Abstract— In vivo reaction space is constrained by complex structures which are made of entwined cytoskeletons and organelles; this create the difference between in vivo and in vitro in respect of molecular mobility, and it may affect reaction processes. Our motivation is to reveal the background mechanisms of the properties of molecular behaviors in vivo by numerical approach. For this object, we reassembled a pseudo-intracellular environment in 3D lattice space, and executed Monte Carlo simulation. By changing the relative amount of non-reactive obstacles in the simulation space, we tested the effect of the level of crowdedness to the molecular mobility and reaction processes. Our results showed that molecules demonstrated anomalous diffusion correlating to the restriction level of the reaction space. Reaction processes also showed distinct characteristics, that is increase of reaction rate at the beginning of reactions, with the decrease of the reaction rate at later time frame of reactions. Our results suggested that the anomalous behaviors at singe molecule level in vivo could bring an essential difference to the reaction processes and the results. I. INTRODUCTION In vivo reaction space is very different from in vitro reaction space because of their crowdedness and inhomogeneity [1]. The conditions of reaction space in classical numerical models are assumed ideal conditions, which differ from the actual conditions of in vivo biochemical reactions [2]. Recently, Aoki et.al. have revealed the differences of reaction processes between in vivo and in vitro, and also the effect of crowding which affects reaction processes by experiments [3]. Although classical models can compute in vivo reactions with sufficient approximation in specific conditions, such approximation does not stand as a general approach. A new method is desired to apply various biological phenomena occurring in non-ideal conditions. We showed in our previous works that the characteristics of in vivo structures with fractal dimension, and the level of anomaly of molecular diffusion in cytoplasmic region, which is considered as a typical in vivo *Research supported by SUNBOR (SUNTORY) grant. N. H., T. O., T. K., K. O. and A. F. are with Department of Biosciences N. H., T. O., T. K., K. O. and A. F. are with Department of Biosciences and Informatics, Keio University, Yokohama, 223-8522 Japan (corresponding author to provide phone: +81-45-566-1584; fax: +81-45-566-1789; e-mail: hiroi@bio.keio.ac.jp). K. I. and A. T. were with Department of Biosciences and Informatics, Keio University, Yokohama, 223-8522 Japan. T. J. K. is with Institute of Industrial Science, the University of Tokyo, Meguro Ward, 153-8505 Japan. environment [4]. In the paper, we also showed that parameter values may not change essential behaviors of in vivo molecules (Supplemental Figures of [4]). We also reconstructed an artificial in vivo reaction environment to test the realistic size distribution and the diffusion constant of non-reactive obstacles (NROs) in vivo [5]. Finally we suggested the significance of the ratio between the surface and its volume of environmental obstacles in physiological environment, and the simple rule could define the size, shape and density of environmental obstacles [6]. By those 3 papers, we showed that there is a specific range of relative amount of NRO to enhance the mean square displacement (MSD) of molecules. The missing point among our former studies for in vivo oriented modeling is the investigation of reaction processes, such as a catalytic process of a substrate with an enzyme to produce a specific product. This kind of test has important meaning, for example to confirm if one of the characteristics of in vivo diffusion, which is slow-exhaustion [4], could have realistic effects to the dynamics of the reaction substrate and the product. Here, we examined Michaelis-Menten Model, which is a popular simulation method for enzymatic reaction, with Monte Carlo simulation. The results showed that the characteristics which was observed in the molecular diffusions were reflected to the results of molecular reaction. II. EXPERIMENTAL PROCEDURES A. Michaelis-Menten kinetics by Monte Carlo simulation in crowded reaction space We assembled intracellular environment with lattices in a 3 dimensional space, and executed Monte Carlo simulations [Fig. 1]. Figure 1. A schematic figure of a Reaction space. Red solid-filled circles: reactants, blue solid-filled circles: non-reactive obstacles, green arrows: mobile direction. in vivo oriented modeling with consideration of intracellular crowding* Noriko Hiroi, Keisuke Iba, Akito Tabira, Takahiro Okuhara, Takeshi Kubojima, Takumi Hiraiwa, Tetsuya J Kobayashi, Kotaro Oka and Akira Funahashi