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Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool.

ABSTRACT: Understanding the fundamental principles of virus architecture is one of the most important challenges in biology and medicine. Crick and Watson were the first to propose that viruses exhibit symmetry in the organization of their protein containers for reasons of genetic economy. Based on this, Caspar and Klug introduced quasi-equivalence theory to predict the relative locations of the coat proteins within these containers and classified virus structure in terms of T-numbers. Here it is shown that quasi-equivalence is part of a wider set of structural constraints on virus structure. These constraints can be formulated using an extension of the underlying symmetry group and this is demonstrated with a number of case studies. This new concept in virus biology provides for the first time predictive information on the structural constraints on coat protein and genome topography, and reveals a previously unrecognized structural interdependence of the shapes and sizes of different viral components. It opens up the possibility of distinguishing the structures of different viruses with the same T-number, suggesting a refined viral structure classification scheme. It can moreover be used as a basis for models of virus function, e.g. to characterize the start and end configurations of a structural transition important for infection.

SUBMITTER: Keef T

PROVIDER: S-EPMC3571114 | biostudies-literature | 2013 Mar

REPOSITORIES: biostudies-literature

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Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool.

Keef Thomas T Wardman Jessica P JP Ranson Neil A NA Stockley Peter G PG Twarock Reidun R

Acta crystallographica. Section A, Foundations of crystallography 20130108 Pt 2

Understanding the fundamental principles of virus architecture is one of the most important challenges in biology and medicine. Crick and Watson were the first to propose that viruses exhibit symmetry in the organization of their protein containers for reasons of genetic economy. Based on this, Caspar and Klug introduced quasi-equivalence theory to predict the relative locations of the coat proteins within these containers and classified virus structure in terms of T-numbers. Here it is shown th ...[more]

PMID: 23403965

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Project description:Judging the poses, sizes, and shapes of objects accurately is necessary for organisms and machines to operate successfully in the world. Retinal images of three-dimensional objects are mapped by the rules of projective geometry and preserve the invariants of that geometry. Since Plato, it has been debated whether geometry is innate to the human brain, and Poincare and Einstein thought it worth examining whether formal geometry arises from experience with the world. We examine if humans have learned to exploit projective geometry to estimate sizes and aspects of three-dimensional shape that are related to relative lengths and aspect ratios. Numerous studies have examined size invariance as a function of physical distance, which changes scale on the retina. However, it is surprising that possible constancy or inconstancy of relative size seems not to have been investigated for object pose, which changes retinal image size differently along different axes. We show systematic underestimation of length for extents pointing toward or away from the observer, both for static objects and dynamically rotating objects. Observers do correct for projected shortening according to the optimal back-transform, obtained by inverting the projection function, but the correction is inadequate by a multiplicative factor. The clue is provided by the greater underestimation for longer objects, and the observation that they seem to be more slanted toward the observer. Adding a multiplicative factor for perceived slant in the back-transform model provides good fits to the corrections used by observers. We quantify the slant illusion with two different slant matching measurements, and use a dynamic demonstration to show that the slant illusion perceptually dominates length nonrigidity. In biological and mechanical objects, distortions of shape are manifold, and changes in aspect ratio and relative limb sizes are functionally important. Our model shows that observers try to retain invariance of these aspects of shape to three-dimensional rotation by correcting retinal image distortions due to perspective projection, but the corrections can fall short. We discuss how these results imply that humans have internalized particular aspects of projective geometry through evolution or learning, and if humans assume that images are preserving the continuity, collinearity, and convergence invariances of projective geometry, that would simply explain why illusions such as Ames' chair appear cohesive despite being a projection of disjointed elements, and thus supplement the generic viewpoint assumption.

Project description:BackgroundThree-dimensional Surface Imaging (3DSI) is a well-established method to objectively monitor morphological changes in the female breast in the field of plastic surgery. In contrast, in radiation oncology we are still missing effective tools, which can objectively and reproducibly assess and document adverse events in breast cancer radiotherapy within the framework of clinical studies. The aim of the present study was to apply structured-light technology as a non-invasive and objective approach for the documentation of cosmetic outcome and early effects of breast radiotherapy as a proof of principle.MethodsWeekly 3DSI images of patients receiving either conventionally fractionated radiation treatment (CF-RT) or hypofractionated radiation treatment (HF-RT) were acquired during the radiotherapy treatment and clinical follow-up. The portable Artec Eva scanner (Artec 3D Inc., Luxembourg) recorded 3D surface images for the analysis of breast volumes and changes in skin appearance. Statistical analysis compared the impact of the two different fractionation regimens and the differences between the treated and the contralateral healthy breast.ResultsOverall, 38 patients and a total of 214 breast imaging sessions were analysed. Patients receiving CF-RT showed a significantly higher frequency of breast erythema compared to HF-RT (93.3% versus 34.8%, p = 0.003) during all observed imaging sessions. Moreover, we found a statistically significant (p < 0.05) volumetric increase of the treated breast of the entire cohort between baseline (379 ± 196 mL) and follow-up imaging at 3 months (437 ± 224 mL), as well as from week 3 of radiotherapy (391 ± 198 mL) to follow-up imaging. In both subgroups of patients undergoing either CF-RT or HF-RT, there was a statistically significant increase (p < 0.05) in breast volumes between baseline and 3 months follow-up. There were no statistically significant skin or volumetric changes of the untreated healthy breasts.ConclusionsThis is the first study utilizing 3D structured-light technology as a non-invasive and objective approach for the documentation of patients receiving breast radiotherapy. 3DSI offers potential as a non-invasive tool to objectively and precisely monitor the female breast in a radiooncological setting, allowing clinicians to objectively distinguish outcomes of different therapy modalities.

Dataset Information

Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool.

Publications

Structural constraints on the three-dimensional geometry of simple viruses: case studies of a new predictive tool.

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