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Up to now, it is not possible to obtain analytical solutions for complex molecular association processes (e.g. Molecule recognition in Signaling or catalysis). Instead Brownian Dynamics (BD) simulations are commonly used to estimate the rate of diffusional association, e.g. to be later used in mesoscopic simulations. Meanwhile a portfolio of diffus...
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... follows the philosophy of JAMES II [17,16], whose plug-in structure is the foundation for FADA. Hence, for each of the three steps different components and methods can be created, allowing a flexible combination and application of them (see Figure 2). However, since the area of application for FADA is the DA process, some of these components have to follow a specific structure. ...
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... Takahashi et al. (2005) stated that effects like molecular crowding, where molecular density is very high, are known to have crucial impact on cellular motion and thus on the final outcome of cell biological systems. To this end, Haack et al. (2010) propose to computationally determine rate constants by exhaustive simulation of models that consider deterministic, continuous motion of molecules and their collision. An alternative would be to define a modeling language with a stochastic semantics that supports continuous molecular motion, including molecule size and collision. ...
For cell-biological processes, it is the complex interaction of their biochemical components, affected by both stochastic and spatial considerations, that create the overall picture. Formal modeling provides a method to overcome the limits of experimental observation in the wet-lab by moving to the abstract world of the computer. The limits of the abstract world again depend on the expressiveness of the modeling language used to formally describe the system under study. In this thesis, reaction constraints for the pi-calculus are proposed as a language for the stochastic and spatial modeling of cell-biological processes. The goal is to develop a language with sufficient expressive power to model dynamic cell structures, like fusing compartments. To this end, reaction constraints are augmented with two language constructs: priority and a global imperative store, yielding two different modeling languages, including non-deterministic and stochastic semantics. By several modeling examples, e.g. of Euglena's phototaxis, and extensive expressiveness studies, e.g. an encoding of the spatial modeling language BioAmbients, including a prove of its correctness, the usefulness of reaction constraints, priority, and a global imperative store for the modeling of cell-biological processes is shown. Thereby, besides dynamic cell structures, different modeling styles, e.g. individual-based vs. population-based modeling, and different abstraction levels, as e.g. provided by reaction kinetics following the law of Mass action or the Michaelis-Menten theory, are considered.
Most modeling and simulation approaches applied in cell biology assume a homogeneous distribution of particles in space, although experimental studies reveal the importance of space to understand the dynamics of cells. There are already numerous spatial approaches focusing on the simulation of cells. Recently, they have been complemented by a set of spatial modeling languages whose operational semantics are tied partly to existing simulation algorithms. These modeling languages allow an explicit description of spatial phenomena, and facilitate analysis of the temporal spatial dynamics of cells by a clear separation between model, semantics, and simulator. With the supported level of abstraction, each of those offers a different perception of the spatial phenomena under study. In this paper, we give an overview of existing modeling formalisms and discuss some ways of combining approaches to tackle the problem the computational costs induced by spatial dynamics.