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Modeling and Parameter Estimation for Heterogeneous Cell Populations

Modeling and Parameter Estimation for Heterogeneous Cell Populations
Author: Jan Hasenauer
Publisher: Logos Verlag Berlin GmbH
Total Pages: 143
Release: 2013
Genre: Mathematics
ISBN: 3832533982

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Most of the modeling performed in biology aims at achieving a quantitative description and understanding of the intracellular signaling pathways within a "typical cell". However, in many biologically important situations even genetically identical cell populations show a heterogeneous response. This means that individual members of the cell population behave differently. Such situations require the study of cell-to-cell variability and the development of models for heterogeneous cell populations. The main contribution of this thesis is the development of unifying modeling frameworks for signal transduction and proliferation processes in heterogeneous cell populations. These modeling frameworks allow for the detailed description of individual cells as well as differences between them. In contrast to many existing modeling approaches, the proposed frameworks allow for a direct comparison of model predictions with available data. Beyond this, the proposed population models can be simulated efficiently and, by exploiting the model structures, we are able to develop model-tailored Bayesian parameter estimation methods. These methods enable the calculation of the optimal parameter estimates, as well as the evaluation of the parameter and prediction uncertainties. The proposed tools allow for novel insights in population dynamics, in particular the model-based characterization of population heterogeneity and cellular subgroups. This is illustrated for two different application examples: pro- and anti-apoptotic signaling, which is interesting in the context of cancer therapy, and immune cell proliferation.


A mathematical modeling framework to simulate and analyze cell type transitions

A mathematical modeling framework to simulate and analyze cell type transitions
Author: Daniella Schittler
Publisher: Logos Verlag Berlin GmbH
Total Pages: 192
Release: 2015-03-20
Genre: Mathematics
ISBN: 3832539352

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The quantitative understanding of changes in cell types, referred to as cell type transitions, is fundamental to advance fields such as stem cell research, immunology, and cancer therapies. This thesis provides a mathematical modeling framework to simulate and analyze cell type transitions. The novel methodological approaches and models presented here address diverse levels which are essential in this context: Gene regulatory network models represent the cell type-determining gene expression dynamics. Here, a novel construction method for gene regulatory network models is introduced, which allows to transfer results from generic low-dimensional to realistic high-dimensional gene regulatory network models. For populations of cells, a generalized model class is proposed that accounts for multiple cell types, division numbers, and the full label distribution. Analysis and solution methods are presented for this new model class, which cover common cell population experiments and allow to exploit the full information from data. The modeling and analysis methods presented here connect formerly isolated approaches, and thereby contribute to a holistic framework for the quantitative understanding of cell type transitions.


Network Bioscience, 2nd Edition

Network Bioscience, 2nd Edition
Author: Marco Pellegrini
Publisher: Frontiers Media SA
Total Pages: 270
Release: 2020-03-27
Genre:
ISBN: 288963650X

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Network science has accelerated a deep and successful trend in research that influences a range of disciplines like mathematics, graph theory, physics, statistics, data science and computer science (just to name a few) and adapts the relevant techniques and insights to address relevant but disparate social, biological, technological questions. We are now in an era of 'big biological data' supported by cost-effective high-throughput genomic, transcriptomic, proteomic, metabolomic data collection techniques that allow one to take snapshots of the cells' molecular profiles in a systematic fashion. Moreover recently, also phenotypic data, data on diseases, symptoms, patients, etc. are being collected at nation-wide level thus giving us another source of highly related (causal) 'big data'. This wealth of data is usually modeled as networks (aka binary relations, graphs or webs) of interactions, (including protein-protein, metabolic, signaling and transcription-regulatory interactions). The network model is a key view point leading to the uncovering of mesoscale phenomena, thus providing an essential bridge between the observable phenotypes and 'omics' underlying mechanisms. Moreover, network analysis is a powerful 'hypothesis generation' tool guiding the scientific cycle of 'data gathering', 'data interpretation, 'hypothesis generation' and 'hypothesis testing'. A major challenge in contemporary research is the synthesis of deep insights coming from network science with the wealth of data (often noisy, contradictory, incomplete and difficult to replicate) so to answer meaningful biological questions, in a quantifiable way using static and dynamic properties of biological networks.


