The last years have witnessed remarkable advances in our understanding of the emergence
and consequences of topological constraints in biological and soft matter. Examples
are abundant in relation to (bio)polymeric systems and range from the characterization
of knots in single polymers and proteins to that of whole chromosomes
and polymer melts. At the same time, considerable advances have been made in the
description of the interplay between topological and physical properties in complex
fluids, with the development of techniques that now allow researchers to control
the formation of and interaction between defects in diverse classes of liquid crystals.
Thanks to technological progress and the integration of experiments with increasingly
sophisticated numerical simulations, topological biological and soft matter is a vibrant
area of research attracting scientists from a broad range of disciplines. However, owing
to the high degree of specialization of modern science, many results have remained
confined to their own particular fields, with different jargon making it difficult for researchers
to share ideas and work together towards a comprehensive view of the diverse
phenomena at play. Compelled by these motivations, here we present a comprehensive
overview of topological effects in systems ranging from DNA and genome organization to
entangled proteins, polymeric materials, liquid crystals, and theoretical physics, with the
intention of reducing the barriers between different fields of soft matter and biophysics.
Particular care has been taken in providing a coherent formal introduction to the
topological properties of polymers and of continuum materials and in highlighting the
underlying common aspects concerning the emergence, characterization, and effects of
topological objects in different systems. The second half of the review is dedicated
to the presentation of the latest results in selected problems, specifically, the effects
of topological constraints on the viscoelastic properties of polymeric materials; their
relation with genome organization; a discussion on the emergence and possible effects
of knots and other entanglements in proteins; the emergence and effects of topological
defects and solitons in complex fluids.
This review is dedicated to the memory of Marek Cieplak.
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The protein folding rate and the geometry and topology of the native state
Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state.
more » « less- PAR ID:
- 10381802
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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