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2001. In vitro assembly of Sindbis virus corelike particles from crosslinked dimers of truncated and mutant capsid proteins
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This article cites 30 articles, 9 of which can be accessed free at:
Evolutionary Trace Residues in Noroviruses: Importance in Receptor Binding, Antigenicity, Virion Assembly, and Strain Diversity
, 2004
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Modelling virus selfassembly pathways: Avoiding dynamics using geometric constraint decomposition
 J. Comp. Biol
, 2006
"... We develop a model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular selfassembly occuring in nature and possesses many features that are desirable whi ..."
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We develop a model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular selfassembly occuring in nature and possesses many features that are desirable while engineering selfassembly at the nanoscale. The model uses static geometric and tensegrity constraints to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The goal is to answer focused questions about the structural properties of a successful assembly pathway. Pathways and their properties are carefully defined and computed using computational algebra and geometry, specifically stateofart concepts in geometric constraint decomposition. The model is analyzable and refinable and avoids expensive dynamics. We show that it has a provably tractable and accurate computational simulation and that its predictions are roughly consistent with known information about viral shell assembly. Justifications for mathematical and biochemical assumptions are provided, and comparisons are drawn with other virus assembly models. A method for more conclusive experimental validation involving specific viruses is sketched. Overall, the paper indicates a strong and direct, mutually beneficial interplay between (a) the concepts underlying macromolecular assembly; and (b) a wide variety of established as well as novel concepts from combinatorial and computational algebra, geometry and algebraic complexity. Key words: selfassembly, geometric constraints nanoscience, viral pathway, tractable modeling. 1.
COMBINATORIAL DECOMPOSITION, GENERIC INDEPENDENCE AND ALGEBRAIC COMPLEXITY OF GEOMETRIC CONSTRAINTS SYSTEMS: APPLICATIONS IN BIOLOGY AND ENGINEERING
, 2006
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"... Eppel et al. R000612002R2 2 We examined the extent of renal medullary blood flow (MBF) autoregulation in pentobarbital anesthetized rabbits. Two methods for altering renal arterial pressure (RAP) were compared; the conventional method of graded suprarenal aortic occlusion, and an extracorporeal c ..."
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Eppel et al. R000612002R2 2 We examined the extent of renal medullary blood flow (MBF) autoregulation in pentobarbital anesthetized rabbits. Two methods for altering renal arterial pressure (RAP) were compared; the conventional method of graded suprarenal aortic occlusion, and an extracorporeal circuit that allows RAP to be increased above systemic arterial pressure. Changes in MBF were estimated by laser Doppler flowmetry, which appears to predominantly reflect red cell velocity, rather than flow per se, in the kidney. We compared responses using a dual fiber needle probe held in place by a micromanipulator, with those from a single fiber probe anchored to the renal capsule, to test whether RAPinduced changes in kidney volume confound medullary laser Doppler flux (MLDF) measurements. MLDF responses were similar for both probe types, and both methods for altering RAP. MLDF changed little as RAP was altered from 50 to at least 170 mmHg (24 ± 22 % change). Within the same RAP range, RBF increased by 296 ± 48%. Urine flow and sodium excretion also increased with increasing RAP. Thus, pressure diuresis/natriuresis proceeds in the absence of measurable increases in medullary erythrocyte velocity estimated by laser Doppler flowmetry. These data do not, however, exclude the possibility that MBF is increased with increasing RAP in this model, because vasa recta recruitment may occur.
Tree Orbits under Permutation Group Action: Algorithm, Enumeration and Application to Viral Assembly
, 2009
"... This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the ca ..."
