Effects of long DNA folding and small RNA stem–loopin thermophoresisYusuke T. Maedaa,b,c, Tsvi Tlustyd,e, and Albert Libchabera,e,1

aCenter for Studies in Physics and Biology, The Rockefeller University, New York, NY 10065; bThe Hakubi Center for Advanced Research, Kyoto University,Yoshida-Ushinomiya-cho, Kyoto 606-8302, Japan; cJapan Science and Technology Agency, PRESTO, Kawaguchi, Saitama 332-0012, Japan; dDepartmentof Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel; and eInstitute for Advanced Study, Princeton, NJ 08540

Contributed by Albert Libchaber, September 14, 2012 (sent for review July 17, 2012)

In thermophoresis, with the fluid at rest, suspensions move alonga gradient of temperature. In an aqueous solution, a PEG polymersuspension is depleted from the hot region and builds a concen-tration gradient. In this gradient, DNA polymers of different sizescan be separated. In this work the effect of the polymer structurefor genomic DNA and small RNA is studied. For genome-size DNA,individual single T4 DNA is visualized and tracked in a PEG solutionunder a temperature gradient built by infrared laser focusing. Wefind that T4 DNA follows steps of depletion, ring-like localization,and accumulation patterns as the PEG volume fraction is increased.Furthermore, a coil–globule transition for DNA is observed fora large enough PEG volume fraction. This drastically affects thelocalization position of T4 DNA. In a similar experiment, with smallRNA such as ribozymes we find that the stem–loop folding of suchpolymers has important consequences. The RNA polymers havinga long and rigid stem accumulate, whereas a polymer with stemlength less than 4 base pairs shows depletion. Such measurementsemphasize the crucial contribution of the double-stranded parts ofRNA for thermal separation and selection under a temperaturegradient. Because huge temperature gradients are present aroundhydrothermal vents in the deep ocean seafloor, this process mightbe relevant, at the origin of life, in an RNA world hypothesis.Ribozymes could be selected from a pool of random sequencesdepending on the length of their stems.

molecular transport | DNA condensation | oligonucleotides sorting

In 1824, Carnot (1) showed that in a two-temperature system,the transformation of heat into mechanical motion is possible.

This implied two thermal reservoirs, one at high temperature tosupply heat and another one at lower temperature to receive thediscarded heat. This led to the second law of thermodynamicsbut also showed how universal the operation of heat engines, thevector for the first industrial revolution, is. However, tempera-ture differences also play essential roles in our planet, leading toplatetectonics (another heat engine) (2) and various aspects ofmeteorology through atmospheric thermal convection (3). Thosephenomena are large in scale, kilometers or more.For smaller scales, it was observed in the 1980s that deep in the

ocean, along the ridges separating tectonic plates, thermal ventsare present (4), injecting enriched water at temperatures up to400 °C into an ocean of surrounding temperature 5 °C. Thosevents are meter length in scale, with a large number of pores inthe vents ranging from micrometers to a millimeter. Thus, smalllength scale temperature gradients in the pores are also part ofnatural phenomena. Thus, applied to all length scales, tempera-ture differences carve continents, the weather, and may be livingsystems as well.It has been suggested that thermal vents could be the location

where life originates, given the presence of seawater, variouschemical compounds emitted by small volcanoes, the high temper-ature of the emitted fluid with cold fluid around, and also completeisolation from devastating UV solar radiation (4). Following suchhypothesis, and assuming an RNA world at the origin of life, weperformed many experiments to test the effect of temperature

gradients on DNA and RNA and showed that accumulation (5),amplification (6), and length-dependent selection of DNA (7) arepossible. We demonstrated that in such temperature gradients onecould accumulate many-fold DNA by combining thermophoresisand convection (5).We showed then that an amplifier ofDNA,PCRtype, can be effective in thermal convection (6), where the timeoscillation of temperature in PCR is replaced by a space oscillationin convection. Finally, we recently demonstrated that a temperaturegradient separates dsDNA of different sizes when it is in solutionwith another polymer of a large volume fraction (7), a phenomenonsimilar to gel electrophoresis. Thus, the typical laboratory manipu-lations are possible in a temperature gradient.In this article we have revisited DNA and RNA in a temper-

