A stochastic model of corneal epithelium maintenance and recovery following perturbation.

Various biological studies suggest that the corneal epithelium is maintained by active stem cells located in the limbus, the so-called limbal epithelial stem cell hypothesis. While numerous mathematical models have been developed to describe corneal epithelium wound healing, only a few have explored the process of corneal epithelium homeostasis. In this paper we present a purposefully simple stochastic mathematical model based on a chemical master equation approach, with the aim of clarifying the main factors involved in the maintenance process. Model analysis provides a set of constraints on the numbers of stem cells, division rates, and the number of division cycles required to maintain a healthy corneal epithelium. In addition, our stochastic analysis reveals noise reduction as the epithelium approaches its homeostatic state, indicating robustness to noise. Finally, recovery is analysed in the context of perturbation scenarios.

Molecular noise induces concentration oscillations in chemical systems with stable node steady states.

It is well known that internal or molecular noise induces concentration oscillations in chemical systems whose deterministic models exhibit damped oscillations. In this article we show, using the linear-noise approximation of the chemical master equation, that noise can also induce oscillations in systems whose deterministic descriptions admit no damped oscillations, i.e., systems with a stable node. This non-intuitive phenomenon is remarkable since, unlike noise-induced oscillations in systems with damped deterministic oscillations, it cannot be explained by noise excitation of the deterministic resonant frequency of the system. We here prove the following general properties of stable-node noise-induced oscillations for systems with two species: (i) the upper bound of their frequency is given by the geometric mean of the real eigenvalues of the Jacobian of the system, (ii) the upper bound of the Q-factor of the oscillations is inversely proportional to the distance between the real eigenvalues of the Jacobian, and (iii) these oscillations are not necessarily exhibited by all interacting chemical species in the system. The existence and properties of stable-node oscillations are verified by stochastic simulations of the Brusselator, a cascade Brusselator reaction system, and two other simple chemical systems involving auto-catalysis and trimerization. It is also shown how external noise induces stable node oscillations with different properties than those stimulated by internal noise.

Steady-state fluctuations of a genetic feedback loop: an exact solution.

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

[Pleural diffusion of amoxicillin 1 and vancomycin in patients treated for post-surgical empyema]. / Empyème après chirurgie d'exérèse pulmonaire: étude de la diffusion pleurale de l'amoxicilline et de la vancomycine.

INTRODUCTION: Treatment of post surgical thoracic empyema consists of chest tube drainage, antibiotic administration, and in some cases surgical lavage of infected spaces. Data in human on the diffusion of antibiotics in pleural cavity after post surgical empyema are lacking. METHODS: We studied on 9 patients with post surgical thoracic empyema (including 6 pneumonectomy) the diffusion of 2 antibiotics commonly used in this situation: amoxicillin (for 7 patients) and vancomycin (for 2 patients). Antibiotics concentrations were measured after at least 3 days of treatment (3-12 days), in order to reach a plateau concentration in the pleural space. RESULTS: The ratio pleural/plasma antibiotic concentration was 1.96 (range: 0.6-4.9). The pleural infection was cured for 8 on 9 patients. The last patients required thoracostomy, and the outcome was favorable after this procedure. CONCLUSION: That the penetration of amoxicillin and vancomycin in pleural space after post surgical empyema is good. Pleural antibiotics concentrations are in the majority of cases higher than plasmatic concentrations.

A systematic investigation of the rate laws valid in intracellular environments.

