Time-constant


An in silico representation of a biological filament should respond to external forces on the appropriate time-scale. A standard measure of this response time is the relaxation time-constant. This can, for our purposes, be defined as the time in which a strained filament will relax to 1/e of its deformed state.


A filament will bend in certain primary modes --any complicated strain state can be described as a linear superposition of these primary modes. The upper right-hand corner of the diagram below shows the first two primary bending modes. The first mode (half-sine wave) is associated with the largest time-constant (tau1). All higher modes of bending quickly relax, leaving the much slower first mode deformation; such behavior can be observed in SimFil by turning Brownian motion On/Off. The tuning method of Alberts (2008) focuses on the 1st bending mode, but higher mode time-constants "just work out" as well.