Glass-forming tendency, percolation of rigidity, and onefold-coordinated atoms in covalent networks

Boolchand, P.; Thorpe, M. F.

doi:10.1103/physrevb.50.10366

Cited by 118 publications

(95 citation statements)

References 14 publications

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“…At each step, singly coordinated atoms are pruned until there are none left, and side groups that do not connect to the rest of the protein via hydrophobic tethers or hydrogen bonds are also removed. This is done because such atoms do not contribute to the rigidity of the protein (32). This procedure allows the results on proteins to be compared directly with those for network glasses, as shown in Figs.…”

Section: Methodsmentioning

confidence: 99%

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Protein unfolding: Rigidity lost

Rader

Hespenheide

Kuhn

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

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We relate the unfolding of a protein to its loss of structural stability or rigidity. Rigidity and flexibility are well defined concepts in mathematics and physics, with a body of theorems and algorithms that have been applied successfully to materials, allowing the constraints in a network to be related to its deformability. Here we simulate the weakening or dilution of the noncovalent bonds during protein unfolding, and identify the emergence of flexible regions as unfolding proceeds. The transition state is determined from the inflection point in the change in the number of independent bond-rotational degrees of freedom (floppy modes) of the protein as its mean atomic coordination decreases. The first derivative of the fraction of floppy modes as a function of mean coordination is similar to the fraction-folded curve for a protein as a function of denaturant concentration or temperature. The second derivative, a specific heat-like quantity, shows a peak around a mean coordination of ͗r͘ ‫؍‬ 2.41 for the 26 diverse proteins we have studied. As the protein denatures, it loses rigidity at the transition state, proceeds to a state where just the initial folding core remains stable, then becomes entirely denatured or flexible. This universal behavior for proteins of diverse architecture, including monomers and oligomers, is analogous to the rigid to floppy phase transition in network glasses. This approach provides a unifying view of the phase transitions of proteins and glasses, and identifies the mean coordination as the relevant structural variable, or reaction coordinate, along the unfolding pathway. Much interest is currently focused on the rapid and faithful folding of proteins from a one-dimensional sequence of amino acids in a random coil, to a three-dimensional biologically functional structure in the native state (1-4). Chemical and thermal denaturation of proteins are standard techniques in protein biochemistry to determine protein folding and unfolding equilibria and kinetics (3,5,6).A general view of protein folding is that it begins with hydrophobic collapse, in which the random coil changes to a compact state, with the hydrophobic groups in the interior region and polar groups at the surface interacting with the surrounding water. The packing is not yet optimal, with hydrophobic groups somewhat free to slide about in the interior of the globule, until residues are locked in place by the formation of specific hydrogen bonds. These hydrogen bonds can be regarded as a sort of Velcro that locks the various structural elements in the folded protein together. Once these interactions are optimized, the native state is predominantly rigid with flexible hinges or loops at the surface-the number and distribution of these depending on the particular protein.There have been many significant theoretical advances in understanding protein folding in recent years-including the concept of a funnel-shaped free-energy landscape (1, 7-9), simplified lattice models that are more tractable for simulations of folding (8, ...

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Section: Methodsmentioning

confidence: 99%

“…This formulation ignores any dangling bonds-i.e., terminal atoms which do not contribute to the global network rigidity (32). Eq.…”

Section: Methodsmentioning

confidence: 99%

Protein unfolding: Rigidity lost

Rader

Hespenheide

Kuhn

et al. 2002

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

261

298

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“…Starting from the local Q 4 and Q 3 units (with respective probabilities 1 − p and p = 2x/(1 − x), the SICA probabilities can be evaluated for different steps of cluster sizes following the procedure described previously and taking into account the 1-fold M cations 52 .…”

