DNA Looping Mediated by Site-Specific SfiIminusDNA InteractionsSridhar Vemulapalli Mohtadin Hashemi Anatoly B Kolomeisky and Yuri L Lyubchenko

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ABSTRACT Interactions between distant DNA segments playimportant roles in various biological processes such as DNArecombination Certain restriction enzymes create DNA loops whentwo sites are held together and then cleave the DNA DNA looping isimportant during DNA synapsis Here we investigated themechanisms of DNA looping by restriction enzyme SfiI by measuringthe properties of the system at various temperatures Different sizedloop complexes mediated by SfiIminusDNA interactions were visualizedwith AFM The experimental results revealed that small loops aremore favorable compared to other loop sizes at all temperatures Ourtheoretical model found that entropic cost dominates at allconditions which explains the preference for short loopsFurthermore specific loop sizes were predicted as favorable froman energetic point of view These predictions were tested by experiments with transiently assembled SfiI loops on a substrate with asingle SfiI site

INTRODUCTION

ProteinminusDNA interactions are critically important forsupporting the majority of fundamental cellular processessuch as transcription DNA repair and DNA recombina-tion1minus3 Complex topological structures can occur when twospatially distant segments on DNA are brought together byspecialized proteins leading to a site-specific proteinminusDNAsynaptic complex called a synaptosome4minus8 The formation ofthe synaptosome is a general phenomenon during transcrip-tional regulation9 (eg by Lac repressor) site-specificrecombination71011 and various gene rearrangement sys-tems12minus14 Synaptosome formation leads to DNA looping bybringing together spatially distant segments15minus19 The size ofthe loops is determined by a variety of structural and chemicalinteractions between protein and DNA molecules Severaltheoretical models have been proposed to describe the role ofdifferent factors such as DNA length proteinminusDNAinteractions DNA mechanics and geometric factors in theloop formation process20minus24 However the molecular mech-anisms of underlying loop formation processes still remain notwell understood In addition there are a limited number ofexperimental studies that might test these theoretical ideasDouble-stranded DNA (dsDNA) can be characterized as a

semiflexible polymer chain with a persistence length lp ofsim150 bp under typical cellular conditions25minus27 Thepersistence length of dsDNA is important for understandingthe processes that involve the interaction of multiple sites onthe same DNA eg due to different proteins binding tospecific sites on the DNA The parameter lp reflects the abilityof the DNA chain to bend and it depends on several factors

including ionic strength DNA sequence DNA defects andtemperature28minus31 Local kinks in dsDNA lead to higherintrinsic bendability and affect the stability of loops formedby proteins283233 However the microscopic picture of theprotein-mediated loop formation is still not fully understoodSfiI is a type IIF restriction endonuclease that can associate

with two distinct cognate sites SfiI binds to DNA as ahomotetramer and attaches to a recognition sequence of 5prime-GGCCNNNN^NGGCC-3prime where N denotes any base and ^marks the cleavage position before cleavage To cleave theDNA chain SfiI requires magnesium ions as cofactorsreplacing Mg2+ with Ca2+ results in the formation of stableSfiIminusDNA synaptic complexes53435 The interaction betweenthe two cognate sites on the same DNA molecule leads to theformation of looped DNA structures35minus37 These propertiesmake SfiI an ideal system to quantitatively characterize theloop formation process and to elucidate the microscopicfactors that affect this processIn this study we employed atomic force microscopy (AFM)

to directly visualize the SfiIminusDNA synaptic complexes TheDNA used in this work contained three specific SfiIrecognition sites resulting in the formation of DNA loopswith 254 bp 532 bp and 786 bp lengths The assembly of the

Received January 27 2021Revised April 21 2021Published April 29 2021

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httpsdoiorg101021acsjpcb1c00763J Phys Chem B 2021 125 4645minus4653

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looped complexes was monitored at 4 25 and 50 degC A simpletheoretical model based on equilibrium polymer physicsarguments was developed and applied to understand theexperimental observations The probability of the formation ofDNA loops of different sizes is explained by considering free-energy changes during the formation of different proteinminusDNA complexes The comparison with experiments reveals theimportance of entropic factors in the protein-mediated DNAlooping under all experimental conditions Theoreticalpredictions for free-energy profiles of DNA loop formationwere further tested by experiments with a single specificprotein binding site making possible transient loop formationPhysicalminuschemical arguments to explain these observations arepresented