ature gradient and in the presence of a large volume fraction ofPEG, a highly soluble polymer in water. Focusing an infraredlaser beam, PEG moves away from the hot region, balanced bydiffusion (5, 7–9). The resulting equilibrium is an exponentiallyincreasing concentration of PEG toward its equilibrium value farfrom the laser beam. This creates an entropic potential well inwhich DNA or RNA polymers localize themselves depending ontheir length, as was shown previously (7).However, the size of a DNA polymer depends on its folding

structure, which is relevant when dealing with long DNA (typi-cally 15 times the persistent length or more). In the presence ofa large amount of another polymer as a crowding agent such asPEG, DNA may fall into a highly compact globule of a few tensof nanometers instead of a random coil, the coil–globule tran-sition (10–17). We present here single-molecule measurementson T4 DNA, where we also observe the coupling of this foldingtransition with transport driven by a temperature gradient.We have previously studied thermal separation of RNA whose

size varies from 100 bp (as small as transfer RNA) to a few thou-sand base pairs (as long as messenger RNA) (7). Small RNA hasa wide range of functions such as ribozyme, riboswitch, and non-coding RNA molecules (18). In those small functional RNAs, thestem–loop structure is the basic motif for RNA folding, with a rigidstem (50-nm persistence length) and a flexible loop. We find thatthe selection of RNA depends on the total length of the stems.Hence, this motif selection induces some sequence selection. Aconsequence of this effect concerns the origin of life hypothesisnear thermal vents where temperature gradients may select ribo-zymes in the pores present in the solid deposits (4, 18, 19).

ResultsThermophoresis of Polymer Mixtures. We use focused laser heatingto create a temperature gradient in a Tris-buffered solutionsupplemented with PEG10000 polymer with up to 5.0% volume

Author contributions: Y.T.M. and A.L. designed research; Y.T.M. and T.T. performed re-search; Y.T.M. analyzed data; and Y.T.M., T.T., and A.L. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1To whom correspondence should be addressed. E-mail: libchbr@rockefeller.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1215764109/-/DCSupplemental.

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fraction (Fig. 1A; Materials and Methods). The maximum tem-perature difference is 5.0 K and typical temperature gradient∼0.25 K/μm. Thermophoresis depletes a PEG polymer from thehot region and builds a concentration gradient of PEG (5). AsPEG concentration increased, we observed that solutes such asDNA and RNA showed depletion, ring-like localization, andaccumulation (Fig. 1B) (7). We have proposed a phenomeno-logical model that takes into account hydrodynamics effectsdriven by the PEG osmotic pressure gradient (7, 20–26). Theequation for the flow of PEG molecule JPEG is

JPEG =−DPEG∇cPEG − cPEGDPEGT ∇T; [1]

where cPEG is the PEG concentration, DPEG is the PEG diffusionconstant, and DPEG

T is the thermal diffusion constant. The PEGconcentration gradient in a radius r from the heated center, atsteady state, yields

cPEG�r�= c0PEG exp

�−SPEGT ðTðrÞ−T0Þ

�; [2]

where SPEGT is the Soret coefficient, defined as SPEGT =DPEGT =DPEG;

TðrÞ and T0 are temperatures at r and at infinity, respectively. Inour experiment SPEGT is 0.064 [1/K].Given the presence of another solute, DNA, of small volume

fraction, whose concentration is c, it experiences thermophoresisand diffusiophoresis, the effect of the PEG concentration-de-pendent restoring forces (21). The flow of DNA (and RNA), J,can be written phenomenologically as

J = −D∇c− cDT∇T + cu; [3]

where u= kBT3η ðSPEGT − 1=TÞλ2cPEG

�r�∇T is the diffusiophoretic ve-

locity of DNA, kB is the Boltzmann constant, η is the viscosity of thebulk solution, and λ is the depth of a steric repulsion of PEG fromthe surface of DNA (7, 25). Given a PEG radius of gyration Rg, itscenter of mass is expelled up to a distance Rg from the DNA, thusλ≈Rg. In addition, in the presence of a temperature gradient, thethermal energy has a spatial dependence kBTðrÞ, which leads to the

