Simulation study of the effects of surface chemistry and temperature on theconformations of ssDNA oligomers near hydrophilic and hydrophobic surfacesRobert M. Elder and Arthi Jayaraman Citation: The Journal of Chemical Physics 140, 155103 (2014); doi: 10.1063/1.4870776 View online: http://dx.doi.org/10.1063/1.4870776 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Mechanism of oil detachment from hybrid hydrophobic and hydrophilic surface in aqueous solution J. Chem. Phys. 140, 164702 (2014); 10.1063/1.4870930 Temperature effect on the small-to-large crossover lengthscale of hydrophobic hydration J. Chem. Phys. 139, 184709 (2013); 10.1063/1.4828459 The effect of pressure on the hydration structure around hydrophobic solute: A molecular dynamics simulationstudy J. Chem. Phys. 136, 114510 (2012); 10.1063/1.3694834 Solubilization of aromatic and hydrophobic moieties by arginine in aqueous solutions J. Chem. Phys. 133, 054902 (2010); 10.1063/1.3469790 Size-dependent hydrophobic to hydrophilic transition for nanoparticles: A molecular dynamics study J. Chem. Phys. 131, 244706 (2009); 10.1063/1.3276915

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THE JOURNAL OF CHEMICAL PHYSICS 140, 155103 (2014)

Simulation study of the effects of surface chemistry and temperatureon the conformations of ssDNA oligomers near hydrophilicand hydrophobic surfaces

Robert M. Elder and Arthi Jayaramana)

Department of Chemical and Biological Engineering, University of Colorado, 3415 Colorado Avenue,UCB 596, Boulder, Colorado 80303, USA

(Received 6 January 2014; accepted 28 March 2014; published online 18 April 2014)

We study the effects of the presence of a hydrophilic and a hydrophobic surface on the conformationsand interactions of a single-stranded DNA (ssDNA) oligomer using atomistic molecular dynamics,umbrella sampling, and temperature-replica exchange. Our simulations capture the expected inter-actions between the ssDNA and the two surfaces (e.g., hydrogen bonds, hydrophobic interactions),but we find that the surface chemistry does not strongly affect the exposure of the relatively hy-drophobic nucleobases or the hydrophilic phosphate backbone in a 16-base ssDNA. Likewise, thesurfaces do not strongly affect the preferred size of the ssDNA compared to bulk solution, althoughthe hydrophilic surface does favor slightly more compact ssDNA conformations than the hydropho-bic surface. In more compact conformations, the negative charge of the ssDNA is more concentrated,and the energetic interactions of the DNA and DNA-bound counterions with the hydrophilic surfaceare more favorable, which consequently favors smaller ssDNA sizes. Increasing temperature, regard-less of the presence or chemistry of a surface, makes it less unfavorable for the ssDNA to assumeboth compact and extended conformations. With increasing temperature the free energy cost of as-suming a compact conformation is reduced to a greater extent than the cost of assuming an extendedconformation. The reason for this difference is the entropically favorable release of DNA-bound wa-ter molecules upon assuming a compact conformation. Increasing temperature decreases water-DNAinteractions while surprisingly increasing counterion-DNA interactions, changes which are attributedto the relative balance of entropic and energetic contributions for water molecules and counterionsbound to the ssDNA. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4870776]

I. INTRODUCTION

Many nano- and bio-technologies rely on the uniqueproperties of single-stranded DNA (ssDNA). The sponta-neous self-assembly of ssDNA is used to construct predefinedtwo- and three-dimensional nanostructures,1, 2 to direct DNA-grafted nanoparticles into specific spatial arrangements,3–7

and to screen solutions for numerous target nucleic acid se-quences simultaneously using DNA microarrays.8, 9 In each ofthese DNA-based technologies, the ssDNA is in close prox-imity to a surface, such as the surface of the microarray ornanoparticle, and the interactions of the ssDNA with thesesurfaces will impact the success of the application. Simi-larly, elevated temperatures or controlled temperature anneal-ing procedures might be used to control the behavior of ss-DNA and improve the performance of these technologies.10, 11

However, the behavior of ssDNA near surfaces, either at roomtemperature or at elevated temperatures, has received com-paratively less attention than the behavior of ssDNA in bulksolution.12 Therefore, the present work aims to elucidate someof the effects of surface chemistry and temperature on the in-terfacial equilibrium structure of ssDNA.

a)Author to whom correspondence should be addressed. Electronic mail:arthi.jayaraman@colorado.edu. Telephone: (303) 492-3087. Fax: (303)492-4341.

