92C42 Systems biology, networks
Multi-valued network models can be described by their topology and a set of parameters capturing the effects of the regulators for each component. Dynamics can then be derived and represented as state transition systems.
Different network models may lead to the same transition system, meaning dynamics analysis of a representative model covers a larger class of models. While rather clear in the Boolean case, the properties contributing to this effect become more involved for multi-valued models. We analyse these properties and present a mathematical description of the resulting model equivalence classes.
Asymptotic behavior is often of particular interest when analyzing asynchronous Boolean networks representing biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called symbolic steady states, can be exploited to investigate attractor properties as well as for model reduction techniques conserving attractors. In this paper, we propose a novel optimization-based method for computing all maximal symbolic steady states and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a short study of a MAPK pathway model.
Constraint-based modeling of genome-scale metabolic network reconstructions has become a widely used approach in computational biology. Flux coupling analysis is a constraint-based method that analyses the impact of single reaction knockouts on other reactions in the network.We present an extension of flux coupling analysis for double and multiple gene or reaction knockouts, and develop corresponding algorithms for an in silico simulation. To evaluate our method, we perform a full single and double knockout analysis on a selection of genome-scale metabolic network reconstructions and compare the results.
Flux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state assumption can be replaced by a much weaker lattice-theoretic property related to the supports of metabolic fluxes. In this paper, we further extend our approach and delevelop an efficient algorithm for general qualitative flux coupling analysis (QFCA). We illustrate our method by thermodynamic flux coupling analysis (tFCA), which allows studying steady-state metabolic models with loop-law thermodynamic constraints. These models do not satisfy the lattice-theoretic properties required in our previous work. For a selection of genome-scale metabolic network reconstructions, we discuss both theoretically and practically, how thermodynamic constraints strengthen the coupling results that can be obtained with classical FCA.
Elementary flux mode (EM) analysis is an important tool in the constraint-based analysis of genome-scale metabolic networks. Due to the combinatorial complexity of these networks, as well as the advances in the level of detail to which they can be reconstructed, an exhaustive enumeration of all EMs is often not practical. Therefore, in recent years interest has shifted towards searching EMs with specific properties. We present a novel method that allows computing EMs containing a given set of target reactions. This generalizes previous algorithms where the set of target reactions consists of a single reaction. In the one-reaction case, our method compares favorably to the previous approaches. In addition, we present several applications of our algorithm for computing EMs containing two target reactions in genome-scale metabolic networks.
Motivation. Modelling, parameter identification, and simulation play an important role in systems biology. Usually, the goal is to determine parameter values that minimise the difference between experimental measurement values and model predictions in a least-squares sense. Large-scale biological networks, however, often suffer from missing data for parameter identification. Thus, the least-squares problems are rank-deficient and solutions are not unique. Many common optimisation methods ignore this detail because they do not take into account the structure of the underlying inverse problem. These algorithms simply return a “solution” without additional information on identifiability or uniqueness. This can yield misleading results, especially if parameters are co-regulated and data are noisy.
Results. The Gauss-Newton method presented in this paper monitors the numerical rank of the Jacobian and converges locally, for the class of adequate problems, to a solution that is unique within the subspace of identifiable parameters. This method has been implemented in BioPARKIN, a software package that combines state-of-the-art numerical algorithms with compliance to system biology standards, most importantly SBML, and an accessible interface.
Availability. The software package BioPARKIN is available for download at http://bioparkin.zib.de .
The huge number of elementary flux modes (EFM) in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes.
We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.
Constraint-based analysis of metabolic networks has become a widely used approach in computational systems biology.
In the simplest form, a metabolic network is represented by a stoichiometric matrix and thermodynamic information on the irreversibility of certain reactions.
Then one studies the set of all steady-state flux vectors satisfying these stoichiometric and thermodynamic constraints.
We introduce a new lattice-theoretic framework for the computational analysis of metabolic networks, which focuses on the support of the flux vectors,
i.e., we consider only the qualitative information whether or not a certain reaction is active, but not its specific flux rate.
Our lattice-theoretic view includes classical metabolic pathway analysis as a special case, but turns out to be much more flexible and general,
with a wide range of possible applications.
We show how important concepts from metabolic pathway analysis, such as blocked reactions, flux coupling, or elementary modes, can be generalized to arbitrary lattice-based models. We develop corresponding general algorithms and present a number of computational results.
Flux variability analysis (FVA) is an important tool to further analyze the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. Standard FVA may predict unbounded fluxes through some reactions in the network even if the nutrient uptake rate is bounded. These fluxes violate the second law of thermodynamics. They may be eliminated by extending flux variability analysis with thermodynamic constraints.
We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analyzing genome-scale metabolic networks. We first show that flux balance analysis with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast flux variability analysis with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved.
In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 out of 716 networks additional irreversible or fixed reactions could be detected.
Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models.
We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model.