24 research outputs found
Modelling Electrostatic Interactions and Solvation in Chromatin: from the single nucleosome towards the chromatin fibre
No full textChromatin is a complex of proteins and DNA found in the nuclei of eukaryotic cells. It reinforces the DNA and its topology tunes DNA transcription and gene expression. It is formed by nucleosomes, structures composed of an octameric protein core and approximately 147 base pairs of DNA. Chromatin is an extremely complex system, the behaviour of which is ruled by both mechanical and electrostatic factors that are depend on its structure, and biomolecular interactions occurring in the cell nucleus. In this thesis, I analyse chromatin compaction from an electrostatic perspective and focus on the role of electrostatics and solvation as determinants of the topology of chromatin. I examine the effect of the histone tails and propose a methodology to connect electrostatic calculations to the structural and functional features of protein-DNA systems. This methodology can also be combined with coarse-grained representations. I study the electrostatic forces acting on the phosphate atoms of the DNA backbone. I investigate the electrostatic origins of effects such as different stages in DNA unwrapping, nucleosome destabilisation upon histone tail truncation, and the role of specific arginines and lysines undergoing Post - Translational Modifications. I find that the positioning of the histone tails can oppose the attractive pull of the histone core, locally deform the DNA, and tune DNA unwrapping. I conduct an analysis of the porosity of nucleosomes and related to the importance of solvation phenomena. I complement and support my computational findings on nucleosome electrostatic interactions experimental Zeta Potential and Dynamic Light Scattering measurements on single nucleosomes under varying ionic concentrations, providing information on the surface charge and the size of nucleosomes. I present a comprehensive study of the electrostatic interactions between nucleosome pairs sampling different translations and rotations. My analysis aims to provide a cohesive description of nucleosome electrostatic interactions in the chromatin fibre, combining information on the energetics of different relative positions of nucleosomes, especially in very tight packing situations. In addition to numerical estimates of electrostatic interaction energy of nucleosomes at different relative distances and orientations, obtained within the Poisson-Boltzmann framework, I present their approximation by analytical asymptotic expressions, where nucleosomes are approximated as monopoles and dipoles centred in dielectric spheres immersed in an electrolytic solution. I am able to identify a non-linearity region around the nucleosomes, and to exploit the fact that that in points outside that region the electrostatic potential can be described by the linearised Poisson-Boltzmann Equation
Charged dielectric spheres interacting in electrolytic solution: A linearized Poisson–Boltzmann equation model
No full textWe present an analytical theory of electrostatic interactions of two spherical dielectric particles of arbitrary radii and dielectric constants, immersed into a polarizable ionic solvent (assuming that the linearized Poisson-Boltzmann framework holds) and bearing arbitrary charge distributions expanded in multipolar terms. The presented development entails a novel two-center re-expansion analytical theory that expands upon and improves the existing ones, bypassing the conventional expansions in modified Bessel functions. On this basis, we develop a specific matrix formalism that facilitates the construction of asymptotic expansions in ascending order of Debye screening terms of potential coefficients, which are then employed to find exact closed-form expressions for the total electrostatic energy. In particular, this work allows us to explicitly and precisely quantify the k-screened terms of the potential coefficients and mutual interaction energy. Specific cases of monopolar and dipolar distributions are described in particular detail. Comprehensive numerical examples and tests of series convergence and the relative balance of leading and higher-order terms of the mutual interaction energy are presented depending on the inter-particle distance and particles' radii. The results of this work find application in soft matter modeling and, in particular, in computational biophysics and colloid science, where the availability of increasingly larger experimental structures at the atomic-level resolution makes numerical treatment challenging and calls for more efficient expressions and an increased range of validity
Coherency and differential Mueller matrices for polarizing media
No full textThe elements of the coherency matrix give the strength of the components of a Mueller matrix in the coherency basis. The Z-matrix (called the polarization-coupling matrix or state-generating matrix) represents a partial sum of the coherency expansion. For transmission through a deterministic medium, the coherency elements can be used directly as generators to calculate the development of polarization upon propagation. The commutation properties of the coherency elements are investigated. New matrices that we call the W-matrix and the X-matrix, both different representations of the Z-matrix in a Jones basis, are introduced. The W-matrix controls the transformation of the Jones vector and also the covariance matrix. The product of the X-matrix with its complex conjugate gives the matrix representation of the Mueller matrix in the Jones basis. The development of Mueller matrix and coherency matrix elements upon propagation through some examples of a uniform medium is investigated. It is shown that the coherency matrix is more easily interpreted than the Mueller matrix. Analytic expressions are presented to calculate the elementary polarization properties from coherency matrix elements or Mueller matrix parameters. (C) 2018 Optical Society of Americ
Polarimetric optical scanning microscopy of zebrafish embryonic development using the coherency matrix
No full textMany of the most important resolution improvements in optical microscopy techniques are based on the reduction of scattering effects. The main benefit of polarimetry-based imaging to this end is the discrimination between scattering phenomena originating from complex systems and the experimental noise. The determination of the coherency matrix elements from the experimental Mueller matrix can take advantage of scattering measurements to obtain additional information on the structural organization of a sample. We analyze the contrast mechanisms extracted from (a) the coherency matrix elements, (b) its eigenvalues and (c) the indices of polarimetric purity at different stages of zebrafish embryos, based on previous work using Mueller matrix optical scanning microscopy. We show that the use of the coherency matrix and related decompositions leads to an improvement in the imaging contrast, without requiring any complicated algebraic operations or any a priori knowledge of the sample, in contrast to standard polarimetric methods