Previous experimental work has shown that ssDNA ex-hibits complex interfacial behavior. Because ssDNA is an am-phiphilic polyelectrolyte, it can adsorb to both hydrophilicand hydrophobic surfaces,13–15 and both the conformationsand dynamic behaviors of adsorbed ssDNA depend on the hy-drophobicity and other properties of the substrate, the lengthand sequence of ssDNA strand, and the temperature.14–17 Toelucidate the molecular-level basis for the complex be-haviors observed using experimental methods, simulationmethods have been employed to study ssDNA adsorbed tocarbon nanotubes 17–19 and solid surfaces,20 and to study thehybridization behavior of surface-grafted ssDNA strands withssDNA strands in solution.21–24 However, few studies haveexamined the molecular-level interactions of ssDNA withfunctionalized surfaces or self-assembled monolayers,25, 26

and the temperature-dependence of DNA-surface interac-tions has also received relatively little attention using sim-ulation methods.17, 27 In our recent publication, we stud-ied the adsorption of short ssDNA oligomers (2–4 bases)to hydrophilic and hydrophobic self-assembled monolayers(SAMs) at 300 K.28 We found that short ssDNA oligomersexhibit a favorable binding energy on both hydrophilic andhydrophobic SAMs. The short ssDNA in the vicinity ofthe hydrophilic SAM forms attractive hydrogen bonds withthe surface species, while experiencing a repulsive forcefrom the dense, strongly adsorbed water molecules near the

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FIG. 1. (a) The hydrophobic (OMe) and hydrophilic (OEG) oligomers usedto construct the model hydrophobic and hydrophilic self-assembled mono-layers (SAMs). (b) Representative simulation snapshots of the cytosine hex-adecamer (C16) ssDNA oligomer at two different values of the reaction co-ordinate, ssDNA size, Rg,DNA, used for umbrella sampling. The reaction co-ordinate, Rg,DNA, is the radius of gyration of the O5′ atoms in the DNA. Aschematic of the OEG SAM is also shown (not to scale with ssDNA). In eachumbrella sampling window, the value of Rg,DNA is biased with a harmonicconstraint between 9 Å and 23 Å in 2 Å increments. For the simulations ofC16 near the OEG or OMe surfaces, the center of mass of the ssDNA oligomeris also constrained to be 10 Å from the top of the SAM (i.e., the center of massof the topmost heavy atoms in the SAM). The surface distance constraint isapplied for all values of Rg,DNA although it is only shown for the extendedconformation in this diagram.

hydrophilic surface. The short ssDNA in the vicinity of thehydrophobic SAM experiences weak hydrophobic attractionto the surface, and a surprising repulsive force associated witha low-density region of water near the hydrophobic surface. Inthis paper we are extending the above study to longer ssDNAoligomers (16 bases) and also exploring the effects of tem-perature on the structure of these ssDNA oligomers on hy-drophilic and hydrophobic surfaces.

Using atomistic molecular dynamics simulations com-bined with umbrella sampling and temperature-replica ex-change, we study how the presence and chemistry of a surfaceaffect the conformations and interactions of ssDNA oligomer(e.g., size, exposure of nucleobases, base-base stacking, hy-drogen bonding). We focus on an ssDNA oligomer com-posed of sixteen cytosine nucleotides (C16) near a modelhydrophilic oligo(ethylene glycol) surface and a model hy-drophobic oligo(methylene) surface (Figure 1). Using um-brella sampling, we calculate the free energy as a function ofssDNA size (Rg,DNA) in bulk solution and near both of thesesurfaces, while simultaneously observing changes in ssDNAstructure and interactions as a function of ssDNA size andsurface chemistry. Temperature-replica exchange, in which aset of simulations (replicas) with increasing temperatures arerun in parallel and are periodically allowed to exchange tem-peratures, allows a biomolecular system to overcome energybarriers in high-temperature replicas, which enhances confor-mational sampling in the low-temperature replicas.29 Further-more, using temperature-replica exchange allows us to exam-ine the temperature-dependence of the DNA size, structure,and interactions in bulk and on the two model surfaces.

