## Borgne. Topology and static response of interaction networks in molecular biology (2006)

Venue: | J R Soc Interface |

Citations: | 9 - 3 self |

### BibTeX

@ARTICLE{Radulescu06borgne.topology,

author = {Ovidiu Radulescu and Rine Lagarrigue and Anne Siegel and Michel Le Borgne},

title = {Borgne. Topology and static response of interaction networks in molecular biology},

journal = {J R Soc Interface},

year = {2006}

}

### OpenURL

### Abstract

molecular biology

### Citations

311 |
Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge
- Kuipers
- 1994
(Show Context)
Citation Context ...lues of the variations are imposed (or known) on the boundary dXi, i2c in G. For biological networks the Dirichlet problem shows its utility when one possesses only a partial knowledge of the system (=-=Kuipers 1994-=-; Siegel et al. inpress). We can define the corresponding Dirichlet static susceptivities c D ij Z vXi ; i 2G; j 2c vXj in G: ð4:8Þ (ii) Linear Neumann problem: determine the variations dXi, i2G every... |

268 |
Thermodynamics and an Introduction to Thermostatstics
- Callen
- 1985
(Show Context)
Citation Context ...dividuals is linear even at large perturbations. In the static case, structural stability (Smale 1980; Ruelle 1989) suggests a simple approach to nonlinear response. Like in classical thermodynamics (=-=Callen 1985-=-), finite static response can be obtained by integrating the (state dependent) differential forms Received 27 June 2005 Accepted 13 September 2005 1 q 2005 The Royal Society2 Static response of inter... |

121 |
of enzyme kinetics
- CORNISH-BOWDEN
- 1979
(Show Context)
Citation Context ... the Jacobian of a chemical kinetics evolution equations. Very related to this is the work of Sontag (Kholodenko et al. 2002) and the older Kacser–Burns connectivity property from metabolic networks (=-=Cornish-Bowden 1995-=-), meaning that the matrix of elasticities (the Jacobian) is the inverse of the matrix of control coefficients (static susceptivities). The dynamical Jacobian is also important in gene networks dynami... |

76 |
Constitutive equations for polymer melts and solutions
- Larson
- 1988
(Show Context)
Citation Context ... in statistical physics (Kubo et al. 1998), electrical, physical and mechanical systems (MacFarlane 1970), chemical and biochemical systems (Oster et al. 1973; Perelson & Oster 1974), complex fluids (=-=Larson 1988-=-), metabolic networks (Kacser & Burns 1973; Heinrich & Rapoport 1974) and gene networks (Kholodenko et al. 2002; Vlad et al. 2004). The basic quantities in such theories are the susceptivities, repres... |

75 |
On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations
- Thomas
- 1981
(Show Context)
Citation Context ...al Jacobian is also important in gene networks dynamics. It defines the interaction graph (Soulé 2003), which is the natural mathematical candidate to represent the biologist’s gene regulation graph (=-=Thomas 1981-=-). Systems of chemical reactions allow for other graphical representations (the interested reader could refer to the comprehensive reviews of Oster et al. 1973; Perelson & Oster 1974). In this paper w... |

66 |
Untangling the wires: a strategy to trace functional interactions in signaling and gene networks
- Kholodenko, Kiyatkin, et al.
- 2002
(Show Context)
Citation Context ...ties of these biological networks, dynamical properties, as well as their inference from experimental data, were the subject of intensive studies (Wagner 2001; de Jong 2002; Kaminski & Friedman 2002; =-=Kholodenko et al. 2002-=-; de Jong et al. 2004; Thieffry & Sanchez 2004; Yamanishi et al. 2004). However, network inference techniques need huge amounts of data which are not always available or often have poor accuracy. Simi... |

66 |
Necessary conditions for multistationarity and stable periodicity
- Snoussi
- 1998
(Show Context)
Citation Context ...s weakness is largely compensated by the fact that many qualitative properties of the dynamics and of steady states depend on topological conditions on the interaction graph (Thomas 1981; Gouzé 1998; =-=Snoussi 1998-=-; Soulé 2003). J. R. Soc. InterfaceStatic response of interaction networks O. Radulescu and others 3 2.2. Boundary Boundary is a key concept of any modular approach trying to reduce the overwhelming ... |

