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 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 site-specific recombination. Characterization of these knots has allowed researchers to dissect the mechanistic details of various site-specific recombinases. Reviews by Sean Colloms  and by Ian Grainge  explain how site-specific recombination systems responsible for the monomerization of bacterial plasmids and of bacterial chromosomes act. Isabel Darcy and Mariel Vazquez  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.
DNA knots form very efficiently when DNA molecules are highly crowded, as in the case of bacteriophage heads. Peter Virnau et al.  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  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.  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 , whereas Andrew Travers and Georgi Muskhelisvili  discuss how DNA supercoiling shapes chromosome organization in prokaryotic and eukaryotic cells. Makkuni Jayaram et al.  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  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.  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 .
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  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.
A further aspect of DNA topology is the formation of DNA loops. Thermodynamics of DNA loop formation is reviewed by Stephen Levene et al. , whereas Wilma Olson et al.  discuss simulations of the role of proteins that are implicated in the formation of DNA loops. Chris Brackley et al.  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 , whereas Arturo Narros González et al.  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  review the structure and dynamics of chromatin fibres at the level of the 30 nm fibre. Angelo Rosa  and Mario Nicodemi and colleagues  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.  review how knots in linear chains such as proteins can be unambiguously detected and characterized. Eric Rawdon et al.  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.  review mechanisms of protein knotting. Piotr Szymczak  discusses the consequences of protein knotting for proteins that need to be translocated through mitochondrial pores. Marek Cieplak and Mateusz Sikora  discuss how topology of proteins affects their stretching resistance. Alexander Kister and Vladimir Potapov  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 papers that are, however, clearly related to biology. Piotr Sułkowski and colleagues  review the enumeration of RNA complexes with various topologies/structures. Greg Chirkijan  reviews how to describe mathematically the local and global geometry of DNA helices forming a knot. Mariel Vazquez and colleagues  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 genome-wide 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.
Topological Aspects of DNA Function and Protein Folding: 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.).
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.