Olaf Wolkenhauer

Experimental Design in Systems Biology, Based on Parameter Sensitivity Analysis Using a Monte Carlo Method: A Case Study for the TNFα-Mediated NF-κ B Signal Transduction Pathway

Mathematical modeling and dynamic simulation of signal transduction pathways is a central theme in systems biology and is increasingly attracting attention in the postgenomic era. The estimation of model parameters from experimental data remains a bottleneck for a major breakthrough in this area. This study’s aim is to introduce a new strategy for experimental design based on parameter sensitivity analysis. The approach identifies key parameters/variables in a signal transduction pathway model and can thereby provide experimental biologists with guidance on which proteins to consider for measurement. The article focuses on applying this approach to the TNFα-mediated NF-κB pathway, which plays an important role in immunity and inflammation and in the control of cell proliferation, differentiation, and apoptosis. A mathematical model of this pathway is proposed, and the sensitivity analysis of model parameters is illustrated for this model by employing the Monte Carlo method over a broad range of parameter values.

Modeling and simulation of intracellular dynamics: choosing an appropriate framework

Systems biology is a reemerging paradigm which, among other things, focuses on mathematical modeling and simulation of biochemical reaction networks in intracellular processes. For most simulation tools and publications, they are usually characterized by either preferring stochastic simulation or rate equation models. The use of stochastic simulation is occasionally accompanied with arguments against rate equations. Motivated by these arguments, we discuss in this paper the relationship between these two forms of representation. Toward this end, we provide a novel compact derivation for the stochastic rate constant that forms the basis of the popular Gillespie algorithm. Comparing the mathematical basis of the two popular conceptual frameworks of generalized mass action models and the chemical master equation, we argue that some of the arguments that have been put forward are ignoring subtle differences and similarities that are important for answering the question in which conceptual framework one should investigate intracellular dynamics.

Fuzzy Clustering of Short Time-Series and Unevenly Distributed Sampling Points

This paper proposes a new algorithm in the fuzzy-c-means family, which is designed to cluster time-series and is particularly suited for short time-series and those with unevenly spaced sampling points. Short time-series, which do not allow a conventional statistical model, and unevenly sampled time-series appear in many practical situations. The algorithm developed here is motivated by common experiments in molecular biology. Conventional clustering algorithms based on the Euclidean distance or the Pearson correlation coefficient are not able to include the temporal information in the distance metric. The temporal order of the data and the varying length of sampling intervals are important and should be considered in clustering time-series. The proposed short time-series (STS) distance is able to measure similarity of shapes which are formed by the relative change of amplitude and the corresponding temporal information. We develop a fuzzy time-series (FSTS) clustering algorithm by incorporating the STS distance into the standard fuzzy clustering scheme. An example is provided to demonstrate the performance of the proposed algorithm.

Minimum Information About a Simulation Experiment (MIASE).

Reproducibility of experiments is a basic requirement for science. Minimum Information (MI) guidelines have proved a helpful means of enabling reuse of existing work in modern biology. The Minimum Information Required in the Annotation of Models (MIRIAM) guidelines promote the exchange and reuse of biochemical computational models. However, information about a model alone is not sufficient to enable its efficient reuse in a computational setting. Advanced numerical algorithms and complex modeling workflows used in modern computational biology make reproduction of simulations difficult. It is therefore essential to define the core information necessary to perform simulations of those models. The Minimum Information About a Simulation Experiment (MIASE, Glossary in Box 1) describes the minimal set of information that must be provided to make the description of a simulation experiment available to others. It includes the list of models to use and their modifications, all the simulation procedures to apply and in which order, the processing of the raw numerical results, and the description of the final output. MIASE allows for the reproduction of any simulation experiment. The provision of this information, along with a set of required models, guarantees that the simulation experiment represents the intention of the original authors. Following MIASE guidelines will thus improve the quality of scientific reporting, and will also allow collaborative, more distributed efforts in computational modeling and simulation of biological processes.

Mathematical Modeling of the Influence of RKIP on the ERK Signaling Pathway

This paper investigates the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signaling pathway through mathematical modeling and simulation. Using nonlinear ordinary differential equations to represent biochemical reactions in the pathway, we suggest a technique for parameter estimation, utilizing time series data of proteins involved in the signaling pathway. The mathematical model allows the simulation the sensitivity of the ERK pathway to variations of initial RKIP and ERK-PP (phosphorylated ERK) concentrations along with time. Throughout the simulation study, we can qualitatively validate the proposed mathematical model compared with experimental results.

The dynamic systems approach to control and regulation of intracellular networks

Systems theory and cell biology have enjoyed a long relationship that has received renewed interest in recent years in the context of systems biology. The term ‘systems’ in systems biology comes from systems theory or dynamic systems theory: systems biology is defined through the application of systems‐ and signal‐oriented approaches for an understanding of inter‐ and intra‐cellular dynamic processes. The aim of the present text is to review the systems and control perspective of dynamic systems. The biologists conceptual framework for representing the variables of a biochemical reaction network, and for describing their relationships, are pathway maps. A principal goal of systems biology is to turn these static maps into dynamic models, which can provide insight into the temporal evolution of biochemical reaction networks. Towards this end, we review the case for differential equation models as a ‘natural’ representation of causal entailment in pathways. Block‐diagrams, commonly used in the engineering sciences, are introduced and compared to pathway maps. The stimulus–response representation of a molecular system is a necessary condition for an understanding of dynamic interactions among the components that make up a pathway. Using simple examples, we show how biochemical reactions are modelled in the dynamic systems framework and visualized using block‐diagrams.

