The reaction-diffusion model is well known as a describing equation for chemical reactions on uniform- or non-uniform- spatial fields. This kind of model has been studied in a point of view of representation for spatio-temporal patterns. On the other hand, living systems use wet systems for signal processing in order to maintain their lives. Thus recently an unconventional computation framework utilizing wet, reaction-diffusion features has attracted researchers. Authors have reported that basic signal processing functions are implemented on reaction-diffusion fields, with non-uniform field characteristics. In these studies, propagation of excitation pulse on a reaction-diffusion (excitable) field corresponds to signal propagation. It has been reported that co-incidence detection between a couple of inputs can be realized by suitable arrangement of reaction-diffusion fields on diffusion field in numerical and experimental studies. In this paper time differences of a couple of inputs can be encoded as the number of output pulses by adopting a bursting model that originated from living systems at the detecting point of output field.

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An actomyosin in vitro motility assay system is one of the effective systems for discussing biological hierarchy at the molecular level. From the movies of the sliding movement of an actin filament observed here, I extracted possible skeletal structures of an actin filament by image analysis and analyzed their movement and windings on the whole filament. The result is that as the velocity of sliding movement increased, the windings decreased and small windings propagated and formed a pattern. Additionally, at the ends of actin filament, the windings show complex patterns e.g.: dissipation, reflection or fusion of a few winding waves. The existence of these complex patterns suggests the possibility of occurrences of not only interaction between nearest neighbor actin molecules but also information processing to coordinate whole actin filament interacting between higher-level classes made by hierarchy.

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The aim of this paper is to investigate the discrete nature of chemically reacting systems. In order to achieve our purpose we propose a systematic method to compare the discrete stochastic model of chemically reacting systems with the continuous stochastic model. We adopt the chemical master equation (CME) as the discrete stochastic model and the chemical Fokker-Planck equation (CFPE) as the continuous stochastic model. By making use of the well-known idea of approximating diffusion processes by birth-death processes, we construct a family of master equations parameterized by the degree of discreteness. This family of master equations bridges CME and CFPE. With full degree of discreteness we obtain CME and as decreasing discreteness the family of master equations converges to CFPE. Our strategy is not to study CME directly but to distinguish the properties of CME by putting CME into the family of master equations bridging CME and CFPE. We examine the usefulness of our construction by two simple examples.

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An amoeboid organism, the true slime mold Physarum, has been studied actively in recent years to explore its spatiotemporal oscillatory dynamics and various computational capabilities. In the authors' previous studies, the amoeba was employed as a computing substrate to construct a neurocomputer. Under optical feedback control to implement a recurrent neural network model, the amoeba grows or withdraws its photosensitive branches by exhibiting a number of spatiotemporal oscillation modes in search of a solution to some combinatorial optimization problems. In this paper, considering the amoeba as a network of oscillators that compete for constant amounts of resources, we model the amoeba-based neurocomputer. The model generates several oscillation modes and produces not only simple behavior to stabilize a single mode but also complex behavior to spontaneously switch among different modes. To explore significances of the oscillatory dynamics in producing the computational capabilities, we establish a test problem that is a kind of optimization problem of how to allocate a limited amount of resource to oscillators so that conflicts among theoscillators can be avoided. We compare the performances of the oscillation modes in solving the problem in a bottom-up manner.

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Class 4 automata are considered to exhibit the essential feature of biochemical systems. Robust but dynamic systems in nature are assumed to be hierarchical, while class 4 automata have no hierarchical structure. The idea of hierarchy itself is self-referential and ambiguous, and these properties have been recently reflected in the term "heterarchy." We propose a model for class 4 behavior as heterarchy, which is constructed by implementing intermediate layers intervening macroscopic and microscopic layers. We propose an analysis for an algebraic structure of ECA based on the lattice derived by rough set analysis (Figure 1-3), and show that class 1 and 2 behavior depend on distributivity of a derived lattice (Figure 4-7). A virtual algebraic structure which characterizes class 1 or 2 ECA which cannot be derived from class 3 rules is assumed in the real class 3 ECA, and the intermediate layer intermediating virtual and real behavior is implemented (Figure 8). This operation results in class 4 behavior (Figure 9, 10).

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