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Mathematical guidance for axons.

Axon guidance by gradients plays an important role in wiring up the developing nervous system. Growth cones seem to sense a concentration difference across their spatial extent, and convert this into a signal to move up or down a gradient. In this article, a simple mathematical framework is developed to understand when and where gradient detection can occur as a function of gradient shape. This framework is applied to two examples:the guidance of axons by target-derived diffusible factors in vivo and in collagen gels, and guidance by substrate-bound gradients of optimal shape, as might be relevant in the retinotectal system.Two distinct spatial limits on guidance emerge: I mm for a target-derived diffusible gradient, and I cm for a substrate-bound gradient.

Animals↗

Physiological and mathematical aspects in setting criteria for decontamination of foods by physical means.

In heat processing, microbial inactivation is traditionally described as log-linear. As a general rule, the relation between rate of inactivation and temperature is also described as a log-linear relation. The model is also sometimes applied in pressure and in pulsed electric field (PEF) processing. The model has proven its value by the excellent safety record of the last 80 years, but there are many deviations from log-linearity. This could lead to either over-processing or under-processing resulting in safety problems or, more likely, spoilage problems. As there is a need for minimal processing, accurate information of the inactivation kinetics is badly needed. To predict inactivation more precisely, models have been developed that can cope with deviations of linearity. As extremely low probabilities of survival must be predicted, extrapolation is almost always necessary. However, extrapolation is hardly possible without knowledge of the nature of nonlinearity. Therefore, knowledge of the physiology of inactivation is necessary. This paper discusses the physiology of denaturation by heat, high pressure and pulse electric field. After discussion of the physiological aspects, the various aspects of the development of inactivation models will be addressed. Both general and more specific aspects are discussed such as choice of test strains, effect of the culture conditions, conditions during processing and recovery conditions and mathematical modelling of inactivation. In addition to lethal inactivation, attention will be paid to sublethal inactivation because of its relevance to food preservation. Finally, the principles of quantitative microbiological risk assessment are briefly mentioned to show how appropriate inactivation criteria can be set.

Bacteria↗

A mathematical model of an aqueous-organic partition-based controlled release system using microporous membranes.

A mathematical model with an exact solution is presented for the membrane-controlled release of small molecules such as nicotine, caffeine, and benzoic acid initially present in solution in the reservoir of the device. Both hollow fiber and flat membrane device geometries are considered. The reservoir is bounded by a microporous membrane, the pores of which are filled with a pore liquid immiscible with the reservoir phase liquid. At the interface between the reservoir and the pore, the solute partitions between the reservoir and the pore liquid phases, before diffusing outward through the membrane pore. The model results compare well with experimental data. Parametric studies reveal the interaction between system parameters and the controlled release behavior. A high partition coefficient of the solute between the reservoir and pore phases is found to effect pseudo-zero order release for an extended time. Similarly, when the ratio of time constants for transport of the solute through the reservoir and membrane regions is small, a constant release rate is achieved for an extended time.

Benzoic Acid↗

Mathematical models of cell variation seen in a heterogeneous malignant cell population.

We established mathematical models for the cell variation seen in a heterogeneous malignant cell population, with the supposition that it occurs as the result of the competition between two types of cells, (A) and (B), leading to a change of stem cells. Models I and II: In the case of differences in the ability of (A) and (B) cells to adapt themselves to an environment, the proportion of cells which are less adaptable to the environment decreases exponentially and eventually disappears. Model III supposes that under certain environmental conditions, the two types of cells exist simultaneously in fixed proportions, and transformations of (B) cell to (A) cell and of (A) cell to (B) cell occur at a certain rate but are independent of each other. This process is considered to follow the Markov's chain theory. Based on this supposition, we established Model III and introduced the concept of "coefficient of cell variation". We found that Model III fits the process of cell variation seen in m cell line and we calculated the coefficients of cell variation seen in this cell line in different environments. The possible mechanism of the cell variation of this cell line is discussed.