−1=T term in u. At steady state J = 0, the distribution of the DNAconcentration cðrÞ is

c�r�= c0exp

�−SDNA

T ðTðrÞ−T0Þ+�c0PEG − cPEG

�r��V�; [4]

where c0 is the DNA concentration at infinity, V = 2πaλ2 (no slipcondition), and a is the radius of DNA. According to this model,ring-like localization results from the interplay between thermopho-resis and diffusiophoresis originating from the osmotic pressure ofPEG near the surface of DNA (7). Small salt ions concentration ispresent in the solution, but we can neglect their effects for thislocalization as they have a large diffusion constant.Fig. 2A shows the phase diagram of the localization patterns as

a function of the DNA length from 250 bp up to 166 kbp of T4DNA (T4 phage genome DNA) as a function of the PEG poly-mer concentration. We find that the position of the radius ofaccumulated dsDNA, rðNDÞ, exhibits a nonmonotonic behavioras a function of DNA length with a minimum at ND = 5 × 103

base pairs (bp) (Fig. 2B). For long DNA from 5.6 to 166 kbp,the diameter of ring localization expands. For short DNA up to5.6 kbp and RNA up to 3 kb (7) the ring diameter decreases,following a behavior analogous to gel electrophoresis. The ringdiameter decreases linearly from 2.0 to 3.5% but changes littlefrom 3.5 to 4.5% (Fig. 2C).

Thermophoresis of T4 DNA in a PEG Solution.Why does dsDNA longerthan 5.6 kbp show a wide range of ring-like localization?This hints at a change in the DNA configuration that occurs

around this length. The origin of this transition is the large dif-ference in the natural length scale of the polymers: PEG hasa persistence length of about aP = 0.35 nm, whereas the persis-tence length of dsDNA is larger by two orders of magnitude: aP =50 nm (150 bp). Thus, short dsDNA of up to a few hundred basepairs has only a few persistence lengths. Such dsDNA is thereforein the semiflexible regime, a rather stiff rod with a few bendssurrounded by the much more flexible PEG. Only longer dsDNAstrands have enough twists and turns to make a polymer blob,which geometrically defines an “inside” and an “outside” anda corresponding PEG concentration gradient. When the DNAlength becomes large enough it is then compressed and movesaway from the trap as if it is a small DNA. Then, the osmoticpressure of PEG of order kBT=a3P will overcome the resistance ofthe DNA blob and lead to intrachain DNA condensation (SIAppendix) (15–17, 27, 28).To verify this hypothesis, we move to single-molecule studies

of the T4 phage genome DNA. Because T4 DNA is 166 kbp longand 57 μm in end-to-end distance, this DNA is large enough tobe detected and tracked as individual DNA.

PEG Induces the Compaction of Single T4 DNA. Single DNA visuali-zation was performed in various PEG concentrations but in theabsence of a temperature gradient. T4 DNA in a water solutionbuffered with Tris elongates and subsequently relaxes to an equi-librium state within a second, like a random coil. The length of T4DNA stretching due to thermal conformational fluctuation, aver-aged over more than 100 molecules, was 3.5 μm. We find a transi-tion for themean length of stretched axis for T4DNAas a functionof PEG volume fraction (Fig. 3). The onset of compaction for T4DNA is around 2.0% PEG volume fraction (Fig. 3A). From 2.0 to5.0%PEG, a certain proportion ofDNA is compacted into a singledot whereas others fluctuate as semiflexible polymers. Further-more, as the PEG concentration is increased, the proportion ofcompacted DNA increases as in a subcritical bifurcation (15, 29).Note that the PEG volume fraction at the onset of the coil–

globule transition is close to the calculated critical volume fractionϕ∗ of 1.5% PEG (30, 31) but smaller than the ϕ∗ of 4.0% obtainedfrom the measurement by Hansen et al. (32). This difference may

A

B

Fig. 1. Thermophoresis of DNA in a PEG solution. (A) Experimental setup.Schematic of the polymer mixture of DNA (blue) and PEG (green) underinfrared laser focusing (red) is shown. (B) Depletion (Left), ring-like locali-zation (Center), and accumulation (Right) of T4 DNA in 0%, 2.5%, and 5.0%PEG solutions respectively. Plot shows the relative concentration of T4 DNAin three different PEG solutions. (Scale bars, 35 μm.)