Phasor approach of Mueller matrix optical scanning microscopy for biological tissue imaging
No full textMueller matrix microscopy is an advanced imaging technique providing a full characterization of the optical polarization fingerprint of a sample. The Lu-Chipman (LC) decomposition, a method based on the modeling of elementary polarimetric arrangements and matrix inversions, is the gold standard to extract each polarimetric component separately. However, this models the optical system as a small number of discrete optical elements and requires a priori knowledge of the order in which these elements occur. In stratified media or when the ordering is not known, the interpretation of the LC decomposition becomes difficult. In this work, we propose a new, to our knowledge, representation dedicated to the study of biological tissues that combines Mueller matrix microscopy with a phasor approach. We demonstrate that this method provides an easier and direct interpretation of the retardance images in any birefringent material without the use of mathematical assumptions regarding the structure of the sample and yields comparable contrast to the LC decomposition. By validating this approach through numerical simulations, we demonstrate that it is able to give access to localized structural information, resulting in a simple determination of the birefringent parameters at the microscopic level. We apply our novel, to our knowledge, method to typical biological tissues that are of interest in the field of biomedical diagnosis
A Table of Some Coherency Matrices, Coherency Matrix Factors, and Their Respective Mueller Matrices
No full textMany books on polarization give tables of Mueller matrices. The coherency matrix has been found useful for interpretetion of the Mueller matrix. Here we give a table of Mueller matrices M, coherency matrices C, and coherency matrix factors F for different polarization components and systems. F is not given for some complicated nondeterministic cases. In many cases, though, F has a very simple form. In particular, we give expressions for F for the general case of an homogeneous elliptic diattenuating retarder. Different coordinate systems for describing diattenuating retarders are compared, on a generalized retardation sphere, analogous to the Poincaré sphere. For the general homogeneous deterministic case, expressions for the Mueller matrix have particularly simple forms for Cartesian or stereographic coordinates in generalized retardation space
The role of histone tails in nucleosome stability: An electrostatic perspective
No full textWe propose a methodology for the study of protein-DNA electrostatic interactions and apply it to clarify the effect of histone tails in nucleosomes. This method can be used to correlate electrostatic interactions to structural and functional features of protein-DNA systems, and can be combined with coarse-grained representations. In particular, we focus on the electrostatic field and resulting forces acting on the DNA. We investigate the electrostatic origins of effects such as different stages in DNA unwrapping, nucleosome destabilization upon histone tail truncation, and the role of specific arginines and lysines undergoing Post-Translational Modifications. We find that the positioning of the histone tails can oppose the attractive pull of the histone core, locally deform the DNA, and tune DNA unwrapping. Small conformational variations in the often overlooked H2A C-terminal tails had significant electrostatic repercussions near the DNA entry and exit sites. The H2A N-terminal tail exerts attractive electrostatic forces towards the histone core in positions where Polymerase II halts its progress. We validate our results with comparisons to previous experimental and computational observations. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology.LCVM
Characterization of the Mueller Matrix: Purity Space and Reflectance Imaging
No full textDepolarization has been found to be a useful contrast mechanism in biological and medical imaging. The Mueller matrix can be used to describe polarization effects of a depolarizing material. An historical review of relevant polarization algebra, measures of depolarization, and purity spaces is presented, and the connections with the eigenvalues of the coherency matrix are discussed. The advantages of a barycentric eigenvalue space are outlined. A new parameter, the diattenuation-corrected purity, is introduced. We propose the use of a combination of the eigenvalues of coherency matrices associated with both a Mueller matrix and its canonical Mueller matrix to specify the depolarization condition. The relationships between the optical and polarimetric radar formalisms are reviewed. We show that use of a beam splitter in a reflectance polarization imaging system gives a Mueller matrix similar to the Sinclair–Mueller matrix for exact backscattering. The effect of the reflectance is canceled by the action of the beam splitter, so that the remaining features represent polarization effects in addition to the reflection process. For exact backscattering, the Mueller matrix is at most Rank 3, so only three independent complex-valued measurements are obtained, and there is insufficient information to extract polarization properties in the general case. However, if some prior information is known, a reconstruction of the sample properties is possible. Some experimental Mueller matrices are considered as examples
Learning to utilize internal protein 3D nanoenvironment descriptors in predicting CRISPR–Cas9 off-target activity
No full textDespite advances in determining the factors influencing cleavage activity of a CRISPR–Cas9 single guide RNA (sgRNA) at an (off-)target DNA sequence, a comprehensive assessment of pertinent physico-chemical/structural descriptors is missing. In particular, studies have not yet directly exploited the information-rich internal protein 3D nanoenvironment of the sgRNA–(off-)target strand DNA pair, which we obtain by harvesting 634 980 residue-level features for CRISPR–Cas9 complexes. As a proof-of-concept study, we simulated the internal protein 3D nanoenvironment for all experimentally available single-base protospacer-adjacent motif-distal mutations for a given sgRNA–target strand pair. By determining the most relevant residue-level features for CRISPR–Cas9 off-target cleavage activity, we developed STING_CRISPR, a machine learning model delivering accurate predictive performance of off-target cleavage activity for the type of single-base mutations considered in this study. By interpreting STING_CRISPR, we identified four important Cas9 residue spatial hotspots and associated structural/physico-chemical descriptor classes influencing CRISPR–Cas9 (off-)target cleavage activity for the sgRNA–target strand pairs covered in this study
