Geometric frustration in the myosin superlattice of vertebrate muscle

Geometric frustration results from an incompatibility between minimum energy arrangements and the geometry of a system, and gives rise to interesting and novel phenomena. Here, we report geometric frustration in a native biological macromolecular system---vertebrate muscle. We analyse the disorder in the myosin filament rotations in the myofibrils of vertebrate striated (skeletal and cardiac) muscle, as seen in thin-section electron micrographs, and show that the distribution of rotations corresponds to an archetypical geometrically frustrated system---the triangular Ising antiferromagnet. Spatial correlations are evident out to at least six lattice spacings. The results demonstrate that geometric frustration can drive the development of structure in complex biological systems, and may have implications for the nature of the actin--myosin interactions involved in muscle contraction. Identification of the distribution of myosin filament rotations with an Ising model allows the extensive results on the latter to be applied to this system. It shows how local interactions (between adjacent myosin filaments) can determine long-range order and, conversely, how observations of long-range order (such as patterns seen in electron micrographs) can be used to estimate the energetics of these local interactions. Furthermore, since diffraction by a disordered system is a function of the second-order statistics, the derived correlations allow more accurate diffraction calculations, which can aid in interpretation of X-ray diffraction data from muscle specimens for structural analysis.

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Faculty Opinions recommendation of Long-range order from local interactions: organization and development of distributed cortical networks.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.733479170.793547406 ◽

2018 ◽

Author(s):

Geoffrey Goodhill ◽

Lilach Avitan

Keyword(s):

Long Range ◽

Range Order ◽

Long Range Order ◽

Cortical Networks ◽

Local Interactions

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Co-existence of long-range order and spin fluctuation in a new geometric frustration series M2(OH)3Cl

Journal of Magnetism and Magnetic Materials ◽

10.1016/j.jmmm.2006.10.442 ◽

2007 ◽

Vol 310 (2) ◽

pp. 1288-1290 ◽

Cited By ~ 6

Author(s):

X.G. Zheng ◽

Masato Hagihala ◽

Takato Toriyi

Keyword(s):

Long Range ◽

Spin Fluctuation ◽

Range Order ◽

Long Range Order ◽

Geometric Frustration

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Faculty Opinions recommendation of NMR characterization of long-range order in intrinsically disordered proteins.

Faculty Opinions – Post-Publication Peer Review of the Biomedical Literature ◽

10.3410/f.3453958.5169057 ◽

2010 ◽

Author(s):

Vladimir Uversky ◽

Bin Xue

Keyword(s):

Long Range ◽

Intrinsically Disordered Proteins ◽

Range Order ◽

Disordered Proteins ◽

Long Range Order ◽

Intrinsically Disordered ◽

Nmr Characterization

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Superfluidity and Superconductivity

10.1093/oso/9780198791942.003.0013 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Magnetic Field ◽

Wave Function ◽

Wave Packet ◽

Long Range ◽

Cooper Pair ◽

Bose Condensation ◽

Range Order ◽

Condensed State ◽

Long Range Order ◽

Coherent Wave

Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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Frustration, ring exchange, and the absence of long-range order in EtMe3Sb[Pd(dmit)2]2 : From first principles to many-body theory

Physical Review Materials ◽

10.1103/physrevmaterials.4.044403 ◽

2020 ◽

Vol 4 (4) ◽

Author(s):

E. P. Kenny ◽

G. David ◽

N. Ferré ◽

A. C. Jacko ◽

B. J. Powell

Keyword(s):

Long Range ◽

First Principles ◽

Range Order ◽

Long Range Order ◽

Many Body ◽

Many Body Theory ◽

Ring Exchange ◽

Body Theory

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Time-Resolved, Laser-Induced Phase Transformation in Aluminum

MRS Proceedings ◽

10.1557/proc-35-87 ◽

1984 ◽

Vol 35 ◽

Cited By ~ 4

Author(s):

S. Williamson ◽

G. Mourou ◽

J.C.M. Li

Keyword(s):

Point Defect ◽

Long Range ◽

Rapid Heating ◽

Range Order ◽

Nucleation Theory ◽

Long Range Order ◽

Time Resolved ◽

Aluminum Films ◽

Thin Aluminum ◽

Initial Nucleus

ABSTRACTThe technique of picosecond electron diffraction is used to time resolve the laser-induced melting of thin aluminum films. It is observed that under rapid heating conditions, the long range order of the lattice subsists for lattice temperatures well above the equilibrium point, indicative of superheating. This superheating can be verified by directly measuring the lattice temperature. The collapse time of the long range order is measured and found to vary from 20 ps to several nanoseconds according to the degree of superheating. Two interpretations of the delayed melting are offered, based on the conventional nucleation and point defect theories. While the nucleation theory provides an initial nucleus size and concentration for melting to occur, the point defect theory offers a possible explanation for how the nuclei are originally formed.

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