EXPERIMENTAL PROCEDUREMaterials SfiI enzyme SfiI restriction enzyme with low

BSA (20 unitsμL) was purchased from the New EnglandBiolabs (Beverly MA)DNA Substrate Two DNA constructs were used in this

study and were obtained by the PCR of a pUC19 plasmid fromBio Basic (Markham ON CA) which included an 885 bpDNA sequence with three SfiI cognate sequences GGCC-TCGAG-GGCC The SfiI recognition sequence was previouslyproposed as the strongest sequence with high specificity34

Three-SfiI-Site DNA Construct PCR was performed toobtain a final construct of 1036 bp with three SfiI sites andtwo flanks of 113 bp and 98 bp as shown in Figure 1 As

shown in Figure 1 the SfiI sites on the DNA were separated by254 bp between the first and second sites and 532 bp betweenthe second and third sites thus there are 786 bp between thefirst and third sites The PCR product was run on a 1 agarosegel the product bands were excised and DNA was extractedand purified using the Qiagen DNA gel extraction kit (QiagenInc Valencia CA) The final DNA concentration wasdetermined by absorbance at 260 nm using a NanoDropspectrophotometer (NanoDrop Technologies WilmingtonDE) A restriction digest reaction using SfiI and the purifiedDNA was run and characterized on a gel to confirm thepresence of recognition sites shown in Figure S1 Sangersequencing of the DNA was also performed to confirm thepresence of three recognition sites shown in Figure S2Single-SfiI-Site DNA Construct PCR was performed to

obtain a construct of 1036 bp with a single SfiI recognition siteflanked by 925 bp and 98 bp arms shown in Figure S3 ThePCR product was purified and quantified as described aboveThe PCR primers for the three-site construct were the

forward primer 5prime-GGGGATGTGCTGCAAGG-3prime and thereverse primer 5prime-TGTGTGGAATTGTGAGCGG-3prime Theprimers for the single-site construct were the forward primer5prime-ATTCTGAGAATAGTGTATGCGG-3prime and the reverseprimer 5prime-CCAAGCACCAGAAGCC-3prime Primers were de-

signed using SnapGene software (version 52 GSL BiotechChicago IL) and ordered from IDT (Coralville IA)

SfiIminusDNA Synaptosome Assembly The synaptosomeassembly reaction mixture consisted of 1 μL of 10times buffer A[10 mM HEPES (pH 75) 50 mM NaCl 2 mM CaCl2 01mM EDTA] 2 μL of DNA substrate (86 ngμL) 1 μL of 1mM DTT 1 μL of SfiI enzyme and 5 μL of DI water Thereaction mixture was prepared incubated for 15 min at thedesired temperature and diluted through serial dilutions toobtain the final concentration used for AFM The sameprocedure was followed for SfiIminusDNA complex assembly at 425 and 50 degC reagents except SfiI protein were pre-equilibrated at the desired temperature before complexassembly and deposition

SfiIminusDNA Transient Loop Assembly Transient loopassembly was performed at 25 degC with the reaction mixtureconsisting of 1 μL of 10times buffer A 1 μL of 1 mM DTT 1 μLof SfiI enzyme and 2 μL of DI water One μL of the reactionmixture was then mixed with 10 μL of 2 nM DNA andimmediately (lt5 s) used for AFM sample preparation

Atomic Force Microscopy A freshly cleaved mica wasfunctionalized with a 167 μM solution of 1-(3-aminopropyl)-silatrane as described previously3839 Five μL of SfiIminusDNAassembly reaction mixture sample was diluted using 1times bufferA and deposited on the functionalized mica surface incubatedfor 2 min rinsed with DI water and dried with a gentle streamof argon In the case of transient loop assembly 5 μL of thereaction mixture was deposited on the functionalized micasurface incubated for 2 min rinsed with DI water and driedwith a gentle stream of argon A typical image of 1 times 1 μm2

with 512 pixelsline was obtained under ambient conditionswith a MultiMode AFM system (Bruker) using TESPA probes(Bruker Nano Camarillo CA USA)

