S-system parameter estimation for noisy metabolic profiles using newton-flow analysis.

Biochemical systems are commonly modelled by systems of ordinary differential equations (ODEs). A particular class of such models called S-systems have recently gained popularity in biochemical system modelling. The parameters of an S-system are usually estimated from time-course profiles. However, finding these estimates is a difficult computational problem. Moreover, although several methods have been recently proposed to solve this problem for ideal profiles, relatively little progress has been reported for noisy profiles. We describe a special feature of a Newton-flow optimisation problem associated with S-system parameter estimation. This enables us to significantly reduce the search space, and also lends itself to parameter estimation for noisy data. We illustrate the applicability of our method by applying it to noisy time-course data synthetically produced from previously published 4- and 30-dimensional S-systems. In addition, we propose an extension of our method that allows the detection of network topologies for small S-systems. We introduce a new method for estimating S-system parameters from time-course profiles. We show that the performance of this method compares favorably with competing methods for ideal profiles, and that it also allows the determination of parameters for noisy profiles.

Neutralizing antibodies in Multiple Sclerosis a model-based analysis of Interferon beta signaling pathway in macrophages

Multiple Sclerosis is the most common non-traumatic cause of neurologicaldisability in young people. There is no cure yet, and until recently, few long-termtherapies existed. Interferon beta (IFNβ) was the first treatment, and remains the mostcommonly prescribed. One of the most significant problems of IFNβ therapy is theproduction of drug specific antibodies. Up to 45% of patients develop neutralizingantibodies (NAbs) to IFNβ products. The neutralizing antibody binds to the biologicalagent preventing its interaction with its receptor, inhibiting the biological action of theprotein, which abrogates the clinical efficacy of IFNβ treatment. Interferon-betamediates its response by binding to its high affinity cell surface receptor and initiatingthe JAK/STAT signalling cascade. In this project we have analyzed the IFNβ signalingpathway in macrophages when neutralizing antibodies are present. The response tothis pathway after IFNβ stimulation shows a transient oscillatory rhythm of STAT1phosphorylation, which varies as NAbs concentration increases. To improve ourunderstanding of that behavior, we extended an existing mathematical model based onnonlinear ordinary differential equations of JAK/STAT pathway by including IFN-NAbassociation and IFN-activation receptor. Combining our theoretical model withexperimental data we could study the role of neutralizing antibodies on the molecularresponse and determine its lifetime after cytokine stimulation.

Equacions diferencials i models

En tot cas, jo voldria que aquesta conferència fos això que he dit: una breu lliçó sobre la importància de les equacions diferencials. Parlaré d'elles des de el punt de vista del models, és a dir, dels fenòmens que modelitzeu. I intentaré explicar que malgrat el seu origen antic, totes elles segueixen presentant avui en dia problemes nous i interessants, tant des de el punt de vista teòric com pràctic.

Estimating parameters for generalized mass action models using constraint propagation.

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.

Integração numérica de leis de velocidade diferenciais com o uso do SCILAB

In this work, we applied the free open source SCILAB software for the numerical integration of differential rate law equations to obtain the concentration profiles of chemical species involved in the kinetics of some complex reactions. An automated method was applied to construct the system of ordinary differential equations (ODE) from the postulated chemical models. The solutions of the ODEs were obtained numerically by standard SCILAB functions. We successfully simulated even complex chemical systems such as pH oscillators. This communication opens up the possibility of using SCILAB in simulations and modeling by our chemistry undergraduate students.

Évaluation in silico des pompes d’assistance ventriculaire de type écoulement mixte

L'insuffisance cardiaque est une maladie à grande incidence dont le traitement définitif est difficile. Les pompes d'assistance ventriculaire ont été proposées comme thérapie alternative à long terme, mais la technologie est relativement jeune et selon son design, axial ou centrifuge, le dispositif favorise soit l'hémolyse, soit la stagnation de l'écoulement sanguin. Les pompes à écoulement mixte, combinant certaines propriétés des deux types, ont été proposées comme solution intermédiaire. Pour évaluer leurs performances, nous avons effectué des comparaisons numériques entre huit pompes, deux axiales, deux centrifuges, et quatre mixtes, en employant un modèle Windkessel du système cardiovasculaire avec paramètres optimisés pour l'insuffisance cardiaque résolu avec une méthode Radau IIA3, une méthode de résolution de système d'équations différentielles ordinaires L-stable appartenant à la famille des méthodes Runge-Kutta implicites. Nos résultats semblent suggérer que les pompes d'assistance mixtes ne démontrent qu'un léger avantage comparativement aux autres types en terme de performance optimale dans le cas de l'insuffisance cardiaque, mais il faudrait effectuer plus d'essais numériques avec un modèle plus complet, entre autres avec contrôles nerveux implémentés.

Modélisation mathématique de la propagation de la malaria.

Un modèle mathématique de la propagation de la malaria en temps discret est élaboré en vue de déterminer l'influence qu'un déplacement des populations des zones rurales vers les zones urbaines aurait sur la persistance ou la diminution de l'incidence de la malaria. Ce modèle, sous la forme d'un système de quatorze équations aux différences finies, est ensuite comparé à un modèle analogue mais en temps continu, qui prend la forme d'équations différentielles ordinaires. Une étude comparative avec la littérature récente permet de déterminer les forces et les faiblesses de notre modèle.

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