Nicole Radde

Modeling gene regulatory networks with piecewise linear differential equations

Abstract Microarray chips generate large amounts of data about a cell’s state. In our work we want to analyze these data in order to describe the regulation processes within a cell. Therefore, we build a model which is capable of capturing the most relevant regulating interactions and present an approach how to calculate the parameters for the model from time-series data. This approach uses the discrete approximation method of least squares to solve a data fitting modeling problem. Furthermore, we analyze the features of our proposed system, i.e., which kinds of dynamical behaviors the system is able to show.

Determinants of robustness in spindle assembly checkpoint signalling

The spindle assembly checkpoint is a conserved signalling pathway that protects genome integrity. Given its central importance, this checkpoint should withstand stochastic fluctuations and environmental perturbations, but the extent of and mechanisms underlying its robustness remain unknown. We probed spindle assembly checkpoint signalling by modulating checkpoint protein abundance and nutrient conditions in fission yeast. For core checkpoint proteins, a mere 20% reduction can suffice to impair signalling, revealing a surprising fragility. Quantification of protein abundance in single cells showed little variability (noise) of critical proteins, explaining why the checkpoint normally functions reliably. Checkpoint-mediated stoichiometric inhibition of the anaphase activator Cdc20 (Slp1 in Schizosaccharomyces pombe) can account for the tolerance towards small fluctuations in protein abundance and explains our observation that some perturbations lead to non-genetic variation in the checkpoint response. Our work highlights low gene expression noise as an important determinant of reliable checkpoint signalling.

Graphical methods for analysing feedback in biological networks-A survey

Observed phenotypes usually arise from complex networks of interacting cell components. Qualitative information about the structure of these networks is often available, while quantitative information may be partial or absent. It is natural then to ask what, if anything, we can learn about the behaviour of the system solely from its qualitative structure. In this article we review some techniques which can be applied to answer this question, focussing in particular on approaches involving graphical representations of model structure. By applying these techniques to various cellular network examples, we discuss their strengths and limitations, and point to future research directions.

A New Approach for Modeling Procaryotic Biochemical Networks With Differential Equations

One major challenge in Computational Biology is the simulation of the processes in a biological cell, which makes it necessary to understand the interactions between cell components. It is convenient to model the entirety of such interactions as biochemical networks. In this paper we present our novel approach to describe these biochemical networks with piecewise linear differential equations and analyze it theoretically. Then we will discuss methods for the parameter estimation from time series measurements including inference of the network topology. Finally we show an application of our model for the bacterium Corynebacterium glutamicum.

Systematic component selection for gene-network refinement

MOTIVATION A quantitative description of interactions between cell components is a major challenge in Computational Biology. As a method of choice, differential equations are used for this purpose, because they provide a detailed insight into the dynamic behavior of the system. In most cases, the number of time points of experimental time series is usually too small to estimate the parameters of a model of a whole gene regulatory network based on differential equations, such that one needs to focus on subnetworks consisting of only a few components. For most approaches, the set of components of the subsystem is given in advance and only the structure has to be estimated. However, the set of components that influence the system significantly are not always known in advance, making a method desirable that determines both, the components that are included into the model and the parameters. RESULTS We have developed a method that uses gene expression data as well as interaction data between cell components to define a set of genes that we use for our modeling. In a subsequent step, we estimate the parameters of our model of piecewise linear differential equations and evaluate the results simulating the behavior of the system with our model. We have applied our method to the DNA repair system of Mycobacterium tuberculosis. Our analysis predicts that the gene Rv2719c plays an important role in this system.

Long-term prediction of fish growth under varying ambient temperature using a multiscale dynamic model.

BackgroundFeed composition has a large impact on the growth of animals, particularly marine fish. We have developed a quantitative dynamic model that can predict the growth and body composition of marine fish for a given feed composition over a timespan of several months. The model takes into consideration the effects of environmental factors, particularly temperature, on growth, and it incorporates detailed kinetics describing the main metabolic processes (protein, lipid, and central metabolism) known to play major roles in growth and body composition.ResultsFor validation, we compared our models predictions with the results of several experimental studies. We showed that the model gives reliable predictions of growth, nutrient utilization (including amino acid retention), and body composition over a timespan of several months, longer than most of the previously developed predictive models.ConclusionWe demonstrate that, despite the difficulties involved, multiscale models in biology can yield reasonable and useful results. The model predictions are reliable over several timescales and in the presence of strong temperature fluctuations, which are crucial factors for modeling marine organism growth. The model provides important improvements over existing models.

