Biology as computation is a paradigm that has been explored many times over the years. Amongst these attempts, the theory of P systems has been one of the most successful, and this handbook showcases the many ramifications of this approach, from its application to a wide variety of biological domains to insights it brings to the understanding of computing.

The primary inspiration behind the P systems formalism is the notion of a membrane that can enclose a multiset of elements, which can be modified via rewrite rules that may involve other elements within the same compartment or ones from outside the compartment. The structures can be recursive in the sense that a compartment may contain other compartments enclosed by membranes. Such structuring is ubiquitous in biology. The most obvious analogy of the dynamics is with metabolic reactions, but small variations in the semantics allow the same overall approach to be used to model systems at different levels, such as populations of cells, splicing of DNA, and neural spiking. The final chapter points the way to some more adventurous extensions that are needed to model domains such as economics and quantum computing.

The chapters in this volume have a decidedly theoretical flavor, with an extensive mathematical analysis of the framework. In particular, the initial chapters end up being somewhat dry, and there is very little discussion of what such a formalism brings to the understanding of biology itself or its aptness to solve open questions in biology. Later chapters, which are authored by contributors, redress this somewhat by presenting running examples from biology to explain the concepts, which brings them alive. However, even in these, there is a natural tendency to capture the abstractions of biology, when what interests a lot of biologists is how any methodology can deal with special, interesting cases.

The editors’ goal seems to be primarily in elucidating P systems. This is done very well by characterizing the languages that are defined by each variation and the properties that are satisfied by the rewriting. However, there are very few instances where alternative approaches are brought to the fore and compared to the P systems model, in terms of expressivity or applicability to the domain. The appeal of this book, particularly to those considering applying the P systems approach, would be greater if it also included insights from biologists who could comment on the usefulness of the formalism.

However, for anyone who would like to know more about how a formal, automata-based paradigm can be adapted to capture many variant ideas on computation, this volume provides an in-depth, well-written introduction. It is particularly suitable for those who have a robust understanding of notions of computability.