Feedback dynamics and cell function: Why systems biology is called Systems Biology

A new paradigm, like Systems Biology, should challenge the way research has been conducted previously. This Opinion article aims to present Systems Biology, not as the application of engineering principles to biology but as a merger of systems- and control theory with molecular- and cell biology. In our view, the central dogma of Systems Biology is that it is system dynamics that gives rise to the functioning and function of cells. The concepts of feedback regulation and control of pathways and the coordination of cell function are emphasized as an important area of Systems Biology research. The hurdles and risks for this area are discussed from the perspective of dynamic pathway modelling. Most of all, the aim of this article is to promote mathematical modelling and simulation as a part of molecular- and cell biology. Systems Biology is a success if it is widely accepted that there is nothing more practical than a good theory.

Stochastic approaches in systems biology

The discrete and random occurrence of chemical reactions far from thermodynamic equilibrium, and low copy numbers of chemical species, in systems biology necessitate stochastic approaches. This review is an effort to give the reader a flavor of the most important stochastic approaches relevant to systems biology. Notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy‐to‐follow presentation of a stochastic framework for modeling subcellular biochemical systems. In particular, we make an effort to show how the notion of propensity, the chemical master equation (CME), and the stochastic simulation algorithm arise as consequences of the Markov property. Most stochastic modeling reviews focus on stochastic simulation approaches—the exact stochastic simulation algorithm and its various improvements and approximations. We complement this with an outline of an analytical approximation. The most common formulation of stochastic models for biochemical networks is the CME. Although stochastic simulations are a practical way to realize the CME, analytical approximations offer more insight into the influence of randomness on systems behavior. Toward that end, we cover the chemical Langevin equation and the related Fokker–Planck equation and the two‐moment approximation (2MA). Throughout the text, two pedagogical examples are used to key illustrate ideas. With extensive references to the literature, our goal is to clarify key concepts and thereby prepare the reader for more advanced texts. Copyright

Regulation of cell cycle checkpoint kinase WEE1 by miR-195 in malignant melanoma.

WEE1 kinase has been described as a major gate keeper at the G2 cell cycle checkpoint and to be involved in tumour progression in different malignant tumours. Here we analysed the expression levels of WEE1 in a series of melanoma patient samples and melanoma cell lines using immunoblotting, quantitative real-time PCR and immunohistochemistry. WEE1 expression was significantly downregulated in patient samples of metastatic origin as compared with primary melanomas and in melanoma cell lines of high aggressiveness as compared with cell lines of low aggressiveness. Moreover, there was an inverse correlation between the expression of WEE1 and WEE1-targeting microRNA miR-195. Further analyses showed that transfection of melanoma cell lines with miR-195 indeed reduced WEE1 mRNA and protein expression in these cells. Reporter gene analysis confirmed direct targeting of the WEE1 3′ untranslated region (3′UTR) by miR-195. Overexpression of miR-195 in SK-Mel-28 melanoma cells was accompanied by WEE1 reduction and significantly reduced stress-induced G2-M cell cycle arrest, which could be restored by stable overexpression of WEE1. Moreover, miR-195 overexpression and WEE1 knockdown, respectively, increased melanoma cell proliferation. miR-195 overexpression also enhanced migration and invasiveness of melanoma cells. Taken together, the present study shows that WEE1 expression in malignant melanoma is directly regulated by miR-195. miR-195-mediated downregulation of WEE1 in metastatic lesions may help to overcome cell cycle arrest under stress conditions in the local tissue microenvironment to allow unrestricted growth of tumour cells.

Quantitative modelling of amyloidogenic processing and its influence by SORLA in Alzheimer's disease

The extent of proteolytic processing of the amyloid precursor protein (APP) into neurotoxic amyloid‐β (Aβ) peptides is central to the pathology of Alzheimers disease (AD). Accordingly, modifiers that increase Aβ production rates are risk factors in the sporadic form of AD. In a novel systems biology approach, we combined quantitative biochemical studies with mathematical modelling to establish a kinetic model of amyloidogenic processing, and to evaluate the influence by SORLA/SORL1, an inhibitor of APP processing and important genetic risk factor. Contrary to previous hypotheses, our studies demonstrate that secretases represent allosteric enzymes that require cooperativity by APP oligomerization for efficient processing. Cooperativity enables swift adaptive changes in secretase activity with even small alterations in APP concentration. We also show that SORLA prevents APP oligomerization both in cultured cells and in the brain in vivo, eliminating the preferred form of the substrate and causing secretases to switch to a less efficient non‐allosteric mode of action. These data represent the first mathematical description of the contribution of genetic risk factors to AD substantiating the relevance of subtle changes in SORLA levels for amyloidogenic processing as proposed for patients carrying SORL1 risk alleles.