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come from the density of DNA in our experiment and the positivecharged ions present. The condensation of T4 DNA occurs ata lower PEG concentration in the presence of small salt, called Ψcondensation (33–35).A dsDNA blob within a PEG solution is subjected to three

forces: the osmotic pressure of PEG due to the lower PEG con-centration inside the blob, the osmotic pressure of the counterionsthat neutralize the charges along theDNA, and the elasticity of theDNA that opposes compression and extension away from the free-chain gyration radius. In thermodynamic equilibrium the threecorresponding pressures should balance each other. Because PEGparticles are free to exchange between the blob and it surrounding,the chemical potential of the PEG is also equilibrated between theinside and the outside. Analysis of the thermodynamic equilibrium(SI Appendix) exhibits a subcritical bifurcation in the folding as

a function of PEG concentration (Fig. 3B): below ϕ∗ ≅ 2.0% theDNA is in a dilute “coil” configuration, whereas above the coilconfiguration coexists with a dense globular state of much smallerDNA particles. Force balance acting on the DNA determines thesize of the coil and the globule. In the coil state the elasticityopposes the expansion driven by the counterion pressure, whereasin the dense globule the elasticity resists the compression due to thePEG concentration gradient.

Dynamics of Single T4 DNA in Temperature Gradient and PEG Con-centration Gradients. We combine single DNA observation with thethermophoresis experiment. Single T4 DNA was clearly detectedwithin the area of ring-like localization in 2.5% PEG solution (Fig.4A). Individual T4 DNA was trapped under a PEG concentrationand temperature gradients with observable fluctuations.We then examined the dynamics of thermophoresis of single T4

DNA. Thermophoreosis excludes DNA away from the hot regionwhereas a PEGconcentration gradient pushes it back to the center.According to this scenario, when T4 DNA forms ring-like locali-zation, two oppositemotions, out fromhot to cold in the center andfrom cold to hot in the periphery, occur. To test this argument wetrack themotion of single T4DNAduring the ring-like localizationin various PEG concentrations.Fig. 4B shows T4DNAparticle trajectories as a function of time.

We detect single T4 DNAmoving along a temperature gradient in1.5%, 2.5%, and 4.0%PEG solutions (36) and show representativetrajectories. In 1.5% PEG, at which ring-like localization occurs,T4DNA exhibited thermal Brownianmotion and graduallymovedto the region of ring-like localization (Fig. S1). In addition, ther-mophoretic motion escaping from the hot region is observed ina part of T4 DNA (Fig. 4B, Left). In 2.5% PEG solution, wherering-like localization occurs, DNA is immediately expelled fromthe hot region, but after about 1 s DNA gradually moves from theperiphery inward (Fig. 4B, Center). From 3.0 to 4.0% PEG sol-utions all T4 DNAmove from the cold periphery to the hot center(Fig. 4B, Right). Motion from hot to cold is rarely observed. Thisresult indicates that the force from the PEG concentration gradi-ent occurs instantaneously and plays a dominant effect for ring-likelocalization, building a potential wall.In both 2.5% and 4.0% PEG, the direction of velocity shows no

correlation effects subsequent to the onset of thermophoresis butless fluctuation as T4 DNA approaches its localization position(Fig. S2). Ichikawa et al. have shown that the relaxation time for T4DNA stretching is ∼3 s (26), which is much longer than the

A B

C

Fig. 2. (A) Phase diagram of depletion, ring-like localization, and accumu-lation for DNA molecules from 250 to 166 kbp. (B) Ring radius rðNDÞ asa function of DNA length ND in 2.5% PEG solution. Lines are fitted to DNAbelow 5.6 kbp (purple line) and above 5.6 kbp (blue line). (C) Ring radiuswith respect to PEG volume fraction.

A

B

Fig. 3. Single T4 DNA in a PEG solution. (A) Single T4 DNAmolecules in 0%, 2.0%, and 5.0% PEG solutions. Scale bars, 4 μm.Actual size of compacted DNA is a few tens of nanometers (15,16) below the diffraction limit of our epifluorescent microscope.(B) (Left) Mean sizes of coil and globule DNA as a function of PEGvolume fraction. Coil–globule transition for T4 DNA occurs at2.0% PEG. (Right) Probability distributions of the stretched axisfor individual T4DNA. Reddotted lines arefitted curveswith twoGaussian functions.

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relaxation observed in our experiment. This implies that the ob-served fluctuation in the T4 DNAmotion is dominantly Brownian.Moreover, we found that the velocity of single T4 DNA

increases from 2 to 3 μm/s, 30 μm away from the localizationspot to 10 μm/s, very close to the localization region in 4.0%PEG solution (Fig. 5). The change from Brownian to persistentmotion with slight acceleration indicates that the PEG potentialwall is sharp close to the localization.

