Green's functions for their generalized equivalents. i.e. a “population” function and a “death” function. The analytical mechanics of utilizing these concepts are formulated, applied to the classical Gompertz and Weibull survival models, and discussed with respect to biological relevance.     

The neutrophil as an information transmitter in tumor inhibition by a streptococcal biological response modifier,OK-432

 Effective treatment of a rat transplanted ascites tumor by i. p. injection of a streptococcal biological response modifier, OK-432, was abrogated by selective in vivo depletion of neutrophils by a monoclonal antibody, RP-3. The mechanisms by which neutrophils participate in the therapeutic action of OK-432 were studied with Winn’s assay using peritoneal exudate cells periodically obtained from rats i. p. injected with this biological response modifier. Intraperitoneal resident macrophages were first activated with OK-432, and within 3 h, tumor-inhibitory activity had moved to the early exuded neutrophils. However, 6 h after injection, exuded macrophages were the only cells involved in tumor inhibition. Considered together with other findings, it is likely that, in this system, neutrophils may transmit information from resident macrophages to exuded inflammatory macrophages in a series of responses induced by i. p. injection of OK-432. Received: 29 April 1996 / Accepted: 27 July 1996     

Brucella abortus synthesizes phosphatidylcholine from choline provided by the host

The Brucella cell envelope is characterized by the presence of phosphatidylcholine (PC), a common phospholipid in eukaryotes that is rare in prokaryotes. Studies on the composition of Brucella abortus 2308 phospholipids revealed that the synthesis of PC depends on the presence of choline in the culture medium, suggesting that the methylation biosynthetic pathway is not functional. Phospholipid composition of pmtA and pcs mutants indicated that in Brucella, PC synthesis occurs exclusively via the phosphatidylcholine synthase pathway. Transformation of Escherichia coli with an expression vector containing the B. abortus pcs homologue was sufficient for PC synthesis upon induction with IPTG (isopropyl-beta-d-thiogalactopyranoside), while no PC formation was detected when bacteria were transformed with a vector containing pmtA. These findings imply that Brucella depends on choline provided by the host cell to form PC. We could not detect any obvious associated phenotype in the PC-deficient strain under vegetative or intracellular growth conditions in macrophages. However, the pcs mutant strain displays a reproducible virulence defect in mice, which suggests that PC is necessary to sustain a chronic infection process.     

Detection of novel genetic markers by mismatch analysis.

Chemical mismatch detection has been used to identify previously unknown genomic sequence variations that represent a new source of markers for genetic analysis. The approach detects all types of sequence changes, and therefore overcomes the limitation of restriction analysis, which identifies only a small fraction of the available sequence variations. Three new markers identified at the 3' end of the human dystrophin gene result from variable numbers of exact tandem repeats of 4bp (two examples) or 5bp (one example). None of these would have been detected as restriction fragment length polymorphisms by established procedures.     

Analysis of complex physiological systems by information flow: a time scale-specific complexity assessment.

In the last two decades conventional linear methods for biosignal analysis have been substantially extended by non-stationary, non-linear, and complexity approaches. So far, complexity is usually assessed with regard to one single time scale, disregarding complex physiology organised on different time scales. This shortcoming was overcome and medically evaluated by information flow functions developed in our research group in collaboration with several theoretical, experimental, and clinical partners. In the present work, the information flow is introduced and typical information flow characteristics are demonstrated. The prognostic value of autonomic information flow (AIF), which reflects communication in the cardiovascular system, was shown in patients with multiple organ dysfunction syndrome and in patients with heart failure. Gait information flow (GIF), which reflects communication in the motor control system during walking, was introduced to discriminate between controls and elderly patients suffering from low back pain. The applications presented for the theoretically based approach of information flow confirm its value for the identification of complex physiological systems. The medical relevance has to be confirmed by comprehensive clinical studies. These information flow measures substantially extend the established linear and complexity measures in biosignal analysis.     

The main biological determinants of tumor line taxonomy elucidated by a principal component analysis of microarray data.

By using principal components analysis (PCA) we demonstrate here that the information relevant to tumor line classification linked to the activity of 1375 genes expressed in 60 tumor cell lines can be reproduced by only five independent components. These components can be interpreted as cell motility and migration, cellular trafficking and endo/exocytosis, and epithelial character. PCA, at odds with cluster analysis methods routinely used in microarray analysis, allows for the participation of individual genes to multiple biochemical pathways, while assigning to each cell line a quantitative score reflecting fundamental biological functions.     

On the complexity of fundamental computational problems in pedigree analysis.

Pedigree analysis is a central component of many current efforts to locate genes that contribute to diseases or to valuable traits. The analysis usually involves solving one of two very computation-intense problems. We analyze the complexity of these two problems. Surprisingly, we show that both problems are NP-hard even for pedigrees that contain no inbreeding loops.