Data Analysis The contour lengths of the free DNA andthe SfiIminusDNA complexes were measured using the FemtoScansoftware (Advanced Technologies Center Moscow Russia)The contour length measurement of free DNA was performedby tracing a line starting from the one end of the DNAcontinuing along the backbone to the other end (Figure S4) Atotal of N = 500 particles were analyzed a histogram wasassembled and the distribution fit with a single Gaussianfunction The peak was at 1037 plusmn 32 bp (standard deviation)(Figure S5) The conversion factor was obtained by dividingthe mean length of DNA in nanometers with the total lengthin bp (1036 bp) the conversion factor was 0335 A similarprocedure was followed to measure the contour length ofsingle-SfiI-site DNA and obtained the conversion factor(0340) details provided (Figure S6)To measure the loop sizes of the DNAminusSfiI complexes a

line starting from the center of the SfiI tetramer (bright featureon the AFM images Figure 2) along the length of the DNAloop back to the center of the tetramer was drawn andanalyzed as shown in Figure S7 A total of N = 1000 SfiIminusDNA synaptosome complexes were analyzed at each temper-ature Statistical analysis was performed by assembling eachdata set in histograms (bin size of 20 bp) and fitting with amultiple peak Gaussian function Data for each peak plusmn2σ weretabulated and compared using a non-parametric KolmogorovminusSmirnov method40 to determine the significance of change foreach peak at different temperaturesIn the case of transient loop assembly with a single SfiI site

construct a total of N = 250 SfiIminusDNA complexes formingloops (Figure 5A) were analyzed Statistical analysis was

Figure 1 Schematic of the three-SfiI-site DNA construct The SfiIsites are represented as red bars The arm lengths and the intersitedistance between the SfiI sites are given in base pairs

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performed and histograms with a bin size of 20 bp indicatedthe most probable loop size around 300minus400 bp as shown inFigure 5B A total of N = 130 SfiIminusDNA transient loopcomplexes were analyzed to measure the length of the shortflank of the DNA to the center of the tetramer (bright featurein Figure S9) to confirm the position of SfiI the histogram isshown in Figure 5C A single-peak Gaussian function estimatesthe peak at 101 plusmn 9 bp indicating the positioning of SfiI on therecognition site All statistical analysis was performed usingOriginPro (Origin Laboratories Northampton MA)

RESULTSDNA with Three and Single SfiI Sites The final product

of PCR was purified and quantified as described in theExperimental Procedure section The purified DNA was

diluted to 2 nM and deposited on APS-functionalized micabefore being imaged under ambient conditions using AFMThe DNA contour lengths were then measured as shown inFigure S4 for DNA with three SfiI sites shown in Figure 1 thecontour length distribution (N = 500) produced a single peakat 1037 plusmn 32 bp (SD) the fit using a Gaussian function isshown in Figure S5 The single SfiI site construct produced abroad distribution approximated by a single peak curve (N =255) at 1039 plusmn 29 bp (SD) shown in Figure S6 Bothconstructs were in good agreement with the designed lengthand theoretical contour length of 1036 bp

SfiIminusDNA Loop Assembly at Different TemperaturesSfiIminusDNA complex assembly was performed in the presence of2 mM CaCl2 which assembles stable synaptosomes Thecomplex assembly dilution and sample deposition wasperformed at 4 25 and 50 degC Experiments at eachtemperature were repeated three times The looped morphol-ogy of the DNA is clearly seen in Figure 2 As expected threedifferent sized DNA loops with SfiI at the DNA intersectionwere observed Yields of looped complexes were 38 58 and49 for 4 25 and 50 degC respectively the data are shown inTable S1 A total of 1000 particles with a single tetramer at theDNA intersection were analyzed for each temperatureLoop size distributions for each temperature were assembled

