When do diffusion-limited trajectories become memoryless? Maciej Dobrzy´ nski CWI (Center for Mathematics and Computer Science) Kruislaan 413, 1098 SJ Amsterdam, The Netherlands Abstract Stochastic description of cellular dynamics by the chemical master equation assumes the exponential distribution of intervals between reaction events. Diffusion-limited reactions violate this assumption. Using the example of the target search we investigate the conditions under which a peaked waiting-time distribution can be approximated by the exponential function. We link the steady-state flux and the dynamic property of the diffusion, the mean first-passage time. 1 Introduction Cellular regulation involves processes with reactants occurring at low copy numbers per cell (e.g. transcription/translation, signaling). Such processes suffer from thermal noise and diffusion-limitation. The concentration of species involved in such reactions fluctuates significantly. Recent single-cell, single-molecule experiments indicate that fluctuations contribute to hetero- geneity of isogenic populations and may be detrimental to cellular informa- tion processing [1, 2]. 1.1 CME description of biochemical reactions A conventional modeling approach that accounts for fluctuations in the dis- crete number of molecules is the chemical master equation (CME) [4, 5]. The equation describes the evolution in time of the probability to occupy 1