timate challenge is to understand how the behavior of an organism, or a part thereof, emerges from the individual behaviors of the cells in the collection. We believe this is best done by focusing on the reactivity of cells and the communication between them.

Concurrency and interaction. The essence of a reactive system is that different parts of the system are simultaneously active (“alive”) and interact with each other. In the case of computerized systems, these can be software processes, hardware components, intelligent agents, or the environment, and in the case of biology they can be molecules and molecular processes, cells, tissues, bacteria, or again, the environment.

The operation that combines several simultaneously active parts of a system is called parallel composition because the individual activities happen concurrently, in “parallel,” rather than sequentially (one after the other). However, in computer science there are several different interpretations of what “in parallel” actually means. At one extreme is the clock synchronous interpretation, where execution proceeds in lockstep with a global clock, as a sequence of discrete steps, with each building block (component) of a system contributing one action to each time unit. This happens, for example, in a clocked hardware circuit built from individual logic gates without combinational loops, where each gate performs one operation per clock tick. At the other extreme is the interleaved asynchronous interpretation, where each action represents the contribution of a single component, but different actions, possibly carried out at different time rates, may represent different components. This happens, for example, in distributed software systems where the individual processes proceed at independent speeds. Implicit to the asynchronous interpretation is a scheduler, which chooses for each step the component that will contribute to that step. The scheduler is usually assumed to be “fair,” the simplest interpretation of which is that it cannot neglect to choose any component forever.

Both kinds of concurrency occur in biology, for example, in molecular processes “running” in parallel, and techniques for capturing both have found their way into biological models. Still, sticking religiously to these two

the process of
modeling a piece
of biology is very
different from
that of modeling
a human-made
system. the
motivation is
different, the goals
are very different,
the people involved
are also different,
and the scales are
different.

interpretations may be inadequate for representing the parallelism that arises in a large collection of individual cells. Cells, for example, often proceed “roughly” in lockstep, but not completely so: some reactions may be a bit faster here but a bit slower there, but biological reactions do not proceed at completely independent rates either. An example of how to adapt useful computer science techniques to biology can be found in the recent compromise between these two called bounded asynchrony. 33 It allows the components of a system (for example, cells) to proceed independently while bounding the differences in their rates. Bounded asynchrony has been used to accurately model some of the experimental observations made about certain cell-cell interactions: it captures the variability observed in cells that, although equally potent, assume distinct fates, and thus can be used to provide mechanistic explanations for some phenomena that are observed during cell-fate determination.

Bounded asynchrony is but one example of how the modeling of biological systems may give rise to new variations of reactive concepts. Once it is agreed upon what the most suitable interpretation of “parallel progress” means for a collection of cells, the communication between these cells needs to be modeled. Again, there are several standard alternatives, designed for modeling hardware and software, which may not be readily adequate for our purposes. Traditionally, the interaction between concurrent processes can happen through sharing state or through sending messages. This distinction has led, for example, to thread-based programming languages on one hand, and actor-based languages on the other. The transfer of molecules between cells seems more akin to message passing, but within that paradigm itself there exists a wide spectrum of design choices, ranging from rendezvous, which stops the execution of two processes until simultaneously the sending process is ready to send and the receiving process is ready to receive a message, to unbounded message buffers, which retain sent messages until they are received. Explicitly spatial models11, 69 are natural candidates for capturing morphogen gradients.