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PubMed2003

From sphere to torus: a topological view of the metazoan body plan.

From the viewpoint of mathematical topology, membrane systems in intact living cells can be described as closed and orientable surfaces, i.e., as surfaces with two sides and no boundary lines so that an 'inside' and an 'outside' can be distinguished. Usually, biomembranes represent topological spheres, often one embedded in another one. Toroidal membranes are occasionally observed, e.g., in specialized structures of plant cells like the prolamellar body. Here, we propose that rules analogous to those that govern the topology of biomembranes hold for the epithelial cell sheets that cover anatomically external as well as internal surfaces of multicellular animals. We suggest to study the emergence of morphological complexity during metazoan development using concepts from mathematical topology, and propose experimental analyses of those topological transitions that appear to be relevant in development and evolution.

Animals↗
PubMed1993

Gesture-speech mismatch and mechanisms of learning: what the hands reveal about a child's state of mind.

Previous work has shown that, when asked to explain a concept they are acquiring, children often convey one procedure in speech and a different procedure in gesture. Such children, whom we label "discordant," have been shown to be in a transitional state in the sense that they are particularly receptive to instruction--indeed more receptive to instruction than "concordant" children, who convey the same procedure in speech and gesture. This study asks whether the discordant state is transitional, not only in the sense that it predicts receptivity to instruction, but also in the sense that it is both preceded and followed by a concordant state. To address this question, children were asked to solve and explain a series of problems instantiating the concept of mathematical equivalence. The relationship between gesture and speech in each explanation was monitored over the series. We found that the majority of children who learned to correctly solve equivalence problems did so by adhering to the hypothesized path: They first produced a single, incorrect procedure. They then entered a discordant state in which they produced different procedures--one in speech and another in gesture. Finally, they again produced a single procedure, but this time a correct one. These data support the notion that the transitional state is characterized by the concurrent activation of more than one procedure, and provide further evidence that gesture can be a powerful source of insight into the processes involved in cognitive development.

Child↗
PubMed1988

Planning and using PB-PK models: an integrated inhalation and distribution model for nickel.

A general method is presented for the use of mathematical modeling in the design, execution, and interpretation of toxicology experiments. To illustrate the use of mathematical modeling toxicology, a case study is presented of how a dosimetry model for inhaled nickel was developed for use in cancer risk estimation. A physiologically based pharmacokinetic (PB-PK) dosimetry model is used to plan animal experiments and to extrapolate nickel kinetics from animals to humans. These data are then used to estimate human lung cancer risks from human exposure to nickel aerosols. To achieve this goal, a PB-PK dosimetry model for the lung was integrated with a PB-PK dosimetry model for the internal organs. Nickel removal from the lung was found to be saturable and to follow Michaelis-Menten kinetics. The PB-PK lung dosimetry model was used to design both short-term (single exposures) and long-term (multiple intermittent exposures) needed to validate the parameters (Km and Vmax) of the lung dosimetry model. A constant infusion experiment was planned using the PB-PK modeling approach to measure the distribution and elimination of intravenously administered nickel. The two PB-PK models were integrated to estimate the fate of nickel after inhalation and are being used to plan experiments for other routes of exposure such as ingestion of drinking water and dermal contact. The integrated model has been used to calculate a human cancer risk estimate in combination with short-term genotoxic experiments. Using PB-PK models in toxicology, as illustrated here, conserves experimental animals, aids in understanding new physiological phenomena (such as saturable clearance from the lung), incorporates in vitro tests with in vivo experiments, and provides a means of extrapolation to human health risks from multiple routes of exposure. Introducing the concepts of mathematical modeling into toxicity experiments at the beginning of the experiment improves the usefulness of the experiments in risk estimation. PB-PK models are suggested as a new basis for experimental design in toxicology.

Administration, Inhalation↗
PubMed2006

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.

Biophysics↗
PubMed2006

The evolutionary psychology of left and right: costs and benefits of lateralization.

