Mathematical Modeling and Immunology An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest pos sible cooperation among scientists working in different fields: biology, im munology, medicine, physics and, we believe, mathematics. Certainly, bi ologists and immunologists will make the greatest contribution to the re search. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such prob lems. We cannot expect mathematicians alone to solve fundamental prob lems in immunology and (in particular) cancer research, but valuable sup port, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field.

The rapid development of new methods for immunological data collection – from multicolor flow cytometry, through single-cell imaging, to deep sequencing – presents us now, for the first time, with the ability to analyze and compare large amounts of immunological data in health, aging and disease. The exponential growth of these datasets, however, challenges the theoretical immunology community to develop methods for data organization and analysis. Furthermore, the need to test hypotheses regarding immune function, and generate predictions regarding the outcomes of medical interventions, necessitates the development of mathematical and computational models covering processes on multiple scales, from the genetic and molecular to the cellular and system scales. The last few decades have seen the development of methods for presentation and analysis of clonal repertoires (those of T and B lymphocytes) and phenotypic (surface-marker based) repertoires of all lymphocyte types, and for modeling the intricate network of molecular and cellular interactions within the immune systems. This e-Book, which has first appeared as a ‘Frontiers in Immunology’ research topic, provides a comprehensive, online, open access snapshot of the current state of the art on immune system modeling and analysis.

Beginning his work on the monograph to be published in English, this author tried to present more or less general notions of the possibilities of mathematics in the new and rapidly developing science of infectious immunology, describing the processes of an organism's defence against antigen invasions. The results presented in this monograph are based on the construc tion and application of closed models of immune response to infections which makes it possible to approach problems of optimizing the treat ment of chronic and hypertoxic forms of diseases. The author, being a mathematician, had creative long-Iasting con tacts with immunologists, geneticist, biologists, and clinicians. As far back as 1976 it resulted in the organization of a special seminar in the Computing Center of Siberian Branch of the USSR Academy of Sci ences on mathematical models in immunology. The seminar attracted the attention of a wide circle of leading specialists in various fields of science. All these made it possible to approach, from a more or less united stand point, the construction of models of immune response, the mathematical description of the models, and interpretation of results.

Many potential applications of synthetic and systems biology are relevant to the challenges associated with the detection, surveillance, and responses to emerging and re-emerging infectious diseases. On March 14 and 15, 2011, the Institute of Medicine's (IOM's) Forum on Microbial Threats convened a public workshop in Washington, DC, to explore the current state of the science of synthetic biology, including its dependency on systems biology; discussed the different approaches that scientists are taking to engineer, or reengineer, biological systems; and discussed how the tools and approaches of synthetic and systems biology were being applied to mitigate the risks associated with emerging infectious diseases. The Science and Applications of Synthetic and Systems Biology is organized into sections as a topic-by-topic distillation of the presentations and discussions that took place at the workshop. Its purpose is to present information from relevant experience, to delineate a range of pivotal issues and their respective challenges, and to offer differing perspectives on the topic as discussed and described by the workshop participants. This report also includes a collection of individually authored papers and commentary.

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).

The Janeway's Immunobiology CD-ROM, Immunobiology Interactive, is included with each book, and can be purchased separately. It contains animations and videos with voiceover narration, as well as the figures from the text for presentation purposes.

This is a pioneering work on the emerging field of artificial immune systems-highly distributed systems based on the principles of the natural system. Like artificial neural networks, artificial immune systems can learn new information and recall previously learned information. This book provides an overview of artificial immune systems, explaining its applications in areas such as immunological memory, anomaly detection algorithms, and modeling the effects of prior infection on vaccine efficacy.

Computational Immunology: Models and Tools encompasses the methodological framework and application of cutting-edge tools and techniques to study immunological processes at a systems level, along with the concept of multi-scale modeling. The book's emphasis is on selected cases studies and application of the most updated technologies in computational modeling, discussing topics such as computational modeling and its usage in immunological research, bioinformatics infrastructure, ODE based modeling, agent based modeling, and high performance computing, data analytics, and multiscale modeling. There are also modeling exercises using recent tools and models which lead the readers to a thorough comprehension and applicability. The book is a valuable resource for immunologists, computational biologists, bioinformaticians, biotechnologists, and computer scientists, as well as all those who wish to broaden their knowledge in systems modeling. - Offers case studies with different levels of complexity - Provides a detailed view on cutting-edge tools for modeling that are useful to experimentalists with limited computational skills - Explores the usage of simulation for hypothesis generation, helping the reader to understand the most valuable points on experimental setting

Clearly, nature has been very effective in creating organisms that are capable of protecting themselves against a wide variety of pathogens such as bacteria, fungi, and parasites. The powerful information-processing capabilities of the immune system, such as feature extraction, pattern recognition, learning, memory, and its distributive nature prov