An Independent Meeting held at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K., 3–7 September 2012, as part of the Isaac Newton
Institute Programme Topological Dynamics in the Physical and Biological Sciences (16 July–21 December 2012). Organized and Edited by Andrew Bates
(University of Liverpool, U.K.), Dorothy Buck (Imperial College London, U.K.), Sarah Harris (University of Leeds, U.K.), Andrzej Stasiak (University of Lausanne,
Switzerland) and De Witt Sumners (Florida State University, U.S.A.).
Topological Aspects of DNA Function and Protein
Folding
Andrzej Stasiak*1 , Andrew D. Bates†, Dorothy E. Buck‡, Sarah A. Harris§ and De Witt Sumners
*Center for Integrative Genomics, Faculty of Biology and Medicine, University of Lausanne, CH-1015 Lausanne, Switzerland, †Institute of Integrative Biology,
University of Liverpool, Liverpool L69 7ZB, U.K., ‡Department of Mathematics, Imperial College, London SW7 2AZ, U.K., §School of Physics and Astronomy,
University of Leeds, Leeds LS2 9JT, U.K., and Department of Mathematics, Florida State University, Tallahassee, FL 32306, U.S.A.
Abstract
The Topological Aspects of DNA Function and Protein Folding international meeting provided an
interdisciplinary forum for biological scientists, physicists and mathematicians to discuss recent
developments in the application of topology to the study of DNA and protein structure. It had 111 invited
participants, 48 talks and 21 posters. The present article discusses the importance of topology and introduces
the articles from the meeting’s speakers.
The structure and function of DNA and proteins are affected
by the topology of the DNA strands or polypeptide chains
respectively. During DNA replication, transcription or recombination, DNA molecules become supercoiled, knotted
or catenated (linked). These processes are dynamic and
are modulated by the activity of site-specific recombinases,
which break double-stranded DNA at specific locations, and
re-assort and rejoin the ends, and DNA topoisomerases,
which permit intra- or inter-molecular strand passages by
mechanisms also involving the breaking and rejoining of
the DNA backbone. The transient DNA breaks induced by
topoisomerases have made them a fruitful target for cytotoxic
antibacterial and anti-tumour drugs. Recent structural and
biochemical studies have elucidated many mechanistic details
of both topoisomerases and recombinases.
Although supercoiling, knotting and catenation have been
intensively studied for over 40 years, the realization that
proteins can also be knotted dates back just one decade. The
number of known proteins that form knots in their native
structure is growing, and we are beginning to understand
Key words: catenane, chromatin, chromosome, DNA, knot, protein folding, recombinase,
supercoiling, topoisomerase.
1
To whom correspondence should be addressed (andrzej.stasiak@unil.ch).
Biochem. Soc. Trans. (2013) 41, 491–493; doi:10.1042/BST20130006
how knotted proteins can fold and the potential structural
advantages of knotted proteins.
Subjects covered included: (i) modelling of DNA molecules subject to topological constraints; (ii) mechanism of
action of DNA topoisomerases; (iii) DNA recombination and
its mechanisms; (iv) chromosomal architecture; (v) folding
mechanisms of knotted proteins; and (vi) function of knots
in proteins.
The 30 reviews written by speakers from the workshop
very well describe the scope of the subjects discussed.
These reviews also illustrate the interesting connections
between the topology of biopolymers and their structure and
function.
The paramount examples of complex topological structures are DNA knots, such as those formed during sitespecific recombination. Characterization of these knots
has allowed researchers to dissect the mechanistic details
of various site-specific recombinases. Reviews by Sean
Colloms [1] and by Ian Grainge [2] explain how site-specific
recombination systems responsible for the monomerization
of bacterial plasmids and of bacterial chromosomes act. Isabel
Darcy and Mariel Vazquez [3] describe so-called difference
topology experiments that characterize DNA knots in order
to deduce the architecture of the recombination protein–
DNA complexes responsible for their formation.
C The
Authors Journal compilation
C 2013
Biochemical Society
Topological Aspects of DNA Function and Protein Folding
Topological Aspects of DNA Function
and Protein Folding
491
492
Biochemical Society Transactions (2013) Volume 41, part 2
Figure 1 Workshop participants
DNA knots form very efficiently when DNA molecules
are highly crowded, as in the case of bacteriophage heads.