Overall, we find that the presence and chemistry of thesurfaces do not strongly affect the preferred size (Rg,DNA) orthe structure of the 16 base ssDNA (e.g., exposure of the nu-cleobases, base-base stacking). Neither hydrogen bonds withthe hydrophilic surface nor hydrophobic “face-on” interac-tions with the hydrophobic surface, which are the expected

DNA-surface interactions based on our previous work,28 aregreatly affected by the size of the ssDNA oligomer. How-ever, the hydrophilic surface does favor slightly more com-pact ssDNA than the hydrophobic surface, which appears tobe connected to stronger energetic interactions between themore-concentrated ssDNA charge in the compact ssDNA andthe polar hydrophilic surface. In general, increasing temper-ature has subtle effects that do not depend on the surfacepresence or chemistry, although several reasonable changesin ssDNA behavior with increasing temperature are observed,such as a reduction in base-base stacking and decreased hy-drogen bonding with water molecules at higher temperatures.While increasing the temperature decreases DNA-water in-teractions, it surprisingly increases DNA-counterion interac-tions, which we attribute to the different balance of favorableenergetic and unfavorable entropic contributions of counte-rions binding to DNA compared to water binding to DNA.Lastly, while increasing temperature flattens the entire freeenergy landscape of ssDNA size, making both compact andextended conformations less unfavorable at higher tempera-ture, the more compact ssDNA conformations show a greaterdecrease in free energy than the more extended ssDNA con-formations. The differential change in free energy betweencompact and extended ssDNA conformations is related to theentropically favorable release of DNA-bound water moleculesby the compact ssDNA molecules.

II. METHODS

A. Surfaces and systems

We constructed hydrophilic (oligoethyleneglycol, OEG)and hydrophobic (oligomethylene, OMe) self-assembledmonolayers (SAMs) from oligomers of hydroxyl-terminatedOEG (chemical formula H(OCH2CH2)5OH) and methyl-terminated OMe (chemical formula CH3(CH2)14CH3), asshown in Figure 1. These SAMs, which are identical to thosein our previous publication,28 were designed to provide modelhydrophobic and hydrophilic interfacial environments. TheSAMs have a depth greater than 1 nm, ensuring that ideal hy-drophobic and hydrophilic environments exist at the top sur-face of the SAMs: if the SAMs were thinner, the water andDNA molecules at the top of the SAM would be affected bythe water molecules at the bottom of the SAM, affecting theapparent hydrophobicity at the top surface of the SAM. Ad-ditionally, having such a thick SAM makes it reasonable toconsider ssDNA interactions with a specific solid substrate(e.g., gold, silica) to be negligible, simplifying the simulationdesign and interpretation of results. We chose a high packingdensity of oligomers (∼5 oligomers/nm2) to minimize the ef-fects of intercalation into the surface, although further workcould be aimed at studying these effects because they mayplay an important role in adsorption.15 Additional details ofsurface construction and equilibration are available in SectionS1 in the supplementary material.57

We studied the conformations (e.g., size, surface areacomposition) and interactions (e.g., hydrogen bonds) of asingle-stranded DNA (ssDNA) oligonucleotide of 16 cytosinebases (C16) near both of the model SAMs and in bulk solution

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(i.e., without a surface). For the bulk solution simulations, weadded 15 Na+ counterions to neutralize the ssDNA charge andthen solvated the system with approximately 15 000 TIP3Pwater molecules in a (77.83 Å)3 box. For the simulationscontaining a surface, we placed the ssDNA oligomer 10 Åabove the OEG or OMe surface, added 15 Na+ counteri-ons, and solvated the system with approximately 7500 TIP3Pwater molecules in (65.1 × 68.7 × 71.3) Å3 box. The dis-tance between the ssDNA oligomer and the SAM is definedby the distance between the center of mass of the ssDNAoligomer and the center of mass of the topmost heavy atoms(i.e., non-hydrogen atoms) in the SAM. The DNA, TIP3P wa-ter molecules, and counterions were parameterized using theAmber ff10 combination of force fields.30–32 Additional de-tails of system construction are available in Section S2 in thesupplementary material.57

