Download or read book Mathematical Models and Algorithms for Genetic Regulatory Networks written by Shuqin Zhang and published by Open Dissertation Press. This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mathematical Models and Algorithms for Genetic Regulatory Networks" by Shuqin, Zhang, 張淑芹, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled MATHEMATICAL MODELS AND ALGORITHMS FOR GENETIC REGULATORY NETWORKS submitted by ZHANG Shu-Qin for the degree of Doctor of Philosophy at The University of Hong Kong in August 2007 Genetic regulatory network is an important research topic in bioinformat- ics, which considers the on-o(R) switches and rheostats of a cell operating at the gene level. Mathematical modeling and computation are indispensable in such studies, especially for the complex patterns of behavior which needs high indus- trialpayo(R)sandisdiculttogettheinformationthroughexperimentalmethods. Booleannetworks(BNs)andprobabilisticBooleannetworks(PBNs)areproposed to model the interactions among the genes and have received much attention in the biophysics community. The study in this thesis is based on the BN and PBN models. With the BN model, several algorithms using gene ordering and feedback vertex sets are devel- opedtoidentifysingletonattractorsandsmallattractorswhichcorrespondtocell types and cell states. The average case time complexities of some proposed al- gorithms are analyzed. Extensive computational experiments are also performed which are in good agreement with the theoretical results. A simple and complete proofforshowingthatndinganattractorwiththeshortestperiodisNP-hardis given. Finding global states incoming to a specied global state is useful for the preprocessingofndingasequenceofcontrolactionsinBooleannetworksandfor identifying the basin of attraction for a given attractor. This problem is shown to be NP-hard in general. New algorithms based on the algorithms for ndingsmall attractors are developed, which are much faster than the naive exhaustive search-based algorithm. Based on the PBN model, an ecient method for the construction of the sparse transition probability matrix is proposed. Power method is then applied to compute the steady-state probability distribution. With this method, the sensitivity of the steady-state distribution to the inuences of input genes, gene connections and Boolean functions is studied. Simulation results are given to illustrate the method and to demonstrate the steady-state analysis. An approxi- mation method is proposed to further reduce the time complexity for computing the steady-state probability distribution by neglecting some BNs with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is givenand theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. Numerical experiments are given to demonstrate the eciency of the proposed method. The ultimate goal of studying the long-term behavior of the genetic regula- tory network is to study the control strategies such that the system can go into the desirable states with larger probabilities. A control model is also proposed for gene intervention here. The problem is formulated as a minimization prob- lem with integer variables to minimize the amount of control cost for a genetic network over a given period of time such that the probabilities of obtaining the target states are as large as possible. Experimental results show that the pro- posed formulation is ecient and e(R)ective for solving the control problem of gene intervention. DOI: 10.5353/th_b3884282 Subjects: Genetics - Mathematical models Algorithms Bioinformatics

Download or read book Simple Mathematical Models of Gene Regulatory Dynamics written by Michael C. Mackey and published by Springer. This book was released on 2016-11-09 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduates students and young researchers with a solid mathematical background (calculus, ordinary differential equations, and probability theory at a minimum), as well as with basic notions of biochemistry, cell biology, and molecular biology. They are meant to serve as a readable and brief entry point into a field that is currently highly active, and will allow the reader to grasp the current state of research and so prepare them for defining and tackling new research problems.

Download or read book Dynamics of Mathematical Models in Biology written by Alessandra Rogato and published by Springer. This book was released on 2016-11-03 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters in this section examine several mathematical models and algorithms available for integration, analysis, and characterization. Once life scientists began to produce experimental data at an unprecedented pace, it become clear that mathematical models were necessary to interpret data, to structure information with the aim to unveil biological mechanisms, discover results, and make predictions. The second annual “Bringing Maths to Life” workshop held in Naples, Italy October 2015, enabled a bi-directional flow of ideas from and international group of mathematicians and biologists. The venue allowed mathematicians to introduce novel algorithms, methods, and software that may be useful to model aspects of life science, and life scientists posed new challenges for mathematicians.

