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PubMed2003

Thyroid hormone production rates in rat liver and intestine in vivo: a novel graph theory and experimental solution.

We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces approximately 31% and whole intestine approximately 6% of whole body T3 from T4. With thyroidal production included, liver contributes approximately 15% and intestine approximately 3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.

Algorithms↗
PubMed1990

Metabolic control theory: a graph-theoretic approach.

The regulatory properties of metabolic pathways are investigated using a graph-theoretic approach. Applying concepts from classical graph theory, analytical expressions are derived for the flux control coefficients of a linear pathway subject to feedback inhibition. It is shown that the relative importance of the various enzymes in the control of flux can be easily established with the aid of this graphical procedure. Another advantage of this technique is that it can be implemented in a step-by-step fashion for simplifying the pathway structure. The graph-theoretic method can also be used for studying the cause-effect relationships of the individual enzymes in a given pathway.

Enzymes↗
PubMed1994

Measurement issues in research on social support and health.

STUDY OBJECTIVE: The aims were: (1) to identify methodological problems that may explain the inconsistencies and contradictions in the research evidence on social support and health, and (2) to validate a frequently used measure of social support in order to determine whether or not it could be used in multivariate analyses of population data in research on social support and health. DESIGN AND METHODS: Secondary analysis of data collected in a cross sectional survey of a multistage cluster sample of the population of the United States, designed to study relationships in behavioural, social support and health variables. Statistical models based on item response theory and graph theory were used to validate the measure of social support to be used in subsequent analyses. PARTICIPANTS: Data on 1755 men and women aged 20 to 64 years were available for the scale validation. RESULTS: Massive evidence of item bias was found for all items of a group membership subscale. The most serious problems were found in relationship to an item measuring membership in work related groups. Using that item in the social network scale in multivariate analyses would distort findings on the statistical effects of education, employment status, and household income. Evidence of item bias was also found for a sociability subscale. When marital status was included to create what is called an intimate contacts subscale, the confounding grew worse. CONCLUSIONS: The composite measure of social network is not valid and would seriously distort the findings of analyses attempting to study relationships between the index and other variables. The findings show that valid measurement is a methodological issue that must be addressed in scientific research on population health.

Adult↗
PubMed2000

Prognostic value of graph theory-based tissue architecture analysis in carcinomas of the tongue.

Several studies on oral squamous cell carcinomas (OSCC) suggest that the clinical value of traditional histologic grading is limited both by poor reproducibility and by low prognostic impact. However, the prognostic potential of a strictly quantitative and highly reproducible assessment of the tissue architecture in OSCC has not been evaluated. Using image analysis, in 193 cases of T1-2 (Stage I-II) OSCC we retrospectively investigated the prognostic impact of two graph theory-derived structural features: the average Delaunay Edge Length (DEL_av) and the average homogeneity of the Ulam Tree (ELH_av). Both structural features were derived from subgraphs of the Voronoi Diagram. The geometric centers of the cell nuclei were computed, generating a two-dimensional swarm of point-like seeds from which graphs could be constructed. The impact on survival of the computed values of ELH_av and DEL_av was estimated by the method of Kaplan and Meier, with relapse-free survival and overall survival as end-points. The prognostic values of DEL_av and ELH_av as computed for the invasive front, the superficial part of the carcinoma, the total carcinoma, and the normal-appearing oral mucosa were compared. For DEL_av, significant prognostic information was found in the invasive front (p < 0.001). No significant prognostic information was found in superficial part of the carcinoma (p = 0.34), in the carcinoma as a whole (p = 0.35), or in the normal-appearing mucosa (p = 0.27). For ELH_av, significant prognostic information was found in the invasive front (p = 0.01) and, surprisingly, in putatively normal mucosa (p = 0.03). No significant prognostic information was found in superficial parts of the carcinoma (p = 0.34) or in the total carcinoma (p = 0.11). In conclusion, strictly quantitative assessment of tissue architecture in the invasive front of OSCC yields highly prognostic information.

Aged↗
PubMed2000

Renormalization-group approach to the vulcanization transition

The vulcanization transition-the cross-link-density-controlled equilibrium phase transition from the liquid to the amorphous solid state-is explored analytically from a renormalization-group perspective. The analysis centers on a minimal model which has previously been shown to yield a rich and informative picture of vulcanized matter at the mean-field level, including a connection with mean-field percolation theory (i.e., random graph theory). This minimal model accounts for both the thermal motion of the constituents and the quenched random constraints imposed on their motion by the cross-links, as well as particle-particle repulsion which suppresses density fluctuations and plays a pivotal role in determining the symmetry structure (and hence properties) of the model. A correlation function involving fluctuations of the amorphous solid order parameter, the behavior of which signals the vulcanization transition, is examined, its physical meaning is elucidated, and the associated susceptibility is constructed and analyzed. A Ginzburg criterion for the width (in cross-link density) of the critical region is derived and is found to be consistent with a prediction due to de Gennes. Inter alia, this criterion indicates that the upper critical dimension for the vulcanization transition is 6. Certain universal critical exponents characterizing the vulcanization transition are computed, to lowest nontrivial order, within the framework of an expansion around the upper critical dimension. This expansion shows that the connection between vulcanization and percolation extends beyond mean-field theory, surviving the incorporation of fluctuations in the sense that pairs of physically analogous quantities (one percolation related and one vulcanization related) are found to be governed by identical critical exponents, at least to first order in the departure from the upper critical dimension (and presumably beyond). The relationship between the present approach to vulcanized matter and other approaches, such as those based on gelation-percolation ideas, is explored in the light of this connection. To conclude, some expectations for how the vulcanization transition is realized in two dimensions, developed with H. E. Castillo, are discussed.