Bayesian inference of gene regulatory networks using gene expression time series data

Differential equations have been established to model the dynamic behavior of gene regulatory networks in the last few years. They provide a detailed insight into regulatory processes at a molecular level. However, in a top down approach aiming at the inference of the underlying regulatory network from gene expression data, the corresponding optimization problem is usually severely underdetermined, since the number of unknowns far exceeds the number of timepoints available. Thus one has to restrict the search space in a biologically meaningful way. We use differential equations to model gene regulatory networks and introduce a Bayesian regularized inference method that is particularly suited to deal with sparse and noisy datasets. Network inference is carried out by embedding our model into a probabilistic framework and maximizing the posterior probability. A specifically designed hierarchical prior distribution over interaction strenghts favours sparse networks, enabling the method to efficiently deal with small datasets. Results on a simulated dataset show that our method correctly learns network structure and model parameters even for short time series. Furthermore, we are able to learn main regulatory interactions in the yeast cell cycle.

Computation of the posterior entropy in a Bayesian framework for parameter estimation in biological networks

In this paper we consider the problem of parameter estimation for intracellular network models with statistical Bayesian approaches. We use systems of nonlinear differential equations in order to describe the dynamics of those networks. In this setting, the posterior distribution has to be investigated via Markov chain Monte Carlo sampling. An estimation of summary statistics of the posterior from these samples requires appropriate density estimation methods. We focus in this study particularly on the influence of kernel density estimators on the expected information content of the posterior. A new method for the calculation of this information content is introduced that uses directly the unnormalized posterior values at the sample points. We exemplarily show its superiority to kernel estimators on a model of secretory pathway control at the trans-Golgi network in mammalian cells.

Trajectory-oriented Bayesian experiment design versus Fisher A-optimal design

Motivation: Experiment design strategies for biomedical models with the purpose of parameter estimation or model discrimination are in the focus of intense research. Experimental limitations such as sparse and noisy data result in unidentifiable parameters and render-related design tasks challenging problems. Often, the temporal resolution of data is a limiting factor and the amount of possible experimental interventions is finite. To address this issue, we propose a Bayesian experiment design algorithm to minimize the prediction uncertainty for a given set of experiments and compare it to traditional A-optimal design. Results: In an in depth numerical study involving an ordinary differential equation model of the trans-Golgi network with 12 partly non-identifiable parameters, we minimized the prediction uncertainty efficiently for predefined scenarios. The introduced method results in twice the prediction precision as the same amount of A-optimal designed experiments while introducing a useful stopping criterion. The simulation intensity of the algorithms major design step is thereby reasonably affordable. Besides smaller variances in the predicted trajectories compared with Fisher design, we could also achieve smaller parameter posterior distribution entropies, rendering this method superior to A-optimal Fisher design also in the parameter space. Availability: Necessary software/toolbox information are available in the supplementary material. The project script including example data can be downloaded from http://www.ist.uni-stuttgart.de/%7eweber/BayesFisher2012. Contact: patrick.weber@ist.uni-stuttgart.de Supplementary Information: Supplementary data are available at Bioinformatics online.

A maximum likelihood estimator for parameter distributions in heterogeneous cell populations

Abstract In many biologically relevant situations, cells of a clonal population show a heterogeneous response upon a common stimulus. The computational analysis of such situations requires the study of cell-cell variability and modeling of heterogeneous cell populations. In this work, we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations. Heterogeneity among individual cells is modeled via differences in parameter values and initial conditions. Both are subject to a distribution function which is part of the cell population model. We present a novel approach to estimate the distribution of parameters and initial conditions from single cell measurements, e.g. flow cytometry and cytometric fluorescence microscopy. Therefore, a maximum likelihood estimator for the distribution is derived. The resulting optimization problem is reformulated via a parameterization of the distribution of parameters and initial conditions to allow the use of convex optimization techniques. To evaluate the proposed method, artificial data from a model of TNF signal transduction are considered. It is shown that the proposed method yields a good estimate of the parameter distributions in case of a limited amount of noise corrupted data.