Thermophoresis and Sequence Dependence of Small RNA. In theRNA world hypothesis, tiny RNA polymers with stable sequen-ces must emerge and be selected from a pool of randomsequences. They might be the precursor motif of ribozymes. Inthis second part, we investigate small RNA and show that ther-mal gradient allows some sequence selection of small RNA.RNA itself can also be selected in a temperature gradient in

the presence of PEG of 5.0% volume fraction. The selection willdepend on the RNA folding state. The stem–loop structure is thebasic motif for RNA folding with a rigid double-stranded stemand a flexible loop. We show that no accumulation is observedfor short poly-thymidine oligodeoxy-ribonucleotides (poly-T) andpoly-uracil oligoribonucleotides (poly-U) where no stems arepresent, whereas accumulation is observed for stem–loop struc-tures. The selection of RNA will depend on the total length of therigid stem. Furthermore, as the stem length increases, the rate ofaccumulation increases. An interesting consequence of this effectis that this size selection implies some sequence selection due tocomplementarity of the stem. This is evidence of selection ofsmall RNA in thermophoresis. Thus, a temperature gradientcould select small ribozymes in the pores present in the soliddeposits of thermal vents.We find that single-stranded RNA (ssRNA) having a stem–

loop module accumulates at the hot region, whereas a poly-U ofssRNA, unable to form stems, exhibits depletion (Fig. 6A). Theaccumulation of small dsDNA depends linearly on the PEGconcentration. The effect of ssRNA or ssDNA as a function ofthe stem length (number of base pairs) is quantified in Fig. 6B.We found that stem–loop RNA/DNA shows an accumulation forstem length longer than 5 bp but a depletion below. The rate ofaccumulation increases as the stem length elongates. Moreover,a self-acylating ribozyme with 6-bp double strand (37, 38) alsoexhibited an accumulation (Fig. 6B). This suggests that the

length of rigid stem is important for the force generated by thePEG concentration gradient.We examined this hypothesis by studying the thermophoresis

of a folded, double-stranded RNA (dsRNA) and dsDNA in thePEG solution. A similar transition curve from depletion to ac-cumulation above 8 bp was observed (Fig. 6C). However, fora conformation of 40 nucleotides poly-U ssRNA and up to 124 nu-cleotides poly-T ssDNA, accumulation was not observed (Fig. 6C).This provides evidence that the Soret effect in the polymer solutionis sensitive to the total length of stems for an RNA or DNA poly-mer. The 8-bp stem length (∼2.7 nm) is comparable to the pore sizeof 5.0% PEG network (∼4 nm). However, the estimated size ofssRNA/ssDNAwithout a 40-bp stem (∼5 nm) is also comparable tothe PEG network (39). This suggests that the polymer rigidity dueto the presence of a double-stranded stem rather than its sizeaffects the osmotic force from a PEG concentration gradient.

Salt Dependence of Sequence Selection. In addition, the accumu-lation is reduced as the concentration of charge salt increases anddsDNA/dsRNA uniformly distribute eventually in 500 mM NaClor 50 mMMgCl2 (Fig. 7). This suggests that charge effects such aselectrostatic screening and dipole interaction between dsDNA/dsRNA and PEG mediate the accumulation, whereas the de-pletion of ssDNA/ssRNA become small in the presence of highconcentration of salts (Fig. 7). The effective Soret coefficient at 500mM NaCl is comparable with the offset of the Soret coefficient inwater. The charge of the salt may change the size of the ssDNAand ssRNA in the measured salt concentrations because the os-motic pressure from PEG compresses RNA, whose electrostaticrepulsion is significantly screened. It may also be likely to considerthe change of molecule size (40, 41) to account for the change ofthe effective Soret coefficient for ssDNA and ssRNA.

ConclusionWe have described an experimental study of thermophoresis forlong-genome DNA and short RNA. In the presence of anotherpolymer of large volume fraction, those biopolymers move towardthe heated center, whereas they are expelled from the hot regionin a simple water solution. The PEG concentration gradient gen-erates entropic forces on DNA counterbalancing thermophoresis.At the intermediate PEG concentration, this interplay localizesDNA as a ring-like pattern. We also observe that the size of ring-

A

B

Fig. 4. Dynamics of single T4 DNA in PEG concentration gradients. (A) T4DNA forms ring-like localization in 2.5% PEG solution. Scale bar, 35 μm. (B)Trajectories of single T4 DNA in X–Y plane and t axis; (Left) 1.5% PEG,(Center) 2.5% PEG, and (Right) 4.0% PEG. Pseudocolor maps at the top arefluorescent images taken at t = 20 s.

