Optimal design of stimulus experiments for robust discrimination of biochemical reaction networks

Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs). Results: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning. Availability: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html. Contact: [email protected] Supplementary information: Supplementary data are are available at Bioinformatics online

Symmetry Breaking and Emergence of Directional Flows in Minimal Actomyosin Cortices

Cortical actomyosin flows, among other mechanisms, scale up spontaneous symmetry breaking and thus play pivotal roles in cell differentiation, division, and motility. According to many model systems, myosin motor-induced local contractions of initially isotropic actomyosin cortices are nucleation points for generating cortical flows. However, the positive feedback mechanisms by which spontaneous contractions can be amplified towards large-scale directed flows remain mostly speculative. To investigate such a process on spherical surfaces, we reconstituted and confined initially isotropic minimal actomyosin cortices to the interfaces of emulsion droplets. The presence of ATP leads to myosin-induced local contractions that self-organize and amplify into directed large-scale actomyosin flows. By combining our experiments with theory, we found that the feedback mechanism leading to a coordinated directional motion of actomyosin clusters can be described as asymmetric cluster vibrations, caused by intrinsic non-isotropic ATP consumption with spatial confinement. We identified fingerprints of vibrational states as the basis of directed motions by tracking individual actomyosin clusters. These vibrations may represent a generic key driver of directed actomyosin flows under spatial confinement in vitro and in living systems.(This article belongs to the Special Issue Symmetry Breaking in Cells and Tissues

Evaluation and improvement of the regulatory inference for large co-expression networks with limited sample size

Abstract Background Co-expression has been widely used to identify novel regulatory relationships using high throughput measurements, such as microarray and RNA-seq data. Evaluation studies on co-expression network analysis methods mostly focus on networks of small or medium size of up to a few hundred nodes. For large networks, simulated expression data usually consist of hundreds or thousands of profiles with different perturbations or knock-outs, which is uncommon in real experiments due to their cost and the amount of work required. Thus, the performances of co-expression network analysis methods on large co-expression networks consisting of a few thousand nodes, with only a small number of profiles with a single perturbation, which more accurately reflect normal experimental conditions, are generally uncharacterized and unknown. Methods We proposed a novel network inference methods based on Relevance Low order Partial Correlation (RLowPC). RLowPC method uses a two-step approach to select on the high-confidence edges first by reducing the search space by only picking the top ranked genes from an intial partial correlation analysis and, then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association. Results We selected six co-expression-based methods with good performance in evaluation studies from the literature: Partial correlation, PCIT, ARACNE, MRNET, MRNETB and CLR. The evaluation of these methods was carried out on simulated time-series data with various network sizes ranging from 100 to 3000 nodes. Simulation results show low precision and recall for all of the above methods for large networks with a small number of expression profiles. We improved the inference significantly by refinement of the top weighted edges in the pre-inferred partial correlation networks using RLowPC. We found improved performance by partitioning large networks into smaller co-expressed modules when assessing the method performance within these modules. Conclusions The evaluation results show that current methods suffer from low precision and recall for large co-expression networks where only a small number of profiles are available. The proposed RLowPC method effectively reduces the indirect edges predicted as regulatory relationships and increases the precision of top ranked predictions. Partitioning large networks into smaller highly co-expressed modules also helps to improve the performance of network inference methods. The RLowPC R package for network construction, refinement and evaluation is available at GitHub: https://github.com/wyguo/RLowPC

Design of robust discrimination experiments for modeling biochemical reaction networks

Biochemical reaction networks in the form of coupled ODEs provide a powerful modeling tool to understand the dynamics of biochemical processes, including metabolism as well as signal transduction in bacteria or mammalian cells. During the modeling process of biochemical systems from scratch, scientists have to cope with numerous challenges, for instance, limited knowledge about the underlying mechanisms, contradicting experimental results as well as lack of sufficient experimental data. As a result, a large pool of competing nonlinear biochemical reaction networks is generated during the early phase of systems understanding, from which the most plausible set has to be selected. At this point, model-based stimulus experiments can be used to drive model responses of competing models furthest away [1]. However, model-based experiments depend on the prediction power of the models, which is typically very low due to large parameter uncertainties in the initial modeling phase. Ther efore, alternative criteria have been proposed, which weight the model differences according to their prediction power [1]. In our contribution we present an efficient methodology for designing optimal stimulus experiments for robust model discrimination using the framework of optimal control, taking model uncertainties explicitly into account. The optimal control problem is formulated as a nonlinear program (NLP) in combination with the sigma point method [2] to propagate uncertainties through the dynamic optimization. The advantage of the sigma point method for nonlinear models compared to linearization or Monte Carlo sampling has been illustrated by many authors, including [2,3]. Due to the efficient transformation of model uncertainties, we can apply the non-symmetric Kullback-Leibler divergence as well as the symmetric model-overlap to measure expected model discrepancies [4, 5]. In our presentation we will demonstrate this method considering several competing biochemical reaction networks, which describe the response of NF-kappaB related signaling proteins (cytosol-to-nucleus translocation, posttranslational modifications, e.g., phosphorylation, sumoylation and complexation) in mammalian cells under genotoxic stress, i.e., gamma-irradiation. Being of high practical relevance, this case study illustrates the high potential of the developed methodology. References [1] B. H. Chen, S. P. Asprey, Ind. Eng. Chem. Res., 2003, 42, 1379–1390. [2] S. Julier, J. Uhlmann, H. F. Durrant-Whyte, Automatic Control, 2000, 45, 477-482. [3] R. Schenkendorf, A. Kremling, M. Mangold, IET Syst. Biol., 2009, 3, 10–23. [4] S. Kullback, R. A. Leibler, Annals of Mathematical Statistics, 1951, 22, 79–86. [5] S. Lorenz, E. Diederichs, R. Telgmann, C. Schuette, Journal of Computational Chemistry, 2007, 28, 1384-139