On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach

We present a meshfree method for the curvature estimation of membrane networks based on the local maximum entropy approach recently presented in [1]. A continuum regularization of the network is carried out by balancing the maximization of the information entropy corresponding to the nodal data, with the minimization of the total width of the shape functions. The accuracy and convergence properties of the given curvature prediction procedure are assessed through numerical applications to benchmark problems, which include coarse grained molecular dynamics simulations of the fluctuations of red blood cell membranes [2] and [3]. We also provide an energetic discrete-to-continuum approach to the prediction of the zero-temperature bending rigidity of membrane networks, which is based on the integration of the local curvature estimates. The local maximum entropy approach is easily applicable to the continuum regularization of fluctuating membranes, and the prediction of membrane and bending elasticities of molecular dynamics models.

Graphical abstract3D density plot of the mean curvature of a healthy red blood cell determined through local maximum entropy regularization of molecular dynamics data.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► LME balances maximization of information entropy & minimization of approximation width. ► LME is well suited for the continuum regularization of membrane networks. ► Convergence studies determine the optimal parameter tuning. ► Mean and Gaussian curvatures of healthy human RBCs are estimated. ► The bending rigidity is estimated through a discrete-to-continuum approach.