Discriminating between rival biochemical network models: three approaches to optimal experiment design

Background  

The success of molecular systems biology hinges on the ability to use computational models to design predictive experiments, and ultimately unravel underlying biological mechanisms. A problem commonly encountered in the computational modelling of biological networks is that alternative, structurally different models of similar complexity fit a set of experimental data equally well. In this case, more than one molecular mechanism can explain available data. In order to rule out the incorrect mechanisms, one needs to invalidate incorrect models. At this point, new experiments maximizing the difference between the measured values of alternative models should be proposed and conducted. Such experiments should be optimally designed to produce data that are most likely to invalidate incorrect model structures.     

SELECTpro: effective protein model selection using a structure-based energy function resistant to BLUNDERs

Background  

Protein tertiary structure prediction is a fundamental problem in computational biology and identifying the most native-like model from a set of predicted models is a key sub-problem. Consensus methods work well when the redundant models in the set are the most native-like, but fail when the most native-like model is unique. In contrast, structure-based methods score models independently and can be applied to model sets of any size and redundancy level. Additionally, structure-based methods have a variety of important applications including analogous fold recognition, refinement of sequence-structure alignments, and de novo prediction. The purpose of this work was to develop a structure-based model selection method based on predicted structural features that could be applied successfully to any set of models.     

Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

Background  

Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.     

Module-based multiscale simulation of angiogenesis in skeletal muscle

Background  

Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.     

Towards the high-resolution protein structure prediction. Fast refinement of reduced models with all-atom force field

Background  

Although experimental methods for determining protein structure are providing high resolution structures, they cannot keep the pace at which amino acid sequences are resolved on the scale of entire genomes. For a considerable fraction of proteins whose structures will not be determined experimentally, computational methods can provide valuable information. The value of structural models in biological research depends critically on their quality. Development of high-accuracy computational methods that reliably generate near-experimental quality structural models is an important, unsolved problem in the protein structure modeling.     

RMBNToolbox: random models for biochemical networks

Background  

There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models.     

Dynamic simulation of regulatory networks using SQUAD

Background  

The ambition of most molecular biologists is the understanding of the intricate network of molecular interactions that control biological systems. As scientists uncover the components and the connectivity of these networks, it becomes possible to study their dynamical behavior as a whole and discover what is the specific role of each of their components. Since the behavior of a network is by no means intuitive, it becomes necessary to use computational models to understand its behavior and to be able to make predictions about it. Unfortunately, most current computational models describe small networks due to the scarcity of kinetic data available. To overcome this problem, we previously published a methodology to convert a signaling network into a dynamical system, even in the total absence of kinetic information. In this paper we present a software implementation of such methodology.     

Bayesian coestimation of phylogeny and sequence alignment

Background  

Two central problems in computational biology are the determination of the alignment and phylogeny of a set of biological sequences. The traditional approach to this problem is to first build a multiple alignment of these sequences, followed by a phylogenetic reconstruction step based on this multiple alignment. However, alignment and phylogenetic inference are fundamentally interdependent, and ignoring this fact leads to biased and overconfident estimations. Whether the main interest be in sequence alignment or phylogeny, a major goal of computational biology is the co-estimation of both.     

Automated Bayesian model development for frequency detection in biological time series

Background

The ability to perform quantitative studies using isotope tracers and metabolic flux analysis (MFA) is critical for detecting pathway bottlenecks and elucidating network regulation in biological systems, especially those that have been engineered to alter their native metabolic capacities. Mathematically, MFA models are traditionally formulated using separate state variables for reaction fluxes and isotopomer abundances. Analysis of isotope labeling experiments using this set of variables results in a non-convex optimization problem that suffers from both implementation complexity and convergence problems.

Results

This article addresses the mathematical and computational formulation of ¹³C MFA models using a new set of variables referred to as fluxomers. These composite variables combine both fluxes and isotopomer abundances, which results in a simply-posed formulation and an improved error model that is insensitive to isotopomer measurement normalization. A powerful fluxomer iterative algorithm (FIA) is developed and applied to solve the MFA optimization problem. For moderate-sized networks, the algorithm is shown to outperform the commonly used 13CFLUX cumomer-based algorithm and the more recently introduced OpenFLUX software that relies upon an elementary metabolite unit (EMU) network decomposition, both in terms of convergence time and output variability.

Conclusions

Substantial improvements in convergence time and statistical quality of results can be achieved by applying fluxomer variables and the FIA algorithm to compute best-fit solutions to MFA models. We expect that the fluxomer formulation will provide a more suitable basis for future algorithms that analyze very large scale networks and design optimal isotope labeling experiments.     

