Fluorescence of nitrobenzoxadiazole (NBD)-labeled lipids in model membranes is connected not to lipid mobility but to probe location

Nitrobenzoxadiazole (NBD)-labeled lipids are popular fluorescent membrane probes. However, the understanding of important aspects of the photophysics of NBD remains incomplete, including the observed shift in the emission spectrum of NBD-lipids to longer wavelengths following excitation at the red edge of the absorption spectrum (red-edge excitation shift or REES). REES of NBD-lipids in membrane environments has been previously interpreted as reflecting restricted mobility of solvent surrounding the fluorophore. However, this requires a large change in the dipole moment (Dm) of NBD upon excitation. Previous calculations of the value of Dm of NBD in the literature have been carried out using outdated semi-empirical methods, leading to conflicting values. Using up-to-date density functional theory methods, we recalculated the value of Dm and verified that it is rather small (B2 D). Fluorescence measurements confirmed that the value of REES is B16 nm for 1,2-dioleoyl-sn-glycero-3- phospho-L-serine-N-(NBD) (NBD-PS) in dioleoylphosphatidylcholine vesicles. However, the observed shift is independent of both the temperature and the presence of cholesterol and is therefore insensitive to the mobility and hydration of the membrane. Moreover, red-edge excitation leads to an increased contribution of the decay component with a shorter lifetime, whereas time-resolved emission spectra of NBD-PS displayed an atypical blue shift following excitation. This excludes restrictions to solvent relaxation as the cause of the measured REES and TRES of NBD, pointing instead to the heterogeneous transverse location of probes as the origin of these effects. The latter hypothesis was confirmed by molecular dynamics simulations, from which the calculated heterogeneity of the hydration and location of NBD correlated with the measured fluorescence lifetimes/REES. Globally, our combination of theoretical and experiment-based techniques has led to a considerably improved understanding of the photophysics of NBD and a reinterpretation of its REES in particular.

Semi-implicit finite strain constitutive integration and mixed strain/stress control based on intermediate configurations

A new semi-implicit stress integration algorithm for finite strain plasticity (compatible with hyperelas- ticity) is introduced. Its most distinctive feature is the use of different parameterizations of equilibrium and reference configurations. Rotation terms (nonlinear trigonometric functions) are integrated explicitly and correspond to a change in the reference configuration. In contrast, relative Green–Lagrange strains (which are quadratic in terms of displacements) represent the equilibrium configuration implicitly. In addition, the adequacy of several objective stress rates in the semi-implicit context is studied. We para- metrize both reference and equilibrium configurations, in contrast with the so-called objective stress integration algorithms which use coinciding configurations. A single constitutive framework provides quantities needed by common discretization schemes. This is computationally convenient and robust, as all elements only need to provide pre-established quantities irrespectively of the constitutive model. In this work, mixed strain/stress control is used, as well as our smoothing algorithm for the complemen- tarity condition. Exceptional time-step robustness is achieved in elasto-plastic problems: often fewer than one-tenth of the typical number of time increments can be used with a quantifiable effect in accuracy. The proposed algorithm is general: all hyperelastic models and all classical elasto-plastic models can be employed. Plane-stress, Shell and 3D examples are used to illustrate the new algorithm. Both isotropic and anisotropic behavior is presented in elasto-plastic and hyperelastic examples.