Rule-based Modeling of Transcriptional Attenuation at the Tryptophan Operon

Transcriptional attenuation at E.coli\u27s tryptophan operon is a prime example of RNA-mediated gene regulation. In this paper, we present a discrete stochastic model for this phenomenon based on chemical reactions. Our model is compact and intelligible, due to n-ary reactions (which preclude object-centric approaches) and to rule schemas that define finite sets of chemical reactions. Stochastic simulations with our model confirm results that were previously obtained by master equations or differential equations. In addition, our approach permits to reflect mutation experiments by simple model modifications, and to re-use model components for transcriptional attenuation in other genes and organisms

Rule-based multi-level modeling of cell biological systems

<p>Abstract</p> <p>Background</p> <p>Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.</p> <p>Results</p> <p>Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.</p> <p>Conclusions</p> <p>Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.</p

The Attributed Pi Calculus

International audienceThe attributed pi calculus (pi(L)) forms an extension of the pi calculus with attributed processes and attribute dependent synchronization. To ensure flexibility, the calculus is parametrized with the language L which defines possible values of attributes. pi(L) 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, the movement processes in the phototaxis of Euglena and the cooperative binding in the gene regulation of the lambda Phage, underline the applicability of pi(L) to systems biology

Rule-based modeling of transcriptional attenuation at the tryptophan operon

International audienceTranscriptional attenuation at E.coli's tryptophan operon is a prime example of RNA-mediated gene regulation. In this paper, we present a discrete stochastic model of the fine-grained control of attenuation, based on chemical reactions. Stochastic simulation of our model confirms results that were previously obtained by master or differential equations. Our approach is easier to understand than master equations, although mathematically well founded. It is compact due to rule schemas that define finite sets of chemical reactions. Moreover, our model makes intense use of reaction rules with more than two reactants. As we show, such n-ary rules are essential to concisely capture the control of attenuation. Our model could not adequately be represented in object-centered modeling languages based on the pi-calculus, because these are limited to binary interactions