Recently there has been significant interest in deducing the form of the rate laws for chemical reactions occurring in the intracellular environment. This environment is typically characterized by low-dimensionality and a high macromolecular content; this leads to a spatial heterogeneity not typical of the well stirred in vitro environments. For this reason, the classical law of mass action has been presumed to be invalid for modeling intracellular reactions. Using lattice-gas automata models, it has recently been postulated [H. Berry, Monte Carlo simulations of enzyme reactions in two dimensions: Fractal kinetics and spatial segregation, Biophys. J. 83 (2002) 1891-1901; S. Schnell, T.E. Turner, Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws, Prog. Biophys. Mol. Biol. 85 (2004) 235-260] that the reaction kinetics is fractal-like. In this article we systematically investigate for the first time how the rate laws describing intracellular reactions vary as a function of: the geometry and size of the intracellular surface on which the reactions occur, the mobility of the macromolecules responsible for the crowding effects, the initial reactant concentrations and the probability of reaction between two reactant molecules. We also compare the rate laws valid in heterogeneous environments in which there is an underlying spatial lattice, for example crystalline alloys, with the rate laws valid in heterogeneous environments where there is no such natural lattice, for example in intracellular environments. Our simulations indicate that: (i) in intracellular environments both fractal kinetics and mass action can be valid, the major determinant being the probability of reaction, (ii) the geometry and size of the intracellular surface on which reactions are occurring does not significantly affect the rate law, (iii) there are considerable differences between the rate laws valid in heterogeneous non-living structures such as crystals and those valid in intracellular environments. Deviations from mass action are less pronounced in intracellular environments than in a crystalline material of similar heterogeneity.

Phase transitions and superuniversality in the dynamics of a self-driven particle.

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.

[Indications of lung transplantation: Patients selection, timing of listing, and choice of procedure]. / Indications de la transplantation pulmonaire : sélection des candidats, critères d'inscription en liste d'attente, choix du type d'intervention.

Lung transplantation (LT) is now considered as an excellent treatment option for selected patients with end-stage pulmonary diseases, such as COPD, cystic fibrosis, idiopathic pulmonary fibrosis, and pulmonary arterial hypertension. The 2 goals of LT are to provide a survival benefit and to improve quality of life. The 3-step decision process leading to LT is discussed in this review. The first step is the selection of candidates, which requires a careful examination in order to check absolute and relative contraindications. The second step is the timing of listing for LT; it requires the knowledge of disease-specific prognostic factors available in international guidelines, and discussed in this paper. The third step is the choice of procedure: indications of heart-lung, single-lung, and bilateral-lung transplantation are described. In conclusion, this document provides guidelines to help pulmonologists in the referral and selection processes of candidates for transplantation in order to optimize the outcome of LT.

[Graft-versus-host disease, a rare complication of lung transplantation]. / La maladie du greffon contre l'hôte, graft-versus-host disease, une complication exceptionnelle de la transplantation pulmonaire.

Graft-versus-host disease (GVHD) is a classic and frequent multisystemic complication of bone marrow allografts. It has also been reported after the transplantation of solid organs such as the liver or gut. Recent cases of GVHD have been reported after lung and heart-lung transplant. Skin, liver, gastrointestinal tract and bone marrow are the organ preferentially affected by GVHD. Corticosteroid is the first line treatment of GVHD. The prognosis reported in solid organ transplants is poor with infectious complications favoured by immunosuppressive therapy. In this article, we report a case of a patient with cystic fibrosis who presented a probable GVHD 18 months after a lung transplant and a literature review of similar cases.

Marked ventricular repolarization abnormalities in highly trained athletes' electrocardiograms: clinical and prognostic implications.

OBJECTIVE: We sought to study the functional, clinical and prognostic implications of marked repolarization abnormalities (MRA) sometimes seen in athletes' electrocardiograms (ECGs). BACKGROUND: The clinical meaning of ECG MRA in athletes is unknown. No relationship has been drawn between either training intensity or any particular type of sport and MRA. Athletes are usually symptom free and do not show any decrease in their physical performance. It is as yet unclear whether MRA may have a negative effect on the performance of such athletes in competitive sports. METHODS: We studied 26 athletes with MRA (negative T waves > or =2 mm in three or more ECG leads at rest). No athletes presented clinical symptoms of cardiac disease or decrease in their physical performance. Clinical and physical examinations, ECG at rest, exercise test and echocardiographic and antimyosin studies were performed in all athletes. Rest/exercise myocardial perfusion single-photon emission computed tomography studies were performed in 17 athletes. The follow-up ranged from 4 to 20 years (mean 6.7 years). RESULTS: Four athletes were excluded due to hypertrophic cardiomyopathy. Echocardiographic studies showed right and left normal ventricular dimensions for highly conditioned athletes. In the exercise test, heart rate was 166 +/- 12.4 beats/min, and exercise tolerance was 15.2 +/- 2.7 metabolic equivalents of the task. All athletes had ECG at rest simulating myocardial ischemia or "pseudoischemia" with a tendency to normalize during exercise. Myocardial perfusion studies were normal in the studied athletes. Antimyosin studies showed mild and diffuse myocardial radiotracer uptake in 15 athletes (68%). No adverse clinical events were observed in the follow-up. CONCLUSIONS: These results suggest that MRA have no clinical or pathological implications in athletes and should, therefore, not preclude physical training or participation in sporting events.

