One obtains in this paper a process algebra RCCS, in the style of CCS, where processes can backtrack. Backtrack, just as plain forward computation, is seen as a synchronization and incurs no additional cost on the communication structure. It is shown that, given a past, a computation step can be taken back if and only if it leads to a causally equivalent past.

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Modelers of molecular signaling networks must cope with the combinatorial explosion of protein states generated by posttranslational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts wherein specific protein-protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the granularity at which rules specify interactions. We present a formal (and automated) method for constructing a coarsegrained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarsegrained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.protein interaction networks ͉ rule-based models ͉ model reduction ͉ distinguishability ͉ information carriers M olecular biology is spectacularly successful in disassembling cellular systems and anchoring cell-biological behaviors of staggering complexity in chemistry. This raises the challenge of reconstituting molecular systems formally, in pursuit of principles that would make their behavior more intelligible and their control more deliberate. This pursuit is as much driven by the practical need to cure disease as it reflects a desire for a theoretical perspective needed to understand the complexity of cellular phenotypes. In achieving such a perspective, we must deal with two broad problems. First, we must be able to represent and analyze molecular interaction systems of combinatorial complexity. Although ubiquitous, such systems are perhaps most notorious in the context of cellular signaling. The posttranslational modification of proteins and their noncovalent association into transient complexes generate an astronomical number of possible molecular species that can relay signals (1). The question then becomes how to reason about system dynamics if we cannot possibly consider a differential equation for each chemical species that can appear in a system. Second, understanding systems requires resisting the temptation of adopting the view of an outside observer. The outside view is indeed appropriate for the chemical analysis of a network, since the experimenter deliberately interacts in specific ways with the network to create measurable distinctions. Yet, the network, as a dynamical system, may not be capable of making these same distinctions. For example, an experi...

We introduce a labelled transition semantics for the reversible π-calculus. It is the first account of a compositional definition of a reversible calculus, that has both concurrency primitives and name mobility.The notion of reversibility is strictly linked to the notion of causality. We discuss the notion of causality induced by our calculus, and we compare it with the existing notions in the literature, in particular for what concerns the syntactic feature of scope extrusion, typical of the π-calculus.

MotivationWe present an overview of the Kappa platform, an integrated suite of analysis and visualization techniques for building and interactively exploring rule-based models. The main components of the platform are the Kappa Simulator, the Kappa Static Analyzer and the Kappa Story Extractor. In addition to these components, we describe the Kappa User Interface, which includes a range of interactive visualization tools for rule-based models needed to make sense of the complexity of biological systems. We argue that, in this approach, modeling is akin to programming and can likewise benefit from an integrated development environment. Our platform is a step in this direction.ResultsWe discuss details about the computation and rendering of static, dynamic, and causal views of a model, which include the contact map (CM), snaphots at different resolutions, the dynamic influence network (DIN) and causal compression. We provide use cases illustrating how these concepts generate insight. Specifically, we show how the CM and snapshots provide information about systems capable of polymerization, such as Wnt signaling. A well-understood model of the KaiABC oscillator, translated into Kappa from the literature, is deployed to demonstrate the DIN and its use in understanding systems dynamics. Finally, we discuss how pathways might be discovered or recovered from a rule-based model by means of causal compression, as exemplified for early events in EGF signaling.Availability and implementationThe Kappa platform is available via the project website at kappalanguage.org. All components of the platform are open source and freely available through the authors’ code repositories.

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