イオンチャネルの開口ビリヤードモデル

Abstract

Hodgkin らはイカの巨大神経繊維の電気的な測定からカリウムイオンの異常な輸送現象を観測した. この異常な輸送現象を説明するものとして Hodgkin らは細長い通路で 2 つの部屋を繋いだようなモデルを構築した. このように容器内に封入された大きさのない粒子が容器の内壁と完全弾性衝突を繰り返した後, 脱出する運動をモデル化したものとして開口ビリヤード系がある. 本研究では, 粒子の大きさを考慮し, 粒子間衝突のある多粒子のビリヤード系についてそのビリヤード内滞在時間の逆冪則に従う確率分布を数値シミュレーションにより求め, 遅い異常輸送との関連について考察する.

Hodgkin and Keynes showed that metabolic inhibitors like dinitrophenol and cyanide produce large changes in the relative magnitude of the fluxes of potassium moving inwards and outwards across the membranes of giant axons from Sepia officinalis and proposed such a mechanical model that two flat compartments are separated by a narrow gap with spacers. In a similar way, it is considered such a situation that point-wise particles repeatedly and elastically collide with the wall of a container without any particle-particle collision and eventually escape through a small window from the container, which can be modeled by an open billiard. In the present study, point-wise particles are replaced with finite-size disks and disk-disk collisions are also considered, and inverse power laws of distributions of dwell time in the container are obtained from numerical simulations. Relationship between the power laws and anomalous transport is discussed.