in histograms and fitted with multiple peak Gaussian functionspresented in Figure 3 Observed loop sizes at 4 degC Figure 3Aproduce three peaks at 261 plusmn 30 bp (SD) 526 plusmn 58 bp (SD)and 788 plusmn 48 bp respectively At 25 degC Figure 3B the loopsare distributed in three peaks at 259 plusmn 29 bp (SD) 519 plusmn 44bp (SD) and 775 plusmn 52 bp respectively At 50 degC Figure 3Cthe three peaks are at 265 plusmn 33 bp (SD) 539 plusmn 45 bp (SD)and 807 plusmn 62 bp respectively All loop distribution peaksregardless of temperature are close to the expected loop sizesof 254 532 and 786 bp Statistical comparison between thedifferent loops at each temperature was performed and theresults are presented in Table S2 Comparison reveals that thedistributions of all loop sizes at all temperatures aresignificantly different at a minimum of 95 confidenceinterval and in many cases at 999Probability distributions of loops at 4 25 and 50 degC are

shown in Figure S8 The areas under the curve (AUC)corresponding to relative probability for short medium andlong loop size at each temperature are as follows 042 036

Figure 2 A typical 1 times 1 μm2 AFM image of SfiI in complex with thethree-site DNA construct at 50 degC Complexes of different loop sizesare indicated with arrows SfiI tetramers are seen as bright features atthe intersection of DNA

Figure 3 Analysis of SfiIminusDNA loop complexes formed at 4 25 and 50 degC Multiple peak Gaussian fits of the histograms with a bin size of 20 bpproduce three peaks at 261 plusmn 30 bp (SD) 526 plusmn 58 bp (SD) and 788 plusmn 48 bp at 4 degC (A) 259 plusmn 29 bp (SD) 519 plusmn 44 bp (SD) and 775 plusmn 52bp at 25 degC (B) and 265 plusmn 33 bp (SD) 539 plusmn 45 bp (SD) and 807 plusmn 62 bp at 50 degC (C) The blue dotted lines indicate the expected loop sizefor each loop The area under the curve (AUC) for each loop is shown under the respective peak

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022 (4 degC) 044 034 022 (25 degC) and 048 033 019 (50degC) These data are shown in Table 1 We assume that theseareas are proportional to the relative fractions for theoccurrences of the loops Comparing the relative fractions ofdifferent loop sizes shows that the smallest loop 254 bp ismore probable than other possible loop sizes The probabilityof formation of the loops follows the trend 254 bp gt 532 bp gt786 bp across all three temperatures Furthermore the relativefraction of 254 bp loops is more probable with increasedtemperature These experimental results are further discussedand explained by our theoretical analysisTheoretical Analysis of SfiIminusDNA Looping and

Comparison with the Experiment Our theoreticalapproach is based on the application of simple polymer-physics arguments to quantitatively describe the distribution ofdifferent loop sizes obtained at different temperatures Themain assumption is that the system can be described usingequilibrium thermodynamics In other words it is assumedthat experimental measurements have been done for timeintervals long enough so that the observed loop sizes reflect theunderlying equilibrated free-energy landscapes Then the freeenergy of formation of the DNA loop of size n (in units of kT)due to Sfil protein forming the complex can be approximatedas41

= + +G nAn

b n E( ) ln( )(1)

where the first term accounts for the polymer bending energythe second term describes the entropic cost of loop formationand the last term is enthalpic due to the chemical interactionsbetween SfiI and DNA at the intersection The coefficient A isproportional to the bending stiffness and it is given in terms ofthe persistence length lp as

π=A l2 2p (2)

The parameter b is related to the scaling exponent of the radiusof gyration for the ideal polymer chain it is known that b = 32 Since dsDNA is not an ideal polymer larger values of b areexpectedLet us also assume that the enthalpic contributions E are the

same for different loop sizes and that they are weaklydependent on the temperature (in the range of experimentalmeasurements from 4 degC until 50 degC) This is a reasonableassumption since the same chemical interactions are presentfor all different loop sizes when the SfiI protein associates toDNA at both specific sites Further support for this assumptioncomes from the fact that SfiI is a thermophile enzyme and hasbeen shown to cleave in a temperature-independentmanner42minus44 However the stability of the enzyme is alsotemperature-dependent and it might influence the formation ofthe loops Additionally the turnover rate does vary withtemperature42minus44 which can contribute to the yield valuesshown in Table S2

Now the only parameters that depend on the temperatureare the persistence length lp and the entropic contributionparameter b The temperature dependence of the DNApersistence length has recently been accurately measured29