Analysis of Single-Cell Data

Analysis of Single-Cell Data
Author: Carolin Loos
Publisher: Springer
Total Pages: 108
Release: 2016-03-17
Genre: Mathematics
ISBN: 3658132345

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Carolin Loos introduces two novel approaches for the analysis of single-cell data. Both approaches can be used to study cellular heterogeneity and therefore advance a holistic understanding of biological processes. The first method, ODE constrained mixture modeling, enables the identification of subpopulation structures and sources of variability in single-cell snapshot data. The second method estimates parameters of single-cell time-lapse data using approximate Bayesian computation and is able to exploit the temporal cross-correlation of the data as well as lineage information.


Mathematical Modeling of the Immune System in Homeostasis, Infection and Disease

Mathematical Modeling of the Immune System in Homeostasis, Infection and Disease
Author: Gennady Bocharov
Publisher: Frontiers Media SA
Total Pages: 278
Release: 2020-02-24
Genre:
ISBN: 2889634612

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The immune system provides the host organism with defense mechanisms against invading pathogens and tumor development and it plays an active role in tissue and organ regeneration. Deviations from the normal physiological functioning of the immune system can lead to the development of diseases with various pathologies including autoimmune diseases and cancer. Modern research in immunology is characterized by an unprecedented level of detail that has progressed towards viewing the immune system as numerous components that function together as a whole network. Currently, we are facing significant difficulties in analyzing the data being generated from high-throughput technologies for understanding immune system dynamics and functions, a problem known as the ‘curse of dimensionality’. As the mainstream research in mathematical immunology is based on low-resolution models, a fundamental question is how complex the mathematical models should be? To respond to this challenging issue, we advocate a hypothesis-driven approach to formulate and apply available mathematical modelling technologies for understanding the complexity of the immune system. Moreover, pure empirical analyses of immune system behavior and the system’s response to external perturbations can only produce a static description of the individual components of the immune system and the interactions between them. Shifting our view of the immune system from a static schematic perception to a dynamic multi-level system is a daunting task. It requires the development of appropriate mathematical methodologies for the holistic and quantitative analysis of multi-level molecular and cellular networks. Their coordinated behavior is dynamically controlled via distributed feedback and feedforward mechanisms which altogether orchestrate immune system functions. The molecular regulatory loops inherent to the immune system that mediate cellular behaviors, e.g. exhaustion, suppression, activation and tuning, can be analyzed using mathematical categories such as multi-stability, switches, ultra-sensitivity, distributed system, graph dynamics, or hierarchical control. GB is supported by the Russian Science Foundation (grant 18-11-00171). AM is also supported by grants from the Spanish Ministry of Economy, Industry and Competitiveness and FEDER grant no. SAF2016-75505-R, the “María de Maeztu” Programme for Units of Excellence in R&D (MDM-2014-0370) and the Russian Science Foundation (grant 18-11-00171).


Computational Methods in Systems Biology

Computational Methods in Systems Biology
Author: Ezio Bartocci
Publisher: Springer
Total Pages: 361
Release: 2016-09-03
Genre: Computers
ISBN: 3319451774

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This book constitutes the refereed proceedings of the 14th International Conference on Computational Methods in Systems Biology, CMSB 2016, held in Cambridge, UK, in September 2016. The 20 full papers, 3 tool papers and 9 posters presented were carefully reviewed and selected from 37 regular paper submissions. The topics include formalisms for modeling biological processes; models and their biological applications; frameworks for model verification, validation, analysis, and simulation of biological systems; high-performance computational systems biology and parallel implementations; model inference from experimental data; model integration from biological databases; multi-scale modeling and analysis methods; and computational approaches for synthetic biology.


