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Since the discovery of the SOM's by T. Kohonen, many results that provide a better description of their behaviour have been found. Most of them are very convincing, but from a mathematical point of view, only a few are actually proved. In this paper, we make a review of some results that are still to be proved and give some framework to formulate various questions.
Temporal changes in the tolerance to alcohol are rarely discussed. In the behavioral theory proposed here, the rate of increase in tolerance during alcohol exposure is described by linear equations with zero intercept. These equations describe the rate of tolerance growth for acute tolerance, the rate of tolerance growth after alcohol dosing (chronic tolerance), and, for cases in which tolerance has been conditioned, the equations also describe changes in the rate of growth of tolerance when the stimulus set changes. This theory does not explain tolerance acquisition, but may be useful in investigating the physiological basis for tolerance acquisition because it provides numerical values for momentary tolerance that can be compared with concurrent physiological changes. The theory is testable and most of the published behavioral data on non-conditioned tolerance are consistent with the proposed theory. New empirical data on conditioned tolerance are needed to evaluate the proposed theory, and the design for an evaluation is suggested here. Despite its limitations, the theory serves as one example of what a mathematical theory for tolerance might be and may stimulate the development of competing theories with which it could be compared empirically.
The current global initiative to eliminate lymphatic filariasis is a major renewed commitment to reduce or eliminate the burden of one of the major helminth infections from resource-poor communities of the world. Mathematical models of filariasis transmission can serve as an effective tool for guiding the scientific development and management of successful community-level intervention programmes by acting as analytical frameworks for integrating knowledge regarding parasite transmission dynamics with programmatic factors. However, the power of these tools for supporting control interventions will be realized fully only if researchers address the current uncertainties and gaps in data and knowledge of filarial population dynamics and the effectiveness of currently proposed filariasis intervention options.
INTRODUCTION: Previous publications from GlaxoSmithKline and University of Toledo laboratories convey our independent attempts to predict the half-lives of xenobiotics in humans using data obtained from rats. The present investigation was conducted to compare the performance of our published models against a common dataset obtained by merging the two sets of rat versus human half-life (hHL) data previously used by each laboratory. METHODS: After combining data, mathematical analyses were undertaken by deploying both of our previous models, namely the use of an empirical algorithm based on a best-fit model and the use of rat-to-human liver blood flow ratios as a half-life correction factor. Both qualitative and quantitative analyses were performed, as well as evaluation of the impact of molecular properties on predictability. RESULTS: The merged dataset was remarkably diverse with respect to physiochemical and pharmacokinetic (PK) properties. Application of both models revealed similar predictability, depending upon the measure of stipulated accuracy. Certain molecular features, particularly rotatable bond count and pK(a), appeared to influence the accuracy of prediction. DISCUSSION: This collaborative effort has resulted in an improved understanding and appreciation of the value of rats to serve as a surrogate for the prediction of xenobiotic half-lives in humans when clinical pharmacokinetic studies are not possible or practicable.
Whole blood samples of known methylene tetrahydrofolate reductase (MTHFR) genotypes from 24 individuals were examined at site C677T. Their amplified DNA products were assessed by two-color fluorescence cross-correlation measurements and agarose gel electrophoresis/capillary gel electrophoresis. DNA subpopulations were identified which were not associated with the proper genotype by primer combinations and cycling conditions called multiplexes. We confirmed that DNA analysis by two-color fluorescence cross-correlation measurements allowed the detection of fluorescence signals specifically associated with the proper genotypes in a mixture of amplified nontarget DNA molecules without DNA sizing. The measurement approach does not require complex, follow-up mathematical analysis and is applicable to any single nucleotide polymorphisms. The simple immunogenetic model showed how the approach works to reveal specific DNA target by preventing detection of nontarget DNA. Under those experimental conditions, a new ultrasensitive, and specific method for clinical immunologists is born.
BACKGROUND: Pulmonary nodules are occasionally difficult to excise using video-assisted thoracic surgery (VATS). METHODS: To predict operative success, mathematical models using preoperative computerized tomography (CT) measurements were tested in 50 consecutive patients who underwent attempted or successful thoracoscopic lung biopsy. Unrelated technical problems resulted in the exclusion of 3 patients. RESULTS: No differences were noted with respect to lobar location, thoracic dimensions, gender, presence of chronic obstructive pulmonary disease, or nodule pathology. The expression S/(D + 1), where S = nodule size (cm) and D = distance (cm) to the nearest visceral pleura, yielded significantly higher values for visible nodules (P < 0.001). Resectable nodules had a higher score using the expression 1/(S + D + 1), (P < 0.001). Simple cases (n = 19) were defined as those in which nodules were both visible and resectable with very basic VATS techniques. All others (n = 28) were considered complex. The derived expression for Simplicity [1/(S(D + 1))] yielded significantly higher values for simple cases (0.8 +/- 0.3 vs. 0.3 +/- 0.2 cm(-2), P < 0.001) and all simple cases had a score > or = 0.4. Logistic regression analysis showed that the formulas for resectability and simplicity were significant independent predictors for resectability and simplicity. CONCLUSIONS: Equations based on objective CT measurements may be useful for planning VATS nodulectomy or studying the outcome of these minimally invasive operations.