50 |
On an inverse boundary value problem
- Calderon
- 1980
(Show Context)
Citation Context ...between the static response of gene networks and the Dirichlet-toNeumann map (Curtis & Morrow 2000), which is a relatively new field in graph theory. This field originated from a problem by Calderon (=-=Calderon 1980-=-) who asked whether it is possible to reconstruct the conductivity of a conducting plate from measurements of injected currents and voltages on its boundary. This problem gave rise to non-trivial deve... |

42 | A class of piecewise linear differential equations arising in biological models, in "Dynamical systems - GOUZÉ, SARI |

38 |
Circular planar graphs and resistor networks, submitted
- Curtis, Ingerman, et al.
(Show Context)
Citation Context ... the reduction of complexity of biological networks. One would like to classify all the graph contractions that preserve the response of the system. This has been done for planar electrical networks (=-=Curtis et al. 1998-=-) in relation to the Dirichlet-toNeumann map. There is no similar work for biological networks. This research was supported by ACI IMPBio, a French Ministry for Research program on interdisciplinarity... |

32 | Practical approaches to analyzing results of microarray experiments - Kaminski, Friedman - 2002 |

27 |
Statistical construction of chemical reaction mechanisms from measured timeseries
- Arkin, Ross
- 1995
(Show Context)
Citation Context ...method is complementary to already well-developed correlation analysis of gene and metabolic networks (Kaminski & Friedman 2002; Yamanishi et al. 2004) or of time-series in chemical reaction systems (=-=Arkin & Ross 1995-=-). Vlad et al. (2004) showed that under the neutrality condition the dynamical susceptivity of a system of chemical reactions with respect to abundance perturbations is the exponential of a connectivi... |

23 |
The Mathematics of Time
- Smale
- 1980
(Show Context)
Citation Context ...of reaction–diffusion systems to special perturbations consisting in changing the abundance of some marked individuals is linear even at large perturbations. In the static case, structural stability (=-=Smale 1980-=-; Ruelle 1989) suggests a simple approach to nonlinear response. Like in classical thermodynamics (Callen 1985), finite static response can be obtained by integrating the (state dependent) differentia... |

21 |
Diminished hepatic response to fasting/refeeding and liver X receptor agonists in mice with selective deficiency of sterol regulatory element-binding protein-1c
- Liang, Yang, et al.
- 2002
(Show Context)
Citation Context ...determined by biochemical measurements. A compilation of recent literature on lipogenesis regulation provides results of such protocols: SREBP, ACL, ACC, FAS and SCD1 decline in liver during fasting (=-=Liang et al. 2002-=-); this state is characterized by an inhibition of fatty acid synthesis and an activation of the fatty acid oxidation. However, Tobin et al. (2000) showed that fasting rats for 24 h increased the hepa... |

19 |
On Global Univalence Theorems
- Parthasarathy
(Show Context)
Citation Context ...graph G has no positive loops whatever the concentrations, equations (4.3)–(4.5) imply that all the minors of the opposite Jacobian KJ are positive. From this and from the Gale–Nikaido–Inada theorem (=-=Parthasarathy 1983-=-) it follows the uniqueness of the equilibrium. The complete proof of Thomas’s conjecture can be found in Soulé (2003). The conditions of the first part of theorem 4.9 are fulfilled by gene networks. ... |

18 |
Toward a systematic determination of complex reaction mechanisms
- Chevalier, Schreiber, et al.
- 1993
(Show Context)
Citation Context ...ults connect network topology and the response to steadystate shift experiments. Steady-state shift experiments are useful tools in chemistry allowing in principle to recover the reaction mechanisms (=-=Chevalier et al. 1993-=-). We argue that similar approaches are well adapted to differential microarray experiments which compare gene expressions between two different states (Kaminski & Friedman 2002). † Author for corresp... |

15 | Cross-talk between fatty acid and cholesterol metabolism mediated by liver X receptor-alpha - Tobin, Steineger, et al. - 2000 |

11 |
The Dirichlet to Neumann Map for a Resistor Network
- Curtis, Morrow
- 1991
(Show Context)
Citation Context ... on the boundary. The corresponding linear mapping L ND : R m /R m (mZ#c in G, L ND ij Z P j,i2P ða G j,i=C j,iÞCð1=C iÞdij) is the equivalent of the Neumann-to-Dirichlet map for electrical networks (=-=Curtis & Morrow 1991-=-). The inverse (if it exists) of this mapping is the Dirichlet-to-Neumann map (Curtis & Morrow 1991). Theorem 4.2 implies the following. Corollary 4.5. If there are no paths in PG connecting two diffe... |

