Anastasis Georgoulas, Allan Clark, Andrea Ocone, S. Gilmore, G. Sanguinetti
{"title":"A subsystems approach for parameter estimation of ODE models of hybrid systems","authors":"Anastasis Georgoulas, Allan Clark, Andrea Ocone, S. Gilmore, G. Sanguinetti","doi":"10.4204/EPTCS.92.3","DOIUrl":"https://doi.org/10.4204/EPTCS.92.3","url":null,"abstract":"We present a new method for parameter identification of ODE system descriptions based on data measurements. Our method works by splitting the system into a number of subsystems and working on each of them separately, thereby being easily parallelisable, and can also deal with noise in the observations.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114584753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Caravagna, Alex Graudenzi, M. Antoniotti, G. Mauri, A. d’Onofrio
{"title":"Effects of delayed immune-response in tumor immune-system interplay","authors":"G. Caravagna, Alex Graudenzi, M. Antoniotti, G. Mauri, A. d’Onofrio","doi":"10.4204/EPTCS.92.8","DOIUrl":"https://doi.org/10.4204/EPTCS.92.8","url":null,"abstract":"Tumors constitute a wide family of diseases kinetically characterized by the co-presence of multiple spatio-temporal scales. So, tumor cells ecologically inte rplay with other kind of cells, e.g. endothelial cells or immune system effectors, producing and exchanging various chemical signals. As such, tumor growth is an ideal object of hybrid modeling where discrete stochastic processes model agents at low concentrations, and mean-field equations mode l chemical signals. In previous works we proposed a hybrid version of the well-known Panetta-Kirschner mean-field model of tumor cells, effector cells and Interleukin-2. Our hybrid model suggested -at variance of the inferences from its original formulation- that immune surveillance, i.e. t umor elimination by the immune system, may occur through a sort of side-effect of large stochastic o scillations. However, that model did not account that, due to both chemical transportation and cellular differentiation/division, the tumorinduced recruitment of immune effectors is not instantaneous but, instead, it exhibits a lag period. To capture this, we here integrate a mean-field equation for I nterleukins-2 with a bi-dimensional delayed stochastic process describing such delayed interpla y. An algorithm to realize trajectories of the underlying stochastic process is obtained by coupling the Piecewise Deterministic Markov process (for the hybrid part) with a Generalized Semi-Markovian clock structure (to account for delays). We (i) relate tumor mass growth with delays via simulations and via parametric sensitivity analysis techniques, (ii) we quantitatively determine probabilistic eradication ti mes, and(iii) we prove, in the oscillatory regime, the existence of a heuristic stochasti c bifurcation resulting in delay-induced tumor eradication, which is neither predicted by the mean-field no r by the hybrid non-delayed models.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125854524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hybrid models of the cell cycle molecular machinery","authors":"V. Noel, D. Grigoriev, S. Vakulenko, O. Radulescu","doi":"10.4204/EPTCS.92.7","DOIUrl":"https://doi.org/10.4204/EPTCS.92.7","url":null,"abstract":"Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off some molecular interactions, simulating cell progression through a series of functioning modes. The advancement through the cell cycle is the archetype of such an organized sequence of events. We present an approach, inspired from tropical geometry ideas, allowing to reduce, hybridize and analyse cell cycle models consisting of polynomial or rational ordinary differential equations.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129599674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Disease processes as hybrid dynamical systems","authors":"P. Lio’, E. Merelli, Nicola Paoletti","doi":"10.4204/EPTCS.92.11","DOIUrl":"https://doi.org/10.4204/EPTCS.92.11","url":null,"abstract":"We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions, heterogeneous methodologies are often employed for describing the different biological scales. Hybrid models provide effective means for complex disease modelling where the action and dosage of a drug or a therapy could be meaningfully investigated: the infection dynamics can be classically described in a continuous fashion, while the scheduling of multiple treatment discretely. We define an algebraic language for specifying general disease processes and multiple treatments, from which a semantics in terms of hybrid dynamical system can be derived. Then, the application of control-theoretic tools is proposed in order to compute the optimal scheduling of multiple therapies. The potentialities of our approach are shown in the case study of the SIR epidemic model and we discuss its applicability on osteomyelitis, a bacterial infection affecting the bone remodelling system in a specific and multiscale manner. We report that formal languages are helpful in giving a general homogeneous formulation for the different scales involved in a multiscale disease process; and that the combination of hybrid modelling and control theory provides solid grounds for computational medicine.