it consists of two anti - parallel , complementary strands governed by base - pairing that follow a right - handed helical path about a central axis ( fig . this double helical structure presents an elegant solution to self - replication , but it also introduces a unique problem . dna - based processes , such as replication , repair , recombination , and transcription , would have to overcome the topological constraints inherent in intertwined strands . to understand the many implications of such constraint , we first need to define a basic terminology for dna topology . ( a ) the relaxed state of the dna double helix consists of ~10 bp per helical turn ( center ) . when dna - based processes exert torsional force on the dna , it manifests as a change in twist or formation of writhe . ( b ) the nucleosome is composed of a left - handed wrapped dna around an octameric core . ( d ) molecular structure of psoralen ( top ) , tri - methyl psoralen ( tmp ) ( middle ) , and biotin - tmp ( bottom ) ( e ) tmp intercalates into the dna double - strand and forms monoadducts and interstrand crosslinks under uv light . one complete helical turn of dna about the central axis consists of ~10 base pairs . in topological terms , this is called the linking number ( lk ) , properly defined as the number of times the double - stranded dna rotates around the axis in the right - handed direction . therefore , a 20 bp fragment has a lk of 2 . in a relaxed dna molecule , lk is equal to the number of times the two strands wind around each other , which is called the twist ( tw ) . however , when the dna is not relaxed , it can lead to altered tw , or to coiling of the double strand about itself , resulting in formation of writhe ( wr ) ( fig .  1a ) . the relationship between these three topological properties , lk , tw , and wr , is summarized by the following equation : lk = tw + wr . for closed , circular dna of a given length where rotation can not dissipate , this equation describes the direct relationship between linking number and the dynamic properties of twist and writhe . although eukaryotic dna is not circular , the basic principle largely applies because the genome is divided into large regions with fixed ends that prevent free rotation , giving rise to supercoiling domains . instead of absolute numbers , the relationship becomes relative such that lk = tw + wr . this equation suggests that when torsional force causes a change in lk , it manifests as a change in tw or a compensatory change in wr , which is often referred to as supercoiling . torsional force can result in over - twisting or under - twisting , forming positive or negative supercoiling , respectively ( fig . as an added complexity , eukaryotic dna is packaged into chromatin by wrapping 147 bp of dna around eight histone proteins in a left - handed direction ( fig . the left - handed wrap of dna around the nucleosome introduces negative wr , thus forming constrained supercoiling . the structure of the nucleosome implies an intricate connection with dna topology . in vitro , negatively supercoiled dna templates readily form nucleosomes whereas positive supercoiling inhibits nucleosome formation , suggesting that torsional events generated in vivo would have a profound impact on nucleosome structure and chromatin organization ( fig . , we discuss how dna topology is altered and managed within the cell , how we detect supercoiling states in vivo , and how generation of torsional stress , particularly during transcription , can re - organize chromatin structure , destabilize nucleosomes , feed back into pol ii regulation , and affect the affinity of other dna - binding proteins . polymerases , in particular , are powerful torsion - generating motors . for example , during replication , the mcm helicase unwinds the two strands for use as templates by dna polymerase , which synthesizes the new copy . this unwinding event alters tw and generates positive torsional stress ahead of the replication fork . similarly , during transcription , the rna polymerase ii ( pol ii ) machinery melts the promoter to access the transcription start site ( tss ) . furthermore , as pol ii transcribes , the melted dna bubble travels downstream , creating positive supercoiling ahead and negative supercoiling behind pol ii . this transcription - generated torsional effect is better known as the twin - supercoil domain model . the amount of torsional stress that pol ii generates can be inferred from single molecule experiments of bacterial rnap , which shows that rnap generates sufficient torque to distort dna structure of arbitrary sequence . modeling of supercoil dynamics reveals that supercoils propagate from pol ii at a rate of two orders of magnitude faster than the rate of pol ii itself in either 1d diffusion along the dna or by a  hopping  mechanism . although transcription - generated supercoiling constraints are not additive , if left unresolved , subsequent transcription events genome - wide would generate a significant amount of strain on dna structure . generates constrained negative supercoiling . another chromatin - based