Marathon runners presented lower serum cholesteryl ester transfer activity than sedentary subjects.

Acute exercise promotes raised HDL cholesterol concentrations by lipolysis stimulation, but this effect is insufficient to explain the more permanent HDL increases seen during regular exercise. During training periods in a group of marathon runners, we measured lipid transfer protein I (LTP-I)-mediated cholesteryl ester transfer activity (CETA) and its relationship to their HDL concentrations. Runners of both sexes showed significantly lower CETA values than those of sedentary controls. Male runners also had significantly lower serum concentrations of triglyceride, VLDL cholesterol and apolipoprotein B, and significantly higher concentrations of HDL cholesterol and apolipoprotein A-I than male controls. Results indicate that regular practice of aerobic exercise promotes modifications of lipoprotein metabolism related not only to lipolysis, but also to lower CETA. Such modifications are associated with reduced risk of atherosclerosis.

Transient alterations in cardiac performance after a six-hour race.

Ten long distance runners were enrolled in a 6-hour competitive race. Immediately after the race technetium-99m-albumin gated blood pool scans were performed and indium-111 antimyosin was injected. Forty-eight hours later antimyosin scans were obtained and control gated blood pool scans were performed. Left ventricular ejection fraction was higher after the race (65 +/- 5 vs 60 +/- 7%, p less than 0.01) due to a decrease in end-systolic counts. Right ventricular ejection fraction was lower after the race (42 +/- 7 vs 54 +/- 12%, p = 0.03) due to an increase in both end-diastolic and end-systolic counts. A longer systolic period was observed after the race (53 +/- 5% of the RR interval vs 39 +/- 3%, p = 0.005). No significant differences were observed in peak filling or peak emptying rates after the race. An increase in pulmonary blood volume (116% of control) was observed after the race. Antimyosin scans were normal in 7 athletes and minimal antimyosin myocardial uptake was seen in 3. Transient alterations in biventricular performance present after the race correspond to function adaptation to strenuous exercise and are not due to irreversible myocyte damage.

Ascorbic acid inhibits the increase in low-density lipoprotein (LDL) susceptibility to oxidation and the proportion of electronegative LDL induced by intense aerobic exercise.

