A grid layout algorithm for automatic drawing of biochemical networks

MOTIVATION: Visualization is indispensable in the research of complex biochemical networks. Available graph layout algorithms are not adequate for satisfactorily drawing such networks. New methods are required to visualize automatically the topological architectures and facilitate the understanding of the functions of the networks. RESULTS: We propose a novel layout algorithm to draw complex biochemical networks. A network is modeled as a system of interacting nodes on squared grids. A discrete cost function between each node pair is designed based on the topological relation and the geometric positions of the two nodes. The layouts are produced by minimizing the total cost. We design a fast algorithm to minimize the discrete cost function, by which candidate layouts can be produced efficiently. A simulated annealing procedure is used to choose better candidates. Our algorithm demonstrates its ability to exhibit cluster structures clearly in relatively compact layout areas without any prior knowledge. We developed Windows software to implement the algorithm for CADLIVE. AVAILABILITY: All materials can be freely downloaded from http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/ SUPPLEMENTARY INFORMATION: http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/     

Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks

Background  

Mathematical modeling and analysis have become, for the study of biological and cellular processes, an important complement to experimental research. However, the structural and quantitative knowledge available for such processes is frequently limited, and measurements are often subject to inherent and possibly large uncertainties. This results in competing model hypotheses, whose kinetic parameters may not be experimentally determinable. Discriminating among these alternatives and estimating their kinetic parameters is crucial to improve the understanding of the considered process, and to benefit from the analytical tools at hand.     

A fast layout algorithm for protein interaction networks

MOTIVATION: Graph drawing algorithms are often used for visualizing relational information, but a naive implementation of a graph drawing algorithm encounters real difficulties when drawing large-scale graphs such as protein interaction networks. RESULTS: We have developed a new, extremely fast layout algorithm for visualizing large-scale protein interaction networks in the three-dimensional space. The algorithm (1) first finds a layout of connected components of an entire network, (2) finds a global layout of nodes with respect to pivot nodes within a connected component and (3) refines the local layout of each connected component by first relocating midnodes with respect to their cutvertices and direct neighbors of the cutvertices and then by relocating all nodes with respect to their neighbors within distance 2. Advantages of this algorithm over classical graph drawing methods include: (1) it is an order of magnitude faster, (2) it can directly visualize data from protein interaction databases and (3) it provides several abstraction and comparison operations for effectively analyzing large-scale protein interaction networks. AVAILABILITY: http://wilab.inha.ac.kr/interviewer/     

A generic algorithm for layout of biological networks

Background  

Biological networks are widely used to represent processes in biological systems and to capture interactions and dependencies between biological entities. Their size and complexity is steadily increasing due to the ongoing growth of knowledge in the life sciences. To aid understanding of biological networks several algorithms for laying out and graphically representing networks and network analysis results have been developed. However, current algorithms are specialized to particular layout styles and therefore different algorithms are required for each kind of network and/or style of layout. This increases implementation effort and means that new algorithms must be developed for new layout styles. Furthermore, additional effort is necessary to compose different layout conventions in the same diagram. Also the user cannot usually customize the placement of nodes to tailor the layout to their particular need or task and there is little support for interactive network exploration.     

Optimal identification of biochemical reaction networks

Advances in biotechnology and computer science are providing the possibility to construct mathematical models for complex biological networks and systematically understand their properties. Traditional network identification approaches, however, cannot accurately recover the model parameters from the noisy laboratory measurements. This article introduces the concept of optimal identification (OI), which utilizes a global inversion algorithm to extract the full distribution of parameters consistent with the laboratory data. In addition, OI integrates suitable computational algorithms with experimental capabilities in a closed loop fashion to maximally reduce the breadth of the extracted parameter distribution. The closed loop OI procedure seeks out the optimal set of control chemical fluxes and data observations that actively filter out experimental noise and enhance the sensitivity to the desired parameters. In this fashion, the highest quality network parameters can be attained from inverting the tailored laboratory data. The operation of OI is illustrated by identifying a simulated tRNA proofreading mechanism, in which OI provides superior solutions for all the rate constants compared with suboptimal and nonoptimal methods.     

Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

Minimal cut sets in biochemical reaction networks

MOTIVATION: Structural studies of metabolic networks yield deeper insight into topology, functionality and capabilities of the metabolisms of different organisms. Here, we address the analysis of potential failure modes in metabolic networks whose occurrence will render the network structurally incapable of performing certain functions. Such studies will help to identify crucial parts in the network structure and to find suitable targets for repressing undesired metabolic functions. RESULTS: We introduce the concept of minimal cut sets for biochemical networks. A minimal cut set (MCS) is a minimal (irreducible) set of reactions in the network whose inactivation will definitely lead to a failure in certain network functions. We present an algorithm which enables the computation of the MCSs in a given network related to user-defined objective reactions. This algorithm operates on elementary modes. A number of potential applications are outlined, including network verifications, phenotype predictions, assessing structural robustness and fragility, metabolic flux analysis and target identification in drug discovery. Applications are illustrated by the MCSs in the central metabolism of Escherichia coli for growth on different substrates. AVAILABILITY: Computation and analysis of MCSs is an additional feature of the FluxAnalyzer (freely available for academic users upon request, special contracts for industrial companies; see web page below). Supplementary information: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer     

Computational functions in biochemical reaction networks.

In prior work we demonstrated the implementation of logic gates, sequential computers (universal Turing machines), and parallel computers by means of the kinetics of chemical reaction mechanisms. In the present article we develop this subject further by first investigating the computational properties of several enzymatic (single and multiple) reaction mechanisms: we show their steady states are analogous to either Boolean or fuzzy logic gates. Nearly perfect digital function is obtained only in the regime in which the enzymes are saturated with their substrates. With these enzymatic gates, we construct combinational chemical networks that execute a given truth-table. The dynamic range of a network's output is strongly affected by "input/output matching" conditions among the internal gate elements. We find a simple mechanism, similar to the interconversion of fructose-6-phosphate between its two bisphosphate forms (fructose-1,6-bisphosphate and fructose-2,6-bisphosphate), that functions analogously to an AND gate. When the simple model is supplanted with one in which the enzyme rate laws are derived from experimental data, the steady state of the mechanism functions as an asymmetric fuzzy aggregation operator with properties akin to a fuzzy AND gate. The qualitative behavior of the mechanism does not change when situated within a large model of glycolysis/gluconeogenesis and the TCA cycle. The mechanism, in this case, switches the pathway's mode from glycolysis to gluconeogenesis in response to chemical signals of low blood glucose (cAMP) and abundant fuel for the TCA cycle (acetyl coenzyme A).     

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein–protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor–ligand binding model and a rule‐based model of interleukin‐12 (IL‐12) signaling in naïve CD4+ T cells. The IL‐12 signaling pathway includes multiple protein–protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo‐equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL‐12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank‐ and flux‐based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule‐based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

A new measure of the robustness of biochemical networks

MOTIVATION: The robustness of a biochemical network is defined as the tolerance of variations in kinetic parameters with respect to the maintenance of steady state. Robustness also plays an important role in the fail-safe mechanism in the evolutionary process of biochemical networks. The purposes of this paper are to use the synergism and saturation system (S-system) representation to describe a biochemical network and to develop a robustness measure of a biochemical network subject to variations in kinetic parameters. Since most biochemical networks in nature operate close to the steady state, we consider only the robustness measurement of a biochemical network at the steady state. RESULTS: We show that the upper bound of the tolerated parameter variations is related to the system matrix of a biochemical network at the steady state. Using this upper bound, we can calculate the tolerance (robustness) of a biochemical network without testing many parametric perturbations. We find that a biochemical network with a large tolerance can also better attenuate the effects of variations in rate parameters and environments. Compensatory parameter variations and network redundancy are found to be important mechanisms for the robustness of biochemical networks. Finally, four biochemical networks, such as a cascaded biochemical network, the glycolytic-glycogenolytic pathway in a perfused rat liver, the tricarboxylic acid cycle in Dictyostelium discoideum and the cAMP oscillation network in bacterial chemotaxis, are used to illustrate the usefulness of the proposed robustness measure.     