process that generates torsion occurs during mitosis where atp - dependent condensins generate positive supercoiling when condensing chromosomes . for example , in vitro , the binding of the general transcription factor tbp induces negative supercoiling . in yeast , indeed , many components of the transcription machinery complex promote dna looping of promoter sequence with enhancer regions often mediated by structural proteins such as cohesins and ctcf . the ubiquity of torsion - generating processes poses a great risk for dna damage unless torsion is relieved . therefore , the activity of topoisomerases , enzymes that relieve torsional strain , is critical to cell survival . virtually all life forms contain topoisomerases , including certain viruses , and the high degree of conservation across eukaryotes underlies their significance . indeed , many antibiotics and anti - cancer drugs inhibit topoisomerases to effect cell death . their primary function is to change dna lk through cleavage , torsion relief , and religation . there are two main types of topoisomerases as classified by the mode of dna cleavage . type i topoisomerases ( topo i ) cleave one strand of the double helix whereas type ii topoisomerases ( topo ii ) cleave both strands . although the end result of torsional relief is the same , the two types appear to have distinct and redundant functions within the cell ( table 1 ) ( see ref . after cleaving one strand , the primary class of topo i in eukaryotes swivels one end of the broken strand around the intact strand . topo i is essential for viability in drosophila with a critical role in all proliferating tissues , suggesting a function in dna replication . in fission yeast , topo i is also required for nucleosome disassembly through its interaction with the nucleosome remodeler hrp1 . topo i , however , is most studied for its role as the primary reliever of transcription - generated torsional stress . it localizes to transcribed genes , has a preference for relieving positive supercoiling , and interacts with the pol ii c - terminal domain ( ctd ) , suggesting that topo i acts on gene bodies ahead of pol ii during active transcription . in addition to its action during elongation , topo i has also been shown to regulate other steps in the transcription process . during initiation , topo i facilitates the binding of tfiid - tfiia to form the pre - initiation complex . furthermore , genes containing a paused pol ii are hypersensitive to topo i inhibition , suggesting that topo i may also function in pol ii pause release . in contrast to topo i , topo ii is the main  writhase  of eukaryotic cells . it generates double - strand breaks on one dna segment to create a gate and translocates another intact double - stranded segment through that gate . aside from its writhase functions , topo ii also has the ability to decatenate sister chromatids during dna replication and cell division as it toggles between writhase and decatenase functions . this toggle may be driven by the condensin - induced positive supercoiling , or by the tension on dna as spindle forces pull on each sister chromatid . topo ii is more effective at relieving superhelical tension in nucleosomal templates than topo i , and in both drosophila and humans , it interacts with chromatin remodeling factors chrac and acf , suggesting a functional role in chromatin remodeling . during transcription , topo ii has a largely secondary role to topo i , mainly acting on promoters of highly transcribed genes . it has also been shown to bind at the 3 end of genes , which , together with its function as a chromatin regulator , may indicate a role in dna looping . the efficiency and redundancy of these enzymes seem to suggest that unconstrained supercoiling is largely absent within cells . however , recent advances in detecting supercoiling in vivo reveal that dna topology is highly dynamic and well regulated . several biochemical techniques are available to detect the effects of torsion on dna . for example , excision and circularization of a dna segments using cre recombinase can trap supercoils ex vivo . however , to examine torsional effects in vivo , most methods rely on the basic properties of the molecule psoralen and its derivative tri - methyl psoralen ( tmp ) . 1d ) is a member of furocoumarins , a group of naturally occurring compounds in certain plant seeds that can freely cross lipid membranes and intercalate between the two strands of the dna double helix . it has a preference for negatively supercoiled dna , and when exposed to uv light , forms monoadducts and interstrand crosslinks between thymine residues ( fig . taking advantage of this crosslinking property , several groups have used psoralen derivatives to map negatively supercoiled dna in bacteria , yeast , 