Animals↗

A mathematical model of "plants-microorganisms" interaction on complete mineral medium and under nitrogen limitation.

A mathematical model concerning the interaction of plants and rhizospheric microorganisms on complete mineral medium and under nitrogen limitation has been constructed. The model takes into account the closeness of plants and microorganisms in terms of the matter released by the plant and consumed by the microorganisms. The effect of rhizospheric microorganisms on plant growth with normal carbon dioxide and complete mineral medium has been demonstrated. Plants interacting with microorganisms have a greater biomass than plants growing without microorganisms. Wheat growth stimulation by metabolites of rhizospheric microorganisms under laboratory conditions on artificial soil has been experimentally demonstrated (Pechurkin, 1997). Under nitrogen limitation, the biomass of plants, with or without microorganisms, is identical, and is substantially reduced as compared with the medium with standard nitrogen.

Biomass↗

Experimental and mathematical models for small aqueous closed ecosystems with spatially separated components.

Experimental and theoretical models of closed "autotroph-heterotroph" (chlorella-yeast, chlorella-protozoa) ecosystems with spatially separated components have been created and studied. The chart of flows and interaction of components of gas-closed "chlorella-yeast" system have formed the basis describe mathematically the functioning of the given system, experimental results have been found to agree with computer solution of the problem in terms of quality. Investigation of the experimental model of the "producer-consumer" trophic chain demonstrated the role of protozoa in nitrogen turnover. "Production-decomposition" and "production-grazing-decomposition" cycle models has been theoretically analyzed and compared. The predator has been shown to be a more intensive mineralizer than the reducer component.

Animals↗

Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions.

All events of the fission yeast cell cycle can be orchestrated by fluctuations of a single cyclin-dependent protein kinase, the Cdc13/Cdc2 heterodimer. The G1/S transition is controlled by interactions of Cdc13/Cdc2 and its stoichiometric inhibitor, Rum1. The G2/M transition is regulated by a kinase-phosphatase pair, Wee1 and Cdc25, which determine the phosphorylation state of the Tyr-15 residue of Cdc2. The meta/anaphase transition is controlled by interactions between Cdc13/Cdc2 and the anaphase promoting complex, which labels Cdc13 subunits for proteolysis. We construct a mathematical model of fission yeast growth and division that encompasses all three crucial checkpoint controls. By numerical simulations we show that the model is consistent with a broad selection of cell cycle mutants, and we predict the phenotypes of several multiple-mutant strains that have not yet been constructed.

Anaphase↗

Mathematical analysis of binary activation of a cell cycle kinase which down-regulates its own inhibitor.

In mammalian cells, the heterodimeric kinase cyclin E/CDK2 (EK2) mediates cell cycle progress from G1 phase into S phase. The protein p27Kip1 (p27) binds to and inhibits EK2; but EK2 can phosphorylate p27, and that leads to the deactivation of p27, presumably liberating more EK2 and forming a positive-feedback loop. It has been proposed that this positive-feedback loop gives rise to binary (all-or-none) release of EK2 from its inactive complex with p27. Binary release suggests a bistable biochemical system in which a stable steady state with low EK2 activity is extinguished in a saddle-node bifurcation, causing the system to shift abruptly to a stable steady state with high EK2 activity. Two mathematical models are discussed, one in which free EK2 deactivates p27 in the EK2-p27 inhibitory complex as well as free p27, and one in which the rate of EK2-catalyzed deactivation of free p27 has saturable kinetics with respect to free p27. In general, if inhibitory binding is approximately in equilibrium, bistability requires that there be a potential unstable steady state where the reaction order of p27 deactivation is greater with respect to EK2 than with respect to p27.

Animals↗

Mathematical formulation of Leibnizian world: a theory of individual-whole or interior-exterior reflective systems.

A world model, suggested by Leibniz's monadology, is formulated as a mathematical axiomatic system. The purpose of this world model is to provide a general scheme for describing a system of individuals having consciousness or internal worlds that communicate with each other and make a unified whole world, and moreover, the latter is reflected into the respective internal worlds and appears as an external world. Examples of such monadological structure of interior-exterior (or individual-whole) reflection can be observed in bio- or socio-systems and recently in computer networks. Moreover, a most elemental version of this structure can be found in the basic level of quantum physics. The model not only gives a prototype of monadological systems but also has an evolutionary ability to produce a hierarchy of monadological systems, which are interpreted as corresponding to various levels of consciousness.

Mathematics↗

Towards a mathematical model of the aortic reservoir.

It is well known from experiments that the circulation is going on under physiological parameters, only if the rigidity of the aortic wall is sufficiently small. We show that the result can be confirmed by the one-dimensional mathematical model describing the dynamics of the aortic reservoir (AR) by means of a hyperbolic system of PDE.

Aorta↗

A mathematical model of cell growth and alkane degradation in Wadden Sea sediment suspensions.

In a series of 16 experiments, hexadecane in different concentrations was mixed with natural Wadden Sea sediments, and the degradation of the alkane was observed under controlled conditions (bioreactor). The aim of the experiments was to quantify the impact of the dissolved oxygen tension and the initial alkane concentration on degradation time and degradation completeness. A mathematical model was constructed which is able to reproduce reasonably well the observed-time series under all conditions: aerobic and nearly anaerobic, diluted and alkane-saturated. The model contains hypotheses on the chain of reactions; it attempts to bridge existing gaps in the understanding of the degradation process.

Aerobiosis↗

Quantitative definition of toxicity: a mathematical description of life and death with dose and time as variables.

This manuscript raises some fundamental issues about the role of time as a variable in toxicology, with implications for all biological sciences and also for disciplines dealing with inanimate systems. The dose-response has taken center stage ever since its formulation by Paracelsus. Time-responses have been considered in the past in various contexts such as time to tumor development or half-life of a compound in an organism. However, there has been, to my knowledge, no successful attempt to tie together dose and time in a generalizable theory. This paper describes toxicity by the minimum number of variables (dose and time) from a macroscopic point of view. Interestingly, these fundamental considerations of the dose- and time-dependence of toxicity led to a simple mathematical formulation, which consists of parts previously recognized as valid under specific conditions of experimentation (Haber's Law of Inhalation Toxicology, Druckrey's Law of Cancer Development).

Animals↗

An improved mathematical approach for the assessment of the medial thickness of pulmonary arteries.

Medial hypertrophy of pulmonary arteries is caused by different acute and chronic diseases complicated by pulmonary hypertension and malformations of the lung. Thus the precise assessment of external radius and relative medial thickness are of importance for clinical and experimental pathology. Different concepts have been proposed to solve this problem. Wall thickness methods which can be applied to obliquely cut arteries suffer from the disadvantage that they require prior injection of vessels. Planimetric methods can be applied to not injected vessels but they fail in assessing the medial thickness of obliquely cut arteries. We describe a mathematical approach which renders even obliquely cut and simultaneously not injected pulmonary arteries able to be assessed accurately for medial thickness and external vessel radius. This method combines the advantages of wall thickness and planimetric methods. This new method and the established wall thickness and planimetric methods were applied to 178 rat pulmonary arteries and 412 injected and 401 not injected human pulmonary arteries. The statistical analysis revealed a satisfying reproducibility (Coefficient of correlation: 0.70-0.90) of the new method. The data assessed by the new method are similar to those of the established methods. We conclude our new method to be a significant tool for the assessment of vessel parameters even in small specimens including only few not injected vessels.

Adolescent↗

Mathematical modelling of oxygen supply and oxygenation in tumor tissues: prognostic, therapeutic, and experimental implications.

