Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines

State Estimation for General Complex Dynamical Networks with Incompletely Measured Information

Estimating uncertain state variables of a general complex dynamical network with randomly incomplete measurements of transmitted output variables is investigated in this paper. The incomplete measurements, occurring randomly through the transmission of output variables, always cause the failure of the state estimation process. Different from the existing methods, we propose a novel method to handle the incomplete measurements, which can perform well to balance the excessively deviated estimators under the influence of incomplete measurements. In particular, the proposed method has no special limitation on the node dynamics compared with many existing methods. By employing the Lyapunov stability theory along with the stochastic analysis method, sufficient criteria are deduced rigorously to ensure obtaining the proper estimator gains with known model parameters. Illustrative simulation for the complex dynamical network composed of chaotic nodes are given to show the validity and efficiency of the proposed method.

Tracking individual membrane proteins and their biochemistry: The power of direct observation

The advent of single molecule fluorescence microscopy has allowed experimental molecular biophysics and biochemistry to transcend traditional ensemble measurements, where the behavior of individual proteins could not be precisely sampled. The recent explosion in popularity of new super-resolution and super-localization techniques coupled with technical advances in optical designs and fast highly sensitive cameras with single photon sensitivity and millisecond time resolution have made it possible to track key motions, reactions, and interactions of individual proteins with high temporal resolution and spatial resolution well beyond the diffraction limit. Within the purview of membrane proteins and ligand gated ion channels (LGICs), these outstanding advances in single molecule microscopy allow for the direct observation of discrete biochemical states and their fluctuation dynamics. Such observations are fundamentally important for understanding molecular-level mechanisms governing these systems. Examples reviewed here include the effects of allostery on the stoichiometry of ligand binding in the presence of fluorescent ligands; the observation of subdomain partitioning of membrane proteins due to microenvironment effects; and the use of single particle tracking experiments to elucidate characteristics of membrane protein diffusion and the direct measurement of thermodynamic properties, which govern the free energy landscape of protein dimerization. The review of such characteristic topics represents a snapshot of efforts to push the boundaries of fluorescence microscopy of membrane proteins to the absolute limit. This article is part of the Special Issue entitled 'Fluorescent Tools in Neuropharmacology'.