Understanding the mechanism by which a polypeptide chain thread itself
spontaneously to attain a knotted conformation has been a major challenge in the
field of protein folding. HP0242 is a homodimeric protein from Helicobacter pylori
with intertwined helices to form a unique pseudo-knotted folding topology. A tandem
HP0242 repeat has been constructed to become the first engineered trefoil-knotted
protein. Its small size renders it a model system for computational analyses to
examine its folding and knotting pathways. Here we report a multi-parametric study
on the folding stability and kinetics of a library of HP0242 variants, including the
trefoil-knotted tandem HP0242 repeat, using far-UV circular dichroism and
fluorescence spectroscopy. Equilibrium chemical denaturation of HP0242 variants
shows the presence of highly populated dimeric and structurally heterogeneous
folding intermediates. Such equilibrium folding intermediates retain significant
amount of helical structures except those at the N- and C-terminal regions in the
native structure. Stopped-flow fluorescence measurements of HP0242 variants show
that spontaneous refolding into knotted structures can be achieved within seconds,
which is several orders of magnitude faster than previously observed for other
knotted proteins. Nevertheless, the complex chevron plots indicate that HP0242
variants are prone to misfold into kinetic traps, leading to severely rolled-over
refolding arms. The experimental observations are in general agreement with the
previously reported molecular dynamics simulations. Based on our results, kinetic
folding pathways are proposed to qualitatively describe the complex folding
processes of HP0242 variants

Coluzza, I.

Jackson, S. E.

Micheletti, Cristian

Miller, M. A.

Apollo (Cambridge)

English

Knots in soft condensed matter.

Coluzza, Ivan

Jackson, Sophie E.

Miller, Mark A.