Peter Virnau et al. [4] review what we know about knotting of
DNA in phage heads and explain a nontrivial chain stiffness
effect on the probability of forming knots under spherical
confinement.
Christine Soteros and Michael Szafron [5] address the
interesting question of topoisomerase-mediated preferential
unknotting and show, using a modelling approach, that
if DNA topoisomerases were able to select DNA–DNA
juxtapositions of a specific geometry, this would result in
preferential unknotting.
Another manifestation of DNA topology is DNA
supercoiling. Jorge Schvartzman et al. [6] review the interplay
between DNA supercoiling and DNA knotting during
ongoing replication of bacterial chromosomes. The role of
DNA supercoiling and a variety of DNA-binding proteins
in the overall control of gene expression in bacterial
chromosomes is reviewed by Charles Dorman [7], whereas
Andrew Travers and Georgi Muskhelisvili [8] discuss how
DNA supercoiling shapes chromosome organization in
prokaryotic and eukaryotic cells. Makkuni Jayaram et al.
[9] review the similarity between partitioning loci in yeast
plasmids and chromosomes while discussing the unusual
positive supercoiling that can be detected in the centromeric
region. DNA supercoiling is also a subject of two reviews:
Tony Maxwell and colleagues [10] discuss how small DNA
circles are affected by DNA supercoiling and present results
of atomistic simulations of supercoiled DNA minicircles, and
David Swigon et al. [11] present studies of DNA supercoiling
using simulations based on Kirchhoff rod theory.
One of the consequences of DNA negative supercoiling is
DNA melting, which can also be induced by DNA stretching,
as reviewed by Andreas Hanke [12].
The extent of negative supercoiling in bacterial cells is
controlled by the opposing actions of DNA gyrase, which
introduces negative supercoiling, and topoisomerase I,
which relaxes it. Alfonso Mondragón and colleagues [13]
review single-molecule studies of DNA relaxation by
topoisomerase I and a second type I topoisomerase, topo
III, which is optimized to decatenate DNA and may have a
role in resolving other unusual DNA structures.
C The
C 2013 Biochemical Society
Authors Journal compilation A further aspect of DNA topology is the formation of
DNA loops. Thermodynamics of DNA loop formation is
reviewed by Stephen Levene et al. [14], whereas Wilma Olson
et al. [15] discuss simulations of the role of proteins that are
implicated in the formation of DNA loops. Chris Brackley
et al. [16] review how formation of DNA and chromatin
loops affect recognition of target sequences by DNA-binding
proteins.
How linear or circular polymers (such as DNA) are
affected by confinement to nanochannels is reviewed by
Zusana Benková and Peter Cifra [17], whereas Arturo Narros
González et al. [18] discuss how knotted ring polymers
interact with each other at high concentration.
Chromatin organization from the level of oligonucleosome
fragments to entire chromosomal territories is subject to
yet another aspect of DNA topology, so-called topological
exclusion. Topological exclusion signifies that approaching
chromatin segments cannot pass freely through one other.
Rosana Collepardo-Guevara and Tamar Schlick [19] review
the structure and dynamics of chromatin fibres at the level
of the 30 nm fibre. Angelo Rosa [20] and Mario Nicodemi
and colleagues [21] review and present results explaining the
known large-scale behaviour of chromatin fibres forming
chromosome territories.
Knotting and topology of proteins constituted the second
leading subject (beside DNA) of our workshop. Kenneth
Millett et al. [22] review how knots in linear chains such as
proteins can be unambiguously detected and characterized.
Eric Rawdon et al. [23] discuss a matrix representation of protein structure that facilitates the analysis of whether a given
protein forms a knot, and also the location of the knotted core
on the linear chain. It also allows comparison of the knotted
character of related proteins. Joanna Sułkowska et al. [24]
review mechanisms of protein knotting. Piotr Szymczak [25]
discusses the consequences of protein knotting for proteins
that need to be translocated through mitochondrial pores.
Marek Cieplak and Mateusz Sikora [26] discuss how topology
of proteins affects their stretching resistance. Alexander
Kister and Vladimir Potapov [27] review several protein
structure prediction methods and outline a novel method.
