HillTau: A fast,compact abstraction for model reduction in biochemical signaling networks

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.     

Modeling biochemical networks: a cellular-automata approach

The potential of the cellular-automata (CA) method for modeling biological networks is demonstrated for the mitogen-activated protein kinase (MAPK) signaling cascade. The models derived reproduced the high signal amplification through the cascade and the deviation of the cascade enzymes from the Michaelis-Menten kinetics, evidencing cooperativity effects. The patterns of pathway change upon varying substrate concentrations and enzyme efficiencies were identified and used to show the ways for controlling pathway processes. Guidance in the selection of enzyme inhibition targets with minimum side effects is one outcome of the study.     

Iterative approach to model identification of biological networks

Background  

Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements.     

Linear systems approach to analysis of complex dynamic behaviours in biochemical networks

Central functions in the cell are often linked to complex dynamic behaviours, such as sustained oscillations and multistability, in a biochemical reaction network. Determination of the specific mechanisms underlying such behaviours is important, e.g. to determine sensitivity, robustness, and modelling requirements of given cell functions. In this work we adopt a systems approach to the analysis of complex behaviours in intracellular reaction networks, described by ordinary differential equations with known kinetic parameters. We propose to decompose the overall system into a number of low complexity subsystems, and consider the importance of interactions between these in generating specific behaviours. Rather than analysing the network in a state corresponding to the complex non-linear behaviour, we move the system to the underlying unstable steady state, and focus on the mechanisms causing destabilisation of this steady state. This is motivated by the fact that all complex behaviours in unforced systems can be traced to destabilisation (bifurcation) of some steady state, and hence enables us to use tools from linear system theory to qualitatively analyse the sources of given network behaviours. One important objective of the present study is to see how far one can come with a relatively simple approach to the analysis of highly complex biochemical networks. The proposed method is demonstrated by application to a model of mitotic control in Xenopus frog eggs, and to a model of circadian oscillations in Drosophila. In both examples we are able to identify the subsystems, and the related interactions, which are instrumental in generating the observed complex non-linear behaviours.     

Combining flux and energy balance analysis to model large-scale biochemical networks

Stoichiometric Network Theory is a constraints-based, optimization approach for quantitative analysis of the phenotypes of large-scale biochemical networks that avoids the use of detailed kinetics. This approach uses the reaction stoichiometric matrix in conjunction with constraints provided by flux balance and energy balance to guarantee mass conserved and thermodynamically allowable predictions. However, the flux and energy balance constraints have not been effectively applied simultaneously on the genome scale because optimization under the combined constraints is non-linear. In this paper, a sequential quadratic programming algorithm that solves the non-linear optimization problem is introduced. A simple example and the system of fermentation in Saccharomyces cerevisiae are used to illustrate the new method. The algorithm allows the use of non-linear objective functions. As a result, we suggest a novel optimization with respect to the heat dissipation rate of a system. We also emphasize the importance of incorporating interactions between a model network and its surroundings.     

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 domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks

Background:  

Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications.     

Stochastic simulation GUI for biochemical networks

MOTIVATION: This article describes the development of a useful graphical user interface for stochastic simulation of biochemical networks which allows model builders to run stochastic simulations of their models and perform statistical analysis on the results. These include the construction of correlations, power-spectral densities and transfer functions between selected inputs and outputs. AVAILABILITY: The software is licensed under the BSD open source license and is available at http://sourceforge.net/projects/jdesigner. In addition, a more detailed account of the algorithms employed in the tool can be found at the Wiki at http://www.sys-bio.org/sbwWiki. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

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 quantum model for controlled enzymic reactions: II. Controlled biochemical networks

Two control units, the switching and the two factor discriminating net are described. They are derived as a consequence of the enzymic oscillatory behavior induced by substrate “perturbation”. A complex network encompassing long sequences of metabolic reactions is constructed and the organization of cellular metabolic activities in well defined “regimes” and “states” inferred.     

A joint latent variable model approach to item reduction and validation

Many applications of biomedical science involve unobservable constructs, from measurement of health states to severity of complex diseases. The primary aim of measurement is to identify relevant pieces of observable information that thoroughly describe the construct of interest. Validation of the construct is often performed separately. Noting the increasing popularity of latent variable methods in biomedical research, we propose a Multiple Indicator Multiple Cause (MIMIC) latent variable model that combines item reduction and validation. Our joint latent variable model accounts for the bias that occurs in the traditional 2-stage process. The methods are motivated by an example from the Physical Activity and Lymphedema clinical trial in which the objectives were to describe lymphedema severity through self-reported Likert scale symptoms and to determine the relationship between symptom severity and a "gold standard" diagnostic measure of lymphedema. The MIMIC model identified 1 symptom as a potential candidate for removal. We present this paper as an illustration of the advantages of joint latent variable models and as an example of the applicability of these models for biomedical research.     

