Analysis of a finite volume method for a cross-diffusion model in population dynamics

The main goal of this paper is to propose a convergent finite volume method for a reactionâeuro"diffusion system with cross-diffusion. First, we sketch an existence proof for a class of cross-diffusion systems. Then the standard two-point finite volume fluxes are used in combination with a nonlinear positivity-preserving approximation of the cross-diffusion coefficients. Existence and uniqueness of the approximate solution are addressed, and it is also shown that the scheme converges to the corresponding weak solution for the studied model. Furthermore, we provide a stability analysis to study pattern-formation phenomena, and we perform two-dimensional numerical examples which exhibit formation of nonuniform spatial patterns. From the simulations it is also found that experimental rates of convergence are slightly below second order. The convergence proof uses two ingredients of interest for various applications, namely the discrete Sobolev embedding inequalities with general boundary conditions and a space-time $L^1$ compactness argument that mimics the compactness lemma due to Kruzhkov. The proofs of these results are given in the Appendix.

Paired activation of two components within muscarinic M3 receptor dimers is required for recruitment of beta-arrestin-1 to the plasma membrane.

beta-Arrestins regulate the functioning of G protein-coupled receptors in a variety of cellular processes including receptor-mediated endocytosis and activation of signaling molecules such as ERK. A key event in these processes is the G protein-coupled receptor-mediated recruitment of beta-arrestins to the plasma membrane. However, despite extensive knowledge in this field, it is still disputable whether activation of signaling pathways via beta-arrestin recruitment entails paired activation of receptor dimers. To address this question, we investigated the ability of different muscarinic receptor dimers to recruit beta-arrestin-1 using both co-immunoprecipitation and fluorescence microscopy in COS-7 cells. Experimentally, we first made use of a mutated muscarinic M(3) receptor, which is deleted in most of the third intracellular loop (M(3)-short). Although still capable of activating phospholipase C, this receptor loses almost completely the ability to recruit beta-arrestin-1 following carbachol stimulation in COS-7 cells. Subsequently, M(3)-short was co-expressed with the M(3) receptor. Under these conditions, the M(3)/M(3)-short heterodimer could not recruit beta-arrestin-1 to the plasma membrane, even though the control M(3)/M(3) homodimer could. We next tested the ability of chimeric adrenergic muscarinic alpha(2)/M(3) and M(3)/alpha(2) heterodimeric receptors to co-immunoprecipitate with beta-arrestin-1 following stimulation with adrenergic and muscarinic agonists. beta-Arrestin-1 co-immunoprecipitation could be induced only when carbachol or clonidine were given together and not when the two agonists were supplied separately. Finally, we tested the reciprocal influence that each receptor may exert on the M(2)/M(3) heterodimer to recruit beta-arrestin-1. Remarkably, we observed that M(2)/M(3) heterodimers recruit significantly greater amounts of beta-arrestin-1 than their respective M(3)/M(3) or M(2)/M(2) homodimers. Altogether, these findings provide strong evidence in favor of the view that binding of beta-arrestin-1 to muscarinic M(3) receptors requires paired stimulation of two receptor components within the same receptor dimer.

Acyl-CoA synthetase 3 promotes lipid droplet biogenesis in ER microdomains.

Control of lipid droplet (LD) nucleation and copy number are critical, yet poorly understood, processes. We use model peptides that shift from the endoplasmic reticulum (ER) to LDs in response to fatty acids to characterize the initial steps of LD formation occurring in lipid-starved cells. Initially, arriving lipids are rapidly packed in LDs that are resistant to starvation (pre-LDs). Pre-LDs are restricted ER microdomains with a stable core of neutral lipids. Subsequently, a first round of"emerging" LDs is nucleated, providing additional lipid storage capacity. Finally, in proportion to lipid concentration, new rounds of LDs progressively assemble. Confocal microscopy and electron tomography suggest that emerging LDs are nucleated in a limited number of ER microdomains after a synchronized stepwise process of protein gathering, lipid packaging, and recognition by Plin3 and Plin2. A comparative analysis demonstrates that the acyl-CoA synthetase 3 is recruited early to the assembly sites, where it is required for efficient LD nucleation and lipid storage.

