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Biological networks, such as vascular networks and neural circuits, are ubiquitous in nature. An understanding of these networks can help us understand their response to damages, which could lead to novel treatments. They can also inspire the design of man-made networks, as evolution has millions of years to figure out optimal designs. The advancement in imaging techniques has created high-dimensional data streams, which is difficult to analyze by conventional approaches. On the other hand, quantitative tools are naturally suited for processing large data sets, and they become more and more important in improving our knowledge on biological networks. Among existing tools ranging from network science to stochastic analysis, here we focus on optimization and dynamical system approach. Optimization links biological functions to corresponding network structures, which can give predictions to be compared with the data. The dynamical system approach is suited for analyzing time series data and complex interaction between the vertices, which is often exploited in biological systems for intricate signalings and regulations. This thesis is devoted to the study of biological networks with optimization and dynamical system, focused on two specific biological systems: microvascular network and bipolar disorder. For microvascular networks, we first study a specific example of embryonic zebrafish trunk network, and reveal the significance of flow uniformity in this network. Then we derive analytical structures of networks with optimal transport efficiency, which is widely regarded as the organizing principle of vascular networks, especially for large vessels such as aorta. To compare the morphologies of transport efficient and uniform flow networks, we develop algorithm that is capable of finding optimal networks with general target functions and constraints, and show that the principle of uniform flow creates more realistic microvascular networks under many different topologies. Finally, we propose an vessel adaptation mechanism based on stress sensing dynamic to explain how microvascular networks stay resilient to noise, and how they grow into uniform flow networks. For bipolar disorder, we mathematically analyze a dynamical model based on the interaction of mood and expectation. We show that bipolar disorder can be viewed as a bifurcation in the direction from normal to cyclic personality. We also consider the case where positive and negative events are sensed differently, and describe the bifurcation in this case. Finally we apply commonly used medicine on the model, and recover clinically observed phenomena on bipolar disorder patients.
Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The textavoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. An Introduction to Systems Biology: Design Principles of Biological Circuits builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.
This book presents the most recent mathematical approaches to the growing research area of networks, oscillations, and collective motions in the context of biological systems. Bringing together the results of multiple studies of different biological systems, this book sheds light on the relations among these research themes. Included in this book are the following topics: feedback systems with time delay and threshold of sensing (dead zone), robustness of biological networks from the point of view of dynamical systems, the hardware-oriented neuron modeling approach, a universal mechanism governing the entrainment limit under weak forcing, the robustness mechanism of open complex systems, situation-dependent switching of the cues primarily relied on by foraging ants, and group chase and escape. Research on different biological systems is presented together, not separated by specializations or by model systems. Therefore, the book provides diverse perspectives at the forefront of current mathematical research on biological systems, especially focused on networks, oscillations, and collective motions. This work is aimed at advanced undergraduate, graduate, and postdoctoral students, as well as scientists and engineers. It will also be of great use for professionals in industries and service sectors owing to the applicability of topics such as networks and synchronizations.
It is the task of computational biology to help elucidate the unique characteristics of biological systems. This process has barely begun, and many researchers are testing computational tools that have been used successfully in other fields. Mathematical and statistical network modeling is an important step toward uncovering the organizational principles and dynamic behavior of biological networks. Undoubtedly, new mathematical tools will be needed, however, to meet this challenge. The workhorse of this effort at present comprises the standard tools from applied mathematics, which have proven to be successful for many problems. But new areas of mathematics not traditionally considered applicable are contributing other powerful tools. This volume is intended to introduce this topic to a broad mathematical audience. The aim is to explain some of the biology and the computational and mathematical challenges we are facing. The different chapters provide examples of how these challenges are met, with particular emphasis on nontraditional mathematical approaches. The volume features a broad spectrum of networks across scales, ranging from biochemical networks within a single cell to epidemiological networks encompassing whole cities. Chapter topics include phylogenetics and gene finding using tools from statistics and algebraic geometry, biochemical network inference using tools from computational algebra, control-theoretic approaches to drug delivery using differential equations, and interaction-based modeling and discrete mathematics applied to problems in population dynamics and epidemiology.
A First Course in Systems Biology is an introduction for advanced undergraduate and graduate students to the growing field of systems biology. Its main focus is the development of computational models and their applications to diverse biological systems. The book begins with the fundamentals of modeling, then reviews features of the molecular inventories that bring biological systems to life and discusses case studies that represent some of the frontiers in systems biology and synthetic biology. In this way, it provides the reader with a comprehensive background and access to methods for executing standard systems biology tasks, understanding the modern literature, and launching into specialized courses or projects that address biological questions using theoretical and computational means. New topics in this edition include: default modules for model design, limit cycles and chaos, parameter estimation in Excel, model representations of gene regulation through transcription factors, derivation of the Michaelis-Menten rate law from the original conceptual model, different types of inhibition, hysteresis, a model of differentiation, system adaptation to persistent signals, nonlinear nullclines, PBPK models, and elementary modes. The format is a combination of instructional text and references to primary literature, complemented by sets of small-scale exercises that enable hands-on experience, and large-scale, often open-ended questions for further reflection.
