Glöckle W G, Nonnenmacher T F
Department of Mathematical Physics, University of Ulm, Germany.
Biophys J. 1995 Jan;68(1):46-53. doi: 10.1016/S0006-3495(95)80157-8.
Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.
由于蛋白质存在大量构象底物，其弛豫过程和反应动力学偏离指数行为。动力学由许多时间尺度控制，因此，弛豫函数或反应物浓度的衰减比指数衰减慢。应用自相似动力学的概念，我们推导了一个分形标度模型，该模型得到一个方程，其中时间导数被非整数阶β的微分(d/dt)β所取代。分数阶微分方程由米塔格-莱夫勒函数求解。它取决于两个参数，一个基本时间尺度τ0和一个分数阶β，分数阶β可解释为动力学的自相似维数。展示了分形模型在肌红蛋白配体再结合和压力释放测量中的应用，并表明了该模型与能垒高度分布考虑因素的联系。
