Communicating oscillatory networks: frequency domain analysis.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Constructing predictive dynamic models of interacting signalling networks remains one of the great challenges facing systems biology. While detailed dynamical data exists about individual pathways, the task of combining such data without further lengthy experimentation is highly nontrivial. The communicating links between pathways, implicitly assumed to be unimportant and thus excluded, are precisely what become important in the larger system and must be reinstated. To maintain the delicate phase relationships between signals, signalling networks demand accurate dynamical parameters, but parameters optimised in isolation and under varying conditions are unlikely to remain optimal when combined. The computational burden of estimating parameters increases exponentially with increasing system size, so it is crucial to find precise and efficient ways of measuring the behaviour of systems, in order to re-use existing work. RESULTS: Motivated by the above, we present a new frequency domain-based systematic analysis technique that attempts to address the challenge of network assembly by defining a rigorous means to quantify the behaviour of stochastic systems. As our focus we construct a novel coupled oscillatory model of p53, NF-kB and the mammalian cell cycle, based on recent experimentally verified mathematical models. Informed by online databases of protein networks and interactions, we distilled their key elements into simplified models containing the most significant parts. Having coupled these systems, we constructed stochastic models for use in our frequency domain analysis. We used our new technique to investigate the crosstalk between the components of our model and measure the efficacy of certain network-based heuristic measures. CONCLUSIONS: We find that the interactions between the networks we study are highly complex and not intuitive: (i) points of maximum perturbation do not necessarily correspond to points of maximum proximity to influence; (ii) increased coupling strength does not necessarily increase perturbation; (iii) different perturbations do not necessarily sum and (iv) overall, susceptibility to perturbation is amplitude and frequency dependent and cannot easily be predicted by heuristic measures.Our methodology is particularly relevant for oscillatory systems, though not limited to these, and is most revealing when applied to the results of stochastic simulation. The technique is able to characterise precisely the distance in behaviour between different models, different systems and different parts within the same system. It can also measure the difference between different simulation algorithms used on the same system and can be used to inform the choice of dynamic parameters. By measuring crosstalk between subsystems it can also indicate mechanisms by which such systems may be controlled in experiments and therapeutics. We have thus found our technique of frequency domain analysis to be a valuable benchmark systems-biological tool.Peer Reviewe

Sophisticated Framework between Cell Cycle Arrest and Apoptosis Induction Based on p53 Dynamics

The tumor suppressor, p53, regulates several gene expressions that are related to the DNA repair protein, cell cycle arrest and apoptosis induction, which activates the implementation of both cell cycle arrest and induction of apoptosis. However, it is not clear how p53 specifically regulates the implementation of these functions. By applying several well-known kinetic mathematical models, we constructed a novel model that described the influence that DNA damage has on the implementation of both the G2/M phase cell cycle arrest and the intrinsic apoptosis induction via its activation of the p53 synthesis process. The model, which consisted of 32 dependent variables and 115 kinetic parameters, was used to examine interference by DNA damage in the implementation of both G2/M phase cell cycle arrest and intrinsic apoptosis induction. A low DNA damage promoted slightly the synthesis of p53, which showed a sigmoidal behavior with time. In contrast, in the case of a high DNA damage, the p53 showed an oscillation behavior with time. Regardless of the DNA damage level, there were delays in the G2/M progression. The intrinsic apoptosis was only induced in situations where grave DNA damage produced an oscillation of p53. In addition, to wreck the equilibrium between Bcl-2 and Bax the induction of apoptosis required an extreme activation of p53 produced by the oscillation dynamics, and was only implemented after the release of the G2/M phase arrest. When the p53 oscillation is observed, there is possibility that the cell implements the apoptosis induction. Moreover, in contrast to the cell cycle arrest system, the apoptosis induction system is responsible for safeguarding the system that suppresses malignant transformations. The results of these experiments will be useful in the future for elucidating of the dominant factors that determine the cell fate such as normal cell cycles, cell cycle arrest and apoptosis