An efficient grid layout algorithm for biological networks utilizing various biological attributes

Background  

Clearly visualized biopathways provide a great help in understanding biological systems. However, manual drawing of large-scale biopathways is time consuming. We proposed a grid layout algorithm that can handle gene-regulatory networks and signal transduction pathways by considering edge-edge crossing, node-edge crossing, distance measure between nodes, and subcellular localization information from Gene Ontology. Consequently, the layout algorithm succeeded in drastically reducing these crossings in the apoptosis model. However, for larger-scale networks, we encountered three problems: (i) the initial layout is often very far from any local optimum because nodes are initially placed at random, (ii) from a biological viewpoint, human layouts still exceed automatic layouts in understanding because except subcellular localization, it does not fully utilize biological information of pathways, and (iii) it employs a local search strategy in which the neighborhood is obtained by moving one node at each step, and automatic layouts suggest that simultaneous movements of multiple nodes are necessary for better layouts, while such extension may face worsening the time complexity.     

Quasi-multiparameter sensitivity measure for robustness analysis of complex biochemical networks

Robustness is the ability to resume reliable operation in the face of different types of perturbations. Analysis of how network structure achieves robustness enables one to understand and design cellular systems. It is typically true that all parameters simultaneously differ from their nominal values in vivo, but there have been few intelligible measures to estimate the robustness of a system's function to the uncertainty of all parameters.We propose a numerical and fast measure of a robust property to the uncertainty of all kinetic parameters, named quasi-multiparameter sensitivity (QMPS), which is defined as the sum of the squared magnitudes of single-parameter sensitivities. Despite its plain idea, it has hardly been employed in analysis of biological models. While QMPS is theoretically derived as a linear model, QMPS can be consistent with the expected variance simulated by the widely used Monte Carlo method in nonlinear biological models, when relatively small perturbations are given. To demonstrate the feasibility of QMPS, it is employed for numerical comparison to analyze the mechanism of how specific regulations generate robustness in typical biological models.QMPS characterizes the robustness much faster than the Monte Carlo method, thereby enabling the extensive search of a large parameter space to perform the numerical comparison between alternative or competing models. It provides a theoretical or quantitative insight to an understanding of how specific network structures are related to robustness. In circadian oscillators, a negative feedback loop with multiple phosphorylations is demonstrated to play a critical role in generating robust cycles to the uncertainty of multiple parameters.     

A graphical notation for biochemical networks

A solid definition and comprehensive graphical representation of biological networks is essential for efficient and accurate dissemination of information on biological models. Several proposals have already been made toward this aim. The most well known representation of this kind is a molecular interaction map, or ‘Kohn Map’. However, although the molecular interaction map is a well-defined and compact notation, there are several drawbacks, such as difficulties in intuitive understanding of temporal changes of reactions and additional complexities arising from particular graphical representations. This article proposes several improvements to the molecular interaction map, as well as the use of the ‘process diagram’ to help understand temporal sequences of reactions.     

A graph layout algorithm for drawing metabolic pathways

MOTIVATION: A large amount of data on metabolic pathways is available in databases. The ability to visualise the complex data dynamically would be useful for building more powerful research tools to access the databases. Metabolic pathways are typically modelled as graphs in which nodes represent chemical compounds, and edges represent chemical reactions between compounds. Thus, the problem of visualising pathways can be formulated as a graph layout problem. Currently available visual interfaces to biochemical databases either use static images or cannot cope well with more complex, non-standard pathways. RESULTS: This paper presents a new algorithm for drawing pathways which uses a combination of circular, hierarchic and force-directed graph layout algorithms to compute positions of the graph elements representing main compounds and reactions. The algorithm is particularly designed for cyclic or partially cyclic pathways or for combinations of complex pathways. It has been tested on five sample pathways with promising results.     

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.     

A dynamical model of genetic networks for cell differentiation

A mathematical model is proposed which is able to describe the most important features of cell differentiation, without requiring specific detailed assumptions concerning the interactions which drive the phenomenon. On the contrary, cell differentiation is described here as an emergent property of a generic model of the underlying gene regulatory network, and it can therefore be applied to a variety of different organisms. The model points to a peculiar role of cellular noise in differentiation and leads to non trivial predictions which could be subject to experimental testing. Moreover, a single model proves able to describe several different phenomena observed in various differentiation processes.