Section: Application To Fast Ionic Conductorsmentioning

confidence: 99%

Rings and rigidity transitions in network glasses

2003

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Three elastic phases of covalent networks, (I) floppy, (II) isostatically rigid and (III) stressed-rigid have now been identified in glasses at specific degrees of cross-linking (or chemical composition) both in theory and experiments.Here we use size-increasing cluster combinatorics and constraint counting algorithms to study analytically possible consequences of self-organization. In the presence of small rings that can be locally I, II or III, we obtain two transitions instead of the previously reported single percolative transition at the mean coordination numberr = 2.4, one from a floppy to an isostatic rigid phase, and a second one from an isostatic to a stressed rigid phase. The width of the intermediate phase ∆r and the order of the phase transitions depend on the nature of medium range order (relative ring fractions). We compare the results to the Group IV chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate phase has been obtained, and for which estimates of ring fractions can be made from structures of high T crystalline phases.

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“…As expected and observed in silicate glasses [38], Si atoms are characterized by 4 BS and 5 BB constraints. H atoms show only 1 BS constraint with their nearest O neighbor [43]. On average, Ca atoms undergo 5 BS constraints.…”

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confidence: 99%

Rigidity Transition in Materials: Hardness is Driven by Weak Atomic Constraints

et al. 2015

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Understanding the composition dependence of the hardness in materials is of primary importance for infrastructures and handled devices. Stimulated by the need for stronger protective screens, topological constraint theory has recently been used to predict the hardness in glasses. Herein, we report that the concept of rigidity transition can be extended to a broader range of materials than just glass. We show that hardness depends linearly on the number of angular constraints, which, compared to radial interactions, constitute the weaker ones acting between the atoms. This leads to a predictive model for hardness, generally applicable to any crystalline or glassy material. DOI: 10.1103/PhysRevLett.114.125502 PACS numbers: 62.20.Qp, 31.15.xv, 61.43.−j Rigidity theory [1-4], or topological constraint theory, is a powerful tool for capturing the atomic topology of glasses by reducing their network to mechanical trusses [5]. Following this mechanical analogy, a glass can be flexible, stressed-rigid, or isostatic, if the number of constraints per atom n c , comprising radial bond stretching (BS) and angular bond bending (BB), is lower, higher, or equal to three, the number of degrees of freedom per atom, respectively. Flexible networks show internal degrees of freedom, the floppy modes [6], which allow for local deformations; whereas stressed-rigid ones are completely locked by their high connectivity. In between, by being rigid but free of eigenstress [7], compositions exhibiting an isostatic behavior show some remarkable properties, such as a space-filling tendency [8], very weak aging [9], and anomalous behaviors, such as maximal fracture toughness [10].One of the major successes of this approach is the design of the Gorilla© Glass 3 by Corning©, which was created by atomic-scale modeling before anything had been melted in the lab [11,12]. Indeed, by capturing the chemical details of glasses that are relevant to macroscopic properties while filtering out those that are not, rigidity theory [13][14][15] has been used to predict the composition dependence of hardness, H, which characterizes resistance to permanent deformations under a load. Hence, topological constraint theory is a promising tool for designing stronger materials, which has recently been identified as a "grand challenge" for the future [16][17][18]. Topological constraint theory has also been applied to studying the folding of proteins [19,20]. However, it is still unknown whether it could be applied to a larger range of materials and, consequently, used to predict mechanical properties like hardness from the mere knowledge of composition.Recently, relying on molecular dynamics (MD) simulations, we showed that rigidity concepts could be applied to calcium-silicate-hydrate, ðCaOÞ x ðSiO 2 Þ 1−x−y ðH 2 OÞ y , or C-S-H, the binding phase of concrete [21]. From a topological point of view, C-S-H is a complex material as (1) it contains several chemical components, (2) its structure is anisotropic, inhomogeneous, and partially crystalline [22][23][24][...

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Glass-forming tendency, percolation of rigidity, and onefold-coordinated atoms in covalent networks

Cited by 118 publications

References 14 publications

Protein unfolding: Rigidity lost

Protein unfolding: Rigidity lost

Rings and rigidity transitions in network glasses

Rigidity Transition in Materials: Hardness is Driven by Weak Atomic Constraints

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