Why do the left and right sides of the vertebrate brain play different functions? Having a lateralized brain, in which each hemisphere carries out different functions, is ubiquitous among vertebrates. The different specialization of the left and right side of the brain may increase brain efficiency--and some evidence for that is reported here. However, lateral biases due to brain lateralization (such as preferences in the use of a limb or, in animals with laterally placed eyes, of a visual hemifield) usually occur at the population level, with most individuals showing similar direction of bias. Individual brain efficiency does not require the alignment of lateralization in the population. Why then are not left--and right-type individuals equally common? Not only humans, but most vertebrates show a similar pattern. For instance, in the paper I report evidence that most toads, chickens, and fish react faster when a predator approaches from the left. I argue that invoking individual brain efficiency (lateralization may increase fitness), evolutionary chance or direct genetic mechanisms cannot explain this widespread pattern. Instead, using concepts from mathematical theory of games, I show that alignment of lateralization at the population level may arise as an "evolutionarily stable strategy" when individually asymmetrical organisms must coordinate their behavior with that of other asymmetrical organisms. Thus, the population structure of lateralization may result from genes specifying the direction of asymmetries which have been selected under "social" pressures.

Animals↗
PubMed2001

Volumetric model determination of the tibia based on 2D radiographs using a 2D/3D database.

We present a new concept with mathematical background for the construction of a three-dimensional (3D) volumetric model of the human tibia based on two conventional orthogonal two-dimensional (2D) radiographic images. This approach is supported by a computer database containing a collection of 80 2D/3D image data sets of individual cadaveric tibiae. For each of these tibiae, the database contains digitized 2D orthogonal radiographic images in both anterior and lateral views, and the corresponding 3D CT data obtained by computerized tomography. To obtain a 3D model of a tibia for a given patient, shape matching is performed. The computer finds the most similar tibia to the patient's tibia among the 2D radiographic images in the database by applying a matching process. To improve accuracy, a 2D image warping procedure can be applied on the slices of the selected bone prior to 3D reconstruction. The warping process is controlled by the contour data of the two orthogonal views. We found that the 3D model thus achieved was useful for virtual preoperative planning and for simulation of the internal fixation of long bones.

Cadaver↗
PubMed1988

The earth and its life: systems perspective.

From the planetary point of view, the Earth can be imagined as a system comprised of interwined natural populations propagated through time via recycling. This recycling, or 'birth/death' process, imposes age patterns on natural populations of the solid earth, hydrosphere, atmosphere and living entities. Mathematically, the concept is analogous to that of population dynamics in living systems. The populations of the Earth system form a hierarchical structure. The hierarchy of geological tectonic realms contains populations of less than or equal to 10(24)-10(26) gr in size, with half-lives in the 10(7)-10(9) yr time range. The approximate parameters for the oceans are less than or equal to 10(24) gr and 10(2)-10(7) yr, for the atmosphere less than or equal to 10(21) gr and 10(-2)-10(7) yr, and for living systems less than or equal to 10(14)-10(19) gr and 10(-3)-10(-2) yr, respectively. In this perspective, and in departure from the GAIA hypothesis, the subordinate populations, such as those of living systems, are constrained to operate within limits imposed by the larger, and slower, hierarchies. They can overstep the imposed limits only on time scales shorter than the response time of the dominant populations. Isotopic record of past sea water shows that on time scales of 10(7) yr the solid earth, hydrosphere, atmosphere and life act as a unified system controlled by tectonics, that is by the hierarchy of the solid earth.

Biological Evolution↗
PubMed2026

Modelling the effects of biological intervention in a dynamical gene network.

Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (1) non-quantitative (or data-based) models which do not describe the probability distribution of gene expressions; (2) quantitative models which fully describe the probability distribution of all genes co-expression; and (3) mechanistic models which allow for a causal interpretation of gene interactions. We propose two rigorous frameworks to model gene alteration in a dynamical GRN, depending on whether the network model is quantitative or mechanistic. We explain how these models can be used for design of experiment, or, if additional alteration data are available, for validation purposes or to improve the parameter estimation of the original model. We apply these methods to the Gaussian graphical model, which is quantitative but non-mechanistic, and to mechanistic models of Bayesian networks and penalized linear regression.

Gene Regulatory Networks↗
PubMed2025

Beyond Level-1: Identifiability of a Class of Galled Tree-Child Networks.

Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in justifying methods. This work obtains strong identifiability results for large sub-classes of galled tree-child semidirected networks. Some of the conditions our proofs require, such as the identifiability of a network's tree of blobs or the circular order of 4 taxa around a cycle in a level-1 network, are already known to hold for many data types. We show that all these conditions hold for quartet concordance factor data under various gene tree models, yielding the strongest results from 2 or more samples per taxon. Although the network classes we consider have topological restrictions, they include non-planar networks of any level and are substantially more general than level-1 networks - the only class previously known to enjoy identifiability from many data types. Our work establishes a route for proving future identifiability results for tree-child galled networks from data types other than quartet concordance factors, by checking that explicit conditions are met.

Mathematical Concepts↗
PubMed2026

Polyploidy Arithmetic.

Polyploidy occurs in plants and animals, and is an important force in speciation and genome evolution. The main focus of this paper is the following fundamental question that was recently posed by Huber and Maher: Given the ploidy numbers of a collection of extant species, or their ploidy profile, what is the smallest number of hybridizations needed in any evolutionary history for these species to completely represent these numbers? In this paper, we shall show that this question can be rephrased in terms of addition chains and the closely related addition sequences, which have been studied for over a century in mathematics and computer science. These are sequences of natural numbers that start with 1, so that each number in the sequence larger than 1 is the sum of two other numbers arising earlier in the sequence. In our first main result, we show that finding the smallest number of hybridization events to explain a ploidy profile, or the hybrid number, is equivalent to solving the so-called addition sequence problem. This immediately implies that computing the hybridization number is computationally intractable. Even so, it also leads to new connections to representing polyploid evolution using networks. More specifically, in our second main result we show that ploidy profiles representable by tree-child networks are exactly the addition chains, implying a polynomial-time algorithm for identifying these profiles. We then consider beaded tree-child networks, which permit the representation of autopolyploidy events, and in our third main result we provide a greedy polynomial-time algorithm to decide whether a given profile can be realized by such a network. We expect that our results can be leveraged in future work through, for example, making use of known algorithms for computing short addition sequences to give bounds for the hybrid number, and in guiding network reconstruction for polyploid species.

Polyploidy↗
PubMed2026

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological↗
PubMed1987

How to use EEG/ERBP phenomena.

Hitherto the study of cerebral slow waves has been mainly empirical phenomenology, in spite of 50 years of effort to discover their origins and possible functions. Since 1970 the increasing use of both analog and digital filters, combined with more sensitive averaging techniques, has led to better understanding of some possible functional significance for the electroencephalogram (EEG) and the endogenous slow waves of event-related brain potentials (ERBP). The developing concepts and mathematics of non-linear dynamicsand coupled oscillators, when considered in the light of cerebral circuit geometry and topology, of local neuronal circuitry, and of both observed and experienced biological behavior, now offer hope for future, more complete, understanding of the development of 'conscious and goal-directed' activity from robotic and reflexive stimulus-response paradigms. Immediate practical results of a biophysical approach to brain waves should be: Models of vertebrate brains as distributed systems of non-linearly coupled oscillators; and revision of traditional methodologies for recording and interpreting EEG/ERBP data.

Afferent Pathways↗
PubMed1982

Protein synthesis after experimental injury in pigs. A comparison of infusion solutions with different amino acid patterns.

This study compared the effect of three amino acid solutions on protein metabolism after injury by measuring plasma amino acid pattern, nitrogen balance, total body protein synthesis and utilisation of administered nitrogen in an experimental protocol using pigs. Protein synthesis and nitrogen utilisation were determined using a 15N-tracer technique with recourse to mathematical model concepts. Control animals which had not undergone surgery had a lower urinary nitrogen excretion, a more favourable nitrogen balance, greater total body protein synthesis and utilisation of the infused amino acids during the infusion of an amino acid solution with a standard pattern of amino acids (A) than the operated animals infused with either solution A or two other test amino acid solutions B and C. Comparison of the post-operative data showed that if solution A is compared with solution (B) whose amino acid content takes account of changes in plasma amino acids following trauma and a solution (C) which contains a high fraction of branched chain amino acids, solution (B) yields the best results in respect of total body protein synthesis and nitrogen utilisation.

Journal Article↗
PubMed1988

Tissue population configuration as a modifier of organ dose response.

