Fluctuation Theorem Applied to Dictyostelium discoideum System

Abstract

Directional cell movement is a fundamental phenomenon exhibited by many biological processes. It has been known that an electric field exists on the surfaces of the tissues of organisms and that it acts as a directional cue for the type of the cell migration known as electrotaxis. Electrotaxis is thought to play important roles in various physiological processes including embryogenesis and wound healing, and the underlying molecular mechanisms of electrotaxis are now extensively studied. 1) In order to elucidate the mechanisms of the electrotactic responses of cells, the cellular slime mold Dictyostelium discoideum [see Fig. 1 (left)] is a suitable organism to study, because of its high motility and strong electrotactic response. With well-established genetic engineering techniques and advanced microscopic techniques, the input–output relationship in the electrotactic response of Dictyostelium cells has been investigated to elucidate the stochastic processes involved in the signaling systems responsible for cell motility and their regulations. 2) In this paper, we analyze the electrotactic movement of Dictyostelium discoideum from the viewpoint of non-equilibrium statistical mechanics. Because we can observe fluctuating behavior of cellular trajectories, we analyze the probability distribution of the trajectories with the aid of the fluctuation theorem. Recently, the validity of the fluctuation theorem was verified in a colloidal system, 3) and it has also been applied to granular systems, 4) turbulent systems, 5) and chemical oscillatory waves 6) to investigate some of their statistical properties that are not yet completely understood. Noting that the fluctuation theorem is potentially applicable to cellular electrotaxis, here we employ it to help us obtain a phenomenological model of this biological system. System. In this study, Dictyostelium discoideum, Ax2 cells (wild type) were starved for up to 4 h, with a pulse of 100 nM cAMP applied every 6 min. The cell suspension was injected into the chamber for electrotactic assay, and the cells were allowed to spread over the coverslip for 20 min at T ¼ 294 K. Direct current was applied to the chamber as illustrated in the paper of Sato et al. 2) The cells in the chamber were observed with a microscope capable of producing differential interference contrast optics. Data acquisition started 5 min after the electric field was first applied, and the electric field remained at a constant strength, E, throughout experiments. Under these conditions, we considered the system to be in a steady state. To analyze the motile activities of the cells under the electric field, cell images were processed automatically with a time resolution of 5 s and converted into binary images by selecting an optimal value of the brightness threshold. In this way, the trajectory of the center position of the observed cellular region, ðxðtÞ; yðtÞÞ, was determined. Because the gradient of the electric field is non-zero only along the x direction, we particularly investigate the trajectories in the x direction for the case that E ¼ 10 V/cm, which is sufficiently large for the response saturation of the cell. 2) Fluctuation theorem. When the electric field is turned on, Dictyostelium cells begin to migrate toward the cathode (the þx direction). In Fig. 1 (right), we plot example trajectories, xðt Þ� xð0Þ and yðt Þ� yð0Þ, as functions of time in the case E ¼ 10 V/cm. The fluctuating behavior of the cell movement was observed. Then, using these fluctuating trajectories