In agreement with theoretical expectations it was foundexperimentally that increasing the temperature lowers thepersistence length29 In other words it is easier to bend theDNA molecule at higher temperaturesOur theoretical analysis is based on the idea that the relative

fractions of different loop sizes f(n) are proportional to theprobabilities of formation of the loops which are determinedby their free energies (more precisely Boltzmann factors) Thelower the free energy of a given conformation the moreprobable it is to observe this conformation in experimentsMore specifically the probability of finding the system in thelooped state of size n can be estimated from

sim =minus

π

minus

ikjjj

yzzz

P nn

( ) eexp

G n

l

n

b( )

2 2p

(3)

Table 1 presents the experimental relative fractions ofdifferent loop sizes at different temperatures and thetemperature-dependent DNA persistent lengths from ref 29It is expected that the differences in these fractions reflect thedifferences in the probability of formation of DNA loops Thisallows us to employ these data in eqs 1 2 and 3 in order toquantify what factors are governing the formation of theprotein-mediated DNA loops More specifically the ratio ofrelative fractions for any two DNA loop sizes can be associatedwith the underlying free-energy landscape via

π= = minusikjjjjj

yzzzzz

Auml

Ccedil

AringAringAringAringAringAringAringAringAringAringikjjjjj

yzzzzz

Eacute

Ouml

NtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildeNtildef nf n

P nP n

nn

ln n

( )( )

( )( )

exp 21 1

b1

2

1

2

2

1

2p

2 1 (4)

We can now analyze the data using eqs 3 and 4 for everytemperature assuming that the parameter b(T) is unknownand can be used as a fitting parameter It is shown then that basymp 90 at 4 degC b asymp 85 for 25 degC (room temperature) and b asymp63 for 50 degC One can see that the entropic contribution startsto decrease with an increase in the temperature This agreeswith expectations that increasing T should bring DNAmolecules closer to being ideal polymer chains because theyare getting more flexible Higher temperatures weakenhydrogen and other secondary structure bonds that hold theDNA molecule together This should also stimulate theappearance of more DNA defects and it will make DNAmore bendable However the amplitudes for the parameter bfrom the fitting procedures are higher than expected fornonideal polymer chains (15 lt b lt 18)Now let us estimate the free energies of the looped

configurations at different temperatures using the expressionfrom eq 1 The results are presented in Table 2 Note that to

Table 1 Fractions of Looped DNA Conformations from Experimental Measurementsa

loop size 4 degC 25 degC 50 degC

short 042 plusmn 0005 (SE) 044 plusmn 0012 (SE) 048 plusmn 002 (SE)medium 036 plusmn 0006 (SE) 034 plusmn 0012 (SE) 033 plusmn 002 (SE)long 022 plusmn 0012 (SE) 022 plusmn 0012 (SE) 019 plusmn 000 (SE)persistence length lp in bpb 160 144 108

aProbabilities are given plusmn standard error bExperimentally measured DNA persistence lengths obtained from ref 29

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understand the distribution of loop sizes only the relativevalues of the free energies are needed

One can see that the entropic contributions dominate theformation of DNA loops at all temperatures In our theoreticalanalysis they are always significantly larger than the bendingcontributions The entropic term domination is stronger forlonger loops while for shorter loops the bending contributionsstart to catch up For a fixed temperature increasing the DNAloop size lowers the bending energy but it also increases theentropic term This result is expected because to create a largerDNA loop requires less bending An increase in the entropicfree-energy term however is observed for longer loopsbecause of the stronger decrease in the allowed degrees offreedom for longer loops in comparison with the free polymerAt the same time for the fixed loop size the increase in thetemperature simultaneously lowers both the bending and theentropic contributions to the overall free energies of thesystem For the bending term it is clearly associated with thedecrease in the persistence length while for the entropic termit is related with the fact that the entropy decrease due tolooping is smaller at higher temperaturesAssuming that our approximate description of the free-

energy cost of looping (eq 1) provides a reasonable descriptionof the process using the fitted values of the parameter b we canconstruct the overall free-energy profiles for the looped DNAconfigurations The results are presented in Figure 4 for threedifferent temperatures We predict that while the short loops(300minus350 bp) are the most probable the larger loops can stillbe observed (although with a smaller probability) due to arelatively slow increase in the entropic contribution as afunction of the size [simln(n)] Note also that very short loops(lt100 bp) have a much lower probability to be observedbecause of the strong increase in the bending energy for smallnTransient SfiIminusDNA Looping on Single-SfiI-Site DNA