Journal Article↗
PubMed2006

A note on the spread of worms in scale-free networks.

This paper considers the spread of worms in computer networks using insights from epidemiology and percolation theory. We provide three new results. The first result refines previous work showing that epidemics occur in scale-free graphs more easily because of their structure. We argue, using recent results from random graph theory that for scaling factors between 0 and approximately 3.4875, any computer worm infection of a scale-free network will become an epidemic. Our second result uses this insight to provide a mathematical explanation for the empirical results of Chen and Carley, who demonstrate that the Countermeasure Competing strategy can be more effective for immunizing networks to viruses or worms than traditional approaches. Our third result uses random graph theory to contradict the current supposition that, for very large networks, monocultures are necessarily more susceptible than diverse networks to worm infections.

Computer Communication Networks↗
PubMed1998

Review of biomedical knowledge and data representation with conceptual graphs.

The basis of conceptual graphs theory is an ontology of types of concepts. Concepts issued from the ontology are interlinked by semantic relationships and constitute canonical conceptual graphs. Canonical graphs may be combined to derive new conceptual graphs by means of formation rules. This formalism allows to separate knowledge representation into a conceptual level and a domain-dependent level, and enables to share and reuse a representation. This paper presents conceptual graph applications to biomedical data and concept representation, classification systems, information retrieval, and natural language understanding and processing. A discussion on the unifying role conceptual graphs theory plays in the implementation of knowledge-based systems is also presented.

Artificial Intelligence↗
PubMed1992

Rationale for using multiple regression analysis with complex interferences.

Non-specificities and interferences may become complex when they involve the analyte as well as other interfering substances. These non-specificities and interferences are known as analyte-dependent and multi-interferent interferences. Multiple regression analysis has proven valuable in analysing this type of interference, but the theoretical foundation for using multiple regression analysis to study the basic mechanisms of interference has not been explicitly demonstrated. Graph theory can depict and model the basic mechanisms of interferences and the possible interactions. The relationship between the analyte, the interferents, and the response of the instrument to these entities can be approximated by a polymial of order three, which includes partial derivatives and cross-terms. The partial derivatives relate to the different interactions found with the graph theory model. Further, the partial derivatives can be associated with the coefficients in the multiple regression analysis when the respective values of the three variables (analyte, interferent one, and interferent two) are multiplied by one another. One can decide to retain or discard the coefficient of a variable, based on the statistical significance of the coefficient. The respective interactions in the graphic model can then be assembled and the framework of the interference mechanism established.

Bilirubin↗
PubMed2005

Unique optimal foldings of proteins on a triangular lattice.

BACKGROUND: A problem for unique protein folding was raised in 1998: are there proteins having unique optimal foldings for all lengths in the hydrophobic-hydrophilic (hydrophobic-polar; HP) model? To such a question, it was proved that on a square lattice there are (i) closed chains of monomers having unique optimal foldings for all even lengths and (ii) open monomer chains having unique optimal foldings for all lengths divisible by four. In this article, we aim to extend the previous work on a square lattice to the optimal foldings of proteins on a triangular lattice by examining the uniqueness property or stability of HP chain folding. METHOD: We consider this protein folding problem on a triangular lattice using graph theory. For an HP chain with length n > 13, generally it is very time-consuming to enumerate all of its possible folding conformations. Hence, one can hardly know whether or not it has a unique optimal folding. A natural problem is to determine for what value of n there is an n-node HP chain that has a unique optimal folding on a triangular lattice. RESULTS AND CONCLUSION: Using graph theory, this article proves that there are both closed and open chains having unique optimal foldings for all lengths >19 in a triangular lattice. This result is not only general from the theoretical viewpoint, but also can be expected to apply to areas of protein structure prediction and protein design because of their close relationship with the concept of energy state and designability.

Algorithms↗
PubMed2005

simBio: a Java package for the development of detailed cell models.

Quantitative dynamic computer models, which integrate a variety of molecular functions into a cell model, provide a powerful tool to create and test working hypotheses. We have developed a new modeling tool, the simBio package (freely available from ), which can be used for constructing cell models, such as cardiac cells (the Kyoto model from Matsuoka et al., 2003, 2004 a, b, the LRd model from Faber and Rudy, 2000, and the Noble 98 model from Noble et al., 1998), epithelial cells (Strieter et al., 1990) and pancreatic beta cells (Magnus and Keizer, 1998). The simBio package is written in Java, uses XML and can solve ordinary differential equations. In an attempt to mimic biological functional structures, a cell model is, in simBio, composed of independent functional modules called Reactors, such as ion channels and the sarcoplasmic reticulum, and dynamic variables called Nodes, such as ion concentrations. The interactions between Reactors and Nodes are described by the graph theory and the resulting graph represents a blueprint of an intricate cellular system. Reactors are prepared in a hierarchical order, in analogy to the biological classification. Each Reactor can be composed or improved independently, and can easily be reused for different models. This way of building models, through the combination of various modules, is enabled through the use of object-oriented programming concepts. Thus, simBio is a straightforward system for the creation of a variety of cell models on a common database of functional modules.

Algorithms↗