Understanding dynamics using sensitivity analysis: caveat and solution

<p>Abstract</p> <p>Background</p> <p>Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.</p> <p>Results</p> <p>A careful interpretation of parametric perturbations used in the PSA is presented here to explain the issue of using this analysis in inferring dynamics. In short, the PSA coefficients quantify the integrated change in the system behaviour due to persistent parametric perturbations, and thus the dynamical information of when a parameter perturbation matters is lost. To get around this issue, we present a new sensitivity analysis based on impulse perturbations on system parameters, which is named impulse parametric sensitivity analysis (iPSA). The inability of PSA and the efficacy of iPSA in revealing mechanistic information of a dynamical system are illustrated using two examples involving switch activation.</p> <p>Conclusions</p> <p>The interpretation of the PSA coefficients of dynamical systems should take into account the persistent nature of parametric perturbations involved in the derivation of this analysis. The application of PSA to identify the controlling mechanism of dynamical behaviour can be misleading. By using impulse perturbations, introduced at different times, the iPSA provides the necessary information to understand how dynamics is achieved, i.e. which parameters are essential and when they become important.</p

Towards a systems biology approach to mammalian cell cycle: modeling the entrance into S phase of quiescent fibroblasts after serum stimulation

Background: The cell cycle is a complex process that allows eukaryotic cells to replicate chromosomal DNA and partition it into two daughter cells. A relevant regulatory step is in the G0/G1phase, a point called the restriction (R) point where intracellular and extracellular signals are monitored and integrated. Results: Subcellular localization of cell cycle proteins is increasingly recognized as a major factor that regulates cell cycle transitions. Nevertheless, current mathematical models of the G1/S networks of mammalian cells do not consider this aspect. Hence, there is a need for a computational model that incorporates this regulatory aspect that has a relevant role in cancer, since altered localization of key cell cycle players, notably of inhibitors of cyclin-dependent kinases, has been reported to occur in neoplastic cells and to be linked to cancer aggressiveness. Conclusion: The network of the model components involved in the G1to S transition process was identified through a literature and web-based data mining and the corresponding wiring diagram of the G1to S transition drawn with Cell Designer notation. The model has been implemented in Mathematica using Ordinary Differential Equations. Time-courses of level and of sub-cellular localization of key cell cycle players in mouse fibroblasts re-entering the cell cycle after serum starvation/re-feeding have been used to constrain network design and parameter determination. The model allows to recapitulate events from growth factor stimulation to the onset of S phase. The R point estimated by simulation is consistent with the R point experimentally determined. The major element of novelty of our model of the G1to S transition is the explicit modeling of cytoplasmic/nuclear shuttling of cyclins, cyclin-dependent kinases, their inhibitor and complexes. Sensitivity analysis of the network performance newly reveals that the biological effect brought about by Cki overexpression is strictly dependent on whether the Cki is promoting nuclear translocation of cyclin/Cdk containing complexes. © 2009 Alfieri et al; licensee BioMed Central Ltd

ATM in focus:a damage sensor and cancer target

The ability of a cell to conserve and maintain its native DNA sequence is fundamental for the survival and normal functioning of the whole organism and protection from cancer development. Here we review recently obtained results and current topics concerning the role of the ataxia-telangiectasia mutated (ATM) protein kinase as a damage sensor and its potential as therapeutic target for treating cancer. This monograph discusses DNA repair mechanisms activated after DNA double-strand breaks (DSBs), i.e. non-homologous end joining, homologous recombination and single strand annealing and the role of ATM in the above types of repair. In addition to DNA repair, ATM participates in a diverse set of physiological processes involving metabolic regulation, oxidative stress, transcriptional modulation, protein degradation and cell proliferation. Full understanding of the complexity of ATM functions and the design of therapeutics that modulate its activity to combat diseases such as cancer necessitates parallel theoretical and experimental efforts. This could be best addressed by employing a systems biology approach, involving mathematical modelling of cell signalling pathways