11 |
Peroxisome proliferators induce mouse liver stearoyl-CoA desaturase 1 gene expression
- Miller, Ntambi
- 1996
(Show Context)
Citation Context ...RNA and inhibiting the cleavage; Jump 2004). SCAP represents the activators of the formation of SREBP-a from SREBP, and is inhibited by PUFA. PPAR directly activates the production of SCD1, D5D, D6D (=-=Miller & Ntambi 1996-=-; Matsuzaka et al. 2002; Tang et al. 2003). The interaction graph for this model is shown in figure 4. Like in the lactose operon example, for each node we have supposed the existence of negative self... |

7 |
Linear Algebra and Geometry
- Bloom
- 1979
(Show Context)
Citation Context ...ned from the inverse matrix J K1 . In this section, the elements of J K1 are connected to the topology of the interaction graph. 4.1. Moduli and loops We start with the following well-known relation (=-=Bloom 1979-=-) J K1 ij Z ðK1Þ iCj D ji D ; ð4:1Þ where Dji is the minor obtained by deleting row j and column i in J, and DZdet(J ). Next, we develop the minor Dji into a sum of principal minors (Bloom 1979) Dji Z... |

6 | Regulation of human Delta-6 desaturase gene transcription: identification of a functional direct repeat-1 element - Tang, Cho, et al. - 2003 |

5 |
Modeling operon dynamics: the tryptophan and lactose operons as paradigms
- Mackey, Santillan, et al.
- 2004
(Show Context)
Citation Context ...lactose (L) metabolism in Escherichia coli are LacY (lactose permease) allowing the uptake of lactose, LacZ (b-galactosidase) catalysing the degradation of lactose to glucose (Yildirim & Mackey 2003; =-=Mackey et al. 2004-=-). The transcriptional regulators for the genes lacY and lacZ are an activator (cAMP receptor protein, CRP) and a repressor (LacI). An inducer (cAMP) binds to the activator and triggers it. Lactose, u... |

3 |
Complex fluids subjected to external influences
- Grmela
- 2001
(Show Context)
Citation Context ... derivatives) of outputs with respect to inputs. Susceptivities (and also response in general) are obtained from constitutive equations that must be compatible with thermodynamics (Oster et al. 1973; =-=Grmela 2001-=-). Nonlinear response theories that apply to large perturbations are generally more difficult to handle (Larson 1988; Grmela 2001). Vlad et al. (2004) showed that under special ‘neutrality’ conditions... |

3 |
Chemical reaction dynamics
- OSTER, PERELSON
- 1974
(Show Context)
Citation Context ...us contexts such as condensed matter and in statistical physics (Kubo et al. 1998), electrical, physical and mechanical systems (MacFarlane 1970), chemical and biochemical systems (Oster et al. 1973; =-=Perelson & Oster 1974-=-), complex fluids (Larson 1988), metabolic networks (Kacser & Burns 1973; Heinrich & Rapoport 1974) and gene networks (Kholodenko et al. 2002; Vlad et al. 2004). The basic quantities in such theories ... |

2 | Dual regulation of mouse Delta(5)and Delta(6)-desaturase gene expression by SREBP-1 and PPARalpha - Matsuzaka, Shimano, et al. - 2002 |

1 | The control of flux - Sci - 1973 |

1 |
Requirement of PPARa in maintaining phospholipid and triacylglycerol homeostasis during energy deprivation
- Lee, Chan, et al.
- 2004
(Show Context)
Citation Context ...hich are the predominant (more than 50%) hepatic lipids and also in phospholipids PL which go into cellular membranes. Moreover PL contribute much less than TG to the total lipid mass. These authors (=-=Lee et al. 2004-=-) show that after 72 h of fasting fatty acids profiles do not change significantly in PL, but there is a strong increase of TG and of their fatty acids constituents, in particular PUFA. Let us recall ... |

1 |
Feedback theory—properties of signal flow graphs
- Mason
- 1953
(Show Context)
Citation Context ...ntations (the interested reader could refer to the comprehensive reviews of Oster et al. 1973; Perelson & Oster 1974). In this paper we generalize Mason–Coates type formulae from electrical circuits (=-=Mason 1953-=-; Coates 1959), providing graphical representations of static susceptivities of gene networks. We also exploit useful connections between the static response of gene networks and the Dirichlet-toNeuma... |

1 | Elements of differentiable dynamics and bifurcation theory - Anal - 1989 |