Download or read book Computational Modeling of Gene Regulatory Networks written by Hamid Bolouri and published by Imperial College Press. This book was released on 2008 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as an introduction to the myriad computational approaches to gene regulatory modeling and analysis, and is written specifically with experimental biologists in mind. Mathematical jargon is avoided and explanations are given in intuitive terms. In cases where equations are unavoidable, they are derived from first principles or, at the very least, an intuitive description is provided. Extensive examples and a large number of model descriptions are provided for use in both classroom exercises as well as self-guided exploration and learning. As such, the book is ideal for self-learning and also as the basis of a semester-long course for undergraduate and graduate students in molecular biology, bioengineering, genome sciences, or systems biology.

Download or read book Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays written by Mehmet Eren Ahsen and published by Birkhäuser. This book was released on 2015-02-25 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.

Download or read book Mathematical Modelling and Parameter Inference of Genetic Regulatory Networks written by Qianqian Wu and published by . This book was released on 2015 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modelling opens the door to a rich pathway to study the dynamic properties of biological systems. Among the many biological systems that would benefit from mathematical modelling, improving our understanding of gene regulatory networks has received much attention from the fields of computational biology and bioinformatics. To understand system dynamics of biological networks, mathematical models need to be constructed and studied. In spite of the efforts that have been given to explore regulatory mechanisms among gene net- works, accurate description of chemical events with multi-step chemical reactions still remains a challenge in biochemistry and biophysics. This dissertation is aimed at developing several novel methods for describing dynamics of multi-step chemical reaction systems. The main idea is introduced by a new concept for the location of molecules in the multi-step reactions, which is used as an additional indicator of system dynamics. Additionally, novel idea in the stochastic simulation algorithm is used to calculate time delay exactly, which shows that the value of time delay depends on the system states. All of these innovations alter the focus of originally complex multi-step structures towards defining novel simplified structures, which simplifies the modelling process significantly. Research results yield substantially more accurate results than published methods.Apart from the well-established knowledge for modelling techniques, there are still significant challenges in understanding the dynamics of systems biology. One of the major challenges in systems biology is how to infer unknown parameters in mathematical models based on experimental datasets, in particular, when data are sparse and networks are stochastic. To tackle this challenge, parameters estimation techniques using Approximate Bayesian Computation (ABC) for chemical reaction system and inference method for dynamic network have been investigated. This dissertation discusses developed ABC methods that have been tested on two stochastic systems. Results on artificial data show certain promising approximations for the unknown parameters in the systems. While unknown parameters are difficult and sometimes even impossible to measure with biological experiments, instead we can study the influence of parameter variation on system properties. Robustness and sensitivity are two major measurements to describe the dynamic properties of a system against the variation of model parameters. For stochastic models of discrete chemical reaction systems, although these two properties have been studied separately, no work has been done so far to investigate these two properties together. In this dissertation, An integrated framework has been proposed to study these two properties for the Nanog gene network simultaneously. It successfully identifies key coefficients that have more impacts on the network dynamics than the others. The proposed inference method to infer dynamic protein-gene interactions is applied to a case study of the human P53 protein, which is a well-known biological network for cancer study. Investigating the dynamics for such regulatory networks through high throughput experimental data has become more popular. To tackle the hindrances with large number of unknown parameters when building detailed mathematical models, a new integrated method is proposed by combining a top-down approach using probability graphical models and a bottom-up approach using differential equation models. Model simulation error, Akaike's information criterion, parameter identifiability and robustness properties are used as criteria to select the optimal network. Results based on random permutations of input gene network structures provide accurate prediction and robustness property. In addition, a comparison study suggests that the proposed approach has better simulation accuracy and robustness property than the earlier one. In particular, the computational cost is significantly reduced. Overall, the new integrated method is a promising approach for investigating the dynamics of genetic regulations.

Download or read book Probabilistic Boolean Networks written by Ilya Shmulevich and published by SIAM. This book was released on 2010-01-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive treatment of probabilistic Boolean networks, unifying different strands of current research and addressing emerging issues.