As our workshop was interdisciplinary and grouped mathematicians and biologists, we finish with three mathematical
Topological Aspects of DNA Function and Protein Folding
papers that are, however, clearly related to biology. Piotr
Sułkowski and colleagues [28] review the enumeration of
RNA complexes with various topologies/structures. Greg
Chirkijan [29] reviews how to describe mathematically
the local and global geometry of DNA helices forming a
knot. Mariel Vazquez and colleagues [30] expose a problem
in standard tables of knots in which enantiomorphs of
chiral knots are placed somewhat haphazardly. This problem
complicates the interpretation of biological experiments in
which DNA knots were formed. The solution to the problem
is proposed.
In conclusion, this was a highly successful interdisciplinary workshop. Posters were displayed during the entire
conference, and the journal Nucleic Acids Research provided
prizes for the outstanding posters. The two winners of Nucleic
Acids Research student poster prizes at our workshop were
Thana Sutthibutpong from the University of Leeds for his
poster, ‘A molecular dynamics study on DNA minicircles’,
and Karin Valencia from Imperial College London for her
poster, ‘Models of site-specific recombination and genomewide rearrangements in ciliates’. The participants enjoyed
an outstanding conference dinner at Christ’s College on the
evening of 5 September 2012.
Open for Business events form part of the Isaac Newton
Institute’s mission to foster links between academic research
and the business world. The aim is to bring together academic
researchers in the mathematical sciences with industrial,
commercial and government organizations and individuals to
enable formal and informal discussion and networking. Keith
Moffatt organized a follow-on Open for Business event to
our workshop on 18 September 2012 at the Newton Institute:
‘Open for Business: Maths Meets Molecular Biology’. Some
key results from the workshop were reported by Dorothy
Buck, De Witt Sumners and Lynn Zechiedrich. These talks
were followed by keynote lectures from Chris Dobson,
Master of St John’s College, and Greg Winter, Master-elect of
Trinity College, Cambridge.
Acknowledgements
We thank the Isaac Newton Institute for Mathematical Sciences for
sponsoring and hosting the workshop. We also thank the Biochemical Society for co-sponsorship. We especially thank Professor Keith
Moffatt for the initial idea to organize this workshop and for his
constant support. We acknowledge the great help of the staff of
the Isaac Newton Institute and the Biochemical Society for all of the
support we benefited from. We thank all speakers and participants
that contributed to the scientific success of our workshop. We are
grateful to all the authors for their timely reviews and we thank Ed
Elloway and his colleagues at Portland Press Ltd for preparing the
papers to be published in Biochemical Society Transactions.
2 Grainge, I. (2013) Simple topology: FtsK-directed recombination at the
dif site. Biochem. Soc. Trans. 41, 595–600
3 Darcy, I.K. and Vazquez, M. (2013) Determining the topology of stable
protein–DNA complexes. Biochem. Soc. Trans. 41, 601–605
4 Virnau, P., Rieger, F.C. and Reith, D. (2013) Influence of chain stiffness on
knottedness in single polymers. Biochem. Soc. Trans. 41, 528–532
5 Soteros, C. and Szafron, M. (2013) Crossing-sign discrimination and knot
reduction for a lattice model of strand passage. Biochem. Soc. Trans. 41,
576–581
6 Schvartzman, J.B., Martı́nez-Robles, M.-L, Hernández, P. and Krimer, D.B.
(2013) The benefit of DNA supercoiling during replication. Biochem. Soc.
Trans. 41, 646–651
7 Dorman, C.J. (2013) Co-operative roles for DNA supercoiling and
nucleoid-associated proteins in the regulation of bacterial transcription.
