Scale invariance in non-equilibrium systems

Täuber, Uwe C.

doi:10.1017/cbo9781139046213.010

Cited by 3 publications

(10 citation statements)

References 242 publications

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“…Our results support the hypothesis that the nerves in the living state are heterogeneous systems far away from thermal equilibrium [13,14], as a generic feature of living matter made of open dissipative systems in a non-equilibrium steady state tuned close to a critical point with typical features of quantum criticality [12]. In fact, near a quantum critical point the structure of living matter would display generic scale invariance and multiscale heterogeneity like critical opalescence [13,14].…”

Section: Discussionsupporting

confidence: 83%

“…Considering the scale of our problem, this is an acceptable average. These results indicate the occurrence of a crystallization-like process in the aged myelin membranes indicative of a transition from a quasi-critical fluctuating state out of equilibrium in the fresh state to a relaxed rigid state with Gaussian distribution approaching equilibrium in the unfresh state, which is in agreement with the hypothesis of criticality for living matter proposed by recent theories [10,[12][13][14][35][36][37].…”

Section: Experimental and Data Analysissupporting

confidence: 90%

“…In fact, near a quantum critical point the structure of living matter would display generic scale invariance and multiscale heterogeneity like critical opalescence [13,14].…”

Section: Discussionmentioning

confidence: 99%

“…As the system moves toward equilibrium, the correlation degree of the disorder is expected to vanish, with the system ending up in an uncorrelated disordered state with Gaussian distribution. The quantitative characterization of the correlated disorder in the functional state is not only of interest for fundamental problems of the physics of life [10][11][12][13][14]36,37], but can open new perspectives, and may have important consequences for the understanding of injury to peripheral nerves and its treatment. This experiment provides a proof of feasibility of studies of statistical physics using scanning micro XRD, opening new perspectives to be explored by further investigations on the dynamics and time evolution of spatial fluctuations of the myelin ultrastructure.…”

Section: Discussionmentioning

confidence: 99%

“…The most significant indicator for proximity to a critical point is critical opalescence, due to the fact that, as the critical point is approached, the sizes of the regions of the two competing phases (ordered and disordered regions) begin to fluctuate over increasingly large length scales [14]. In order to experimentally probe spatial fluctuations in the myelin ultrastructure, there is a need for unique probes that probe the spatial distribution in the real space of the order in the k-space.…”

Section: Introductionmentioning

confidence: 99%

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Correlated Disorder in Myelinated Axons Orientational Geometry and Structure

et al. 2017

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While the ultrastructure of myelin is considered a quasi-crystalline stable system, nowadays its multiscale complex dynamics appear to play a key role in its functionality, degeneration and repair processes following neurological diseases and trauma. In this work, we investigated the fluctuation of the myelin supramolecular assembly by measuring the spatial distribution of orientation fluctuations of axons in a Xenopus Laevis sciatic nerve associated with nerve functionality. To this end, we used scanning micro X-ray diffraction (SµXRD), a non-invasive technique that has already been applied to other heterogeneous systems presenting complex geometries from microscale to nanoscale. We found that the orientation of the spatial fluctuations of fresh axons show a Levy flight distribution, which is a clear indication of correlated disorder. We found that the Levy flight distribution was missing in the aged nerve prepared in an unfresh state. This result shows that the spatial distribution of axon orientation fluctuations in unfresh nerve state loses the correlated disorder and assumes a random disorder behavior. This work provides a deeper understanding of the ultrastructure-function nerve relation and paves the way for the study of other materials and biomaterials using the SµXRD technique to detect fluctuations in their supramolecular structure.

