As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science.

Runtime verification is an area of formal methods that studies the dynamic analysis of execution traces against formal specifications. Typically, the two main activities in runtime verification efforts are the process of creating monitors from specifications, and the algorithms for the evaluation of traces against the generated monitors. Other activities involve the instrumentation of the system to generate the trace and the communication between the system under analysis and the monitor. Most of the applications in runtime verification have been focused on the dynamic analysis of software, even though there are many more potential applications to other computational devices and target systems. In this paper we present a collection of challenges for runtime verification extracted from concrete application domains, focusing on the difficulties that must be overcome to tackle these specific challenges. The computational models that characterize these domains require to devise new techniques beyond the current state of the art in runtime verification.

We address the problem of specifying and detecting emergent behavior in networks of cardiac myocytes, spiral electric waves in particular, a precursor to atrial and ventricular fibrillation. To solve this problem we: (1) apply discrete mode abstraction to the cycle-linear hybrid automata (CLHA) we have recently developed for modeling the behavior of myocyte networks; (2) introduce the new concept of spatial superposition of CLHA modes; (3) develop a new spatial logic, based on spatial superposition, for specifying emergent behavior; (4) devise a new method for learning the formulae of this logic from the spatial patterns under investigation; and (5) apply bounded model checking to detect the onset of spiral waves. We have implemented our methodology as the EMERALD tool suite, a component of our EHA framework for specification, simulation, analysis, and control of excitable hybrid automata. We illustrate the effectiveness of our approach by applying EMERALD to the scalar electrical fields produced by our CELLEXCITE simulation environment for excitable-cell networks.