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The TAM (Model Tile Assembly Model) is a mathematical paradigm for modeling DNA self-assembling according to various given shapes, using DNA-tiles (rectangular shape) with sticky ends on each of the four edges that bound together on various shapes desired by the researcher. Although there are various models in the literature, the focus in this manuscript is on a rule based model, specifically the authors present an overview of the one-dimensional hierarchical self-assembly model of DNA tiles. The authors also present the evolution of number of tiles in partial assemblies, the average assembly size and of the number of partial assemblies of sizes 2 through 10 over the total running time. All simulations were run using the NFSim simulator on a preset period of time. [ABSTRACT FROM AUTHOR]

One approach to modelling complex biological systems is to start from an abstract representation of the biological process and then to incor-porate more details regarding its reactions or reactants through an itera-tive refinement process. The refinement should be done so as to ensure the preservation of the numerical properties of the model, such as its numerical fit and validation. Such approaches are well established in software engineering: starting from a formal specification of the system, one refines it step-by-step towards an implementation that is guaranteed to satisfy a number of logical properties. We introduce here the concepts of (quantitative) data refinement and process refinement of a biomolc-cular. reaction-based model. We choose as a case study a recently pro-posed model for the heat shock response and refine it to include some details of its acetylation-induced control. Although the refinement pro-cess produces a substantial increase in the number of kinetic parameters and variables, the methodology we propose preserves all the numerical properties of the model with a minimal computational effort. [ABSTRACT FROM AUTHOR]

In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid phase of tetramers laterally associating into unit-length filaments and a slow phase of filament elongation. We focus in this paper on a systematic quantitative investigation of two molecular models for filament assembly, recently proposed in (Kirmse et al. J. Biol. Chem. 282, 52 (2007), 18563-18572), through mathematical modeling, model fitting, and model validation. We analyze the quantitative contribution of each filament elongation strategy: with tetramers, with unit-length filaments, with longer filaments, or combinations thereof. In each case, we discuss the numerical fitting of the model with respect to one set of data, and its separate validation with respect to a second, different set of data. We introduce a high-resolution model for vimentin filament self-assembly, able to capture the detailed dynamics of filaments of arbitrary length. This provides much more predictive power for the model, in comparison to previous models where only the mean length of all filaments in the solution could be analyzed. We show how kinetic observations on low-resolution models can be extrapolated to the high-resolution model and used for lowering its complexity. [ABSTRACT FROM PUBLISHER]