Download or read book Differential Equation Models and Numerical Methods for Reverse Engineering Genetic Regulatory Networks written by Miun Yoon and published by . This book was released on 2010 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation develops and analyzes dierential equation-based mathematical models and efficient numerical methods and algorithms for genetic regulatory network identication. The primary objectives of the dissertation are to design, analyze, and test a general variational framework and numerical methods for seeking its approximate solutions for reverse engineering genetic regulatory networks from microarray datasets using the approach based on differential equation modeling. In the proposed variational framework, no structure assumption on the genetic network is presumed, instead, the network is solely determined by the microarray profile of the network components and is identified through a well chosen variational principle which minimizes a biological energy functional. The variational principle serves not only as a selection criterion to pick up the right biological solution of the underlying differential equation model but also provides an effective mathematical characterization of the small-world property of genetic regulatory networks which has been observed in lab experiments. Five specific models within the variational framework and efficient numerical methods and algorithms for computing their solutions are proposed and analyzed in the dissertation. Model validations using both synthetic network datasets and real world subnetwork datasets of Saccharomyces cerevisiae (yeast) and E. coli are done on all five proposed variational models and a performance comparison vs some existing genetic regulatory network identification methods is also provided. As microarray data is typically noisy, in order to take into account the noise effect in the mathematical models, we propose a new approach based on stochastic differential equation modeling and generalize the deterministic variational framework to a stochastic variational framework which relies on stochastic optimization. Numerical algorithms are also proposed for computing solutions of the stochastic variational models. To address the important issue of post-processing computed networks to reflect the small-world property of underlying genetic regulatory networks, a novel threshholding technique based on the Random Matrix Theory is proposed and tested on various synthetic network datasets.

Download or read book Identification Analysis and Control of Discrete and Continuous Models of Gene Regulation Networks written by Christian Breindl and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systems biological approach towards cellular networks promises a better understanding of how these systems work. The development of mathematical models is however inherently complicated, as the involved molecules and their interactions are mostly difficult to measure. Focusing on gene regulation networks, this work therefore intends to provide systems theoretic tools that support the process of model development and analysis in presence of such incomplete knowledge. The contributions are threefold. First, the problem of identifying interconnections between genes from noisy data is addressed. Existing solutions formulated in a discrete framework are reviewed and simplified significantly with the help of tools from convex optimization theory. Second, a novel method for model verification and discrimination is introduced. It is based on concepts from robust control theory and allows to quantify the capability of a model to reproduce experimentally observed stationary behaviors. As the proposed formalism only requires a vague knowledge about the interactions between the molecules, the method is intended to test and compare early modeling hypotheses. Third, the problem of controlling gene regulation networks in presence of qualitative information only is studied. Methods from discrete event systems theory are adapted to obtain stimulation strategies that will steer the network toward a desired attractor. The benefits of all contributions are illustrated with examples in the individual chapters.

Download or read book Mathematical Models for Biological Networks and Machine Learning with Applications written by Yushan Qiu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Mathematical Models for Biological Networks and Machine Learning With Applications" by Yushan, Qiu, 邱育珊, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Systems biology studies complex systems which involve a large number of interacting entities such that their dynamics follow systematical regulations for transition. To develop computational models becomes an urgent need for studying and manipulating biologically relevant systems. The properties and behaviors of complex biological systems can be analyzed and studied by using computational biological network models. In this thesis, construction and computation methods are proposed for studying biological networks. Modeling Genetic Regulatory Networks (GRNs) is an important topic in genomic research. A number of promising formalisms have been developed in capturing the behavior of gene regulations in biological systems. Boolean Network (BN) has received sustainable attentions. Furthermore, it is possible to control one or more genes in a network so as to avoid the network entering into undesired states. Many works have been done on the control policy for a single randomly generated BN, little light has been shed on the analysis of attractor control problem for multiple BNs. An efficient algorithm was developed to study the attractor control problem for multiple BNs. However, one should note that a BN is a deterministic model, a stochastic model is more preferable in practice. Probabilistic Boolean Network (PBN), was proposed to better describe the behavior of genetic process. A PBN can be considered as a Markov chain process and the construction of a PBN is an inverse problem which is computationally challenging. Given a positive stationary distribution, the problem of constructing a sparse PBN was discussed. For the related inverse problems, an efficient algorithm was developed based on entropy approach to estimate the model parameters. The metabolite biomarker discovery problem is a hot topic in bioinformatics. Biomarker identification plays a vital role in the study of biochemical reactions and signalling networks. The lack of essential metabolites may result in triggering human diseases. An effective computational approach is proposed to identify metabolic biomarkers by integrating available biomedical data and disease-specific gene expression data. Pancreatic cancer prediction problem is another hot topic. Pancreatic cancer is known to be difficult to diagnose in the early stage, and early research mainly focused on predicting the survival rate of pancreatic cancer patients. The correct prediction of various disease states can greatly benefit patients and also assist in design of effective and personalized therapeutics. The issue of how to integrating the available laboratory data with classification techniques is an important and challenging issue. An effective approach was suggested to construct a feature space which serves as a significant predictor for classification. Furthermore, a novel method for identifying the outliers was proposed for improving the classification performance. Using our preoperative clinical laboratory data and histologically confirmed pancreatic cancer samples, computational experiments are conducted successfully with the use of Support Vector Machine (SVM) to predict the status of patients. Subjects: Biomathematics Biology - Mathematical models