Simplification de modèles mathématiques représentant des cultures cellulaires

L’utilisation de cellules vivantes dans un procédé industriel tire profit de la complexité inhérente au vivant pour accomplir des tâches complexes et dont la compréhension est parfois limitée. Que ce soit pour la production de biomasse, pour la production de molécules d’intérêt ou pour la décomposition de molécules indésirables, ces procédés font appel aux multiples réactions formant le métabolisme cellulaire. Afin de décrire l’évolution de ces systèmes, des modèles mathématiques composés d’un ensemble d’équations différentielles sont utilisés. Au fur et à mesure que les connaissances du métabolisme se sont développées, les modèles mathématiques le représentant se sont complexifiés. Le niveau de complexité requis pour expliquer les phénomènes en jeu lors d’un procédé spécifique est difficile à définir. Ainsi, lorsqu’on tente de modéliser un nouveau procédé, la sélection du modèle à utiliser peut être problématique. Une des options intéressantes est la sélection d’un modèle provenant de la littérature et adapté au procédé utilisé. L’information contenue dans le modèle doit alors être évaluée en fonction des phénomènes observables dans les conditions d’opération. Souvent, les modèles provenant de la littérature sont surparamétrés pour l’utilisation dans les conditions d’opération des procédés ciblées. Cela fait en sorte de causer des problèmes d’identifiabilité des paramètres. De plus, l’ensemble des variables d’état utilisées dans le modèle n’est pas nécessairement mesuré dans les conditions d’opération normales. L’objectif de ce projet est de cibler l’information utilisable contenue dans les modèles par la simplification méthodique de ceux-ci. En effet, la simplification des modèles permet une meilleure compréhension des dynamiques à l’oeuvre dans le procédé. Ce projet a permis de définir et d’évaluer trois méthodes de simplification de modèles mathématiques servant à décrire un procédé de culture cellulaire. La première méthode est basée sur l’application de critères sur les différents éléments du modèle, la deuxième est basée sur l’utilisation d’un critère d’information du type d’Akaike et la troisième considère la réduction d’ordre du modèle par retrait de variables d’état. Les résultats de ces méthodes de simplification sont présentés à l’aide de quatre modèles cellulaires provenant de la littérature

Mathematical Modeling of Multi-Level Behavior of the Embryonic Stem Cell System during Self-Renewal and Differentiation

Embryonic stem cells (ESC) are pluripotent cells derived from the inner cell mass of the blastocyst. These cells have the unique properties of unlimited self-renewal and differentiation capability. ESC therefore hold huge potential for use in therapeutic applications in regenerative medicine. This potential has been demonstrated in vitro by directing differentiation of ESC to various cell types by modulating the soluble and insoluble cues to which the cells are exposed. Despite their great potential, current differentiation methods are still limited in the yield and functionality of the ESC-derived mature phenotype. We hypothesize the lack of mechanistic understanding of the complex differentiation process to be the primary reason behind their restricted success. Mathematical models, coupled to experimental data, can aid in this understanding. While the past several decades have seen advances in the mathematical analysis of biological systems, mathematical approaches to the ESC system have received limited attention. Furthermore, variability of ESC restricts direct application of deterministic approaches towards drawing mechanistic insight. The goal of the current work is to obtain a more thorough mechanistic understanding of the ESC system through mathematical modeling. In ESC, extracellular cues guide single cell behavior in a non-deterministic fashion, giving rise to heterogeneous populations. Therefore, in this work we focus on modeling three levels of the ESC system: intracellular, extracellular, and population. We first developed an optimization framework to identify intracellular gene regulatory interactions from time series data. We show that incorporation of the bootstrapping technique into the formulism allows for accurate prediction of robust interactions from noisy data. A regression approach was then utilized to identify extracellular substrate features influential to cellular behavior. We apply this model to identify fibrin microstructural features which guide differentiation of mESC. Finally, we developed a stochastic model to capture heterogeneous population dynamics of hESC. We demonstrate the usefulness of the model to obtain mechanistic information of cell cycle transition and lineage commitment during differentiation. Through development and utilization of different mathematical approaches to analyze multilevel behavior and variability of ESC self-renewal and differentiation, we demonstrate the applicability of mathematical models in extracting mechanistic information from the ESC system

DYNAMICAL SENSITIVITY ANALYSES OF KINETIC MODELS IN BIOLOGY

Ph.DDOCTOR OF PHILOSOPH