Acyl-CoA synthetase 3 promotes lipid droplet biogenesis in ER microdomains.

Control of lipid droplet (LD) nucleation and copy number are critical, yet poorly understood, processes. We use model peptides that shift from the endoplasmic reticulum (ER) to LDs in response to fatty acids to characterize the initial steps of LD formation occurring in lipid-starved cells. Initially, arriving lipids are rapidly packed in LDs that are resistant to starvation (pre-LDs). Pre-LDs are restricted ER microdomains with a stable core of neutral lipids. Subsequently, a first round of"emerging" LDs is nucleated, providing additional lipid storage capacity. Finally, in proportion to lipid concentration, new rounds of LDs progressively assemble. Confocal microscopy and electron tomography suggest that emerging LDs are nucleated in a limited number of ER microdomains after a synchronized stepwise process of protein gathering, lipid packaging, and recognition by Plin3 and Plin2. A comparative analysis demonstrates that the acyl-CoA synthetase 3 is recruited early to the assembly sites, where it is required for efficient LD nucleation and lipid storage.

The blood-brain barrier: cellular basis.

Perfusion experiments with horseradish peroxidase have established that the morphological substrate of the blood-brain barrier is represented by microvascular endothelial cells. They are characterized by complexly arranged tight junctions and a very low rate of transcytotic vesicular transport. They express transport enzymes, carrier systems and brain endothelial cell-specific molecules of unknown function not expressed by any other endothelial cell population. These blood-brain barrier properties are not intrinsic to these cells but are inducible by the surrounding brain tissue. Type I astrocytes injected into the anterior eye chamber of the rat or onto the chick chorioallantoic membrane are able to induce a host-derived angiogenesis and some blood-brain barrier properties in endothelial cells of non-neural origin. Recently we have shown that this cellular interaction is due to the secretion of a soluble astrocyte derived factor(s). Astrocytes are also implicated in the maintenance, functional regulation and the repair of the blood-brain barrier. Complex interactions between other constituents of the microenvironment surrounding the endothelial cells, such as the basement membrane, pericytes, nerve endings, microglial cells and the extracellular fluid, take place and are required for the proper functioning of the blood-brain barrier, which in addition is regionally different as reflected by endothelial cell heterogeneity.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

In silico pathway reconstruction: Iron-sulfur cluster biogenesis in Saccharomyces cerevisiae

Background: Current advances in genomics, proteomics and other areas of molecular biology make the identification and reconstruction of novel pathways an emerging area of great interest. One such class of pathways is involved in the biogenesis of Iron-Sulfur Clusters (ISC). Results: Our goal is the development of a new approach based on the use and combination of mathematical, theoretical and computational methods to identify the topology of a target network. In this approach, mathematical models play a central role for the evaluation of the alternative network structures that arise from literature data-mining, phylogenetic profiling, structural methods, and human curation. As a test case, we reconstruct the topology of the reaction and regulatory network for the mitochondrial ISC biogenesis pathway in S. cerevisiae. Predictions regarding how proteins act in ISC biogenesis are validated by comparison with published experimental results. For example, the predicted role of Arh1 and Yah1 and some of the interactions we predict for Grx5 both matches experimental evidence. A putative role for frataxin in directly regulating mitochondrial iron import is discarded from our analysis, which agrees with also published experimental results. Additionally, we propose a number of experiments for testing other predictions and further improve the identification of the network structure. Conclusion: We propose and apply an iterative in silico procedure for predictive reconstruction of the network topology of metabolic pathways. The procedure combines structural bioinformatics tools and mathematical modeling techniques that allow the reconstruction of biochemical networks. Using the Iron Sulfur cluster biogenesis in S. cerevisiae as a test case we indicate how this procedure can be used to analyze and validate the network model against experimental results. Critical evaluation of the obtained results through this procedure allows devising new wet lab experiments to confirm its predictions or provide alternative explanations for further improving the models.

Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock

Background: Understanding the relationship between gene expression changes, enzyme activity shifts, and the corresponding physiological adaptive response of organisms to environmental cues is crucial in explaining how cells cope with stress. For example, adaptation of yeast to heat shock involves a characteristic profile of changes to the expression levels of genes coding for enzymes of the glycolytic pathway and some of its branches. The experimental determination of changes in gene expression profiles provides a descriptive picture of the adaptive response to stress. However, it does not explain why a particular profile is selected for any given response. Results: We used mathematical models and analysis of in silico gene expression profiles (GEPs) to understand how changes in gene expression correlate to an efficient response of yeast cells to heat shock. An exhaustive set of GEPs, matched with the corresponding set of enzyme activities, was simulated and analyzed. The effectiveness of each profile in the response to heat shock was evaluated according to relevant physiological and functional criteria. The small subset of GEPs that lead to effective physiological responses after heat shock was identified as the result of the tuning of several evolutionary criteria. The experimentally observed transcriptional changes in response to heat shock belong to this set and can be explained by quantitative design principles at the physiological level that ultimately constrain changes in gene expression. Conclusion: Our theoretical approach suggests a method for understanding the combined effect of changes in the expression of multiple genes on the activity of metabolic pathways, and consequently on the adaptation of cellular metabolism to heat shock. This method identifies quantitative design principles that facilitate understating the response of the cell to stress.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

Background: During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.

Effectiveness of early detection on breast cancer mortality reduction in Catalonia (Spain)

Background: At present, it is complicated to use screening trials to determine the optimal age intervals and periodicities of breast cancer early detection. Mathematical models are an alternative that has been widely used. The aim of this study was to estimate the effect of different breast cancer early detection strategies in Catalonia (Spain), in terms of breast cancer mortality reduction (MR) and years of life gained (YLG), using the stochastic models developed by Lee and Zelen (LZ). Methods: We used the LZ model to estimate the cumulative probability of death for a cohort exposed to different screening strategies after T years of follow-up. We also obtained the cumulative probability of death for a cohort with no screening. These probabilities were used to estimate the possible breast cancer MR and YLG by age, period and cohort of birth. The inputs of the model were: incidence of, mortality from and survival after breast cancer, mortality from other causes, distribution of breast cancer stages at diagnosis and sensitivity of mammography. The outputs were relative breast cancer MR and YLG. Results: Relative breast cancer MR varied from 20% for biennial exams in the 50 to 69 age interval to 30% for annual exams in the 40 to 74 age interval. When strategies differ in periodicity but not in the age interval of exams, biennial screening achieved almost 80% of the annual screening MR. In contrast to MR, the effect on YLG of extending screening from 69 to 74 years of age was smaller than the effect of extending the screening from 50 to 45 or 40 years. Conclusion: In this study we have obtained a measure of the effect of breast cancer screening in terms of mortality and years of life gained. The Lee and Zelen mathematical models have been very useful for assessing the impact of different modalities of early detection on MR and YLG in Catalonia (Spain).

Hormonal regulation of (Na+,K+)-ATPase biosynthesis in the toad bladder. Effect of aldosterone and 3,5,3'-triiodo-L-thyronine.

Aldosterone stimulates transepithelial Na+ transport in the toad bladder, and thyroid hormone antagonizes this mineralocorticoid action. In the present study, we assessed the influence of these two hormones on the biosynthesis of (Na+,K+)ATPase, the major driving force of Na+ transport. Rates of enzyme synthesis were estimated by immunoprecipitation with monospecific alpha (96,000 daltons) and beta (60,000 daltons) subunit antibodies. After a 30-min pulse of intact tissue with [35S]methionine, the anti-alpha-serum recognized the 96,000-dalton alpha subunit and the anti-beta-serum, a 42,000-dalton protein, in total cell extracts. The biosynthesis rates of both these proteins were increased 2.8- and 2.4-fold respectively, over controls by 80 nM aldosterone after 18 h of hormone treatment. The hormonal effect was not apparent up to 3 h of incubation and was dose dependent between 0.2 and 20 nM aldosterone. The hormonal induction was antagonized by spironolactone (500-fold excess) but not by amiloride. The action of aldosterone thus seems to be a receptor-mediated process and a primary event independent of the Na+ permeability of the apical membrane. Thyroid hormone, on the other hand, had no effect on either basal or aldosterone-stimulated synthesis rates of both enzyme proteins. The results demonstrate a direct effect of aldosterone on gene expression of the (Na+,K+)-ATPase. Ultimately, this phenomenon could be linked to the late mineralocorticoid action of this hormone. On the other hand, thyroid hormone, in contrast to the situation in mammals, does not stimulate de novo enzyme synthesis in amphibia. Neither can the antimineralocorticoid action of thyroid hormone in the toad bladder be explained by an inhibition of the (Na+,K+)-ATPase synthesis.