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117240167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Expressing and Monitoring Oscillatory Dynamics","authors":"Petr Dluhos, L. Brim, David Šafránek","doi":"10.4204/EPTCS.92.6","DOIUrl":"https://doi.org/10.4204/EPTCS.92.6","url":null,"abstract":"To express temporal properties of dense-time real-valued\u0000signals, the Signal Temporal Logic (STL) has been defined by\u0000Maler et al. The work presented a monitoring algorithm deciding\u0000the satisfiability of STL formulae on finite discrete samples\u0000of continuous signals. The logic has been used to express and\u0000analyse biological systems, but it is not expressive enough to\u0000sufficiently distinguish oscillatory properties important in\u0000biology. In this paper we define the extended logic STL* in\u0000which STL is augmented with a signal-value freezing operator\u0000allowing us to express (and distinguish) detailed properties of\u0000biological oscillations. The logic is supported by a monitoring\u0000algorithm prototyped in Matlab. The monitoring procedure of\u0000STL* is evaluated on a biologically-relevant case study.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127741404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nicolas Mobilia, Alexandre Donzé, J. Moulis, E. Fanchon
{"title":"A Model of the Cellular Iron Homeostasis Network Using Semi-Formal Methods for Parameter Space Exploration","authors":"Nicolas Mobilia, Alexandre Donzé, J. Moulis, E. Fanchon","doi":"10.4204/EPTCS.92.4","DOIUrl":"https://doi.org/10.4204/EPTCS.92.4","url":null,"abstract":"This paper presents a novel framework for the modeling of biological networks. It makes use of recent tools analyzing the robust satisfaction of properties of (hybrid) dynamical systems. The main challenge of this approach as applied to biological systems is to get access to the relevant parameter sets despite gaps in the available knowledge. An initial estimate of useful parameters was sought by formalizing the known behavior of the biological network in the STL logic using the tool Breach. Then, once a set of parameter values consistent with known biological properties was found, we tried to locally expand it into the largest possible valid region. We applied this methodology in an effort to model and better understand the complex network regulating iron homeostasis in mammalian cells. This system plays an important role in many biological functions, including erythropoiesis, resistance against infections, and proliferation of cancer cells.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131868082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hybrid Automata and ε-Analysis on a Neural Oscillator","authors":"A. Casagrande, T. Dreossi, C. Piazza","doi":"10.4204/EPTCS.92.5","DOIUrl":"https://doi.org/10.4204/EPTCS.92.5","url":null,"abstract":"In this paper we propose a hybrid model of a neural oscillator, obtained by partially discretizing a well-known continuous model. Our construction points out that in this case the standard techniques, based on replacing sigmoids with step functions, is not satisfactory. Then, we study the hybrid model through both symbolic methods and approximation techniques. This last analysis, in particular, allows us to show the differences between the considered approximation approaches. Finally, we focus on approximations via e-semantics, proving how these can be computed in practice.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115971380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Analysis of parametric biological models with non-linear dynamics","authors":"Romain Testylier, T. Dang","doi":"10.4204/EPTCS.92.2","DOIUrl":"https://doi.org/10.4204/EPTCS.92.2","url":null,"abstract":"In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to two case studies of biological systems: one is a cardiac cell model for studying the conditions for cardiac abnormalities, and the second is a model of insect nest-site choice.","PeriodicalId":102233,"journal":{"name":"International Workshop on Hybrid Systems Biology","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127691797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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