Function approximation approach to the inference of reduced NGnet models of genetic networks

Background  

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.     

Parameter inference for discretely observed stochastic kinetic models using stochastic gradient descent

Background  

Stochastic effects can be important for the behavior of processes involving small population numbers, so the study of stochastic models has become an important topic in the burgeoning field of computational systems biology. However analysis techniques for stochastic models have tended to lag behind their deterministic cousins due to the heavier computational demands of the statistical approaches for fitting the models to experimental data. There is a continuing need for more effective and efficient algorithms. In this article we focus on the parameter inference problem for stochastic kinetic models of biochemical reactions given discrete time-course observations of either some or all of the molecular species.     

Systematic calibration of a cell signaling network model

Background  

Mathematical modeling is being applied to increasingly complex biological systems and datasets; however, the process of analyzing and calibrating against experimental data is often challenging and a rate limiting step in model development. To address this problem, we developed a systematic methodology for calibrating quantitative models of dynamic biological processes and illustrate its utility by validating a model of TRAIL (Tumor necrosis factor Related Apoptosis-Inducing Ligand)-induced cell death.     

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

Background  

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.     

MetaMQAP: A meta-server for the quality assessment of protein models

Background  

Computational models of protein structure are usually inaccurate and exhibit significant deviations from the true structure. The utility of models depends on the degree of these deviations. A number of predictive methods have been developed to discriminate between the globally incorrect and approximately correct models. However, only a few methods predict correctness of different parts of computational models. Several Model Quality Assessment Programs (MQAPs) have been developed to detect local inaccuracies in unrefined crystallographic models, but it is not known if they are useful for computational models, which usually exhibit different and much more severe errors.     

Simulation-based model checking approach to cell fate specification during Caenorhabditis elegans vulval development by hybrid functional Petri net with extension

Background  

Model checking approaches were applied to biological pathway validations around 2003. Recently, Fisher et al. have proved the importance of model checking approach by inferring new regulation of signaling crosstalk in C. elegans and confirming the regulation with biological experiments. They took a discrete and state-based approach to explore all possible states of the system underlying vulval precursor cell (VPC) fate specification for desired properties. However, since both discrete and continuous features appear to be an indispensable part of biological processes, it is more appropriate to use quantitative models to capture the dynamics of biological systems. Our key motivation of this paper is to establish a quantitative methodology to model and analyze in silico models incorporating the use of model checking approach.     

Understanding dynamics using sensitivity analysis: caveat and solution

Background  

Parametric sensitivity analysis (PSA) has become one of the most commonly used tools in computational systems biology, in which the sensitivity coefficients are used to study the parametric dependence of biological models. As many of these models describe dynamical behaviour of biological systems, the PSA has subsequently been used to elucidate important cellular processes that regulate this dynamics. However, in this paper, we show that the PSA coefficients are not suitable in inferring the mechanisms by which dynamical behaviour arises and in fact it can even lead to incorrect conclusions.     

When the optimal is not the best: parameter estimation in complex biological models

Background

The vast computational resources that became available during the past decade enabled the development and simulation of increasingly complex mathematical models of cancer growth. These models typically involve many free parameters whose determination is a substantial obstacle to model development. Direct measurement of biochemical parameters in vivo is often difficult and sometimes impracticable, while fitting them under data-poor conditions may result in biologically implausible values.

Results

We discuss different methodological approaches to estimate parameters in complex biological models. We make use of the high computational power of the Blue Gene technology to perform an extensive study of the parameter space in a model of avascular tumor growth. We explicitly show that the landscape of the cost function used to optimize the model to the data has a very rugged surface in parameter space. This cost function has many local minima with unrealistic solutions, including the global minimum corresponding to the best fit.

Conclusions

The case studied in this paper shows one example in which model parameters that optimally fit the data are not necessarily the best ones from a biological point of view. To avoid force-fitting a model to a dataset, we propose that the best model parameters should be found by choosing, among suboptimal parameters, those that match criteria other than the ones used to fit the model. We also conclude that the model, data and optimization approach form a new complex system and point to the need of a theory that addresses this problem more generally.     

MIRIAM Resources: tools to generate and resolve robust cross-references in Systems Biology

Background  

The Minimal Information Requested In the Annotation of biochemical Models (MIRIAM) is a set of guidelines for the annotation and curation processes of computational models, in order to facilitate their exchange and reuse. An important part of the standard consists in the controlled annotation of model components, based on Uniform Resource Identifiers. In order to enable interoperability of this annotation, the community has to agree on a set of standard URIs, corresponding to recognised data types. MIRIAM Resources are being developed to support the use of those URIs.