A B

Fig. 5. Velocity of single T4 DNA molecule as a function of time. Traces ofvelocity evolution in five different DNA are shown in (A) 2.5% PEG and (B)4.0% PEG. The fitted curve (dashed line) indicates the proportional increaseof velocity as time advances.

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like localization of DNA has a singular point at around 5.6 kbp.The model based on the semiflexible polymer chain surrounded byPEGmolecules predicts that the effect of condensation appears at∼10 kbp, which is in good agreement with our experiment. Indeed,our single-molecule observation confirmed that long DNA such asT4 DNA is compacted in the presence of more than 2.0% PEG,and this dramatically changes the DNA size from 3.5-μm length ofthe long major axis to less than 0.5 μm (15, 17). The reduction ofeffective DNA size may decrease the entropic force from PEG

concentration gradient and result in the wider range of ring lo-calization from 2.0 to 4.5%PEG.We also measured the local PEGconcentration where T4 DNA was localized. The obtained valueswere correspondingly 1.8–3.5% PEG. In this PEG range DNAis condensed.The tracking of individual single T4 DNA allowed us to ana-

lyze the dynamics of thermophoresis in a polymer solution. Onekey observation was the acceleration of T4 DNA when it ap-proaches the stable point where T4 DNA localizes. The velocityof T4 DNA is proportional to the gradient of PEG concentrationand it migrates toward the localization point (7). There the DNAmolecule has fastest velocity and this mechanism is consistentwith our observation.In the second part we studied thermophoresis of short RNA

such as a ribozyme (18, 37). Given the small radius of gyration ofPEG, entropic force can act on short RNA and DNA. It leads toaccumulation in a temperature gradient.The interesting result is that this entropic force overcomes

thermophoresis only for a long enough stem in stem–loop RNA.Thermal separation of DNA and RNA might be relevant tomolecular evolution at the origin of life: Separation of small RNAfrom a large library of RNA world might occur at the thermalvent. Thus, separation and accumulation are physically feasible ina temperature gradient at the early stage of life (4, 5, 7).Intriguingly, we have shown recently that we can trap shorter

RNA (1.0 kb) of a small volume fraction in a gradient of longerRNA (rRNA) of large volume fraction (Fig. S3). This resultmeans that our finding is a general phenomenon, and does notdepend on the PEG specificity.

Materials and MethodsExperimental Setups for Thermophoresis. The solution is enclosed in a poly-dimethylsiloxane (PDMS, Sylgard 184; Dow Corning) microchannel. A singlechannel 10 μm thick and 500 μmwide was closed with a cleaned glass slide tosuppress thermal convection and sealed with a fast-curing epoxy (AralditeRapid, Huntsman). The whole experiment was maintained at room tem-perature (T0 = 24 °C). The temperature gradient ∇T was built by focusing aninfrared laser beam (FOL1402PNJ; Furukawa Electronics, λ = 1480 nm) on thePDMS chamber with the objective lens ×32. Dieletrophoresis due to theelectric field of laser light is negligible. Temperature difference at the radialdistance was measured by the intensity drop of fluorescent dye 2′,7′-bis(-2-

A

B C Fig. 6. Selection of stem–loop RNA in the PEGconcentration gradient. (A) Stem–loop RNA with12-bp stem (Upper) and ssRNA poly-U of 15nucleotides (Lower). Plot shows the relative con-centration of stem–loop RNA (red line) and thepoly-U (black line). Scale bars, 35 μm. (B) Accu-mulation of stem–loop RNA (green circles), stem–

loop DNA (red circles), and a ribozyme (blue cir-cle). We use the effective Soret coefficient SeffT (thedefinition is shown in Materials and Methods).Positive values of SeffT represents accumulation,whereas negative values of SeffT correspond todepletion. (C) Comparison of accumulation ordepletion of dsDNA, dsRNA, ssDNA poly-T, andssRNA poly-U.