Durham Research Online

Knots in soft condensed matterIvan Coluzza∗, Sophie E. Jackson†, Cristian Micheletti‡, Mark A. Miller§13 July 2015The full potential of fundamental research is sometimes only realised a long time after the work wasinitiated, and may take a form that could not have been predicted at the outset. This has certainly beenthe case for research on the scientific properties of knots. The first systematic tabulations of knottedtopologies were carried out by P. G. Tait [1] in the late nineteenth century, motivated by the long-sinceabandoned vortex theory of atoms [2] due to William Thomson (later created Lord Kelvin). Fortunately,the demise of Thomson’s theory did not deter mathematicians from developing a sophisticated under-standing of the topological properties of knots in their own right (for an accessible introduction, see thebook by Adams [3]). The resulting theoretical framework is now finding applications in a wide rangeof fields in the physical sciences that could not even have been imagined when Tait was carrying out hisseminal investigations.Because of the diversity of sub-disciplines in which knots are playing an increasingly important role,developments in one area are not always communicated to others where they may be relevant. Theaim of this Special Issue of Journal of Physics: Condensed Matter is to promote cross-fertilisation ofideas between research communities by gathering together the latest contributions to some of the majorcontemporary knot-related topics in condensed matter. In a similar spirit, a CECAM workshop entitledKnots in Soft Condensed Matter was held from 10 to 13 September 2014 at the University of Vienna toprovide a forum for direct discussions. Topics represented at the meeting were diverse: linear and ringpolymers, proteins, DNA, liquid crystals, soap films, organic synthesis, magnetohydrodynamics, andtoplogical glasses, as well as matters of more general analysis such as entangled networks and methodsfor loop closure. This issue includes accounts some of the work that was presented at the Vienna meetingbut is not restricted to it.One of the broad themes that emerges from the collection of articles presented here and from theCECAM meeting is a drive to understand how dynamic processes affect, and are affected by knots.Indeed, this Special Issue could almost have been entitled “Knots in action”. While questions of structurecan often be considered in general or abstract terms, it is usually harder to separate questions of dynamicsfrom the physical nature of the system in which they occur. Hence, the consequences of knotted topologyare particularly rich when it comes to dynamic properties, and the manifestation of knots in real physicalsystems can give rise to interesting new phenomena, as illustrated by the articles in this Special Issue.Knotted molecules of various kinds feature strongly in the collection of articles, and the Issue openswith a wide-ranging review by Lim and Jackson [4] on the structure, formation and properties of molec-ular knots, covering DNA, RNA, proteins and synthetic molecular knots.Three of the research articles focus on knots in DNA. Suma et al. [5] use Langevin dynamics sim-ulations to look at spontaneous knot formation in DNA chains confined inside nanochannels of widthcomparable to the DNA persistence length. The study focuses, in particular, on the very different timescales associated with the lifetimes of knotted and unknotted states in DNA chains of different lengths,and relates them to the occurrence of backfolding events at the chain ends. Liu and Chan [6] proposea model for how type-2 topoisomerases might harness local geometrical features or supercoiled DNA∗Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria; ivan.coluzza@univie.ac.at†University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, U.K.; sej13@cam.ac.uk‡SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy; michelet@sissa.it§Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K.; m.a.miller@durham.ac.uk1filaments to carry out the selective strand passages required to control the linking number distribution.Building on their previous work, the authors suggest that the local geometrical clues exploited by thetopoisomerases arise from the geometrical variations of the so-called hooked DNA juxtapositions. Ue-hara and Deguchi [7] use stochastic simulations to sample the equilibrium population of DNA rings andestablish the incidence of knots upon varying both the contour length of the rings and also their thickness(which captures the effective electrostatic screening operated by counterions). The data are used to es-tablish the characteristic length scales that govern the decay of the unknotted population upon increasingchain length at fixed thickness.New work on knotted proteins is presented in five papers, covering both experiments and simula-tions. Chwastyk and Cieplak [8] present a molecular dynamics study of the folding of knotted proteinsusing structure-based potentials. Thanks to the computationally accessible model, they are able to showhow the knot formation probability is enhanced by the simultaneous folding and synthesis of the proteinfrom the ribosome. Wang et al. [9] present an experimental study of the variants of the HP0242 proteinfrom Helicobacter pylori. By employing a variety of spectroscopic tools, the authors have systematicallycharacterised the folding–unfolding transition of HP0242 variants. The analysis of the equilibrium andkinetic properties reveals a complex refolding pathway, that