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"Prior, Christopher"
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The SKMT Algorithm: A method for assessing and comparing underlying protein entanglement
We present fast and simple-to-implement measures of the entanglement of protein tertiary structures which are appropriate for highly flexible structure comparison. These are performed using the SKMT algorithm, a novel method of smoothing the C α backbone to achieve a minimal complexity curve representation of the manner in which the protein’s secondary structure elements fold to form its tertiary structure. Its subsequent complexity is characterised using measures based on the writhe and crossing number quantities heavily utilised in DNA topology studies, and which have shown promising results when applied to proteins recently. The SKMT smoothing is used to derive empirical bounds on a protein’s entanglement relative to its number of secondary structure elements. We show that large scale helical geometries dominantly account for the maximum growth in entanglement of protein monomers, and further that this large scale helical geometry is present in a large array of proteins, consistent across a number of different protein structure types and sequences. We also show how these bounds can be used to constrain the search space of protein structure prediction from small angle x-ray scattering experiments, a method highly suited to determining the likely structure of proteins in solution where crystal structure or machine learning based predictions often fail to match experimental data. Finally we develop a structural comparison metric based on the SKMT smoothing which is used in one specific case to demonstrate significant structural similarity between Rossmann fold and TIM Barrel proteins, a link which is potentially significant as attempts to engineer the latter have in the past produced the former. We provide the SWRITHE interactive python notebook to calculate these metrics.
Journal Article
Computation of Winding-Based Magnetic Helicity and Magnetic Winding Density for SHARP Magnetograms in Spherical Coordinates
Magnetic helicity has been used widely in the analysis and modelling of solar active regions. However, it is difficult to evaluate and interpret helicity in spherical geometry since coronal magnetic fields are rooted in the photosphere and helicity is susceptible to gauge choices. Recent work extended a geometrical definition of helicity from Cartesian to spherical domains, by interpreting helicity as the average, flux-weighted pairwise winding of magnetic-field lines. In this paper, by adopting the winding-based definition of helicity, we compute helicity and winding in spherical coordinates for SHARP (Spaceweather HMI Active Region Patches) magnetograms. This is compared with results obtained in Cartesian coordinates to quantitatively investigate the effect of spherical geometry. We find that the Cartesian approximations remain mostly valid, but for active regions with large spatial extents or strong field strengths (usually leading to flares and coronal mass ejections) there are significant deviations due to surface curvature that must be accounted for.
Journal Article
Magnetic winding
Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In this article, we give a detailed description of what magnetic winding describes, how to calculate it and how to interpret it in relation to helicity. We show how magnetic winding provides a clear topological description of magnetic fields (open or closed) and we give examples to show how magnetic winding and helicity can behave differently, thus revealing different and important information about the underlying magnetic field.
Journal Article
Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods
We consider a geometrically accurate model for a helically wound rope constructed from two intertwined elastic rods. The line of contact has an arbitrary smooth shape which is obtained under the action of an arbitrary set of applied forces and moments. We discuss the general form the theory should take along with an insight into the necessary geometric or constitutive laws which must be detailed in order for the system to be complete. This includes a number of contact laws for the interaction of the two rods, in order to fit various relevant physical scenarios. This discussion also extends to the boundary and how this composite system can be acted upon by a single moment and force pair. A second strand of inquiry concerns the linear response of an initially helical rope to an arbitrary set of forces and moments. In particular we show that if the rope has the dimensions assumed of a rod in the Kirchhoff rod theory then it can be accurately treated as an isotropic inextensible elastic rod. An important consideration in this demonstration is the possible effect of varying the geometric boundary constraints; it is shown the effect of this choice becomes negligible in this limit in which the rope has dimensions similar to those of a Kirchhoff rod. Finally we derive the bending and twisting coefficients of this effective rod.