 drosophila , and human cells . for example , one group used a biotin - conjugated tmp ( btmp ) to pull - down btmp crosslinked dna fragments . another group enriched for tmp - crosslinked fragments by thermally denaturing all dna fragments followed by gel electrophoresis . tmp - crosslinked fragments snap back into the double stranded form upon denaturation , and migrate slower in a gel . in the yeast study , the authors enriched for double - stranded crosslinks by a combination of denaturation and digestion with exo i , a single - strand specific exonuclease . the tmp - crosslinked fragments re - nature efficiently and are thus protected from exo i digestion . in all three variations , the crosslinked fragment was used as template for producing labeled probes to hybridize in microarrays , generating a global view of supercoiling states in yeast and human cells with varying resolution levels ( table 2 ) . to achieve a higher degree of resolution applying this method to drosophila s2 cells , we observed high and low tmp crosslinking upstream and downstream , respectively , of tsss . furthermore , consistent with the twin - supercoil domain model , expressed genes were found to experience more torsional strain relative to silent genes ( fig . this torsional strain was exacerbated upon topoisomerase inhibition . specifically , topo i inhibition resulted in a greater change in supercoiling relative to topo ii ( fig . 2b ) , providing further evidence that topo i is the major relaxer of transcription - generated torsional strain . inhibition of topo ii primarily altered the supercoiling states of the highest expressed genes , also consistent with its role as a secondary relaxer when topo i is outpaced by the rate of transcription . indeed , topo ii is primarily localized at highly transcribed genes whereas topo i is present in most genes . figure  2 . transcribed gene regions experience torsional stress ( a ) method for mapping dna supercoiling genome - wide using next - generation sequencing . ( i ) following exo i - enrichment of crosslinked strands , illumina paired - end ( pe ) adapters were ligated . ( ii ) lambda exonuclease ( exo  ) was used to resect the 5 strand until the crosslinking site . ( iii ) using a primer complementary to pe adapters , several rounds of primer extension were performed . ( iv ) the single - stranded products were appended with ribo - gs at the 3 ends using terminal transferase , ( v ) followed by ligation with a double - stranded pe adaptor with a ccc overhang . ( vi ) after a single round of primer extension to generate a double - stranded fragment , the products were amplified using pe sequencing primers . sequencing from the ccc overhang allowed for the precise mapping of tmp - crosslinked sites throughout the whole genome . ( b ) genes in drosophila genome were split as expressed ( top ) or silent ( bottom ) . high - resolution genome - wide maps of tmp crosslinking surrounding the transcription start site ( tss ) and transcription end site ( tes ) are shown under normal conditions ( black ) , topo i inhibition ( orange ) , and topo ii inhibition ( teal ) . expressed genes experience higher torsional stress , consistent with the twin - supercoil domain model . we have discussed how nucleosome assembly and chromosome condensation generate torsional stress , but , in a feedback manner , torsion can also affect chromatin structure and organization , despite the structural plasticity of chromatin fibers during torsional stress . in one study , the authors delineated large - scale supercoiling domains in human chromosome 11 with a median size of 100 kb that are dependent on transcriptional activity . furthermore , the authors found that chromatin of underwound domains are more de - compacted than those of overwound domains . regions of chromatin compaction , similar to supercoiling domains , are dependent on transcriptional activation . from these data , the authors proposed a model whereby transcription - generated supercoiling domains regulate chromatin compaction and organization . this is consistent with another study , which showed that large - scale chromatin movements are dependent on polymerases and topo ii , further implicating torsion in chromatin structure and dynamics . single molecule studies indicate that increased dna torsion facilitates rapid h2a - h2b dimer exchange , further suggesting that dna torsion mediates nucleosome structure and stability . we recently showed that in vivo , when topoisomerases are inhibited , the resulting accumulation of torsional strain results in increased nucleosome turnover within gene bodies . nucleosome turnover is also dependent on transcription , as pol ii inhibition results in decreased nucleosome turnover for transcribed genes . when topoisomerases are inhibited , genes that experience the highest change in torsion also have the highest increase in nucleosome turnover ( fig . in contrast , genes that change the least in torsion also change the least in nucleosome turnover ( fig . genes were grouped based on change in torsional stress as measured by change in tmp crosslinking before and after topo i or ii inhibition . the highest ( high td ) and lowest ( low td ) 20% of genes are shown . for these two groups , the change in nucleosome turnover ( a ) , the change in pol ii pausing ( b ) , and the change in pol ii elongation as measured by nascent rna production ( c ) are plotted for