Investigating the dynamic behavior of biochemical networks using model families

MOTIVATION: Supporting the evolutionary modeling process of dynamic biochemical networks based on sampled in vivo data requires more than just simulation. In the course of the modeling process, the modeler is typically concerned not only with a single model but also with sequences, alternatives and structural variants of models. Powerful automatic methods are then required to assist the modeler in the organization and the evaluation of alternative models. Moreover, the structure and peculiarities of the data require dedicated tool support. SUMMARY: To support all stages of an evolutionary modeling process, a new general formalism for the combinatorial specification of large model families is introduced. It allows for automatic navigation in the space of models and excludes biologically meaningless models on the basis of elementary flux mode analysis. An incremental usage of the measured data is supported by using splined data instead of state variables. With MMT2, a versatile tool has been developed as a computational engine intended to be built into a tool chain. Using automatic code generation, automatic differentiation for sensitivity analysis and grid computing technology, a high performance computing environment is achieved. MMT2 supplies XML model specification and several software interfaces. The performance of MMT2 is illustrated by several examples from ongoing research projects. AVAILABILITY: http://www.simtec.mb.uni-siegen.de/ CONTACT: wiechert@simtec.mb.uni-siegen.de.     

Bridging from molecular simulation to biochemical networks

How can we make the connection between the three-dimensional structures of individual proteins and understanding how complex biological systems involving many proteins work? The modelling and simulation of protein structures can help to answer this question for systems ranging from multimacromolecular complexes to organelles and cells. On one hand, multiscale modelling and simulation techniques are advancing to permit the spatial and temporal properties of large systems to be simulated using atomic-detail structures. On the other hand, the estimation of kinetic parameters for the mathematical modelling of biochemical pathways using protein structure information provides a basis for iterative manipulation of biochemical pathways guided by protein structure. Recent advances include the structural modelling of protein complexes on the genomic level, novel coarse-graining strategies to increase the size of the system and the time span that can be simulated, and comparative molecular field analyses to estimate enzyme kinetic parameters.     

Modelling biochemical networks with intrinsic time delays: a hybrid semi-parametric approach

Background  

This paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.     

A constitutive model for the time-dependent,nonlinear stress response of fibrin networks

Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin–Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.     

A systematic approach to biochemical profiling

Sequencing of the Arabidopsis thaliana genome is complete. The analytical tools for determining gene function by altering and monitoring gene expression are relatively well developed, and are generating large volumes of valuable data. Recent advances in techniques for the analysis of small molecules allow researchers to apply biochemical profiling as another powerful approach to functional genomics and metabolic research.     

A biochemical approach to essential hypertension

Using multivariate statistical analysis, an attempt has been made to select hypertensive and normotensive sub-groups of subjects on the basis of certain parameters of their blood serum, such as the inhibition of purified Na,K-ATPase by serum and the content of two proteins with molecular masses of 12 and 15 kDa. An analysis of 20 human beings (10 hypertensive and 10 normotensive individuals) revealed that the best division into sub-groups is achieved only through the use of a combination of these three parameters.     

Flux module decomposition for parameter estimation in a multiple-feedback loop model of biochemical networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Since few quantitative values are measured in vivo, the values for unmeasured parameters should be estimated so that the simulation agrees with the experimental data. Considering the sparsity and error rates of experimentally measured data, the first thing is not to find a numerically exact and global solution but to explore a variety of the plausible parameter solutions. To find many plausible parameter solutions without any biases, we developed the two-phase search (TPS) method. However, calculation complexity makes it hard for TPS to optimize a large-scale dynamic model. In this study divide-and-conquer methods are used to solve this problem. The flux module decomposition (FMD) is first proposed that separates a complex, large-scale dynamic model into multiple flux modules without deteriorating its basic control architectures. FMD is combined with TPS, named FMD-TPS, to find many plausible parameter solutions for a dynamic model. To demonstrate the feasibility of FMD-TPS, it is applied to the E. coli ammonia assimilation system that consists of multiple-feedback loops. The variability of the solutions is verified by measuring the space distribution of the parameter solution vectors and by defining the binary vectors checking the consistency with biological behaviors. Compared with non-decomposition methods, FMD-TPS efficiently explored a variety of plausible parameter solutions that reproduce the dynamic behaviors in vivo.