BACKGROUND: We have previously reported the finding of an acute increment in the susceptibility of low-density lipoprotein (LDL) to oxidation and in the proportion of electronegative LDL [LDL(-)] after intense exercise. We have now studied the effect of oral supplementation with 1 g ascorbic acid, immediately before a 4-h athletic race, on the susceptibility of LDL to oxidation, the proportion of LDL(-), and the alpha-tocopherol and lipid peroxides content in LDL, in order to inhibit such deleterious changes, and to confirm the oxidative nature of modifications of LDL induced by exercise. METHODS: We studied seven highly trained runners who received a supplement of 1 g ascorbic acid and a control group of seven who did not receive the supplement. The susceptibility of LDL to oxidation was assessed by measurement of conjugated dienes after CuSO4-induced oxidation, the proportion of LDL(-) was determined by anion exchange chromatography, alpha-tocopherol was quantified by reverse-phase high performance liquid chromatography, and lipid peroxides were measured by the thiobarbituric acid-reactive substances (TBARS) method. RESULTS: After exercise, in the control group there was an increase in both the susceptibility of LDL to oxidation (change in lag phase from 51.4 +/- 4.7 min to 47.0 +/- 4.6 min, P < 0.05) and the proportion of LDL(-) (from 11.1 +/- 1.4% to 13.0 +/- 2.2%, P < 0.05), but these did not occur in the ascorbic acid group (change in lag phase from 49.7 +/- 2.3 min to 50.4 +/- 4.2 min, and in LDL(-) from 9.7 +/- 1.7% to 10.1 +/- 1.7%). No significant changes in the absolute amount of LDL alpha-tocopherol were observed after exercise (ascorbic acid group: 6.65 +/- 0.94 mol/mol apoB before the race, 7.13 +/- 0.88 mol/mol apoB after the race; control group: 7.34 +/-0.69 mol/mol apoB before the race, 7.06 +/- 0.69 mol/mol apoB after the race), but significant differences were found when increments or decrements of alpha-tocopherol were tested (alpha-tocopherol increased 9.9 +/- 11.5% in the ascorbic acid group, and decreased 0.6 +/- 7.3% in the control group; P < 0.018). TBARS did not change after exercise. CONCLUSIONS: We conclude that 1 g ascorbic acid inhibits the increase in LDL susceptibility to oxidation after exercise, preventing this acute pro-atherogenic effect. In addition, the observation that LDL(-) enhancement is prevented by ascorbic acid supports the hypothesis that at least some of the circulating LDL(-) originates from oxidative processes.

Accurate discretization of advection-diffusion equations.

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.

Many-body theory of chemotactic cell-cell interactions.

We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling epsilon , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient D(R)--an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that D(R) is renormalized to zero at a critical value of epsilon, indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that D(R) approximately epsilon(-2) , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion.

[Biventricular functional adaptation during a prolonged race. An analysis of global and regional ventricular function]. / Adaptación funcional biventricular durante una carrera de larga duración. Análisis de la función ventricular global y regional.

To determine the effects of a six-hour competitive race on left and right ventricular performance, 99mTc gated blood pool scans were performed to 6 long distance runners before the race (rest), each hour during the race and one hour after concluding the exercise (recovery). Heart rate increased during the race, peaking at 4th hour of competition (55 +/- 3 to 110 +/- 9 lpm; p = 0.001). Evolution of right ventricular ejection fraction showed a similar behavior with the evolution of left ventricular ejection fraction during the competition (r = 0.39; p = 0.006). Blood volume in the lungs increased at the end of the race (index 1.13 +/- 0.14) normalizing at recovery (index 1.03 +/- 0.03). Left and right ventricular peak filling rate had an inverse correlation with pulmonary blood volume (r = -0.31; p = 0.041 and r = -0.47; p = 0.001 respectively). Both left and right ventricular ejection fraction had an inverse correlation with pulmonary blood volume (r = -0.38; p = 0.006 and r = -0.34; p = 0.01 respectively). The anteroseptal regional ejection fraction showed an inverse correlation with end-systolic and end-diastolic volume (r = -0.32; p = 0.03 and r = -0.4; p less than 0.01 respectively). The posterolateral region showed a parallel evolution with the global ejection fraction for both left and right ventricles (r = 0.57; p less than 0.0001 and r = 0.38; p = 0.009 respectively). In conclusion, a transient biventricular functional adaptation during a prolonged race is related to pulmonary blood volume redistribution and to a higher preload for both ventricles and a greater afterload for the right ventricle. The posterolateral and inferoapical regions show a similar behavior as both left and right ventricular ejection fraction, response that does not occur with the anteroseptal regional ejection fraction.

[Circumferential profiles versus visual analysis in studies of myocardial perfusion during exertion using thallium-201]. / Perfiles circunferenciales versus análisis visual en los estudios de perfusión miocárdica de esfuerzo con talio-201.

