A unified framework for the numerical evaluation of the Q-subtractive Kramers-Kronig relations and application to the reconstruction of optical constants of quartz.

The direct usage of the Kramers-Kronig (KK) relations is complicated by two factors: limited frequency range of the available spectra and experimental errors. Here, we reconsider the application of the KK relations to experimental data for the construction of a self-consistent set of optical constants over a wide spectral range: the real part of the complex optical constant, F1, is reconstructed using the imaginary part F2, obtained from an experiment. The focus is on multiply (Q-)subtractive KK relations, which in contrast to the standard KK transformation, exploit information about F1 at a certain number Q of anchor frequencies. We develop a general mathematical framework of the Q-subtractive KK relations and analyze all sources of errors contributing to the inaccuracy of the reconstructed F1. We show that for the reconstruction of F1 only a single evaluation of the standard KK relation is needed together with a correction term given by an approximate evaluation of the error in the standard KK. It is demonstrated that in the classical form of the Q-subtractive KK relations, this correction term coincides with the Lagrange interpolation polynomial of the error with nodes at the anchor frequencies. Another correction term can also be constructed as a lower degree polynomial through a least squares fit, a particular realization of which is taking the average of Q singly subtractive KK relations. As a result, recommendations for the application of Q-subtractive KK relations are given. The accuracy of the considered approaches is illustrated on synthetic examples and experimental data of fused SiO2.

Structural determinants of a permeation barrier of the SecYEG translocon in the active state.

The SecYEG translocon is a channel in bacteria, which provides a passage for secretory proteins across as well as integration of membrane proteins into the plasma membrane. The molecular mechanism, by which SecYEG manages protein transport while preventing water and ion leakage through the membrane, is still controversial. We employed molecular dynamics simulations to assess the contribution of the major structural elements - the plug and the pore ring (PR) - to the sealing of SecYEG in the active state, i.e., with a signal sequence helix occupying the lateral gate. We found, that the PR alone can provide a very tight seal for the wild-type translocon in the active state for both water and ions. Simulations of the mutant I403N, in which one of the PR-defining isoleucine residues is replaced with asparagine, suggest that hydrophobic interactions within the PR and between the PR and the plug are important for maintaining a tight conformation of the wild-type channel around the PR. Disruption of these interactions results in strong fluctuations of helix TM7 and water leakage of the translocon.

ARGOS: An adaptive refinement goal-oriented solver for the linearized Poisson-Boltzmann equation.

An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal-oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS-CoV-2 and the ACE2 receptor. All the calculations are repeated by using the well-known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.

Driving Forces of Translocation Through Bacterial Translocon SecYEG.

This review focusses on the energetics of protein translocation via the Sec translocation machinery. First we complement structural data about SecYEG's conformational rearrangements by insight obtained from functional assays. These include measurements of SecYEG permeability that allow assessment of channel gating by ligand binding and membrane voltage. Second we will discuss the power stroke and Brownian ratcheting models of substrate translocation and the role that the two models assign to the putative driving forces: (i) ATP (SecA) and GTP (ribosome) hydrolysis, (ii) interaction with accessory proteins, (iii) membrane partitioning and folding, (iv) proton motive force (PMF), and (v) entropic contributions. Our analysis underlines how important energized membranes are for unravelling the translocation mechanism in future experiments.

Theory of FRET "Spectroscopic Ruler" for Short Distances: Application to Polyproline.

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.