Intrinsically disordered proteins often form dynamic complexes with their ligands. Yet, the speed and amplitude of these motions are hidden in classical binding kinetics. Here, we directly measure the dynamics in an exceptionally mobile, high-affinity complex. We show that the disordered tail of the cell adhesion protein E-cadherin dynamically samples a large surface area of the protooncogene β-catenin. Single-molecule experiments and molecular simulations resolve these motions with high resolution in space and time. Contacts break and form within hundreds of microseconds without a dissociation of the complex. The energy landscape of this complex is rugged with many small barriers (3 to 4 k B T ) and reconciles specificity, high affinity, and extreme disorder. A few persistent contacts provide specificity, whereas unspecific interactions boost affinity.
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Experimental observations of fractal landscape dynamics in a dense emulsion
Many soft and biological materials display so-called ‘soft glassy’ dynamics; their constituents undergo
anomalous random motions and complex cooperative rearrangements. A recent simulation model of one
soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the
system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that
the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably
quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For
a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively
reproduces the high-dimensional fractal geometry of the configuration path and its associated local energy
minima generated using a computational model. That geometry in turn drives the droplets’ complex random
motion observed in real space. Our results indicate that experimental studies can elucidate whether the
similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.
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- PAR ID:
- 10536730
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 19
- Issue:
- 35
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 6805 to 6813
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Glasses have the interesting feature of being neither integrable nor fully chaotic. They thermalize quickly within a subspace but thermalize much more slowly across the full space due to high free energy barriers which partition the configuration space into sectors. Past works have examined the Rosenzweig-Porter (RP) model as a minimal quantum model which transitions from localized to chaotic behavior. In this work we generalize the RP model in such a way that it becomes a minimal model which transitions from glassy to chaotic behavior, which we term the “Block Rosenzweig-Porter” (BRP) model. We calculate the spectral form factors of both models at all timescales larger than the inverse spectral width. Whereas the RP model exhibits a crossover from localized to ergodic behavior at the Thouless timescale, the new BRP model instead crosses over from glassy to fully chaotic behavior, as seen by a change in the steepness of the ramp of the spectral form factor.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D3SM00852E