Biochem. Soc. Trans. 41, 542–547
8 Travers, A.A. and Muskhelishvili, G. (2013) DNA thermodynamics shape
chromosome organization and topology. Biochem. Soc. Trans. 41,
548–553
9 Jayaram, M., Chang, K.-M., Ma, C.-H., Huang, C.-C., Liu, Y.-T. and Sau, S.
(2013) Topological similarity between the 2μm plasmid partitioning
locus and the budding yeast centromere: evidence for a common
evolutionary origin? Biochem. Soc. Trans. 41, 501–507
10 Bates, A.D., Noy, A., Piperakis, M.M., Harris, S.A. and Maxwell, A. (2013)
Small DNA circles as probes of DNA topology. Biochem. Soc. Trans. 41,
565–570
11 Swigon, D., Lim, S. and Kim, Y. (2013) Dynamical simulations of DNA
supercoiling and compression. Biochem. Soc. Trans. 41, 554–558
12 Hanke, A. (2013) Denaturation transition of stretched DNA. Biochem.
Soc. Trans. 41, 639–645
13 Terekhova, K., Marko, J.F. and Mondragón, A. (2013) Studies of bacterial
topoisomerases I and III at the single-molecule level. Biochem. Soc.
Trans. 41, 571–575
14 Levene, S.D., Giovan, S.M., Hanke, A. and Shoura, M.J. (2013) The
thermodynamics of DNA loop formation, from J to Z. Biochem. Soc.
Trans. 41, 513–518
15 Olson, W.K., Grosner, M.A., Czapla, L. and Swigon, D. (2013) Structural
insights into the role of architectural proteins in DNA looping deduced
from computer simulations. Biochem. Soc. Trans. 41, 559–564
16 Brackley, C.A., Cates, M.E. and Marenduzzo, D. (2013) Effect of DNA
conformation on facilitated diffusion. Biochem. Soc. Trans. 41, 582–588
17 Benková, Z. and Cifra, P. (2013) Comparison of linear and ring DNA
macromolecules moderately and strongly confined in nanochannels.
Biochem. Soc. Trans. 41, 625–629
18 Narros, A., Moreno, A.J. and Likos, C.N. (2013) Effective interactions of
knotted ring polymers. Biochem. Soc. Trans. 41, 630–634
19 Collepardo-Guevara, R. and Schlick, T. (2013) Insights into chromatin
fibre structure by in vitro and in silico single-molecule stretching
experiments. Biochem. Soc. Trans. 41, 494–500
20 Rosa, A. (2013) Topological constraints and chromosome organization in
eukaryotes: a physical point of view. Biochem. Soc. Trans. 41, 612–615
21 Barbieri, M., Chotalia, M., Fraser, J., Lavitas, L.-M., Dostie, J., Pombo, A.
and Nicodemi, M. (2013) A model of the large-scale organization of
chromatin. Biochem. Soc. Trans. 41, 508–512
22 Millett, K.C., Rawdon, E.J., Stasiak, A. and Sułkowska, J.I. (2013)
Identifying knots in proteins. Biochem. Soc. Trans. 41, 533–537
23 Rawdon, E.J., Millett, K.C., Sułkowska, J.I. and Stasiak, A. (2013) Knot
localization in proteins. Biochem. Soc. Trans. 41, 538–541
24 Sułkowska, J.I., Noel, J.K., Ramı́rez-Sarmiento, C.A., Rawdon, E.J., Millett,
K.C. and Onuchic, J.N. (2013) Knotting pathways in proteins. Biochem.
Soc. Trans. 41, 523–527
25 Szymczak, P. (2013) Tight knots in proteins: can they block the
mitochondrial pores? Biochem. Soc. Trans. 41, 620–624
26 Cieplak, M. and Sikora, M. (2013) Topological features in stretching of
proteins. Biochem. Soc. Trans. 41, 519–522
27 Kister, A. and Potapov, V. (2013) Amino acid distribution rules predict
protein fold. Biochem. Soc. Trans. 41, 616–619
28 Andersen, J.E., Chekhov, L.O., Penner, R.C., Reidys, C.M. and Sułkowski, P.
(2013) Enumeration of RNA complexes via random matrix theory.
Biochem. Soc. Trans. 41, 652–655
29 Chirikjian, G. (2013) Framed curves and knotted DNA. Biochem. Soc.
Trans. 41, 635–638
30 Brasher, R., Scharein, R.G. and Vazquez, M. (2013) New biologically
motivated knot table. Biochem. Soc. Trans. 41, 606–611
References
1 Colloms, S.D. (2013) The topology of plasmid-monomerizing Xer
site-specific recombination. Biochem. Soc. Trans. 41, 589–594
Received 24 January 2013
doi:10.1042/BST20130006
C The
C 2013 Biochemical Society
Authors Journal compilation 493