B. Simulation protocol

After constructing the above systems, they were sub-jected to the minimization and equilibration procedure de-scribed in Section S2 in the supplementary material priorto use in production simulations where we combined um-brella sampling with temperature-replica exchange moleculardynamics.57

1. Umbrella sampling and temperature-replicaexchange protocols

To accelerate the sampling of ssDNA conformations, weemployed the umbrella sampling method33 using NAMD34

for all simulations. The reaction coordinate defining ssDNAconformation was the radius of gyration of the O5′ atoms inthe ssDNA (Rg,DNA). Only the O5′ atoms were used to in-crease computational efficiency relative to using all of theDNA atoms in the definition of Rg,DNA. Umbrella samplingwindows with values of Rg,DNA from 9 Å to 23 Å in 2 Åincrements were used, and a harmonic spring with a forceconstant of 2.5 kcal/mol-Å2 was used to bias the conforma-tion of the ssDNA near each value of Rg,DNA. All biasingpotentials were applied with the collective variables mod-ule of NAMD.35 This force constant (2.5 kcal/mol-Å2) pro-duced a wide enough distribution of the value of the re-action coordinate, Rg,DNA, in each umbrella sampling win-dow such that neighboring windows (each separated by2 Å) partially overlap and so the entire range of Rg,DNA

was well sampled (i.e., there are no gaps between win-dows). Representative conformations of the ssDNA oligomerat two different values of Rg,DNA are shown schematically inFigure 1(b). Initial configurations for each umbrella samplingwindow were generated in a stepwise fashion as follows. First,the C16 ssDNA oligomer was simulated in bulk solution at300 K without any biasing potential for 20 ns; the initial con-figuration for this simulation was a single strand from a ds-DNA helix in canonical B-DNA conformation generated us-ing nucleic acid builder in the Amber software suite. The fi-nal configuration from this unbiased simulation had roughlyRg,DNA = 15 Å and was used as the initial configuration for

the umbrella sampling window with a biasing potential atRg,DNA = 15 Å. Then, the ssDNA configuration after 1 nsof equilibration in the Rg,DNA = 15 Å window was used asthe initial configuration for the adjacent umbrella samplingwindows (13 Å and 17 Å). In those adjacent windows, theRg,DNA constraint was gradually changed from 15 Å to thevalue of the current window (13 Å or 17 Å) over 200 ps be-fore beginning umbrella sampling in that window. The ini-tial configurations for the next set of adjacent windows (13–11 Å and 17–19 Å) were generated in the same fashion, andso on. Temperature-replica exchange, described below, wasused during this process to accelerate equilibration, and theinitial structure for each temperature-replica came from thecorresponding temperature-replica from the preceding um-brella sampling window (i.e., all of the temperature-replicasfor a given umbrella sampling window had different startingconformations).

As an alternative to Rg,DNA, we could have used the end-to-end distance of the ssDNA oligomer to define ssDNA con-formation (e.g., the distance between the oxygen atoms at the5′ and 3′ terminals). However, the end-to-end distance has alarger range of values than the radius of gyration: the end-to-end distance ranges from approximately 3 Å (i.e., the van derWaals contact distance of two oxygen atoms) up to approxi-mately 54 Å (i.e., 16 bases by 4.3 Å per base, which is the dis-tance between bases in ssDNA)36, while the radius of gyrationonly spans the range of 9–23 Å. The smaller range of relevantvalues of Rg,DNA requires a smaller number of umbrella sam-pling windows and hence lesser computational expense thanthe end-to-end distance. Additionally, the radius of gyrationdefines the size of the ssDNA more uniquely than the end-to-end distance would: for example, in a globular conformation,where Rg,DNA is unequivocally low, the end-to-end distancecan take on a wide range of values from approximately 3 Åup to values larger than Rg,DNA. Hence, although the end-to-end distance of the ssDNA oligomer could certainly be usefulin other situations, we chose to use Rg,DNA to define ssDNAconformations in this case.