One of the specific conclusions of our theory is that loops withsizes of 300minus350 bp are the most probable species in thelooped assemblies under given experimental conditions To

test this theoretical prediction we investigated the formationof transient loops formed by SfiI bound to a specific andnonspecific site In these experiments DNA of the same lengthbut containing a single SfiI recognition site was designed Ouridea is that the loop sizes are determined by bending andentropic contributions to the free energy and they are notdependent on specific enthalpic interactions This means thatthe distribution of transiently formed loops with nonspecificprotein interactions also should follow the free-energy profilespredicted by our theoretical argumentsThe SfiI site was located at 98 bp from one end of the DNA

and 925 bp from the other (Figure S3) SfiI binds thisrecognition site and probes other parts of the DNA in the sitesearch process forming transient loops that are unstable due toa low affinity of SfiI to nonspecific sites To detect suchtransient states of SfiI stabilized loops DNA was mixed withSfiI for a short period of time (5 s) and rapidly prepared for theAFM imaging This procedure allowed us to minimize theformation of stable bimolecular trans complexes held togetherby SfiI bound to specific sites on two DNA molecules Arepresentative image is shown in Figure 5A in which thelooped structure is indicated with a wide arrow Linear DNAmolecules with SfiI bound are indicated with ldquo1rdquo and the transbimolecular complex is indicated with ldquo2rdquo A total of 250looped SfiIminusDNA complexes with a single tetramer at theDNA intersection (highlighted in Figure 5A) were analyzedMore examples of the transient loops are shown in Figure S9The length distribution for the short flank of the looped

structures is narrow with the maximum 101 plusmn 9 (SD) bpshown in Figure 5C which coincides with the position of theSfiI binding site so transient loops are formed between theprotein bound to a specific site and another nonspecific DNAsequence The histogram of the size distribution of the loops ispresented in Figure 5B The distribution is asymmetric withmost of the transient loops being between 300 and 400 bpwhich is very close to the predicted range of the most favorableloop size of 300minus350 (Figure 4) The asymmetry of thehistogram with sharp decay toward short loops is alsoconsistent with our theoretical predictions (Figure 4)

DISCUSSION

The direct measurement of DNA loops formed by SfiIrestriction enzyme allowed us to characterize the effect of sizeand temperature on the assembly of SfiIminusDNA loops Thisprovided the information to clarify microscopic features ofprotein-mediated DNA loop formation The specific details areoutlined in the following paragraphs

Table 2 Estimated Free Energies (in kT Units) from eq 1

4 degC 4 degC 25 degC 25 degC 50 degC 50 degC

loop size bending entropic bending entropic bending entropic

short 124 498 112 471 84 346medium 59 565 53 534 40 392long 40 600 36 567 27 417

Figure 4 Graphs for the free-energy cost of looping G(n) as a function of n for three different temperatures from eq 1 at 4 degC (A) 25 degC (B) and50 degC (C) For all calculations E = minus20 is assumed

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Loops of 254 bp Are Predominant at All Temper-atures Our experimental results suggest that the smallest loop(254 bp) is the most probable outcome in the SfiI-mediatedDNA loop formation for all temperatures At first this is asurprising observation since this loop size is only slightly largerthan the persistence length (lp = 160 bp at 4 degC) and bendingcontributions to the free energy are expected to be significantHowever the entropic cost of making short loops is not aslarge as that for the longer loops Our theoretical analysissuggests that entropic factors are the biggest contributors inthe free energy and they effectively determine the probabilityof the formation of loops of different sizes The smallestentropic changes are predicted for short loops and this fullyagrees with our experimental observations Increasing the DNAloop size at a given temperature lowers the bendingcontribution to the free energy4546 as expected from eq 1but this effect is fully compensated by the increase in theentropic cost of the loop formation (see Table 2) As a resultour theoretical model predicts that short loops should beobserved most frequently under all conditions and this agreeswith experimental observations

Our data suggest that SfiI prefers the formation of relativelyshort DNA loops However making very short loops(comparable or smaller than the persistence length) will notbe a favorable process because the bending energy will be toohigh This is illustrated in Figure 4 We predict that there is aspecific size of the loop that will be the most favorable from anenergetic point of view For all temperatures the loops withsizes of 300minus350 bp are expected to be the dominantpopulation (see Figure 4) Note also that although the shortloops are preferred we could simultaneously observe the loopsof much larger sizes although with a smaller frequency Onecould speculate that the parameters of this system areoptimized in the following way so that the range of possibleloop sizes can be reached and this allows the system to bemore flexible Interestingly the theoretical prediction of thespecific size of loops favorable from an energetic point of viewmatches with our experimental results with a single SfiIrecognition site construct as shown in Figure 5B This gives anadditional support to our approximate description of the free-energy cost for the formation of DNA loops

Figure 5 Transient loops for SfiIminusDNA complexes at 25 degC (A) A typical 1 times 1 μm2 AFM image of transient SfiIminusDNA loops assembled usingDNA with a single SfiI site A looped structure is indicated with a wide arrow Linear DNA molecules with SfiI bound are indicated with ldquo1rdquo andthe trans bimolecular complex is indicated with ldquo2rdquo (B) Distribution of loop sizes observed for N = 250 transient loops at 25 degC The blue dottedlines indicate the region of the predominant loops predicted by the theory (C) The single peak Gaussian fit of histograms gives a peak at 101 plusmn 9bp (SD) indicating the positioning of SfiI is close to 98 bp (indicated by the dotted line) the expected position Statistical analysis was performedusing OriginPro (Origin Laboratories MA)

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Temperature Dependence of the DNA Loop For-mation As shown in Figure 2 three different loop sizes (254bp 532 bp and 784 bp) can be simultaneously observed in ourexperimental system However the frequency of finding theloops of different sizes is not the same because of the differentfree energies of the proteinminusDNA looped conformations Asdiscussed above the short loops are preferred in the systemdue to the high entropic cost of making loops of larger sizesTable 1 quantifies this effect by presenting the relative fractionsof different-size loops at various temperatures At 4 degC theshort loop is the most probable ( f = 042) and increasing thetemperature makes the short loop even more preferred ( f =048 at 50 degC) Interestingly the relative fractions of mediumsize (532 bp) and long size (784 bp) loops show a non-monotonic behavior as a function of the temperature At 4 degCthe relative fraction of the loops with the medium size is f =036 and it drops to f = 034 at 25 degC however increasing thetemperature further decreases the fraction of the medium loopsto f = 033 The trend is also observed for long loops startingfrom f = 022 at 4 degC it remains at f = 022 at 25 degC beforelowering to f = 019 at 50 degC This is the consequence of thefree-energy changes for each loop size when the temperatureincreases Lowering of the bending energy for larger loop sizesis not equally compensated by the increase in the entropic cost(see Table 2)Table 2 presents our theoretical estimates (from eq 1) for

the free-energy contributions of the loop formation One cansee that entropic terms are always larger than the bendingcontributions For short loops the entropic term is 40minus41times larger than the bending energy while for medium loopsthis ratio increases to 96minus98 times and becomes even largerfor long loops increasing to 150minus154 times the bendingenergy These results clearly show that the entropic cost ofcreating DNA loops dominates the overall process anddetermines which loop sizes will be observed in the systemOne could also notice that both bending and entropic termsdecrease with an increase in temperature with the effect beingslightly stronger for the bending than for the entropiccontributionNature of Entropic Contributions Although the semi-