Journal Article
Using topology to locate the position where fully three-dimensional reconnection occurs
In two-dimensional magnetic reconnection, involving neutral sheets and magnetic islands it is generally a straightforward task to recognize reconnection sites when detailed data sets or simulations are available. In fully three-dimensional reconnection, their analogues can be challenging to identify. In this study, we demonstrate how locations of high reconnective activity can be detected in highly complex turbulent plasmas. We use a recently developed topological measure of reconnection based on the magnetic winding number, which measures the entanglement of pairs of field lines, to identify sub-regions of magnetic field lines which are reconnecting. This diagnostic is combined with established measures of magnetic field complexity, such as quasi-separatrix layers and regions of high magnetic twisting, to characterize the spatial and temporal distributions of reconnective activity of the field. It is demonstrated that the regions with the highest reconnective activity do not always coincide with the largest QSL signatures are, thus indicating this is a more complete methodology for quantifying reconnective activity than standard methods. This framework can serve as a model for reconnection analysis in future studies, in combination with established methods for identifying the specific form of reconnection once its location is established.
Journal Article
A Brotherhood of Britons? Public Schooling, esprit de corps and Colonial Officials in Africa, c.1900-1939
Historians have tended to suggest that Britain's colonial officials demonstrated an esprit de corps, and that this is testament to the efficacy of public schooling in generating social cohesion. Examining Britain's officials in seven different colonies in sub-Saharan Africa, this article will argue that differences in working conditions, approaches to work and officials' backgrounds, such as conflicts between officials from 'military' and 'civilian' backgrounds, all caused deep fragmentations in the colonial services. Most significantly, officials were irreconcilably torn between a need for company as a means of maintaining morale, and a desire for freedom from the constraints of colonial society. Living in insular communities driven by gossip and marked by the need to keep up appearances for fear of ostracism from their peers, officials felt unable to experience an 'authentic' Africa and live out the romanticized dreams of individualism that had motivated many to leave for Africa in the first place. This sense of feeling trapped bred resentment towards one's fellow officials. Consequently, public schools were unable to surmount other factors in shaping how officials regarded one other.
Journal Article
A Brotherhood of B ritons? Public Schooling, esprit de corps and Colonial Officials in A frica, c .1900–1939
Historians have tended to suggest that Britain's colonial officials demonstrated an esprit de corps , and that this is testament to the efficacy of public schooling in generating social cohesion. Examining Britain's officials in seven different colonies in sub‐Saharan Africa, this article will argue that differences in working conditions, approaches to work and officials' backgrounds, such as conflicts between officials from ‘military’ and ‘civilian’ backgrounds, all caused deep fragmentations in the colonial services. Most significantly, officials were irreconcilably torn between a need for company as a means of maintaining morale, and a desire for freedom from the constraints of colonial society. Living in insular communities driven by gossip and marked by the need to keep up appearances for fear of ostracism from their peers, officials felt unable to experience an ‘authentic’ Africa and live out the romanticized dreams of individualism that had motivated many to leave for Africa in the first place. This sense of feeling trapped bred resentment towards one's fellow officials. Consequently, public schools were unable to surmount other factors in shaping how officials regarded one other.
Journal Article
DEER and RIDME Measurements of the Nitroxide-Spin Labelled Copper-Bound Amine Oxidase Homodimer from Arthrobacter Globiformis
In the study of biological structures, pulse dipolar spectroscopy (PDS) is used to elucidate spin–spin distances at nanometre-scale by measuring dipole–dipole interactions between paramagnetic centres. The PDS methods of Double Electron Electron Resonance (DEER) and Relaxation Induced Dipolar Modulation Enhancement (RIDME) are employed, and their results compared, for the measurement of the dipolar coupling between nitroxide spin labels and copper-II (Cu(II)) paramagnetic centres within the copper amine oxidase from
Arthrobacter globiformis
(AGAO). The distance distribution results obtained indicate that two distinct distances can be measured, with the longer of these at c.a. 5 nm. Conditions for optimising the RIDME experiment such that it may outperform DEER for these long distances are discussed. Modelling methods are used to show that the distances obtained after data analysis are consistent with the structure of AGAO.
Journal Article