Download or read book Modeling the Dynamics of Gene Regulatory Networks written by Aparna Das and published by . This book was released on 2012 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to describe the dynamic behavior of gene regulatory networks different formalisms have been introduced. In this thesis, we describe first the discrete approach of René Thomas and piecewise linear differential equations approach. Then we proposed a correspondence result between the two approaches and based on it we proposed an automatic computational technique to understand the global behavior of such complex systems using MAPLE programming language. The proposed code provides a way to compute the trajectories of the discrete version of a gene regulatory network model given an initial condition, in the same way as usual numerical algorithms give the "true" solution of a differential model from an initial condition. Knowing a discrete trajectory is less precise than knowing a true trajectory but correspondence theorems shows the link between the two approaches. Hence, it is a mathematical tool for analysing gene regulatory networks models. Finally, we illustrate both discrete and piecewise linear approaches, theircorrespondence and the use of our Maple code on a specific example: a mathematical model of the circadian clock. Our first two presented 8 and 4 variables models are the simplification of a model proposed by Leloup and Goldbeter. We deliberately choose to push the simplicity of the model as far as possible, focusing only on a few biological behaviors of interest. The hope is to get nevertheless the essential abstract causalities that govern these behaviors.

Download or read book Gene Regulatory Networks written by Guido Sanguinetti and published by Humana. This book was released on 2018-12-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores recent techniques for the computational inference of gene regulatory networks (GRNs). The chapters in this book cover topics such as methods to infer GRNs from time-varying data; the extraction of causal information from biological data; GRN inference from multiple heterogeneous data sets; non-parametric and hybrid statistical methods; the joint inference of differential networks; and mechanistic models of gene regulation dynamics. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, descriptions of recently developed methods for GRN inference, applications of these methods on real and/ or simulated biological data, and step-by-step tutorials on the usage of associated software tools. Cutting-edge and thorough, Gene Regulatory Networks: Methods and Protocols is an essential tool for evaluating the current research needed to further address the common challenges faced by specialists in this field.

Download or read book Mathematical Models in Biology written by Valeria Zazzu and published by Springer. This book was released on 2015-11-26 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy. The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content useful as it addresses existing challenges in identifying the gaps between mathematical modeling and biological research. The shared solutions will aid and promote further collaboration between life sciences and mathematics.