Two methods of analysis for perfusion myocardial studies with thallium are compared: the conventional visual analysis, and a quantitative method which shows results as circumferential profiles. Three hundred and ninety myocardial segments in 65 patients were studied. Visual analysis showed abnormalities in 44/65 (68%) patients, the quantitative method did it in 53/65 (81%). When localization and/or extension discrepancy between the two methods was found, angiography was always concordant with circumferential profiles findings. Total agreement between the two methods was present in 20/65 (31%) patients. The quantitative method is more sensitive than the visual analysis. It is also more precise in defining localization and extension of thallium defects.

[The effect of a race 4 hours in duration on the production of beta-endorphin and adrenocorticotropic hormone]. / Efecto de una carrera de cuatro horas de duración sobre la producción de betaendorfina y hormona adrenocorticotropa.

BACKGROUND: Physiological hormone adaptation to a prolonged and submaximum exercise is not well known. The present study was designed to evaluate changes in plasma levels of beta-endorphin and ACTH before and after a 4 hour pedestrian race. SUBJECTS AND METHOD: Fourteen amateur athletes enrolled in a 4-hour race were studied. Beta-endorphin and ACTH determinations were performed (double antibody IRMA) 10 minutes before and after the race. Simultaneously, heart rate and blood pressure were registered. RESULTS: After the race beta-endorphin level increased 2.8 times with respect to basal values (X [DE]) (42.2 [20,5] VS 14.9 [5.1] pM/I; p < 0.0001), and ACTH level increased 3.5 times (110.8 [72.9] vs 31.4 [14.2] pg/ml; p < 0.0001). There was a positive correlation between the increase of beta-endorphin and ACTH and the distance covered by each athlete (r = 0.617, p < 0.001 and r = 0.533, p < 0.05, respectively), and between the increase of basal and post-race values of both hormones (r = 0.935; p < 0.001). CONCLUSION: Prolonged and submaximum exercise provokes beta-endorphin and ACTH increase, and is related to the amount of performed exercise. There is a positive correlation between the increase of plasma levels of both hormones. Therefore, exercise amount could be one of the main modulator mechanism of beta-endorphin and ACTH release.

[Does antifungal therapy influence postoperative morbidity or long-term survival after surgical resection for pulmonary aspergilloma?]. / Un traitement antifongique périopératoire influence-t-il la morbidité postopératoire et la survie à long terme après une résection pulmonaire pour aspergillome ?

BACKGROUND: Surgical resection of pulmonary aspergilloma is associated with symptoms control, complications prevention, and improved survival, given that the disease is localized and the patient fit enough to undergo surgery. In these operable forms, the impact of perioperative antifungal therapy remains controversial. The purpose of this study was to analyze the impact of antifungal therapy on postoperative morbidity and overall survival in patients with operable pulmonary aspergilloma. METHODS: The clinical records of 113 patients who underwent thoracic surgery for aspergilloma in our institution from January 1989 to December 2010 were retrospectively reviewed. Of these, 64 patients received antifungal therapy in the perioperative period and were included in group 1, and 49 patients did not receive antifungal therapy and were included in group 2. RESULTS: Postoperative complication rates were 31.2% in group 1 and 20.4% in group 2 (P = 0.30). Univariable analysis showed that immunocompromised status (P < 0.001), past history of cancer (P = 0.50), preoperative purulent sputum (P = 0.024), and pneumonectomy (P < 0.001) were significantly associated with postoperative complications, but that antifungal therapy was not. Five- and 10-year overall survival rates were respectively 78.3% and 57.8% in group 1 vs. 85.9% and 65.7% in group 2 (P = 0.23). Multivariate analysis revealed that age higher than 50, immunocompromised status and pneumonectomy were significantly associated with adverse long-term survival (χ(2) = 6.59, df = 5, P < 0.001), but that antifungal therapy was not. CONCLUSION: Antifungal therapy has no significant impact on postoperative morbidity or long-term survival following surgical resection of pulmonary aspergilloma. Such procedure is associated with acceptable postoperative morbidity and long-term survival.