The weighted histogram analysis method (WHAM)37

was used to calculate the free energy as a function of Rg,DNA,using a freely available implementation.38 In the WHAM pro-cedure, we used 111 bins to generate the histogram. We esti-mated the uncertainty of our free energy profiles using MonteCarlo bootstrap error analysis, which is implemented in thefreely available WHAM code.38 The Monte Carlo bootstrapprocedure requires a correlation time, which we estimatedby observing where the autocorrelation function of Rg,DNA

reaches zero (approximately 200 ps) and using twice thisvalue (400 ps) as the correlation time (Figure S1 in the sup-plementary material).57 The error bars on the free energy asa function of Rg,DNA are the standard deviation produced bythe bootstrapping method. In each window, 7 ns of simu-lation were conducted, and the first 1 ns was discarded asequilibration time, yielding 6 ns of sampling per window. Al-though this is a relatively short simulation time, the samplingwas accelerated by the using replica exchange, as describednext.

In each umbrella sampling window, we also used thereplica exchange method to accelerate sampling of the

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internal degrees of freedom of the ssDNA and to ob-tain information about the temperature dependence of DNAconformations.29 The replicas had temperatures ranging from273 K to 473 K. The highest temperature, 473 K, was cho-sen by observing the frequency of base-base stacking overa range of temperatures, which reaches a minimum value ataround 473 K. Temperatures higher than 473 K did not sub-stantially decrease the prevalence of base-base stacking com-pared to 473 K, so we reasoned that using higher temper-atures would unduly increase the computational cost with-out a corresponding increase in the speed of conformationalsampling. The number of replicas was chosen to yield ex-change acceptance ratio of approximately 20%–30%, whichis the range of acceptance ratios that is the most computa-tionally efficient.39, 40 The temperatures of the replicas weredistributed exponentially between the lowest and highest tem-peratures to maintain constant acceptance ratio across thereplicas.29 In bulk solution simulations, 36 replicas were used,while in the near surface simulations, which have a greaternumber of atoms and therefore require a greater number ofreplicas to achieve a given exchange acceptance ratio, 72replicas were used. Adjacent replicas were allowed to ex-change temperatures every 1 ps if they met the Metropoliscriterion.29

We conducted several analyses to assess whether theseumbrella sampling temperature-replica exchange simulationsyielded converged free energy profiles and sampled many dif-ferent ssDNA conformations. First, we verified that the freeenergy profiles as a function of Rg,DNA have converged withinthe given sampling time of 7 ns per window by monitoring thechange in the free energy profiles with increasing amounts ofsampling time (Figure S1 in the supplementary material). Sec-ond, the autocorrelation of Rg,DNA is approximately 200 ps,suggesting that we are sampling a wide variety of indepen-dent conformations over the 7 ns simulations (Figure S1 inthe supplementary material).57 Third, we observed the move-ment of each replica through the range of temperatures and wefound that each replica traverses the entire temperature rangeseveral times over the course of the 7 ns simulations. Finally,we conducted a cluster analysis of the DNA structure in theRg,DNA = 15 Å umbrella sampling window at 300 K, usingthe functionality in VMD with a root-mean-square-deviation(RMSD) cut off of 5.0 Å of all non-hydrogen atoms in thessDNA. We found that several clusters are generated during7 ns of sampling (10 clusters containing 5% or more of thestructures per cluster). The most populous cluster, containingapproximately 40% of the ssDNA structures, does not con-tain the starting structure, which suggests that the ssDNA hasrelaxed from its initial configuration and explored many dif-ferent conformations.

2. Additional simulation details

After the equilibration protocol described in SectionS2 in the supplementary material,57 production simulationswere conducted in the constant temperature and constant vol-ume ensemble (NVT). We discuss the choice and limitationsof constant volume simulations rather than constant pres-

sure simulations in the conclusion. A Langevin thermostatwas used to control the temperature (damping coefficient of1 ps−1) at the temperature of each replica. The SHAKE al-gorithm was used to constrain all bonds involving hydrogen,and a time step of 2 fs was used.41, 42 Electrostatic interactionswere treated with the particle mesh Ewald (PME) summationmethod, with a tolerance of 1 × 10−6 and interpolation orderof 4.43 The non-bonded cutoff was 9.0 Å, and the non-bondedlist, which had a cutoff of 10 Å, was updated every 10 steps.Snapshots were recorded every 2 ps. In the near surface simu-lations, the center of mass of the ssDNA was held at approxi-mately 10 Å from the topmost heavy atoms in the SAM usinga harmonic constraint with a 10 kcal/mol-Å2 force constant.In the bulk solution simulations, no such center-of-mass con-straint was applied to the ssDNA.