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Section: Discussionsupporting

confidence: 83%

Section: Experimental and Data Analysissupporting

confidence: 90%

“…In fact, near a quantum critical point the structure of living matter would display generic scale invariance and multiscale heterogeneity like critical opalescence [13,14].…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Correlated Disorder in Myelinated Axons Orientational Geometry and Structure

et al. 2017

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Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure

et al. 2017

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Ultrastructural fluctuations at nanoscale are fundamental to assess properties and functionalities of advanced out-of-equilibrium materials. We have taken myelin as a model of supramolecular assembly in out-of-equilibrium living matter. Myelin sheath is a simple stable multilamellar structure of high relevance and impact in biomedicine. Although it is known that myelin has a quasi-crystalline ultrastructure, there is no information on its fluctuations at nanoscale in different states due to limitations of the available standard techniques. To overcome these limitations, we have used scanning micro X-ray diffraction, which is a unique non-invasive probe of both reciprocal and real space to visualize statistical fluctuations of myelin order of the sciatic nerve of Xenopus laevis. The results show that the ultrastructure period of the myelin is stabilized by large anticorrelated fluctuations at nanoscale, between hydrophobic and hydrophilic layers. The ratio between the total thickness of hydrophilic and hydrophobic layers defines the conformational parameter, which describes the different states of myelin. Our key result is that myelin in its out-of-equilibrium functional state fluctuates point-to-point between different conformations showing a correlated disorder described by a Levy distribution. As the system approaches the thermodynamic equilibrium in an aged state, the disorder loses its correlation degree and the structural fluctuation distribution changes to Gaussian. In a denatured state at low pH, it changes to a completely disordered stage. Our results aim to clarify the degradation mechanism in biological systems by associating these states with ultrastructural dynamic fluctuations at nanoscale.

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Myelin Basic Protein dynamics from out-of-equilibrium functional state to degraded state in myelin

Gioacchino

Bianconi

Burghammer

et al. 2019

Preprint

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Living matter is a quasi-stationary out-of-equilibrium system; in this physical condition, structural fluctuations at nano-and meso-scales are needed to understand the physics behind its biological functionality. Myelin has a simple ultrastructure whose fluctuations show correlated disorder in its functional out-of-equilibrium state. However, there is no information on the relationship between this correlated disorder and the dynamics of the intrinsically disordered Myelin Basic Protein (MBP) which is expected to influence the membrane structure and overall functionality. In this work, we have investigated the role of this protein structural dynamics in the myelin ultrastructure fluctuations in and out-of-equilibrium conditions, by using synchrotron Scanning micro X Ray Diffraction and Small Angle X ray Scattering. We have induced the crossover from out-of-equilibrium functional state to in-equilibrium degeneration changing the pH far away from physiological condition. While the observed compression of the cytosolic layer thickness probes the unfolding of the P2 protein and of the cytoplasmic P0 domain (P0 cyt ), the intrinsic large MBP fluctuations preserve the cytosol structure also in the degraded state. Thus, the transition of myelin ultrastructure from correlated to uncorrelated disordered state, is significantly affected by the unfolding of the P2 and P0 proteins, which in this latter state do not act in synergistic manner with MBP to determine the membrane functionality. STATEMENT OF SIGNIFICANCEA better comprehension of myelin degenerative process and the role of protein dynamics in this biological membrane is a topic issue in today's scientific community. The myelin ultrastructural fluctuations exhibit correlated disorder in its functional state, that becomes uncorrelated as it degenerates. In this work we elucidate the interplay of protein structural dynamics and myelin ultrastructure in the transition from its functional state to the degraded state. The results highlight that the intrinsically disordered Myelin Basic Protein (MBP) allows to preserve the myelin structure following both the small correlated fluctuations in physiological state and the large disordered fluctuations in degraded conditions, where the myelin functionality is close to being lost and the MBP remains the single active protein.

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Scale invariance in non-equilibrium systems

Cited by 3 publications

References 242 publications

Correlated Disorder in Myelinated Axons Orientational Geometry and Structure

Correlated Disorder in Myelinated Axons Orientational Geometry and Structure

Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure

Myelin Basic Protein dynamics from out-of-equilibrium functional state to degraded state in myelin

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