regions surrounding the tss . indeed , one of the earliest indications of this relationship is that inhibition of both types of topoisomerases leads to an effective block of transcription of ribosomal genes in budding yeast . recently , we showed that inhibition of individual topoisomerases affect specific aspects of pol ii kinetics . upon topo i or ii inhibition , pol ii pausing downstream of the tss increased dramatically for all genes , although genes that experienced a greater change in torsional stress showed a greater increase in paused pol ii ( fig . whereas a previous study has shown that genes regulated by a paused pol ii are more sensitive to topo i inhibition , this result suggests that torsional relief by topoisomerases affects the kinetics of pol ii initiation and/or release from pause site . topo i inhibition affected pol ii elongation , as measured by nascent rna production , much more strongly than topo ii inhibition ( fig . 3c ) , consistent with previous studies . surprisingly , topo i inhibition resulted in increased pol ii elongation , particularly in genes that experienced the most change in torsional stress . one possible explanation for this result is that the increase in nucleosome destabilization due to the accumulation of torsion transiently allows pol ii to proceed a short distance . some evidence also suggests that dna supercoiling affects the affinity of dna - binding proteins . for example , local melting of the c - myc promoter due to pol ii - generated negative supercoiling facilitates the binding of activators and repressors . dna topology also influences the binding affinity of the tumor suppressor p53 . in our recent study , we examined the effects of topoisomerase inhibition on the affinity of dna binding proteins as measured by low - salt extraction . low salt preferentially extracts euchromatic nucleosomes , but has also been used to map binding of sequence - specific and general transcription factors . using this technique , we observed a strong peak of binding at the tss , representing a cumulative view of dna - binding proteins at the tsss of all genes ( fig . topo i or topo ii inhibition did not affect the averaged pattern of binding at the tss ( fig . however , when the changes in binding were examined on a gene - by - gene basis using a heatmap , we observed variegated changes in binding due to topoisomerase inhibition ( fig .  4b ) . when we performed unbiased k - means clustering with k = 2 , we detected two main groups of genes ( fig . group 1 showed increased binding at the tss whereas group 2 showed strong decrease in binding . furthermore , genes in group 2 following topo i inhibition strongly overlapped with those in group 2 of topo ii - inhibited samples ( fig . 4d ) , suggesting that tf binding at the tss of these genes is hypersensitive to torsional stress . gene ontology analysis of group 2 genes showed enrichment for ribosomal constituents and dna binding proteins ( fig . these data suggest that the torsional state of dna affects the affinity of dna binding factors on some promoter regions . ( a ) micrococcal nuclease digested chromatin is extracted using low salt and sequenced using the paired - end illumina platform . reads were parsed computationally by size , with short fragments representing sites for dna binding protein . the global pattern of short fragments from low - salt extraction of chromatin is analyzed for all genes surrounding the tss before and after topo i or ii inhibition . ( b ) the change in short fragments after topo i ( left ) or ii ( right ) inhibition relative to control is displayed as a heat map for all genes arranged by expression level in untreated cells . ( c ) unbiased k - means clustering of ( b ) with k = 2 . ( d ) venn diagram of group 2 genes in topo i ( orange ) and topo ii ( teal ) inhibited samples . however , these constraints were generally overlooked in investigation of mechanisms behind many cellular processes such as dna replication , transcription , and chromatin organization , because of the use of unconstrained dna templates . now , newly developed methods to study dna topology in vivo have revealed the importance of dna structural dynamics . as most dna - based processes generate torsional stress , the resulting dna strain in turn affects the same processes . this relationship creates a feedback loop based on dna topology , with topoisomerases acting as regulatory modulators to fine - tune dna structure .
the double helical structure of dna lends itself to topological constraints . 
 many dna - based processes alter the topological state of dna , generating torsional stress , which is efficiently relieved by topoisomerases . 
 maintaining this topological balance is crucial to cell survival , as excessive torsional strain risks dna damage . here , we review the mechanisms that generate and modulate dna torsion within the cell . 
 in particular , we discuss how transcription - generated torsional stress affects pol ii kinetics and chromatin dynamics , highlighting an emerging role of dna torsion as a feedback mediator of torsion - generating processes .