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Abstract
Systems biology is a lively interdisciplinary research field that has received considerable attention in recent years. While traditional molecular biology studies the various components of a biological system (genes, RNAs, proteins,...) in isolation, systems biology aims to understand how these components interact in order to perform higher-level functions. Mathematical modeling then plays a major role not only in capturing and analyzing complex networks governing biological processes, but also as a way to verify hypotheses based on observational evidence and in designing efficient experiments to further the understanding of the system. The goal of this project is to pool our knowledge on discrete, deterministic and stochastic modeling of biological systems to pave the way towards efficient hybrid models (discrete/continuous, deterministic/stochastic) for elaborate biological networks.
Heads
Prof. Dr. Alexander Bockmayr (FUB)
Prof. Dr. Dr. h.c. Peter Deuflhard (ZIB)
Members
Laszlo David (FUB)
Hannes Klarner (FUB)
Dr. Susanna Röblitz (ZIB)
Dr. Heike Siebert (FUB)
Claudia Stötzel (ZIB)
Dr. Patrick Winkert (TUB)
Funding
DFG Research Center Matheon "Mathematics for key technologies"
Duration
01.06.2010 - 31.05.2014
Background
Systems biology is a lively interdisciplinary research field that has received considerable attention in recent years.
While traditional molecular biology studies the various components of a biological system (genes, RNAs, proteins,…) in isolation, systems biology aims to understand how these components interact in order to perform higher-level functions. Mathematical modeling then plays a major role not only in capturing and analyzing complex networks governing biological processes, but also as a way to verify hypotheses based on observational evidence and in designing efficient experiments to further the understanding of the system. Traditionally, differential equations are used to model time-dependent concentrations of reacting species. A number of efficient algorithms and software implementations for the solution of such systems have been developed over the years. Although these tools simplify the modeling process, the main challenge is still parameter identification. A common problem particular to biological systems as opposed to, for example, applications in physics, is the lack of reliable experimental data, e.g. kinetic parameters. Given this situation, a possible alternative to differential equation modeling is to translate the available information into a set of constraints. This in general does not allow for deterministic predictions, but permits to identify system characteristics, and a set of possible behaviors. The idea of constraint-based modeling leads to the application of discrete methods, for example steady-state analysis of metabolic networks based on stoichiometric and thermodynamic constraints, or the representation of regulatory networks as discrete dynamical systems.
A further difficulty to be considered when modeling biological systems are low copy numbers. As the number of participating molecules decreases, stochastic fluctuations come into play. In this case, modeling chemical reaction systems solely by means of the classical equations of reaction kinetics is not sufficient anymore. Rather, the chemical master equation (CME) in high dimensions has to be utilized, a discrete partial differential equation that describes the time-evolution of the probability density for the copy number of each species. The considerations above highlight some important aspects of modeling biological systems, and of course many systems call for modeling frameworks capable of combining several of those aspects. Hybrid discrete/continuous methods offer possibilities to enhance discrete dynamics with continuous processes, e.g., adding a continuous time evolution that allows for integration of more quantitative data. Hybrid continuous/stochastic methods, e.g.; integrate the chemical master equation into reaction kinetics allowing for analysis of high-dimensional models with a rather low-dimensional, yet time-dependent subspace of low copy numbers. In general, hybrid methods extend modeling power considerably, allowing for a continual model development in a comprehensive framework.
Software
BioPARKIN (Biology related Parameter Identification in Large Kinetic networks)
FFCA (Feasibility-based Flux Coupling Analysis)
ERDA (Edge Refinement and Data Assessment)
Publications
S. A. Marashi , L. David and A. Bockmayr. On flux coupling analysis of metabolic subsystems. J. Theoretical Biology, in press, 2012.
M. Rügen, A. Bockmayr, J. Legrand, and G. Cogne. Network reduction in metabolic pathway analysis: Elucidation of the key pathways involved in the photoautotrophic growth of the green alga Chlamydomonas reinhardtii. Metabolic Engineering, in press, 2012.
H. M. T. Boer, C. Stötzel, S. Röblitz, and H. Woelders. A differential equation model to investigate the dynamics of the bovine estrous cycle. In Advances in Systems Biology, volume 736 of Advances in Experimental Medicine and Biolog, pages 59-606. Springer, 2012.
S. Jamshidi, H. Siebert, and A. Bockmayr. Comparing discrete and piecewise affine differential equation models of gene regulatory networks. In Proc. 9th Int. Conf. Information Processing in Cells and Tissues, IPCAT 2012, Cambridge, UK, 2012. To appear
H .M. T. Boer, S. Röblitz, C. Stötzel, B. Kemp, R. F. Veerkamp, and H. Woelders. Mechanisms regulating follicle wave patterns in the bovine estrous cycle investigated with a mathematical model. J. Dairy Sci., 94(12):5987-6000, 2011.
H .M. T. Boer, C. Stötzel, S. Röblitz, P. Deuhard, R. F. Veerkamp, and H. Woelders. A simple mathematical model of the bovine estrous cycle: follicle development and endocrine interactions. J. Theoret. Biol., 278(1):20-31, 2011.
G. Cogne, M. Rügen, A. Bockmayr, M. Titica, C. G. Dussap, J. F. Cornet, and J. Legrand. A model-based method for investigating bioenergetic processes in autotrophically growing eukaryotic microalgae: Application to the green algae Chlamydomonas reinhardtii. Biotechnology Progress, 27/3:631-40, 2011.
L. David, S. A. Marashi, A. Larhlimi, B. Mieth, and A. Bockmayr. FFCA: a feasibility-based method for ux coupling analysis of metabolic networks. BMC Bioinformatics, 12:236, 2011.
M. Hegland and J. Garcke. On the numerical solution of the chemical master equation with sums of rank one tensors. In Proc. 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, volume 52 of ANZIAM J., pages C628-C643, 2011
H. Klarner, H. Siebert, and A. Bockmayr. Parameter inference for ansynchronous logical networks using discrete times series. Computational Methods in Systems Biology, CMSB 2011, Paris, 2011.
S.A. Marashi and A. Bockmayr. Flux coupling analysis of metabolic networks is sensitive to missing reactions. BioSystems, 103:57-66, 2011.
A. Palinkas and A. Bockmayr. Petri nets for integrated models of metabolic and gene regulatory 10 networks. Workshop on Constraint based Methods for Bioinformatics, WCB'11, Perugia, 2011.
A. Rezola, L.F. de Figueiredo, M. Brock, J. Pey, A. Podhorski, C. Wittmann, S. Schuster, A. Bockmayr, and F. J. Planes. Exploring metabolic pathways in genome-scale networks via generating ux modes. Bioinformatics, 27/4:534-540, 2011.
H. Siebert. Analysis of discrete bioregulatory networks using symbolic steady states. Bull. Math. Biol., 73:873-898, 2011.
S. Twardziok, H. Siebert, and A. Heyl. Stochasticity in reactions: a probabilistic boolean modeling approach. Computational Methods in Systems Biology, CMSB 2010, Trento, Italy, pages 76-85. ACM, 2010.