This volume presents a timely and comprehensive overview of biological networks at all organization levels in the spirit of the complex systems approach. It discusses the transversal issues and fundamental principles as well as the overall structure, dynamics, and modeling of a wide array of biological networks at the molecular, cellular, and population levels. Anchored in both empirical data and a strong theoretical background, the book therefore lends valuable credence to the complex systems approach. Sample Chapter(s). Chapter 1: Scale-Free Networks in Biology (821 KB). Contents: Scale-Free Networks in Biology (E Almaas et al.); Modularity in Biological Networks (R V Sol(r) et al.); Inference of Biological Regulatory Networks: Machine Learning Approaches (F d''Alch(r)-Buc); Transcriptional Networks (F K(r)p s); Protein Interaction Networks (K Tan & T Ideker); Metabolic Networks (D A Fell); Heterogeneous Molecular Networks (V Schnchter); Evolution of Regulatory Networks (A Veron et al.); Complexity in Neuronal Networks (Y Fr(r)gnac et al.); Networks of the Immune System (R E Callard & J Stark); A History of the Study of Ecological Networks (L-F Bersier); Dynamic Network Models of Ecological Diversity, Complexity, and Nonlinear Persistence (R J Williams & N D Martinez); Infection Transmission through Networks (J S Koopman). Readership: Graduate students and industry experts in systems biology and complex systems; biologists; chemists; physicists; mathematicians; computer scientists
Networked systems are all around us. The accumulated evidence of systems as complex as a cell cannot be fully understood by studying only their isolated constituents, giving rise to a new area of interest in research OCo the study of complex networks . In a broad sense, biological networks have been one of the most studied networks, and the field has benefited from many important contributions. By understanding and modeling the structure of a biological network, a better perception of its dynamical and functional behavior is to be expected. This unique book compiles the most relevant results and novel insights provided by network theory in the biological sciences, ranging from the structure and dynamics of the brain to cellular and protein networks and to population-level biology. Sample Chapter(s). Chapter 1: Introduction (61 KB). Contents: Networks at the Cellular Level: The Structural Network Properties of Biological Systems (M Brilli & P Li); Dynamics of Multicellular Synthetic Gene Networks (E Ullner et al.); Boolean Networks in Inference and Dynamic Modeling of Biological Systems at the Molecular and Physiological Level (J Thakar & R Albert); Complexity of Boolean Dynamics in Simple Models of Signaling Networks and in Real Genetic Networks (A D az-Guilera & R ulvarez-Buylla); Geometry and Topology of Folding Landscapes (L Bongini & L Casetti); Elastic Network Models for Biomolecular Dynamics: Theory and Application to Membrane Proteins and Viruses (T R Lezon et al.); Metabolic Networks (M C Palumbo et al.); Brain Networks: The Human Brain Network (O Sporns); Brain Network Analysis from High-Resolution EEG Signals (F De Vico Fallani & F Babiloni); An Optimization Approach to the Structure of the Neuronal layout of C elegans (A Arenas et al.); Cultured Neuronal Networks Express Complex Patterns of Activity and Morphological Memory (N Raichman et al.); Synchrony and Precise Timing in Complex Neural Networks (R-M Memmesheimer & M Timme); Networks at the Individual and Population Levels: Ideas for Moving Beyond Structure to Dynamics of Ecological Networks (D B Stouffer et al.); Evolutionary Models for Simple Biosystems (F Bagnoli); Evolution of Cooperation in Adaptive Social Networks (S Van Segbroeck et al.); From Animal Collectives and Complex Networks to Decentralized Motion Control Strategies (A Buscarino et al.); Interplay of Network State and Topology in Epidemic Dynamics (T Gross). Readership: Advanced undergraduates, graduate students and researchers interested in the study of complex networks in a wide range of biological processes and systems."
Recent studies have developed preliminary wiring diagrams for a number of important biological networks. However, the design principles governing the construction and operation of these networks remain mostly unknown. To discover design principles in these networks, we investigated and developed a set of computational tools described below. First, we looked into the application of optimization techniques to explore network topology, parameterization, or both, and to evaluate relative fitness of networks operational strategies. In particular, we studied the ability of an enzymatic cycle to produce dynamic properties such as responsiveness and transient noise filtering. We discovered that non-linearity of the enzymatic cycle allows more effective filtering of transient noise. Furthermore, we found that networks with multiple activation steps, despite being less responsive, are better in filtering transient noise. Second, we explored a method to construct compact models of signal transduction networks based on a protein-domain network representation. This method generates models whose number of species, in the worst case, scales quadratically to the number of protein-domain sites and modification states, a tremendous saving over the combinatorial scaling in the more standard mass-action model was estimated to consist of more that 107 species and was too large to simulate; however, a simplified model consists of only 132 state variables and produced intuitive behavior. The resulting models were utilized to study the roles of a scaffold protein and of a shared binding domain to pathway functions.
The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.