Flow through thin-wall axisymmetric tubes has long been of interest to physiologists. Analysis is complicated by the fact that such tubes will collapse when the transmural pressure (internal minus external pressure) is near zero. Because of the absence of any body of related knowledge in other sciences or engineering, previous workers have directed their efforts towards experimental studies of flow in collapsible tubes. More recently, some attention has been given towards analytical studies. Results of an extensive series of experiments show that the significant system parameter is transmural pressure. The cross-sectional area of the tube depends upon the transmural pressure, and changes in cross-section in turn affect the flow geometry. Based on experimental studies, a lumped parameter system model is proposed for the collapsible tube. The mathematical model is simulated on a hybrid computer. Experimental data were used to define the functional relationship between cross-sectional area and transmural pressure as well as the relation between the energy loss coefficient and cross-sectional area. Computer results confirm the validity of the model for both steady and transient flow conditions.
Ability to predict the dynamic response of oxygen, carbon dioxide tensions, and pH in blood and tissues to abrupt changes in ventilation is important in the mathematical modeling of the respiratory system. In this study, the controlled plant (the amount and distribution of O(2) and CO(2)) of the respiratory system is modeled. Although the body tissues are divided into a finite number of "compartments" (three tissue groups), in contrast to earlier models, the blood and tissue gas tensions within each compartment are considered to be continuously distributed in time and in one spatial coordinate. The mass conservation equations for oxygen and carbon dioxide involved in the blood-tissue gas exchange are described by a set of partial differential equations which take into account convection of O(2) and CO(2) caused by the flow of blood as well as diffusion due to local tension gradients. Nonlinear algebraic equations for the dissociation curves, which take into account the Haldane and Bohr effects in blood, are used to obtain the relationships between concentrations and partial pressures. Time-variable delays caused by the arterial and venous transport of the respiratory gases are also included. The model so constructed successfully reproduced actual O(2) and CO(2) tensions in arterial blood, and in muscle venous and mixed venous blood when ventilation was abruptly changed.
A mathematical model for the hormonal interactions of the human menstrual cycle is presented. The feedback effects of estrogen on the release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) are considered, including a mechanism describing the midcycle LH peak. Computer simulation with this model yields results which are periodic and in good agreement with physiological data.
This paper deals with the physical interpretation of existing mathematical models which describe the transient sodium conductance changes in excitable membranes. It is shown that there are clear limitations to the specificity of inferences which may be drawn about physical mechanism from the behavior of abstract models. Within these limitations, it is shown that a pronounced inactivation shift is not necessarily evidence for coupling between the events responsible for the rise and inactivation of the sodium conductance, but that the inactivation shift may be associated with an event whose rate explicitly depends on the rate of continuous voltage change or magnitude of instantaneous voltage change.
A dynamical mathematical model of the acute myeloblastic leukemic state is proposed in which normal neutrophils and their precursors, and leukemic myeloblasts, proliferate as distinct but interacting cell populations. Each population has a Go compartment, consisting of resting cells, that acts as a control center to determine the rate of proliferation. These rates are assumed to depend on the total number of cells in the combined populations. The presence of the leukemic population destabilizes the homeostatic state of the normal population, which is stable in the absence of leukemic cells, and drives the system to a new stable state consisting entirely of leukemic cells and no normal cells. Calculations based on the theory suggest that it is able to simulate the kinetic features of this disease state, at least in its typical manifestations.
Based on our previous mathematical model of the acute myeloblastic leukemic (AML) state in man, we superimpose a chemotherapeutic drug treatment regimen. Our calculations suggest that small changes in the protocol can have significant effects on the result of treatment. Thus, the optimal period between drug doses is the S-phase interval of the leukemic cells--about 20h--and the greater the number of doses administered in a given course treatment, the longer the rest interval should be before the next course is administered. For a patient with a "slow" growing AML cell population, remission can be achieved with one or two courses of treatment, and further suppression of the leukemic population can be achieved with continued courses of treatment. However, for patients with a "fast" growing AML cell population, a similar aggressive treatment regimen succeeds in achieving remission status only at the cost of very great toxic effects on the normal neutrophil population and its precursors.
The inhibitory effect of glucose upon 45Ca efflux from prelabeled pancreatic islets was simulated in a mathematical model for Ca2+-cyclic AMP interaction in the process of glucose-induced insulin release. At variance with a previous interpretation, it was postulated that glucose inhibits 45Ca efflux by facilitating the uptake of the cation by the vacuolar system. The latter facilitation did not hinder glucose from provoking a rapid accumulation of cytosolic Ca2+ and, hence, insulin release. The postulated facilitation was also suitable in simulating the effect of glucose upon 45Ca efflux, uptake, and intracellular distribution in the pancreatic islets.
Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.
