Binding site identification of G protein-coupled receptors through a 3D Zernike polynomials-based method: application to C. elegans olfactory receptors

Studying the binding processes of G protein-coupled receptors (GPCRs) proteins is of particular interest both to better understand the molecular mechanisms that regulate the signaling between the extracellular and intracellular environment and for drug design purposes. In this study, we propose a new computational approach for the identification of the binding site for a specific ligand on a GPCR. The method is based on the Zernike polynomials and performs the ligand-GPCR association through a shape complementarity analysis of the local molecular surfaces. The method is parameter-free and it can distinguish, working on hundreds of experimentally GPCR-ligand complexes, binding pockets from randomly sampled regions on the receptor surface, obtaining an Area Under ROC curve of 0.77. Given its importance both as a model organism and in terms of applications, we thus investigated the olfactory receptors of the C. elegans, building a list of associations between 21 GPCRs belonging to its olfactory neurons and a set of possible ligands. Thus, we can not only carry out rapid and efficient screenings of drugs proposed for GPCRs, key targets in many pathologies, but also we laid the groundwork for computational mutagenesis processes, aimed at increasing or decreasing the binding affinity between ligands and receptors.

Expansion of the Laser Beam Wavefront in Terms of Zernike Polynomials in the Problem of Turbulence Testing

The results of a study of the wavefront distortions of laser radiation caused by artificial turbulence obtained in laboratory conditions using a fan heater are presented. Decomposition of the wavefront in terms of Zernike polynomials is a standard procedure that traditionally is used to investigate the set of existing aberrations. In addition, the spectral analysis of the wavefront dynamics makes it possible to estimate the fraction of the energy distributed between different Zernike modes. It is shown that the fraction of energy related to the low-order polynomials is higher compared to the high-order polynomials. Also, one of the consequences of Taylor’s hypothesis is confirmed—low-order aberrations are slower compared to the higher-order ones.

Contribution of wave aberrations represented by Zernike polynomials to the cross-correlation function between distorted and actual speckle patterns

Speckles are sensitive to the slightest inhomogeneities of the medium, which is used in optical research methods such as speckle interferometry. However, the stochastic nature of propagation of speckle fields complicates their accurate detection and processing. For example, aberrations in the optical system result in the decorrelation of the image of speckles with the actual speckles that are observed in free space. The report will consider the main types of wave aberrations of optical system and their influence on the correlation properties of speckle patterns. The research results can be used to optimize optical systems in which speckles play a significant role, for example, in classical ghost imaging.

Assessment about Luneberg integrals and application to digital in-line holography

In this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg’s integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg’s integrals, the propagation of a vectorial electromagnetic field (Hertz potentials) is developed and a new approach of the computation have been proposed based on Zernike polynomials. With this new approach simulations of holograms is illustrated in the case of the digital in-line holography with an opaque disk.

Using Generalized Basis for Functional Expansion

Functional expansion has been rigorously studied as a promising method in stochastic neutron transport and multi-physics coupling. It is a method to represent data specified on a desired domain as an expansion of basis set in a continuous manner. For convenience, the basis set for functional expansion is typically chosen to be orthogonal. In cylindrical PWR pin-cell simulations, the orthogonal Zernike polynomials have been used. The main advantage of using functional expansion in nuclear modeling is that it requires less memory to represent temperature and nuclide variations in fuel then using a fine discretization. Fewer variables are involved in the data storage and transfer process. Each nuclide can have its unique expansion order, which becomes very important for depletion problems. In a recent study, performance analysis was conducted on Zernike-based FETs on a 2D PWR geometry. For reaction rates like the absorption rate of U-238, however, many orders are needed with Zernike-based FETs to achieve a reasonable accuracy. This gap inspires the study in this paper on alternative basis set that can better capture the steep gradient with fewer orders. In this paper, a generalized functional expansion method is established. The basis set can be an arbitrary series of independent functions. To capture the self-shielding effect of U-238 absorption rate, an exponential basis set is chosen. The results show that the expansion order utilizing exponential basis can reduce by half of that from using orthogonal Zernike polynomials while achieving the same accuracy. The integrated reaction rate is also demonstrated to be preserved. This paper also shows that the generalized functional expansion could be a heuristic method for further investigation on continuous depletion problems.