A divide-and-conquer approach to analyze underdetermined biochemical models

Motivation: To obtain meaningful predictions from dynamic computational models, their uncertain parameter values need to be estimated from experimental data. Due to the usually large number of parameters compared to the available measurement data, these estimation problems are often underdetermined meaning that the solution is a multidimensional space. In this case, the challenge is yet to obtain a sound system understanding despite non-identifiable parameter values, e.g. through identifying those parameters that most sensitively determine the model’s behavior. Results: Here, we present the so-called divide-and-conquer approach—a strategy to analyze underdetermined biochemical models. The approach draws on steady state omics measurement data and exploits a decomposition of the global estimation problem into independent subproblems. The solutions to these subproblems are joined to the complete space of global optima, which can be easily analyzed. We derive the conditions at which the decomposition occurs, outline strategies to fulfill these conditions and—using an example model—illustrate how the approach uncovers the most important parameters and suggests targeted experiments without knowing the exact parameter values.

A divide-and-conquer approach to analyze underdetermined biochemical models

Motivation: To obtain meaningful predictions from dynamic computational models, their uncertain parameter values need to be estimated from experimental data. Due to the usually large number of parameters compared to the available measurement data, these estimation problems are often underdetermined meaning that the solution is a multidimensional space. In this case, the challenge is yet to obtain a sound system understanding despite non-identifiable parameter values, e.g. through identifying those parameters that most sensitively determine the model's behavior. Results: Here, we present the so-called divide-and-conquer approach—a strategy to analyze underdetermined biochemical models. The approach draws on steady state omics measurement data and exploits a decomposition of the global estimation problem into independent subproblems. The solutions to these subproblems are joined to the complete space of global optima, which can be easily analyzed. We derive the conditions at which the decomposition occurs, outline strategies to fulfill these conditions and—using an example model—illustrate how the approach uncovers the most important parameters and suggests targeted experiments without knowing the exact parameter values. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Unfolding RNA 3D structures for secondary structure prediction benchmarking

Les acides ribonucléiques (ARN) forment des structures tri-dimensionnelles complexes stabilisées par la formation de la structure secondaire (2D), elle-même formée de paires de bases. Plusieurs méthodes computationnelles ont été créées dans les dernières années afin de prédire la structure 2D d’ARNs, en partant de la séquence. Afin de simplifier le calcul, ces méthodes appliquent généralement des restrictions sur le type de paire de bases et la topologie des structures 2D prédites. Ces restrictions font en sorte qu’il est parfois difficile de savoir à quel point la totalité des paires de bases peut être représentée par ces structures 2D restreintes. MC-Unfold fut créé afin de trouver les structures 2D restreintes qui pourraient être associées à une structure secondaire complète, en fonction des restrictions communément utilisées par les méthodes de prédiction de structure secondaire. Un ensemble de 321 monomères d’ARN totalisant plus de 4223 structures fut assemblé afin d’évaluer les méthodes de prédiction de structure 2D. La majorité de ces structures ont été déterminées par résonance magnétique nucléaire et crystallographie aux rayons X. Ces structures ont été dépliés par MC-Unfold et les structures résultantes ont été comparées à celles prédites par les méthodes de prédiction. La performance de MC-Unfold sur un ensemble de structures expérimentales est encourageante. En moins de 5 minutes, 96% des 227 structures ont été complètement dépliées, le reste des structures étant trop complexes pour être déplié rapidement. Pour ce qui est des méthodes de prédiction de structure 2D, les résultats indiquent qu’elles sont capable de prédire avec un certain succès les structures expérimentales, particulièrement les petites molécules. Toutefois, si on considère les structures larges ou contenant des pseudo-noeuds, les résultats sont généralement défavorables. Les résultats obtenus indiquent que les méthodes de prédiction de structure 2D devraient être utilisées avec prudence, particulièrement pour de larges molécules.Ribonucleic acids (RNA) adopt complex three dimensional structures which are stabilized by the formation of base pairs, also known as the secondary (2D) structure. Predicting where and how many of these interactions occur has been the focus of many computational methods called 2D structure prediction algorithms. These methods disregard some interactions, which makes it difficult to know how well a 2D structure represents an RNA structure, especially when large amounts of base pairs are ignored. MC-Unfold was created to remove interactions violating the assumptions used by prediction methods. This process, named unfolding, extends previous planarization and pseudoknot removal methods. To evaluate how well computational methods can predict experimental structures, a set of 321 RNA monomers corresponding to more than 4223 experimental structures was acquired. These structures were mostly determined using nuclear magnetic resonance and X-ray crystallography. MC-Unfold was used to remove interactions the prediction algorithms were not expected to predict. These structures were then compared with the structured predicted. MC-Unfold performed very well on the test set it was given. In less than five minutes, 96% of the 227 structure could be exhaustively unfolded. The few remaining structures are very large and could not be unfolded in reasonable time. MC-Unfold is therefore a practical alternative to the current methods. As for the evaluation of prediction methods, MC-Unfold demonstrated that the computational methods do find experimental structures, especially for small molecules. However, when considering large or pseudoknotted molecules, the results are not so encouraging. As a consequence, 2D structure prediction methods should be used with caution, especially for large structures