Organ tissue populations exist in different spatial configurations. There are the idealized "volume" configuration (bone marrow), the "monolayer" (skin basal cell or large vessel endothelial populations), the "linear" (microvascular endothelial populations) and the "isolated unit" (capillaries, intestinal crypt). This defines the size of the irradiated population (No) and influences the absolute number of cells (N) that survive per unit of tissue dimension to permit repopulation. A proliferative cell that survives irradiation replaces cells lost from distant locations according to its spatial dimension. However, in the isolated unit configuration, a proliferative cell can replace those cells lost from the unit, but an anatomical barrier prevents cell replacement extending to adjacent units. Recovery of a tissue following irradiation depends not only on the number of surviving proliferative cells, but also on the organization of those cells into sub-populations. A regenerative unit is a subpopulation capable of being regenerated from the survival of a single cell. A tissue "functional unit" is a subcomponent of the tissue which contributes independently to overall tissue function, and whose loss results in an irreversible incremental loss of function. Survival of the functional unit depends critically on the degree of interdependence among component regenerative units, and such interdependence is strongly influenced by the tissue's spatial organization. Using these concepts, a mathematical formulation expresses a tissue's functional response to irradiation in terms of cell survival parameters, the spatially-related parameters of regenerative unit size, and the number of interdependent regenerative units comprising a functional unit. It is argued that this provides a more realistic approach toward simulating the radiation response of an organ than one based on tissue bulk cell survival parameters alone.

Cell Division↗
PubMed2004

Kinetics of gel formation in dilute dispersions with strong attractive particle interactions.

We report a combined experimental and modeling study to investigate the kinetics of the transformation of a colloidal dispersion with strong attractive particle interactions into a gel. In the model, a two step mechanism is proposed, where an initial aggregation step is followed by an interconnection step leading to a particle network spanning the entire system volume. Using the Smoluchowski aggregation equation for the first step, we introduce a criterion to determine when the aggregation process is arrested and clusters become caged. In the second step the caged clusters diffuse over short distances and interconnect to form the particle network. The reliability of the gelation times computed by the model has been tested by comparison with a suitable set of experimental data. In addition, we show that the concept of mathematical gelation within the Smoluchowski aggregation equation is not appropriate for the description of the entire gel formation process in this system.

Journal Article↗
PubMed2002

Toxicological evaluation of chemical mixtures.

This paper addresses major developments in the safety evaluation of chemical mixtures during the past 15 years, reviews today's state of the art of mixture toxicology, and discusses challenges ahead. Well-thought-out tailor-made mechanistic and empirical designs for studying the toxicity of mixtures have gradually substituted trial-and-error approaches, improving the insight into the testability of joint action and interaction of constituents of mixtures. The acquired knowledge has successfully been used to evaluate the safety of combined exposures and complex mixtures such as, for example, the atmosphere at hazardous waste sites, drinking water disinfection by-products, natural flavouring complexes, and the combined intake of food additives. To consolidate the scientific foundation of mixture toxicology, studies are in progress to revisit the biological concepts and mathematics underlying formulas for low-dose extrapolation and risk assessment of chemical mixtures. Conspicuous developments include the production of new computer programs applicable to mixture research (CombiTool, BioMol, Reaction Network Modelling), the application of functional genomics and proteomics to mixture studies, the use of nano-optochemical sensors for in vivo imaging of physiological processes in cells, and the application of optical sensor micro- and nano-arrays for complex sample analysis. Clearly, the input of theoretical biologists, biomathematicians and bioengineers in mixture toxicology is essential for the development of this challenging branch of toxicology into a scientific subdiscipline of full value.

Air Pollutants↗
PubMed2003

Cardiac computed tomography imaging: a history and some future possibilities.

Cardiac computed tomography (CT) is a special subset of CT, a subject about which much has been written in terms of the underlying concepts and mathematics and the sociologic impact. Cardiac CT has passed through three, chronologically overlapping, developmental stages and is now in its fourth stage of development. The first stage was fluoroscopy-based CT (1972-1995) stimulated by physiologic research needs, and the next was clinical CT-based exploration (1975-1980) of the potential of clinical CT in cardiology. This was followed by the electron beam CT-based stage (1980-present), which was the first CT approach applicable to clinical cardiology. Finally, volume-scanning CT imaging methods achieved with multislice scanning approaches of helical CT and by flat panel-based CT (1990-present), show great promise for clinically applicable CT of the cardiovascular system.

Animals↗