Communication in the context of distributed computation on distributed data structures is one of the brightest frontiers in information processing. Locally, it involves the transmission of a signal from one object to another. The signal may change the state of the receiver and it may represent the state of the sender. Possibly the most primitive communication is seen in exothermic chemical reactions: one molecule changes state and the energy released by this change is absorbed by a neighbor, in which it initiates a similar change in state. Globally, the result is exothermic (for example, combustion). Such a primitive presence suggests that meaningful communication could be universal. And it is, apppearing most mysterious in multicellular life where the resulting time-and-space morphogenesis (for example, five fingers on each hand, the complex architecture of plants, the reliable beating of a heart) is undeniable evidence of communication within a network. This beautiful puzzle was first framed and solved by Alan Turing [1].

Recently, the study of these systems has become a serious research front, involving several researchers [2,3,4], including Atakan. This text frames the issues in terms of hardware: the absorption of cells and proteins by other cells, gap junctions (this important piece of biology has too long been ignored by computation theorists and mathematicians), diffusion, nanorobots, and other topics. This is the approach one would expect in an engineering text, and it is not absent from the work of Abelson et al. [2]. But all of those mentioned above [2,3,4] extend their efforts to include programmed networks, abstract models of computation such as irregular and asynchronous nets of automata, and bits of classical computation theory. And they are always chasing the holy grail of understanding morphogenesis. Nevertheless, there is a need for multiple points of view in any developing frontier and Atakan’s approach is welcome.

Chapter 1, “Molecular Communication Among Nanomachines,” is an introduction to the text. Chapter 2, “Passive Molecular Communication Through Absorbers,” is a largely mathematical review of the physics of diffusion, absorption, decay, and gradient sensing (I enjoyed this!). Reaction-diffusion mechanisms are discussed, but without any mention of Turing. The second chapter ends with “Communication Theories and Techniques for Passive Molecular Communication,” but Shannon is conspicuously absent from this section.

Chapter 3, “Passive Molecular Communication Through Ligand-Receptor Binding,” expands the diffusion modeling of chapter 2. There is some interesting classical engineering mathematics here, especially dealing with the accuracy of gradient sensing. The subsection on gene regulatory networks seems out of place. Finally, in chapter 4, “Active Molecular Communications,” some interesting biology is discussed: molecular motors, adenosine triphosphate (ATP), microtubules (which provide tightly focused long-distance delivery of messages and more), and communication between bacteria (there is also a return to gap junctions). Mathematics similar to that described above is found all the way to the last page.

The classical mathematics presented in this text is the mathematics of physics and engineering, not the mathematics of information theory or of computation theory. There are problems. For example, in 2.6.5, the author writes, “The [transmitter] emits a single molecule ... to transmit bit 1 ... [and then] for the transmission of bit 0, the [transmitter] emits no molecule and it is assumed to be successfully delivered if the [receiver] does not receive any molecule.” Here he seems not to be aware of the computational significance of partial functions (whose absence was the fatal flaw in Gödel’s primitive recursion functions as a model for computation). Less dramatically, he seems to expect synchronization to open the future for absolutely distributed information processing even though it does not exist in nature! But this is, or was, a common view back when asynchronous information processing seemed to be self-contradictory, something we all saw yet couldn’t believe was possible.

This presentation could have benefited from an understanding of computation theory, but Atakan’s book will have a place in my library.