Modular parameter identification of biomolecular networks

The increasing complexity of dynamic models in systems and synthetic biology poses computational challenges especially for the identification of model parameters. While modularization of the corresponding optimization problems could help reduce the “curse of dimensionality,” abundant feedback and crosstalk mechanisms prohibit a simple decomposition of most biomolecular networks into subnetworks, or modules. Drawing on ideas from network modularization and multiple-shooting optimization, we present here a modular parameter identification approach that explicitly allows for such interdependencies. Interfaces between our modules are given by the experimentally measured molecular species. This definition allows deriving good (initial) estimates for the inter-module communication directly from the experimental data. Given these estimates, the states and parameter sensitivities of different modules can be integrated independently. To achieve consistency between modules, we iteratively adjust the estimates for inter-module communication while optimizing the parameters. After convergence to an optimal parameter set---but not during earlier iterations---the intermodule communication as well as the individual modules\' state dynamics agree with the dynamics of the nonmodularized network. Our modular parameter identification approach allows for easy parallelization; it can reduce the computational complexity for larger networks and decrease the probability to converge to suboptimal local minima. We demonstrate the algorithm\'s performance in parameter estimation for two biomolecular networks, a synthetic genetic oscillator and a mammalian signaling pathway

Bacterial adaptation through distributed sensing of metabolic fluxes

We present a large-scale differential equation model of E. coli's central metabolism and its enzymatic, transcriptional, and posttranslational regulation. This model reproduces E. coli's known physiological behavior.We found that the interplay of known interactions in E. coli's central metabolism can indirectly recognize the presence of extracellular carbon sources through measuring intracellular metabolic flux patterns.We found that E. coli's system-level adaptations between glycolytic and gluconeogenic carbon sources are realized on the molecular level by global feedback architectures that overarch the enzymatic and transcriptional regulatory layers.We found that the capability for closed-loop self-regulation can emerge within metabolism itself and therefore, metabolic operation may adapt itself autonomously to changing carbon sources (not requiring upstream sensing and signaling)

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis

Comparison of evolutionary algorithms in gene regulatory network model inference

Background: The evolution of high throughput technologies that measure gene expression levels has created a data base for inferring GRNs (a process also known as reverse engineering of GRNs). However, the nature of these data has made this process very di±cult. At the moment, several methods of discovering qualitative causal relationships between genes with high accuracy from microarray data exist, but large scale quantitative analysis on real biological datasets cannot be performed, to date, as existing approaches are not suitable for real microarray data which are noisy and insu±cient. Results: This paper performs an analysis of several existing evolutionary algorithms for quantitative gene regulatory network modelling. The aim is to present the techniques used and o®er a comprehensive comparison of approaches, under a common framework. Algorithms are applied to both synthetic and real gene expression data from DNA microarrays, and ability to reproduce biological behaviour, scalability and robustness to noise are assessed and compared. Conclusions: Presented is a comparison framework for assessment of evolutionary algorithms, used to infer gene regulatory networks. Promising methods are identi¯ed and a platform for development of appropriate model formalisms is established