The mitogen-activated protein kinase (MAPK) cascade is an important signaling cascade in eukaryotes. We use the approach of generalized modeling to analyze the dynamics of the MAPK cascade and identify key mechanisms of instability. Furthermore, we report sustained multi-mode oscillations and potentially chaotic behavior caused by a sequestration-based feedback mechanism. Finally, we investigate the interplay between sequestration and external feedback loops. Our analysis thereby confirms, extends and generalizes previous results obtained by conventional modeling and points out the diversity of dynamics that sequestration can bring about.

Bone remodeling is regulated by pathways controlling the interplay of osteoblasts and osteoclasts. In this work, we apply the method of generalized modeling to systematically analyse a large class of models of bone remodeling. Our analysis shows that osteoblast precursors can play an important role in the regulation of bone remodeling. Further, we find that the parameter regime most likely realized in nature lies close to bifurcation lines, marking qualitative changes in the dynamics. Although proximity to a bifurcation facilitates adaptive responses to changing external conditions, it entails the danger of losing dynamical stability. Some evidence implicates such dynamical transitions as a potential mechanism leading to forms of Paget's disease.

Abstract. We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two-and three-dimensional random-field Ising systems with a Gaussian distribution of the random fields. Our algorithm is based on an approach of Frontera and Vives which, in some cases, does not yield the true first excited states. Using the corrected algorithm, we find that the order-disorder phase transition for three dimensions is visible via crossings of the excitations-energy curves for different system sizes, while in two-dimensions these crossings converge to zero disorder. Furthermore, we obtain in three dimensions a fractal dimension of the excitations cluster of ds = 2.42(2). We also provide analytical droplet arguments to understand the behavior of the excitation energies for small and large disorder as well as close to the critical point.

Abstract. The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to analyze low-energy excitations for the three-dimensional RFIM with Gaussian distributed disorder that appear in the form of clusters of connected spins. We analyze several properties of these clusters. Our results support the validity of the droplet-model description for the RFIM.

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