The articles which appear in this book reflect the topics discussed in the course ``Dynamical modeling in biotechnology'' held at ISI (Turin, Italy) in June 1996. It is immediately apparent that the course aimed less at to be exhaustive in this topic; rather, it focused on introducing interested scientists with varied backgrounds to active research in a wide spectrum of different areas broadly related to what has come to be called ``Dynamical modeling in biology''. This is an attempt to formalize various branches of biology by a variety of models derived from dynamical system theory. While much of biomathematics (such as models of physiological processes and ecological systems) doesn't deal with dynamical modeling it is now emerging that in biotechnology the most important information is the dynamical property of the system. Another aspect faced by the course (and the book) is that the communication between theoreticians and experimentalists is severely hampered by the use of a different reporting language, i.e. the use of different symbols and names for the variables and parameters of our mathematical models.
A general discussion on the role of modelization in biology can be found in the contribution Mathematical Biotechnology ? by M. Buiatti and S. Ruffo, next to this one, and in the contribution The immune system and why modeling it make sense by F. Celada, in the last section.
The pattern emerging from the book (and the course) is that very similar and simple models can be applied successfully to interacting objects (populations) of different scale and dynamics: antibodies, ribosomes, viruses, cells, organisms and species.
Topics were chosen not only for their intrinsic interest, but also to illustrate some of the connections among them. There is a certain amount of unavoidable repetition so that each article can be read as a self-contained whole. The book is divided into four sections - mathematical methods, population dynamics, DNA analysis and modeling, immune system modeling - and each section is divided into lectures and contributions, reflecting the organization of the course itself.
In the first paper, Franco Bagnoli provides a comprehensive overview of cellular automata and offers his personal perspective on why this approach is a flexible and powerful modelization tool for biological systems.
The paper by Pikovsky describes the fundamentals of dynamical system theory. This paper offers a wide range of examples, from low dimensional to complex systems, introducing the concepts of map, trajectories in a phase space, stability, bifurcations, fluctuations, attractors and chaos. Since numerical methods are also discussed, it gives a different, robust perspective, based on the ``continuum hypothesis'' of biological system modeling with respect the ``discrete'' approach of using cellular automata.
Jean-Pierre Nadal will present thereafter an introduction and selected bibliography to a increasingly used tool: neural networks and supervised learning.
In the contribution section, Franco Bagnoli, Nino Boccara and Paolo Palmerini describe research employing various of the topics described in the first paper; the paper presents the analysis of the behaviour of a probabilistic cellular automata having two absorbing states and addresses questions concerning phase transitions and the analogy with percolation models.
Robin Engelhardt's paper deals with pattern formation that is a central issue in biology because of the close dependence between morphology (structure) and function. The author discusses the ``chemical'' mechanisms of pattern formation and the biological constraints related to the presence of morphogenetic gradients during the development and remodelling processes and the control of gene expression as a source of positional information.
In the section about population dynamics, Dietrich Stauffer shows a review of several birth-death models. He aims to model ageing and he is able to show that simple Montecarlo models can be very successful in describing complex behaviours.
In the paper by Nino Boccara, the reader finds the application of some concepts introduced in the first section. Boccara discusses the modeling of ecological and epidemiological systems starting from very simple to complex systems and presents a clear analysis of the ``classic'' Lotka-Volterra equations on prey-predator model and of the refinements proposed.
Giovanna Guasti is exploring the possibility of modeling translation process and ribosome dynamics in bacteria. This gives the opportunity of understanding the relationships between a macroscopic quantity - bacterial population growth - in term of a microscopic parameter - ribosomes and tRNA abundances and composition.
In the contribution section, a mathematical treatment of problems that are very important in bioreactor technology is presented. Peter Goetz discusses the kinetics of microbial growth in various conditions, linking the biomass production with the bacterial metabolism and growth. Particularly the model takes into account the delay time between the change of conditions in the bioreactor and the intracellular concentration of metabolites. Markus Rarbach and Peter Goetz consider the problem of mixed bacterial cultures that is nowadays of great importance in bioreactor technology in order to set up complex biotechnology processes. The authors study the stability of a system of two microbial species with commensalistic and mutualistic interactions and compare it with mathematical models of pure culture.
The section concerning DNA covers several aspects of the current studies, including statistics. Michael Peyrard analyzes the dynamical properties of DNA opening that is the most important characteristic of the molecule because of DNA replication and transcription processes. He stresses the importance of nonlinearity in the description of many systems and how the idea of nonlinear energy localization can be applied to analyze DNA thermal denaturation and transcription. As in Engelhardt's paper, Peyrard's paper addresses the question of the physical basis underlying a biological process and the development of the biological control.
Several aspects of DNA sequence statistics and mutation dynamics are investigated by Pietro Lió. Information theory can elucidate some aspects of DNA-protein interaction and can discriminate between coding and non coding DNA sequences. Markov models play an important role in tracing back the evolutive history of different species.
The section includes two contributions that give some fundamentals on the statistics of DNA molecular markers and their use in finding genes involved in complex genetic diseases, such as diabetes type I, and the information on bioinformatics tools available from Internet.
The last section is dedicated to the modelization of the immunitary system. The immunitary system is a cellular and molecular system that attempts to recognize and mount a multi-pronged attack against what doesn't belong to the body. The two basic properties of self-not self recognition and the cell proliferation signalling and regulation need a very complex and distributed system because of the very large antigen variability, the human genetic variability and the various cell types show different dynamics in the recognition, signalling and attack processes. This system is also a product of evolution and thus, the evolutive history should be kept in mind when we try to understand how it works.
Franco Celada presents a comprehensive description of the immune system and offers his perspective on its modelization. Michele Bezzi examines some key models of the immune system and analyzes in details the Celada-Seiden model for humoral response. Phil Seiden describes a two dimensional cellular automaton model of the dynamics of populations of migrating, contact-inhibited cells.
Ulrich Behn and co-workers presents a model of the behaviour of lymphocyte T helper of class 1 and 2; these cells show reciprocal inhibitory action and differ in their pattern of cytokine production. The understanding of the regulation of the concentrations of these two classes of lymphocyte T is thought to be of key importance in the future treating of viral, and bacterial infections and auto-immune diseases.
Models like the Celada-Seiden are computationally very expensive even using powerful workstation. Castiglione and co-workers describe a parallel platform optimization of this model. In the following paper, Castiglione gives details of the program and language of the parallel implementation of the Celada-seiden model.
In summary, this collection of papers treating biological systems modelization from a dynamical point of view, and with a particular attention to biotechnology related problems, provides insight into a new fascinating and fast growing area of biology. For mathematicians and theoretical biologists this area is a new challenging frontier in modelling.
Mathematics has long held a central position in the physical sciences where systems in closely controlled environments change in repeatable ways. For biological systems, however, observations show much greater variability and thus breakthroughs and important results can only depend on a close collaborative efforts between theoretical scientists and ``wet-lab'' scientists.