## ABSTRACT APPROACHES TO COMPLEXITY REDUCTION IN A SYSTEMS BIOLOGY

### BibTeX

@MISC{Perrone_abstractapproaches,

author = {L. F. Perrone and F. P. Wiel and J. Liu and B. G. Lawson and D. M. Nicol and R. M. Fujimoto},

title = {ABSTRACT APPROACHES TO COMPLEXITY REDUCTION IN A SYSTEMS BIOLOGY},

year = {}

}

### OpenURL

### Abstract

Due to the complexity of biochemical reaction networks, socalled complexity reduction algorithms play a crucial role for making simulations efficient and for dissecting biochemical networks into meaningful subnetworks for analysis. Here, different approaches are presented, which we are developing in the context of a computational research environment for systems biology (SYCAMORE). These approaches are based on time-scale decomposition, sensitivity analysis, and hybrid simulation methods. 1

### Citations

2070 | Matrix Computations - Golub, Loan - 1996 |

446 |
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
- Gillespie
(Show Context)
Citation Context ... equations for describing reaction systems and the possibility to take intrinsic fluctuations into account using simulations based on discrete particle numbers, e.g., employing Gillespie’s algorithm (=-=Gillespie 1976-=-). The latter methodology being of central importance if low number of identical molecules are present in the system. In those cases random effects can not be neglected and one must resort to stochast... |

163 |
Understanding the control of metabolism
- Fell
- 1997
(Show Context)
Citation Context ...ences some property of a model are called sensitivities. One well established formalism to deal with sensitivities in the context of biochemical reaction networks is Metabolic Control Analysis (MCA) (=-=Fell 1997-=-). MCA defines matrices of so-called control coefficients. They describe how a steady state of the systems changes if the overall rate of a individual reaction is changed. Usually the coefficients are... |

124 | 2002. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics - Haseltine, Rawlings |

69 | Metabolic control theory: a structural approach - Reder - 1988 |

62 |
Accurate hybrid stochastic simulation of a system of coupled chemical or biological reactions
- Salis, Kaznessis
(Show Context)
Citation Context ...particles) none of the traditional simulation methods alone is appropriate any longer. Therefore a number of hybrid methods (Haseltine and Rawlings 2002, Kiehl et al. 2004, Puchalka and Kierzek 2004, =-=Salis and Kaznessis 2005-=-, Alfonsi et al. 2005) have been proposed that try to combine the advantages of the complementary deterministic and stochastic approaches. Parts of the biochemical system are simulated Surovtsova, Sah... |

60 |
Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations
- Petzold
- 1983
(Show Context)
Citation Context ...bed by ordinary differential equation systems (ODEs). There exist a variety of very efficient numerical integration methods even for the very stiff ODEs, which often arise in biochemical simulations (=-=Petzold 1983-=-). The actual numbers of particles in the system do not affect the simulation speed. This continuous approach, however, is based on the notion of continuously changing variables. It breaks down in the... |

51 |
AUTO: Software for continuation and bifurcation problems in ordinary differential equations
- Doedel, Kernevez
- 1986
(Show Context)
Citation Context ...nuation can be considered as a generalization of sensitivity analysis. Continuation is a numerical method that is well established in the field of nonlinear dynamics—with software packages like AUTO (=-=Doedel 1996-=-)—but that has been used in systems biology only rather recently (e.g., Chickarmane et al. 2005). Continuation follows a solution of the model equations over a whole range of parameter values and also... |

50 | The CSP method for simplifying kinetics
- Lam, Goussis
- 1994
(Show Context)
Citation Context ...n, to several hours, e.g., in some cases of gene expression). The most prominent examples building on the concept of time-scale decomposition are the Computational Singular Perturbation (CSP) method (=-=Lam and Goussis 1994-=-) and the so-called Intrinsic Low-Dimensional Manifolds (ILDM) (Maas and Pope 1992). Several variants of these two methods have been successfully used, e.g., in atmospheric and combustion chemistry mo... |

25 | Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. Eric Cancès - ALFONSI, CANCÈS, et al. - 2005 |

19 | Sensitivity analysis of complex kinetic systems. tools and applications
- Turányi
- 1990
(Show Context)
Citation Context ... the reduction of the underlying biochemical network in a time-dependent manner. The second very popular approach—sensitivity analysis—has been widely used to analyze chemical and biological systems (=-=Turanyi 1990-=-, Turanyi et al. 1989) primarily to examine their behavior with respect to disturbances or tosdetermine the robustness of parameter estimation. In addition, principal component analysis can be used to... |