Autocrine ligands have been demonstrated to regulate cell proliferation, cell adhesion, and cell migration in a number of different systems and are believed to be one of the underlying causes of malignant cell transformation. Binding of these ligands to their cellular receptors can be compromised by diffusive transport of ligand away from the secreting cell. Exogenous addition of antibodies or solution receptors capable of competing with cellular receptors for these autocrine ligands has been proposed as a means of inhibiting autocrine-stimulated cell behavioral responses. Such "decoys" complicate cellular binding by offering alternative binding targets, which may also be capable of aiding or abating transport of the ligand away from the cell surface. We present a mathematical model incorporating autocrine ligand production and the presence of competing cellular and solution receptors. We elucidate effects of key system parameters including ligand diffusion rate, binding rate constants, cell density, and secretion rate on the ability of solution receptors to inhibit cellular receptor binding. Both plated and suspension cell systems are considered. An approximate analytical expression relating the key parameters to the critical concentration of solution "decoys" required for inhibition is derived and compared to the numerical calculations. We find that in order to achieve essentially complete inhibition of surface receptor binding, the concentration of decoys may need to be as much as four to eight orders of magnitude greater than the equilibrium disociation constant for ligand binding to surface receptors.
Multiple amphipathic alpha-helical candidate domains have been identified in exchangeable apolipoproteins by sequence analysis and indirect experimental evidence. The distribution of charged residues can differ within and between these apolipoproteins. Segrest et al. (Segrest, J. P., H. DeLoof, J. G. Dohlman, C. G. Brouillette, and G. M. Anantharamaiah. 1990. Proteins. 8:103-117.) argued that these differences are correlated with lipid affinity. A mathematically defined motif for the particular charge distribution associated with high lipid affinity (class A) is proposed. Primary sequence data from protein segments proposed previously to have an amphipathic alpha-helical structure are scanned. Counting formulas are presented for determining the conditional probability that the match between an observed charge distribution and the proposed motif would occur by chance. Because the preselected helical segments are short (the modal length is 22) and the motif definition imposes multiple constraints on the acceptable distributions, the computer-based algorithm is quite feasible computationally. 19 of the 20 segments previously assigned to class A match the motif sufficiently well (the remaining one is borderline), while very few others "erroneously" pass the screening test. These results confirm the original assignments of the candidate domains and, thus, support the hypothesis that there is a distinguishable subset of helixes having high lipid affinity. This counting approach is applicable to a growing subset of protein sequence analysis problems in which the segment lengths are short and the motif is complex.
Variation in the amplitude of miniature postsynaptic currents (mPSCs) generated by individual quanta of neurotransmitter is a major contributor to the variance of evoked synaptic responses. Here we explore the possible origins of this variability by developing a mathematical description of mPSC generation and consider the contribution of "off-center" release to this variability. By "off-center" release we mean variation in the distance between the position where a presynaptic vesicle discharges its content of neurotransmitter into the synaptic cleft and the center of a cluster of postsynaptic receptors (PRCs) that responds to those transmitter molecules by generating an mPSC. We show that when the time course of quantal discharge through a fusion pore (noninstantaneous release) is considered, elementary analytical descriptions of the subsequent diffusion of transmitter within the synaptic cleft (with or without uptake) predict the development of significant gradients of transmitter concentration during the rising phase of mPSCs. This description of diffusion is combined with a description of the pharmacodynamics of receptors in the PRC and of the time dependence of the gradient of transmitter concentration over the area of the PRC to reconstruct the time course and amplitude of an mPSC for a synapse of a given geometry. Within the constraints of known dimensions of presynaptic active zones and postsynaptic receptor clusters at CNS synapses, our analysis suggests that "off-center" release, produced by allowing release to occur anywhere within an anatomically defined presynaptic active zone, can be an important contributor to mPSC variability. Indeed, modulation of the influence of "off-center" release may be a novel way of controlling synaptic efficacy. We also show how noninstantaneous release can serve to focus the action of neurotransmitter within a given synapse and thereby reduce cross-talk between synapses.
Corticotropin-releasing hormone (CRH) is an important regulator of adrenocorticotropin (ACTH) secretion from pituitary corticotroph cells. The intracellular signaling system that underlies this process involves modulation of voltage-sensitive Ca2+ channel activity, which leads to the generation of Ca2+ action potentials and influx of Ca2+. However, the mechanisms by which Ca2+ channel activity is modulated in corticotrophs are not currently known. We investigated this process in a Hodgkin-Huxley-type mathematical model of corticotroph plasma membrane electrical responses. We found that an increase in the L-type Ca2+ current was sufficient to generate action potentials from a previously resting state of the model. The increase in the L-type current could be elicited by either a shift in the voltage dependence of the current toward more negative potentials, or by an increase in the conductance of the current. Although either of these mechanisms is potentially responsible for the generation of action potentials, previous experimental evidence favors the former mechanism, with the magnitude of the shift required being consistent with the experimental findings. The model also shows that the T-type Ca2+ current plays a role in setting the excitability of the plasma membrane, but does not appear to contribute in a dynamic manner to action potential generation. Inhibition of a K+ conductance that is active at rest also affects the excitability of the plasma membrane.