A

B

Fig. 7. Salt dependence for dsDNA of 20 bp and ssDNA polyT of 40nucleotides. In the presence of NaCl (A) and MgCl2 (B), the effective Soretcoefficient was close to zero value, indicating that the accumulation of smallRNA and DNA was suppressed.

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carboxyethyl)-5-(6)-carboxyfluorescein (BCECF, Molecular Probes) at 1 mMsolution. Fluorescence of BCECF decreases linearly with a slope −1.3%/K.Maximal temperature increase is ΔTmax = 5 K for T4 DNA experiment andΔTmax = 3 K for small RNA/DNA experiment. We used smaller temperaturegradient to fit to exponential distribution (see SeffT in Effective Soret Co-efficient for Small RNA) without ring-like localization. Small RNA can showthe localization as well under a bigger temperature gradient.

Visualization and Imaging. For thermophoresis experiment, we visualized T4DNA, small RNA, and small DNA with SYBR gold fluorescent dye (MolecularProbes). Fluorescence of DNA and RNA molecules was detected using anepifluorescence microscope (Olympus; IX70) and recorded with the RetigaCCD camera (QImaging). SYBR gold dye depends on temperature with linearslopes of –3.2%/K and –1.1%/K for ssDNA/ssRNA and dsDNA/dsRNA, re-spectively. We thus obtained relative concentration of DNA/RNA after therescaling of this temperature dependence.

We tracked single T4 DNA stained by YOYO-1 instead of SYBR gold.Time-lapse movies of thermophoresis for single T4 DNA were taken ata camera set for 10 frames/s, maximum binning, region of interest of85 μm × 85 μm. Image analysis was performed with MATLAB software(MathWorks). We measured the center of mass of single DNA from fluo-rescent intensity profile by fitting a 2D Gaussian distribution function

I�x; y

�= I0 + I1 exp

�− ðx − xGÞ2

σ2x− ðy − yGÞ2

σ2y

�(ref. 36).

Single DNA visualization for coil-globule transition was performed usingan epifluorescence microscope (Nikon; ECLIPSE) with a ×100 objective lensand recorded with an electron multiplying CCD camera (Andor; iXon).

Chemical Reagents. Polyethylene glycol 10,000 (PEG) was purchased fromAlfa Aesar. The powder of PEG was dissolved in 10 mM Tris·HCl buffer (pH

7.5). We mixed DNA and RNA in a PEG10000 solution of various volumefractions. DNA–PEG solutions were kept at 4 °C for at least 24 hafter mixing.

T4 DNA was purchased from Nippon Gene, Ltd. T4 DNA was dissolved in10 mM Tris·HCl buffer solution (pH 7.4) at 100 ng/μL. After 1,000× dilution ofT4 DNA solution (ϕDNA ∼ 0.02%), we mixed YOYO-1 fluorescent dye thatintercalates into base pairs in DNA with T4 DNA at a ratio of 1,000:1.

Short DNA and RNA were hybridized from oligonucleotide primers. Re-peated heating and cooling between 60 and 16 °C was done to make ho-mogeneous and thermodynamically stable folding in DNA and RNA.Nucleotide sequences are shown in SI Materials and Methods.

Effective Soret Coefficient for Small RNA. To measure the transition fromdepletion to accumulation for small DNA and RNA, we defined the effectiveSoret coefficient SeffT as cðrÞ= c0exp½SeffT ðTðrÞ− T0Þ�. SeffT is related to Eq. 4 asSeffT ≈−ST + c0PEGS

PEGT V (SI Appendix). V depends on the stem length and it

subsequently affects RNA accumulation. The positive sign of SeffT means anaccumulation, whereas a negative sign corresponds to depletion. Its valuereflects the rate of accumulation or depletion.

ACKNOWLEDGMENTS. We thank A. Buguin and A. Grosberg for theoreticalmodel, P. Kumar and J. Merrin for discussions and comments on themanuscript, and F. Scott, Y. Shimamoto, T. M. Kapoor, and M. Ichikawa forsingle DNA visualization. This work was supported by a fellowship for re-search abroad from Japan Society for the Promotion of Science, a Marie-Josée Henry Kravis Fellowship from the Rockefeller University, PrecursoryResearch for Embryonic Science and Technology from Japan Science andTechnology Agency (all to Y.T.M.); and National Science Foundation GrantPHY-0848815 and Florence J. Gould Fellowship at Institute for AdvancedStudy (both to A.J.L.).

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