Radiation response of some tumors is dependent on the oxygenation of the tumor tissue. To improve tissue oxygenation, attempts to increase a reduced hemoglobin concentration or to shift the dissociation curve of hemoglobin have been made. The aim of this paper is to estimate the influence of such measures on the volume of radiobiologically hypoxic tissue by means of a mathematical model. In addition, the influence of blood velocity and metabolic status of tumor tissues on tissue oxygenation is evaluated. The calculations show a strong influence on hypoxic tissue volume over a modest range of variation of physiological parameters, especially when interactions of several parameters may occur.

Hematocrit↗

Use of mathematical derivatives (time-domain differentiation) on chromatographic data to enhance the detection and quantification of an unknown 'rider' peak.

Two samples of an anticancer prodrug, AQ4N, were submitted for HPLC assay and showed an unidentified impurity that eluted as a 'rider' on the tail of the main peak. Mathematical derivatization of the chromatograms offered several advantages over conventional skimmed integration. A combination of the second derivative amplitude and simple linear regression gave a novel method for estimating the true peak area of the impurity peak. All the calculation steps were carried out using a widely available spreadsheet program.

Chromatography, High Pressure Liquid↗

Mathematics anxiety and working memory: support for the existence of a deficient inhibition mechanism.

A current theory of anxiety effects in cognition claims that anxiety disrupts normal processing within the working memory system. We examined this theory in the context of a reading task, for participants who were high or low in assessed mathematics anxiety. The task was designed to measure the ability to inhibit attention to distracting information and the effects of this ability on explicit memory performance. The results suggested that math-anxious individuals have a deficient inhibition mechanism whereby working memory resources are consumed by task-irrelevant distracters. A consequence of this deficiency was that explicit memory performance was poorer for high-anxious individuals. Based on these results, the recommendation is made that Eysenck and Calvo's (1992) processing efficiency theory be integrated with Connelly, Hasher, and Zack's (1991) inhibition theory to portray more comprehensively the relation between anxiety and performance.

Adolescent↗

A mathematical model for calculation of 90Sr absorbed dose in dental tissues: elaboration and comparison to EPR measurements.

A mathematical model for calculation of the 90Sr absorbed doses in dental tissues is presented. The results of the Monte-Carlo calculations are compared to the data obtained by EPR measurements of dental tissues. Radiometric measurements of the 90Sr concentrations. TLD and EPR dosimetry investigations were performed in animal (dog) study. The importance of the irregular 90Sr distribution in the dentine for absorbed dose formation has been shown. The dominant dose formation factors (main source-tissues) were identified for the crown dentine and enamel. The model has shown agreement with experimental data which allows to determine further directions of the human tooth model development.

Animals↗

Neither high-pass filtering nor mathematical differentiation of the EMG signals can considerably reduce cross-talk.

Using mathematical simulation of motor unit potentials (MUPs), detected by a point and rectangular plate electrode, we have shown that the muscle tissue does not act like a low-pass frequency filter on MUPs. Depending on the electrode type and its longitudinal position, the relative weight of the terminal phases (reflecting the excitation extinction) in MUPs and thus of high frequencies in the MUP power spectrum, increase with the MU depth. Therefore, high-pass filtering or differentiating signals detected neither monopolarly nor bipolarly could eliminate the cross-talk produced by high frequency components of MUPs from deep MUs. Such methods could be effective against the main components but not against the MUP leading edge and terminal phases. To reduce the cross-talk, position of the detecting electrodes should correspond to anatomy of muscles producing the cross-talk. Monopolar electrode should be located above the ends of the muscles. Cross-talk of the muscles located beyond the muscle of interest could be higher than that produced above the end-plate of deep muscles. On the contrary, under detection by a longitudinal bipolar electrode, the cross-talk is much smaller above the end-plate region or beyond deep muscles. The cross-talk is the greatest above the ends of the deep muscles.

Action Potentials↗