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This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the capsid is modeled by a polyhedron whose facets represent the monomers. The assembly process is modeled by a rooted tree, the leaves representing the facets of the polyhedron, the root representing the assembled polyhedron, and the internal vertices representing intermediate stages of assembly (subsets of facets). Besides its virological motivation, the enumeration of orbits of trees under the action of a finite group is of independent mathematical interest. If G is a finite group acting on a finite set X, then there is a natural induced action of G on the set TX of trees whose leaves are bijectively labeled by the elements of X. If G acts simply on X, then X : = Xn  = n · G, where n is the number of Gorbits in X. The basic combinatorial results in this paper are (1) a formula for the number of orbits of each size in the action of G on TXn, for every n, and (2) a simple algorithm to find the stabilizer of a tree τ ∈ TX in G that runs in linear time and does not need memory in addition to its input tree.
Modeling Virus SelfAssembly Pathways Using Computational Algebra and Geometry
 APPLICATIONS OF COMPUTER ALGEBRA (ACA2004)
, 2004
"... We develop a tractable model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular selfassembly occuring in nature and possesses many features that are d ..."
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We develop a tractable model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular selfassembly occuring in nature and possesses many features that are desirable while engineering selfassembly at the nanoscale. The model uses static geometric constraints to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The goal is to answer focused questions about the structural properties of a successful assembly pathway. Pathways and their
COUNTING AND ENUMERATION OF SELFASSEMBLY PATHWAYS FOR SYMMETRIC MACROMOLECULAR STRUCTURES
"... We consider the problem of explicitly enumerating and counting the assembly pathways by which an icosahedral viral shell forms from identical constituent protein monomers. This poorly understood assembly process is a remarkable example of symmetric macromolecular selfassembly occuring in nature and ..."
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We consider the problem of explicitly enumerating and counting the assembly pathways by which an icosahedral viral shell forms from identical constituent protein monomers. This poorly understood assembly process is a remarkable example of symmetric macromolecular selfassembly occuring in nature and possesses many features that are desirable while engineering selfassembly at the nanoscale. We use the new model of���that employs a static geometric constraint graph to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The model was developed to answer focused questions about the structural properties of the most probable types of successful assembly pathways. Specifically, the model reduces the study of pathway types and their probabilities to the study of the orbits of the automorphism group of the underlying geometric constraint graph, acting on the set of pathways. Since these are highly symmetric polyhedral graphs, it seems a viable approach to explicitly enumerate these orbits and count their sizes. The contribution of this paper is to isolate and simplify the core combinatorial questions, list related work and indicate the advantages of an explicit enumerative approach. 1.
THE INFLUENCE OF SYMMETRY ON THE PROBABILITY OF ASSEMBLY PATHWAYS FOR ICOSAHEDRAL VIRAL SHELLS
"... This paper motivates and sets up the mathematical framework for a new program of investigation: to isolate and clarify the precise influence of symmetry on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable open questions are posed. Besid ..."
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This paper motivates and sets up the mathematical framework for a new program of investigation: to isolate and clarify the precise influence of symmetry on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable open questions are posed. Besides its virology motivation, the topic is of independent mathematical interest for studying constructions of symmetric polyhedra. Preliminary results are presented: a natural, structural classification of subsets of facets of T = 1 polyhedra, based on their stabilizing subgroups of the icosahedral group; and a theorem that uses symmetry to formalize why increasing depth increases the numeracy (and hence probability) of an assembly pathway type (or symmetry class) for a T = 1 viral shell. 1.
Role of Surface Charge Density in NanoparticleTemplated Assembly of Bromovirus Protein Cages
"... n the past few years increased evidence was provided that established symmetric protein cages as a common architectural paradigm of the subcellular world. Intracellularly, protein cages may serve as microreactors, concentrators, or vehicles for metabolites.1 For example, clathrin cages are involv ..."
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n the past few years increased evidence was provided that established symmetric protein cages as a common architectural paradigm of the subcellular world. Intracellularly, protein cages may serve as microreactors, concentrators, or vehicles for metabolites.1 For example, clathrin cages are involved in endocytosis,2 carboxysomes in CO2 fixation,3 and ferritin cages in iron metabolism.4 In all these cases, the cages shield their cargo from the influence of external conditions and provide a controlled microenvironment, which is chemically welldefined by virtue of their regular nature. Protein cages also represent