[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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Modern Applied Statistics With S

CA : A Cancer Journal for Clinicians

It has become increasingly difficult to find an area of cell biology in which lipids do not have important, if not key, roles as signalling and regulatory molecules. The rapidly expanding field of bioactive lipids is exemplified by many sphingolipids, such as ceramide, sphingosine, sphingosine-1-phosphate (S1P), ceramide-1-phosphate and lyso-sphingomyelin, which have roles in the regulation of cell growth, death, senescence, adhesion, migration, inflammation, angiogenesis and intracellular trafficking. Deciphering the mechanisms of these varied cell functions necessitates an understanding of the complex pathways of sphingolipid metabolism and the mechanisms that regulate lipid generation and lipid action.

Principles of bioactive lipid signalling: lessons from sphingolipids

Preface Introduction 1 Graphical representation of biochemical systems 2 Models of biochemical systems 3 From maps to equations 4 Computer simulation 5 Parameter estimation 6 Analytical steady-state evaluation 7 Sensitivity analysis 8 Case study 1 - Anaerobic fermentation pathway in Saccharomyces cerevisiae 9 Case study 2 - diagnosis and refinement of a model of the tricarboxylic acid cycle in Dictyostelium discoideum 10 Case study 3 - A sequence of models describing purine metabolism 11 Case study 4 - Algebraic analysis of the initial steps of the Glycolytic-Glycogenolytic pathway in perfused rat liver 12 Epilogue-Canonical modeling beyond biochemistry Appendix Hints and solutions References Author index Subject index

Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists

The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

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Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems

Rationale: Modern molecular biology is generating data of unprecedented quantity and quality. Particularly exciting for biochemical pathway modeling and proteomics are comprehensive, time-dense profiles of metabolites or proteins that are measurable, for instance, with mass spectrometry, nuclear magnetic resonance or protein kinase phosphorylation. These profiles contain a wealth of information about the structure and dynamics of the pathway or network from which the data were obtained. The retrieval of this information requires a combination of computational methods and mathematical models, which are typically represented as systems of ordinary differential equations.

Results: We show that, for the purpose of structure identification, the substitution of differentials with estimated slopes in non-linear network models reduces the coupled system of differential equations to several sets of decoupled algebraic equations, which can be processed efficiently in parallel or sequentially. The estimation of slopes for each time series of the metabolic or proteomic profile is accomplished with a 'universal function' that is computed directly from the data by cross-validated training of an artificial neural network (ANN).

Conclusions: Without preprocessing, the inverse problem of determining structure from metabolic or proteomic profile data is challenging and computationally expensive. The combination of system decoupling and data fitting with universal functions simplifies this inverse problem very significantly. Examples show successful estimations and current limitations of the method.

Availability: A preliminary Web-based application for ANN smoothing is accessible at http://bioinformatics.musc.edu/webmetabol/. S-systems can be interactively analyzed with the user-friendly freeware PLAS© (http://correio.cc.fc.ul.pt/~aenf/plas.html) or with the MATLAB module BSTLab (http://bioinformatics.musc.edu/bstlab/), which is currently being beta-tested.

Decoupling dynamical systems for pathway identification from metabolic profiles

An enormous variety of nonlinear differential equations and functions have been recast exactly in the canonical form called an S-system. This is a system of nonlinear ordinary differential equations, each with the same structure: the change in a variable is equal to a difference of products of power-law functions. We review the development of S-systems, prove that the minimum for the range of equations that can be recast as S-systems consists of all equations composed of elementary functions and nested elementary functions of elementary functions, give a detailed example of the recasting process, and discuss the theoretical and practical implications. Among the latter is the ability to solve numerically nonlinear ordinary differential equations in their S-system form significantly faster than in their original form through utilization of a specially designed algorithm.

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Recasting nonlinear differential equations as S-systems: a canonical nonlinear form

Facility in the targeted manipulation of the genetic and metabolic composition of organisms, combined with unprecedented computational power, is forging a niche for a new subspecialty of biotechnology called metabolic engineering. First published in 2002, this book introduces researchers and advanced students in biology and engineering to methods of optimizing biochemical systems of biotechnological relevance. It examines the development of strategies for manipulating metabolic pathways, demonstrates the need for effective systems models, and discusses their design and analysis, while placing special emphasis on optimization. The authors propose power-law models and methods of biochemical systems theory toward these ends. All concepts are derived from first principles, and the text is richly illustrated with numerous graphs and examples throughout. Special features include: nontechnical and technical introductions to models of biochemical systems; a review of basic methods of model design and analysis; concepts of optimization; and detailed case studies.

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Eberhard O. Voit

Papers

Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists

Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems

Decoupling dynamical systems for pathway identification from metabolic profiles

Recasting nonlinear differential equations as S-systems: a canonical nonlinear form

Pathway Analysis and Optimization in Metabolic Engineering