phenomenological expression given in eq 1 seems to describethe experimental observations reasonably well it is importantto note that it relies on the simplified assumption that only twotypes of energies contribute to the free-energy landscapebending and entropic factors While the bending energies wereestimated from known results about the DNA persistencelength in assigning the energy of the entropic term theparameter b was fitted However the fact that this parameter isof the order 6minus9 instead of the expected 15minus18 frompolymer physics arguments suggests a more complex pictureof proteinminusDNA interactions in the system that are not fullyaccounted for by eq 1 It seems that there are additionalstabilizing interactions (beyond the simple loop entropyarguments) when the protein brings together two distinctDNA segments which are also probably dependent on theloop size It could be that when the short loops are formed theenthalpic interactions between the protein and DNA arestronger while for longer loops it might be weaker Severalfactors might contribute to this including steric and electro-static effects It is expected that atomic details of the proteinmolecule forming a loop while associated with two differentsegments of DNA which are not yet available will help to

understand the microscopic picture for these additionalinteractions

CONCLUSIONSInteractions between SfiI proteins and DNA are investigatedusing a combination of experimental and theoretical methodsIt was shown that DNA loops of different sizes can besimultaneously observed at several temperatures although withdifferent probabilities To quantify the differences in therelative fractions of loop sizes a polymer-physics-based simpletheoretical model was developed We found that short loopsare preferred under all experimental conditions and theseobservations are explained by the domination of entropicfactors during the loop formation Increasing the temperaturemakes short loops even more probable while the relativecontributions of medium and long loops decrease with thetemperature It is argued that making the long loops leads to alarger decrease in the degrees of freedom for the DNAmolecules and this explains the dominating contributions ofthe entropic factors in the protein-mediated loop formationWe also speculate that the parameters of the system areoptimized in such a way so that a large range of loop sizes canbe created allowing the protein to efficiently function undercellular conditions this assumption was verified usingexperiments with transiently formed loops assembled by asingle-recognition-site construct At the same time our analysissuggests that there are additional stabilizing proteinminusDNAinteractions which might depend on the loop size

ASSOCIATED CONTENTsı Supporting InformationThe Supporting Information is available free of charge athttpspubsacsorgdoi101021acsjpcb1c00763

A detailed description of the restriction digest reactionwith SfiI Sanger sequencing data of the three-SfiI-siteconstruct schematic of the single-recognition-siteconstruct description of contour length measurementcontour length histogram for three-site DNA contourlength histogram for single-site DNA loop sizemeasurement description transient SfiIminusDNA loopingon the single-site construct along with a histogram offlanking arm length measurements to determine the SfiIposition (PDF)

AUTHOR INFORMATIONCorresponding Authors

Anatoly B Kolomeisky minus Department of Chemistry-MS60Rice University Houston Texas 77005-1892 United Statesorcidorg0000-0001-5677-6690 Phone 713-348-5672

Email tolyariceeduYuri L Lyubchenko minus Department of PharmaceuticalSciences College of Pharmacy University of NebraskaMedical Center Omaha Nebraska 68198-6025 UnitedStates orcidorg0000-0001-9721-8302 Phone 402-559-1971 Email ylyubchenkounmcedu

AuthorsSridhar Vemulapalli minus Department of PharmaceuticalSciences College of Pharmacy University of NebraskaMedical Center Omaha Nebraska 68198-6025 UnitedStates

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Mohtadin Hashemi minus Department of Pharmaceutical SciencesCollege of Pharmacy University of Nebraska Medical CenterOmaha Nebraska 68198-6025 United States orcidorg0000-0003-2698-9761

Complete contact information is available athttpspubsacsorg101021acsjpcb1c00763

Author ContributionsYLL and ABK designed the project SV and MHperformed the AFM experiments and data analysis ABKprovided the theoretical model All authors contributed towriting the manuscript

NotesThe authors declare no competing financial interest

ACKNOWLEDGMENTS

This work was supported by NSF grant MCB- 19410491941106 to YLL ABK acknowledges the support from theWelch Foundation (C-1559) from the NSF (CHE-1953453and MCB-1941106) and from the Center for TheoreticalBiological Physics sponsored by the NSF (PHY-2019745) Wethank L Shlyakhtenko (University of Nebraska MedicalCenter) for useful insights and all of the YLL lab membersfor their fruitful discussions The authors thank Tommy DStormberg (University of Nebraska Medical Center) forproofreading the manuscript The UNMC Genomics CoreFacility receives partial support from the NIGMS INBRE -P20GM103427-19 as well as the NCI center grant for Fred ampPamela Buffett Cancer Center - P30CA036727

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