has long-lived intermediates essential forproper folding, but is fast compared to many other known knotted proteins. Haglund [10] discusses theimportance of entangelment stabilised by covalent disulfide bonds in the biological function of singleproteins. The fascinating message is that disulfide bonds act as on/off switches for pierced lasso bundles,not only affecting the state of the protein but also acting as sensors for the reductive power of the cell.Burban et al. [11] present an experimental NMR study of refolding in the minimal tied trefoil protein.The work identifies the role of side-chain contacts, and in particular the influence of proline 62. Re-laxation of this residue from the native-state trans conformation to a cis conformation when denatured,induces strong hysteresis in the unfolding–folding cycle. In a computational study, Dabrowski-Tumanskiet al. [12] pick apart the interactions in the smallest knotted protein (2efv in the Protein Data Bank) todetermine how they affect knotting and folding. The native contact interactions are sufficient for theknotted structure to fold, but an additional subset of “native-like” contacts in the loop region greatlyenhances the kinetics, and certain non-native contacts accelerate the rate still further.Moving away from properties of individual molecules, two articles provide contrasting illustrationsof more collective phenomena that result from knotted topology. Trefz and Virnau [13] use extensivemolecular dynamics simulations to sample the conformational space of ring polymers of different topol-ogy in melts. They examine the scaling properties both of the size of the rings and of their knottedportion. Ravnik et al. [14] consider the defects created by colloidal inclusions in a nematic liquid crystal.In particular, they examine the modifications of the defect lines introduced when the colloidal particleschange their shape and genus, and discuss the observed variety of ensuing complex topologies.On a more abstract note that is relevant to knots in any context, Hyde et al. [15] devise methods forassessing knot complexity by showing how the topology of a knot emerges from the topology of segmentsof the structure as the length of the segment is continuously increased. The resulting fingerprints providea visualisation of fine structure and can be mapped onto a planar graph for further analysis. Although thearticle concentrates on tight knots, the methods can be applied to any closed curve.We hope that this collection of articles will provide a valuable point of reference as research on knotscontinues apace. We are grateful to the editorial board and staff of Journal of Physics: Condensed Matterfor their support in preparing this Special Issue, and we thank all the authors for their contributions.References[1] P. G. Tait. On knots, part II. Trans. Roy. Soc. Edinburgh, 32:318–334, 1884.[2] W. Thomson. On vortex atoms. Philos. Mag. A, 34:15–24, 1867.[3] C. C. Adams. The Knot Book. American Mathematical Society, Providence, 2004.2[4] N. C. H. Lim and S. E. Jackson. Molecular knots in biology and chemistry. J. Phys.: Condens.Matter, 27:364001, 2015.[5] A. Suma, E. Orlandini, and C. Micheletti. Knotting dynamics of DNA chains of different lengthconfined in nanochannels. J. Phys.: Condens. Matter, 27:364002, 2015.[6] Z. Liu and H. S. Chan. Consistent rationalization of type-2 topoisomerases’ unknotting, decatenat-ing, supercoil-relaxing actions and their scaling relation. J. Phys.: Condens. Matter, 27:364003,2015.[7] E. Uehara and T. Deguchi. Characteristic length of the knotting probability revisited. J. Phys.:Condens. Matter, 27:364004, 2015.[8] M. Chwastyk and M. Cieplak. Cotranslational folding of deeply knotted proteins. J. Phys.: Con-dens. Matter, 27:364005, 2015.[9] L.-W. Wang, Y.-N. Liu, P.-C. Lju, S. E. Jackson, and S.-T. D. Hsu. Comparative analysis of the fold-ing dynamics and kinetics of an engineered knotted protein and its variants derived from HP0242of helicobacter pylori. J. Phys.: Condens. Matter, 27:364006, 2015.[10] E. Haglund. Engineering covalent loops in proteins can serve as an on/off switch to regulatethreaded topologies. J. Phys.: Condens. Matter, 27:364007, 2015.[11] D. J. Burban, E. Haglund, D. T. Capraro, and P. A. Jennings. Heterogeneous side chain conforma-tion highlights a network of interactions implicated in hysteresis of the knotted protein, MinimalTied Trefoil (MTTTm). J. Phys.: Condens. Matter, 27:364008, 2015.[12] P. Dabrowski-Tumanski, A. I. Jarmolinska, and J. I. Sułkowska. Prediction of the optimal set ofcontacts to fold the smallest knotted protein. J. Phys.: Condens. Matter, 27:364009, 2015.[13] B. Trefz and P. Virnau. Scaling behavior of topologically constrained polymer rings in a melt. J.Phys.: Condens. Matter, 27:364010, 2015.[14] M. Ravnik, S. Čopar, and S. Žumer. Particles with changeable topology in nematic colloids. J.Phys.: Condens. Matter, 27:364011, 2015.[15] D. A. B. Hyde, J. Henrich, E. J. Rawdon, and K. C. Millett. Knot fingerprints resolve knot com-plexity and knotting pathways in ideal knots. J. Phys.: Condens. Matter, 27:364012, 2015.3

Knots in soft condensed matter

Sissa Digital Library

Knots in soft condensed matter Preface

Jackson, S.E.

Micheletti, C.

Miller, M.A.

SISSA Digital Library

Ivan Coluzza

Sophie E Jackson

Cristian Micheletti

Mark A Miller

Crossref

Journal of Physics Condensed Matter

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Knots in soft condensed matter Preface

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