14 | Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation - Wolf, Heinrich - 2000 |

9 | Dynamic dimension reduction in ODE models - Deuflhard, Heroth - 1996 |

8 |
Intrinsic low-dimensional manifolds of strained and unstrained flames, in
- Blasenbrey, Schmidt, et al.
- 1997
(Show Context)
Citation Context ... Intrinsic Low-Dimensional Manifolds (ILDM) (Maas and Pope 1992). Several variants of these two methods have been successfully used, e.g., in atmospheric and combustion chemistry modeling (see, e.g., =-=Schmidt et al. 1998-=-). We describe here the adaptation of an ILDM method for the use in the computational decomposition and analysis of biochemical systems with respect to time-scales. In comparison to the ILDM methods f... |

4 |
Hybrid simulation of cellular behavior.” Bioinformatics 20:3
- Kiehl, Mattheyses, et al.
- 2004
(Show Context)
Citation Context ...sduction (few particles) and metabolism (many particles) none of the traditional simulation methods alone is appropriate any longer. Therefore a number of hybrid methods (Haseltine and Rawlings 2002, =-=Kiehl et al. 2004-=-, Puchalka and Kierzek 2004, Salis and Kaznessis 2005, Alfonsi et al. 2005) have been proposed that try to combine the advantages of the complementary deterministic and stochastic approaches. Parts of... |

4 |
Reaction Rate Analysis of Complex Kinetic Systems
- Turanyi, Berces, et al.
- 1989
(Show Context)
Citation Context ... of the underlying biochemical network in a time-dependent manner. The second very popular approach—sensitivity analysis—has been widely used to analyze chemical and biological systems (Turanyi 1990, =-=Turanyi et al. 1989-=-) primarily to examine their behavior with respect to disturbances or tosdetermine the robustness of parameter estimation. In addition, principal component analysis can be used to understand the inter... |

3 |
A new time-dependent complexity reduction method for biochemical systems
- Zobeley, Lebiedz, et al.
- 2005
(Show Context)
Citation Context ...this can aid in network dissection. 2 TIME SCALE DECOMPOSITION In this section, we describe the adaptation of the method of Intrinsic Low-Dimensional Manifolds (ILDM) to biochemical systems (see also =-=Zobeley et al. 2005-=-). Originally, the ILDM techniques were introduced by Maas and Pope (1992) for the mathematical equations of combustion problems. In contrast, our method has an additional focus on reducing Surovtsova... |

2 | Advances in metabolic control analysis. Biotechnol. Prog - Liao, Delgado - 1993 |

1 | Kummer COPASI: Complex Pathway Simulator - Surovtsova, Pahle - 2006 |

1 |
Simplifying chemical reaction kinetics: intrinsic low-dimensional manifolds in composition space. Combustion and Flame 88:239
- Maas, Pope
- 1992
(Show Context)
Citation Context ...mples building on the concept of time-scale decomposition are the Computational Singular Perturbation (CSP) method (Lam and Goussis 1994) and the so-called Intrinsic Low-Dimensional Manifolds (ILDM) (=-=Maas and Pope 1992-=-). Several variants of these two methods have been successfully used, e.g., in atmospheric and combustion chemistry modeling (see, e.g., Schmidt et al. 1998). We describe here the adaptation of an ILD... |

1 |
Reduced mechanisms for propane pyrolysis. Industrial & Engineering Chemistry Research 34:3749–3760
- Tomlin, Pilling, et al.
- 1995
(Show Context)
Citation Context ... disturbances or tosdetermine the robustness of parameter estimation. In addition, principal component analysis can be used to understand the interaction between reactions and their grouped behavior (=-=Tomlin et al. 1995-=-). For SYCAMORE, we are following another strategy, that we believe to be quite promising for investigating biochemical networks — an approach based on parameter scans and second order sensitivities. ... |

1 | IRINA SUROVTSOVA is a Research Associate at EML Research gGmbH. She received the Ph.D. degree in 1997 at the St. Petersburg State University. Her fields of interests are system biology, complexity reduction, fluid–structure interaction, blood flow and ela - BIOGRAPHIES |

1 | is a research associate at EML Research gGmbH. Being trained as a physicist, he received a Ph.D. in 2005 from Tübingen University. He works on methods and tools for simulations in systems biology, with a focus on nonlinear dynamics. He is one of the main - SAHLE |