Once and for all - How people change strategy to ignore irrelevant information in visual tasks

Ignoring irrelevant visual information aids efficient interaction with task environments. We studied how people, after practice, start to ignore the irrelevant aspects of stimuli. For this we focused on how information reduction transfers to rarely practised and novel stimuli. In Experiment 1, we compared competing mathematical models on how people cease to fixate on irrelevant parts of stimuli. Information reduction occurred at the same rate for frequent, infrequent, and novel stimuli. Once acquired with some stimuli, it was applied to all. In Experiment 2, simplification of task processing also occurred in a once-for-all manner when spatial regularities were ruled out so that people could not rely on learning which screen position is irrelevant. Apparently, changes in eye movements were an effect of a once-for-all strategy change rather than a cause of it. Overall, the results suggest that participants incidentally acquired knowledge about regularities in the task material and then decided to voluntarily apply it for efficient task processing. Such decisions should be incorporated into accounts of information reduction and other theories of strategy change in skill acquisition.

Cost-effectiveness of early detection of breast cancer in Catalonia (Spain)

Background: Breast cancer (BC) causes more deaths than any other cancer among women in Catalonia. Early detection has contributed to the observed decline in BC mortality. However, there is debate on the optimal screening strategy. We performed an economic evaluation of 20 screening strategies taking into account the cost over time of screening and subsequent medical costs, including diagnostic confirmation, initial treatment, follow-up and advanced care. Methods: We used a probabilistic model to estimate the effect and costs over time of each scenario. The effect was measured as years of life (YL), quality-adjusted life years (QALY), and lives extended (LE). Costs of screening and treatment were obtained from the Early Detection Program and hospital databases of the IMAS-Hospital del Mar in Barcelona. The incremental cost-effectiveness ratio (ICER) was used to compare the relative costs and outcomes of different scenarios. Results: Strategies that start at ages 40 or 45 and end at 69 predominate when the effect is measured as YL or QALYs. Biennial strategies 50-69, 45-69 or annual 45-69, 40-69 and 40-74 were selected as cost-effective for both effect measures (YL or QALYs). The ICER increases considerably when moving from biennial to annual scenarios. Moving from no screening to biennial 50-69 years represented an ICER of 4,469€ per QALY. Conclusions: A reduced number of screening strategies have been selected for consideration by researchers, decision makers and policy planners. Mathematical models are useful to assess the impact and costs of BC screening in a specific geographical area.

Two component systems: physiological effect of a third component

Signal transduction systems mediate the response and adaptation of organisms to environmental changes. In prokaryotes, this signal transduction is often done through Two Component Systems (TCS). These TCS are phosphotransfer protein cascades, and in their prototypical form they are composed by a kinase that senses the environmental signals (SK) and by a response regulator (RR) that regulates the cellular response. This basic motif can be modified by the addition of a third protein that interacts either with the SK or the RR in a way that could change the dynamic response of the TCS module. In this work we aim at understanding the effect of such an additional protein (which we call ‘‘third component’’) on the functional properties of a prototypical TCS. To do so we build mathematical models of TCS with alternative designs for their interaction with that third component. These mathematical models are analyzed in order to identify the differences in dynamic behavior inherent to each design, with respect to functionally relevant properties such as sensitivity to changes in either the parameter values or the molecular concentrations, temporal responsiveness, possibility of multiple steady states, or stochastic fluctuations in the system. The differences are then correlated to the physiological requirements that impinge on the functioning of the TCS. This analysis sheds light on both, the dynamic behavior of synthetically designed TCS, and the conditions under which natural selection might favor each of the designs. We find that a third component that modulates SK activity increases the parameter space where a bistable response of the TCS module to signals is possible, if SK is monofunctional, but decreases it when the SK is bifunctional. The presence of a third component that modulates RR activity decreases the parameter space where a bistable response of the TCS module to signals is possible.