Forces in a biological context

Abstract

Theoretical modelling of the microtubule-Dam1-ring force generation mechanism and the pulling of tubes from surface-supported lipid bilayers are presented and discussed. Atomic force microscopy (AFM) force data of tube pulling experiments is analysed and compared with theoretical predictions. Featurescommonto recent computational models are simplified and examined independently where possible. In particular, the steric confinement of the Dam1 ring on a microtubule (MT) by protofilaments (PFs), the powerstroke produced by curling PFs, the depolymerisation of the MT, and the binding attraction between Dam1 and the MT are modelled. Model parameters are fitted to data. Functional force generation is equally demonstrated when attachment is maintained by steric confinement alone (protofilament model) or by a binding attraction alone (binding model). Moreover, parameters amenable to experimental modification are shown to induce differences between the protofilament model and the binding model. Changing the depolymerisation rate of MTs, the diffusion coefficient of the Dam1 ring, or applying an oscillating load force will allow discrimination of these two different mechanisms of force generation and kinetochore attachment. A previously described theoretical model of pulling lipid bilayer tubes from vesicles is modified for the case of pulling tubes from surface-supported lipid bilayers. A shape equation for axisymmetric membranes is derived variationally and solved numerically for zero pressure. Free energy profiles and force curves are calculated for various AFM probe sizes and compared to experimental data where a ground flat AFM probe is used to pull tubes from surface-supported lipid bilayers. The predicted force curves partially fit the experimental data, although not at short distances, and estimates of the bilayer surface tension are given. Pressure and volume profiles are calculated for the extension of the model to the nonzero pressure case