Physica A 391 (2012) 686–692 Contents lists available at SciVerse ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Dynamics of macroautophagy: Modeling and oscillatory behavior Kyungreem Han a , Hyun Woong Kwon b , Hyuk Kang c , Jinwoong Kim a,* , Myung-Shik Lee d , M.Y. Choi b,** a College of Pharmacy, Seoul National University, Seoul 151-742, Republic of Korea b Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University, Seoul 151-747, Republic of Korea c National Institute for Mathematical Sciences, Daejeon 305-340, Republic of Korea d Department of Medicine, Samsung Medical Center, and School of Medicine, Sungkyunkwan University, Seoul 135-710, Republic of Korea article info Article history: Received 25 February 2011 Received in revised form 17 August 2011 Available online 6 September 2011 Keywords: Modeling Numerical simulation Macroautophagy Oscillation Autophagosome Autolysosome Protein and organelle ATP Amino acid abstract We propose a model for macroautophagy and study the resulting dynamics of autophagy in a system isolated from its extra-cellular environment. It is found that the intracellular concentrations of autophagosomes and autolysosomes display oscillations with their own natural frequencies. Such oscillatory behaviors, which are interrelated to the dynamics of intracellular ATP, amino acids, and proteins, are consistent with the very recent biological observations. Implications of this theoretical study of autophagy are discussed, with regard to the possibility of guiding molecular studies of autophagy. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Autophagy is evolutionarily conserved and strictly regulated mechanism for the sequestration of cytoplasmic materials into lysosomes. It is classified into several main classes depending on how cytoplasmic materials are delivered from cytosol to lysosomal lumens: (macro)autophagy, microautophagy, chaperone-mediated autophagy, crinophagy, and so on. Often autophagy stands for macroautophagy which is characterized by the double membranes, called phagophores, which engulf cytoplasmic materials before lysosomal sequestration [1]. Usually, autophagy is regarded as a means of protein recycling for the self-energy production during energy starvation [2–9]. In eukaryotic cells, however, it has achieved extra fundamental functions such as regulation of homeostasis and ultimately complex signaling pathways which are essential for life and death of cells [10]. Autophagy is an ongoing process at a steady pace. Nevertheless, it plays different roles, depending on the degree of its activation. Constitutive (basal-level) autophagy protects cells from stress, including starvation, oxidative stress, or other harmful conditions. In this way, it contributes to health and longevity via important housekeeping and quality control functions. On the other hand, excessive-level autophagy destroys important regulatory molecules and micro-organelles, and eventually induces spontaneous cell death [10]. Therefore, proper regulation of autophagy is essential for maintaining * Corresponding author. ** Corresponding author. Tel.: +82 2 880 6615. E-mail addresses: jwkim@snu.ac.kr (J. Kim), mychoi@snu.ac.kr (M.Y. Choi). 0378-4371/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physa.2011.08.046