Managing Complexity, Reducing Perplexity

Managing Complexity, Reducing Perplexity
Author: Marcello Delitala
Publisher: Springer
Total Pages: 140
Release: 2014-06-04
Genre: Mathematics
ISBN: 3319037595

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”Managing Complexity, Reducing Perplexity” is devoted to an overview of the status of the art in the study of complex systems, with particular focus on the analysis of systems pertaining to living matter. Both senior scientists and young researchers from diverse and prestigious institutions with a deliberately interdisciplinary cut were invited, in order to compare approaches and problems from different disciplines. The common aim of the contributions was to analyze the complexity of living systems by means of new mathematical paradigms that are more adherent to reality and which are able to generate both exploratory and predictive models that are capable of achieving a deeper insight into life science phenomena.


Population Parameters

Population Parameters
Author: Hamish McCallum
Publisher: John Wiley & Sons
Total Pages: 360
Release: 2008-04-15
Genre: Science
ISBN: 0470757426

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Ecologists and environmental managers rely on mathematical models, both to understand ecological systems and to predict future system behavior. In turn, models rely on appropriate estimates of their parameters. This book brings together a diverse and scattered literature, to provide clear guidance on how to estimate parameters for models of animal populations. It is not a recipe book of statistical procedures. Instead, it concentrates on how to select the best approach to parameter estimation for a particular problem, and how to ensure that the quality estimated is the appropriate one for the specific purpose of the modelling exercise. Commencing with a toolbox of useful generic approaches to parameter estimation, the book deals with methods for estimating parameters for single populations. These parameters include population size, birth and death rates, and the population growth rate. For such parameters, rigorous statistical theory has been developed, and software is readily available. The problem is to select the optimal sampling design and method of analysis. The second part of the book deals with parameters that describe spatial dynamics, and ecological interactions such as competition, predation and parasitism. Here the principle problems are designing appropriate experiments and ensuring that the quantities measured by the experiments are relevant to the ecological models in which they will be used. This book will be essential reading for ecological researchers, postgraduate students and environmental managers who need to address an ecological problem through a population model. It is accessible to anyone with an understanding of basic statistical methods and population ecology. Unique in concentrating on parameter estimation within modelling. Fills a glaring gap in the literature. Not too technical, so suitable for the statistically inept. Methods explained in algebra, but also in worked examples using commonly available computer packages (SAS, GLIM, and some more specialised packages where relvant). Some spreadsheet based examples also included.


Systems Immunology

Systems Immunology
Author: Jayajit Das
Publisher: CRC Press
Total Pages: 355
Release: 2018-09-03
Genre: Science
ISBN: 1498717411

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"Taken together, the body of information contained in this book provides readers with a bird’s-eye view of different aspects of exciting work at the convergence of disciplines that will ultimately lead to a future where we understand how immunity is regulated, and how we can harness this knowledge toward practical ends that reduce human suffering. I commend the editors for putting this volume together." –Arup K. Chakraborty, Robert T. Haslam Professor of Chemical Engineering, and Professor of Physics, Chemistry, and Biological Engineering, Massachusetts Institute of Technology, Cambridge, USA New experimental techniques in immunology have produced large and complex data sets that require quantitative modeling for analysis. This book provides a complete overview of computational immunology, from basic concepts to mathematical modeling at the single molecule, cellular, organism, and population levels. It showcases modern mechanistic models and their use in making predictions, designing experiments, and elucidating underlying biochemical processes. It begins with an introduction to data analysis, approximations, and assumptions used in model building. Core chapters address models and methods for studying immune responses, with fundamental concepts clearly defined. Readers from immunology, quantitative biology, and applied physics will benefit from the following: Fundamental principles of computational immunology and modern quantitative methods for studying immune response at the single molecule, cellular, organism, and population levels. An overview of basic concepts in modeling and data analysis. Coverage of topics where mechanistic modeling has contributed substantially to current understanding. Discussion of genetic diversity of the immune system, cell signaling in the immune system, immune response at the cell population scale, and ecology of host-pathogen interactions.


Mathematical Biology II

Mathematical Biology II
Author: James D. Murray
Publisher: Springer Science & Business Media
Total Pages: 814
Release: 2006-05-31
Genre: Mathematics
ISBN: 0387224386

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This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS