Fig. 1
Descriptions of the membrane-crosslinker model. (A) Two different views in mathematical modeling for the confined Brownian motion of crosslinkers based on conventional elasticity (left) and the modulus density theory proposed in this work (right). (A, left) The conventional viewpoint. Similar to an elastic spring on the solid membrane, the crosslinker force at a fixed time point is calculated using a constant elastic modulus. (A, right) The alternative viewpoint (in this work). As a modeling treatment, the average distribution of the mobile crosslinker was considered to calculate the crosslinker force. (B‒D) An example configuration calculated using the finite element model of membrane-crosslinker complexes. (B) The elastic modulus density is shown in the surface map. (C) Lateral lipid number strain of the membrane is shown in the surface map. (D) The bending moduli of different lipid classes in the membrane are shown in the surface map. (E) Description of how to index the group of crosslinkers in this model. (F) Description of how the constant \({\varphi }_{c}\) can be split into real numbers assigned over a parametric surface using two degrees of freedom (DOFs) at each point. The functions \({K}_{1c}\) and \({K}_{2c}\) determine values for the two DOFs. With two DOFs, both “positive” and “negative” values can be independently considered at each point during the decomposition of \({\varphi }_{c}\). Such a mathematical strategy may maximize the variability of the shape of the modulus density function \({M}_{c}\) made from the given \({\varphi }_{c}\) value. The illustration here depicts the region where the modulus density is non-zero (except the boundary).
