Mathias John

A Spatial Extension to the π Calculus

Spatial dynamics receive increasing attention in Systems Biology and require suitable modeling and simulation approaches. So far, modeling formalisms have focused on population-based approaches or place and move individuals relative to each other in space. SpacePi extends the @p calculus by time and space. @p processes are embedded into a vector space and move individually. Only processes that are sufficiently close can communicate. The operational semantics of SpacePi defines the interplay between movement, communication, and time-triggered events. A model describing the phototaxis of the Euglena micro-organism is presented as a practical example. The formalisms use and generality is discussed with respect to the modeling of molecular biological processes like diffusion, active transportation in cell signaling, and spatial structures.

Combining micro and macro-modeling in DEVS for computational biology

In computational biology there is an increasing need to combine micro and macro views of the system of interest. Therefore, explicit means to describe micro and macro level and the downward and upward causation that link both are required. Multi-Level-DEVS (or m^-DEVS) supports an explicit description of macro and micro level, information at macro level can be accessed from micro level and vice versa, micro models can be synchronously activated by the macro model and also the micro models can trigger the dynamics at macro level. To link both levels, different methods are combined, to those belong, value coupling, synchronous activations, variable ports, and invariants. The execution semantic of the formalism is given by an abstract simulator and its use is illustrated based on an small extract of the Wnt pathway.

The attributed pi-calculus with priorities

We present the attributed π−calculus for modeling concurrent systems with interaction constraints depending on the values of attributes of processes. The λ-calculus serves as a constraint language underlying the π−calculus. Interaction constraints subsume priorities, by which to express global aspects of populations. We present a non-deterministic and a stochastic semantics for the attributed π−calculus. We show how to encode the π−calculus with priorities and polyadic synchronization π−@ and thus dynamic compartments, as well as the stochastic π−calculus with concurrent objects spico. n nWe illustrate the usefulness of the attributed π−calculus for modeling biological systems at two particular examples: Euglenas spatial movement in phototaxis, and cooperative protein binding in gene regulation of bacteriophage lambda. Furthermore, population-based model is supported beside individual-based modeling. A stochastic simulation algorithm for the attributed π−calculus is derived from its stochastic semantics. We have implemented a simulator and present experimental results, that confirm the practical relevance of our approach.

The Attributed Pi Calculus

The attributed pi calculus

Biochemical reaction rules with constraints

({phi({mathcal L})})

Visual analysis of bipartite biological networks

forms an extension of the pi calculus with attributed processes and attribute dependent synchronization. To ensure flexibility, the calculus is parametrized with the language

Initial receptor-ligand interactions modulate gene expression and phagosomal properties during both early and late stages of phagocytosis.

{mathcal L}

Dynamic Compartments in the Imperative Π-Calculus

which defines possible values of attributes.

Modeling leucine's metabolic pathway and knockout prediction improving the production of surfactin, a biosurfactant from Bacillus subtilis

{phi({mathcal L})}

Integrating diverse reaction types into stochastic models: a signaling pathway case study in the imperative π-calculus

can express polyadic synchronization as in pi@ and thus diverse compartment organizations. A non-deterministic and a stochastic semantics, where rates may depend on attribute values, is introduced. The stochastic semantics is based on continuous time Markov chains. A simulation algorithm is developed which is firmly rooted in this stochastic semantics. Two examples underline the applicability of