An innovative analytical/computational approach is presented to provide maximum allowed probabilities (MAPs) of conformations in protein domains not rigidly connected. The approach is applied to calmodulin and to its adduct with alpha-synuclein. Calmodulin is a protein constituted by two rigid domains, each of them composed by two calcium-binding EF-hand motifs, which in solution are largely free to move with respect to one another. We used the N60D mutant of calmodulin, which had been engineered to selectively bind a paramagnetic lanthanide ion to only one of its four calcium binding sites, specifically in the second EF-hand motif of the N-terminal domain. In this way, pseudocontact shifts (pcs's) and self-orientation residual dipolar couplings (rdc's) measured on the C-terminal domain provide information on its relative mobility with respect to the domain hosting the paramagnetic center. Available NMR data for terbium(III) and thulium(III) calmodulin were supplemented with additional data for dysprosium(III), analogous data were generated for the alpha-synuclein adduct, and the conformations with the largest MAPs were obtained for both systems. The MAP analysis for calmodulin provides further information on the variety of conformations experienced by the system. Such variety is somewhat reduced in the calmodulin-alpha-synuclein adduct, which however still retains high flexibility. The flexibility of the calmodulin-alpha-synuclein adduct is an unexpected result of this research.

Abstract. The MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) instrument on the Envisat (Environmental satellite) satellite has provided vertical profiles of the atmospheric composition on a global scale for almost ten years. The MIPAS mission is divided in two phases: the full resolution phase, from 2002 to 2004, and the optimized resolution phase, from 2005 to 2012, which is characterized by a finer vertical and horizontal sampling attained through a reduction of the spectral resolution. While the description and characterization of the products of the ESA processor for the full resolution phase has been already described in previous papers, in this paper we focus on the performances of the latest version of the ESA (European Space Agency) processor, named ML2PP V6 (MIPAS Level 2 Prototype Processor), which has been used for reprocessing the entire mission. The ESA processor had to perform the operational near real time analysis of the observations and its products needed to be available for data assimilation. Therefore, it has been designed for fast, continuous and automated analysis of observations made in quite different atmospheric conditions and for a minimum use of external constraints in order to avoid biases in the products. The dense vertical sampling of the measurements adopted in the second phase of the MIPAS mission resulted in sampling intervals finer than the instantaneous field of view of the instrument. Together with the choice of a retrieval grid aligned with the vertical sampling of the measurements, this made ill-conditioned the retrieval problem of the MIPAS operational processor. This problem has been handled with minimal changes to the original retrieval approach but with significant improvements nonetheless. The Levenberg–Marquardt method, already present in the retrieval scheme for its capability to provide fast convergence for nonlinear problems, is now also exploited for the reduction of the ill-conditioning of the inversion. An expression specifically designed for the regularizing Levenberg–Marquardt method has been implemented for the computation of the covariance matrices and averaging kernels of the retrieved products. The regularization of the Levenberg–Marquardt method is controlled by the convergence criteria and is deliberately kept weak. The resulting oscillations of the retrieved profile are a posteriori damped by an innovative self-adapting Tikhonov regularization. The convergence criteria and the weakness of the self-adapting regularization ensure that minimum constraints are used and the best vertical resolution obtainable from the measurements is achieved in all atmospheric conditions. Random and systematic errors, as well as vertical and horizontal resolution are compared in the two phases of the mission for all products, namely: temperature, H2O, O3, HNO3, CH4, N2O, NO2, CFC-11, CFC-12, N2O5 and ClONO2. The use in the two phases of the mission of different optimized sets of spectral intervals ensures that, despite the different spectral resolutions, comparable performances are obtained in the whole MIPAS mission in terms of random and systematic errors, while the vertical resolution and the horizontal resolution are significantly better in the case of the optimized resolution measurements.

Conformational heterogeneity is key to the function of many biomacromolecules, but only a few groups have tried to characterize it until recently. Now, thanks to the increased throughput of experimental data and the increased computational power, the problem of the characterization of protein structural variability has become more and more popular. Several groups have devoted their efforts in trying to create quantitative, reliable and accurate protocols for extracting such information from averaged data. We analyze here different approaches, discussing strengths and weaknesses of each. All approaches can roughly be clustered into two groups: those satisfying the maximum entropy principle and those recovering ensembles composed of a restricted number of molecular conformations. In the first case, the solution focuses on the features that are common to all the infinite solutions satisfying the experimental data; in the second case, the reconstructed ensemble shows the conformational regions where a large probability can be placed. The upper limits for conformational probabilities (MaxOcc) can also be calculated. We also give an overview of the mainstream experimental observables, with considerations on the assumptions underlying their usage.

Calmodulin is a two-domain protein which in solution can adopt a variety of conformations upon reorientation of its domains. The maximum occurrence (MO) of a set of calmodulin conformations that are representative of the overall conformational space possibly sampled by the protein, has been calculated from the paramagnetism-based restraints. These restraints were measured after inclusion of a lanthanide binding tag in the C-terminal domain to supplement the data obtained by substitution of three paramagnetic lanthanide ions to the calcium ion in the second calcium binding loop of the N-terminal domain. The analysis shows that the availability of paramagnetic restraints arising from metal ions placed on both domains, reduces the MO of the conformations to different extents, thereby helping to identify those conformations that can be mostly sampled by the protein.

We study the inverse problem of the determination of the most favoured relative orientations of moving protein domains from residual dipolar coupling measurements. We present a numerical procedure based on the simplex method for the efficient determination of the maximum probability of a given relative orientation. We prove the convergence of the algorithm and present the results obtained both on synthetic and on experimental data.