Download or read book Evolutionary Computation in Gene Regulatory Network Research written by Hitoshi Iba and published by John Wiley & Sons. This book was released on 2016-01-20 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing a handbook for gene regulatory network research using evolutionary computation, with applications for computer scientists, computational and system biologists This book is a step-by-step guideline for research in gene regulatory networks (GRN) using evolutionary computation (EC). The book is organized into four parts that deliver materials in a way equally attractive for a reader with training in computation or biology. Each of these sections, authored by well-known researchers and experienced practitioners, provides the relevant materials for the interested readers. The first part of this book contains an introductory background to the field. The second part presents the EC approaches for analysis and reconstruction of GRN from gene expression data. The third part of this book covers the contemporary advancements in the automatic construction of gene regulatory and reaction networks and gives direction and guidelines for future research. Finally, the last part of this book focuses on applications of GRNs with EC in other fields, such as design, engineering and robotics. • Provides a reference for current and future research in gene regulatory networks (GRN) using evolutionary computation (EC) • Covers sub-domains of GRN research using EC, such as expression profile analysis, reverse engineering, GRN evolution, applications • Contains useful contents for courses in gene regulatory networks, systems biology, computational biology, and synthetic biology • Delivers state-of-the-art research in genetic algorithms, genetic programming, and swarm intelligence Evolutionary Computation in Gene Regulatory Network Research is a reference for researchers and professionals in computer science, systems biology, and bioinformatics, as well as upper undergraduate, graduate, and postgraduate students. Hitoshi Iba is a Professor in the Department of Information and Communication Engineering, Graduate School of Information Science and Technology, at the University of Tokyo, Toyko, Japan. He is an Associate Editor of the IEEE Transactions on Evolutionary Computation and the journal of Genetic Programming and Evolvable Machines. Nasimul Noman is a lecturer in the School of Electrical Engineering and Computer Science at the University of Newcastle, NSW, Australia. From 2002 to 2012 he was a faculty member at the University of Dhaka, Bangladesh. Noman is an Editor of the BioMed Research International journal. His research interests include computational biology, synthetic biology, and bioinformatics.

Download or read book Computational and Mathematical Modeling of Gene Regulatory Networks written by Taylor White and published by . This book was released on 2011 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Models of Gene Regulatory Networks and Other Biological Systems written by Andrew Keith Miller and published by . This book was released on 2011 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modelling of biological processes is important in systems biology, because it facilitates understanding of the nature and behaviour of biological systems. This thesis is in two parts, the first on constructing and validating Gene Regulatory Network (GRN) models, and the second on mathematical model representation. A method, BaSeTraM, for identifying transcription factor (TF) binding sites from position weight matrices was developed. The sites identi_ed were used to build a GRN by identifying genes near each site. BaSeTraM performed comparably to a widely used method when validated against experimental data, with the advantage that the selectivity-sensitivity trade-o_ is controlled by adjusting the posterior probability. A classifier for detecting genes with missing regulators in a GRN model was developed, using regression to convert a qualitative model into a quantitative model, with an iterative method to predict expression levels in gene knock-out strains. Errors for each gene were used to predict which genes were missing regulators. Validation of the classifier to detect regulators deleted from a yeast GRN model showed that it out-performed random guessing. Finally, a method was developed for validating entire models by converting to a quantitative model, and predicting gene expression by regulator levels. Validating models built using BaSeTraM against human microarray data showed that degraded models had lower errors than the original in > 50% of all predictions. The bimodal distribution of per-gene proportion of higher errors suggests that the original model described some genes more accurately. This method provides a general framework within which to validate GRN models against genome-wide gene expression data sets. An API for working with CellML models was developed, allowing applications to process mathematical models more easily. A model representation language, ModML, for representing models as a transformation from a domain specific language (DSL) into a data structure describing differential-algebraic equations was developed, along with tools for performing numerical simulations from models. Two DSLs based on ModML were developed; ModML Units, for equations with physical units, and ModML Reactions, for reaction systems. The utility of the DSLs has been demonstrated by expressing existing models in them. The development of ModML and DSLs built on top of it mean that models describing components of a system in different ways can be more easily composed to facilitate understanding of the system.

Download or read book Models and Algorithms for Biomolecules and Molecular Networks written by Bhaskar DasGupta and published by John Wiley & Sons. This book was released on 2016-01-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: By providing expositions to modeling principles, theories, computational solutions, and open problems, this reference presents a full scope on relevant biological phenomena, modeling frameworks, technical challenges, and algorithms. Up-to-date developments of structures of biomolecules, systems biology, advanced models, and algorithms Sampling techniques for estimating evolutionary rates and generating molecular structures Accurate computation of probability landscape of stochastic networks, solving discrete chemical master equations End-of-chapter exercises