C. Analysis methods

We assess hydrogen bonding with geometric criteria in-volving the three atoms that participate in the hydrogen bond(donor, acceptor, and hydrogen): if the distance between thedonor and acceptor is less than 3.5 Å and the angle formedby the three atoms is greater than 120◦, they are character-ized as forming a hydrogen bond. We quantify the hydrogenbonding frequency, which is defined as the percentage of sim-ulation time that a particular type of hydrogen bond is formed.When we calculate hydrogen bonds between the ssDNA andother molecules, we consider all possible hydrogen bondingpartners (donors and acceptors) on the ssDNA rather thanonly the Watson-Crick hydrogen bonding partners. We nor-malize the frequency to the total number of hydrogen bond-ing partners on the ssDNA. Hydrogen bonding partners aredefined as all oxygen and nitrogen atoms and any hydrogenatoms covalently bonded to those oxygen and nitrogen atoms.Hydrogen bonds are only counted when all three requiredatoms are present (donor, hydrogen, and acceptor atoms).

Base-base stacking is quantified by applying a geometriccriteria involving the distance between two bases and the nor-mal vectors of the planes of the two bases involved. We definethe base plane by the plane formed between three atoms in thecytosine nucleobases: N1, C2, and C1′.44 The supplementarymaterial of our previous publication shows a diagram of theseatoms.28 If the angle between the normal of two base planesis less than 45◦ and the distance between the centers of massof the two nucleobases is less than 4.5 Å, we consider thebases stacked. These geometric cutoffs are chosen becausethey yield approximately 90% stacking in B-form double-stranded DNA. We introduce another form of analysis, relatedto base-base stacking, to quantify hydrophobic interactionsbetween the DNA and the surface. These “face-on” conforma-tions, where a nucleobase is lying parallel to the surface, fa-cilitate hydrophobic interactions between the nucleobase andthe surface. If the center of mass of a base is within 4.5 Åin the z-direction of the center of mass of the topmost heavyatoms in the surface and the base normal is within 45◦ of thesurface normal, which we define as the z-axis for simplicity,we consider the base to be interacting “face-on” with the sur-face. The base normal for a face-on conformation is defined

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155103-5 R. M. Elder and A. Jayaraman J. Chem. Phys. 140, 155103 (2014)

in the same way as for base-base stacking. As with hydrogenbonds, we quantify the frequency of base-base stacking andface-on conformations, and we normalize the frequency (i.e.,the percentage of the entire simulation time that an interactionoccurs) to the total possible number of base-base stacking in-teractions or face-on conformations.

We calculate the surface area of the ssDNA, and of var-ious components of the ssDNA, using the solvent-accessiblesurface area (SASA) calculation method in VMD,45 with thedefault solvent probe radius of 1.4 Å. We calculate the to-tal surface area of the ssDNA, the surface area of the nucle-obases (i.e., all the atoms in the nucleobase including hydro-gen atoms, but no atoms in the sugar-phosphate backbone),and the surface area of the phosphate backbone (i.e., theatoms in the sugar-phosphate backbone, as defined in VMD,but also including hydrogen atoms, which are not defined as“backbone” atoms by VMD). We note that the C1′, C2′, andO4′ atoms of the deoxyribose sugar, and the hydrogen atomsattached to those heavy atoms, are not included in the defi-nition of either the nucleobases or the sugar-phosphate back-bone, so the sum of the nucleobase and phosphate backbonesurface areas is slightly less than the total ssDNA surface area.For the near surface simulations, we note that these surfaceareas are not the solvent-accessible surface areas because weignore the SAMs in these calculations, so portions of the DNAthat are in contact with the SAMs, and hence are not acces-sible by the solvent, contribute to the surface area. Althoughwe have also calculated the strictly solvent-accessible surfacearea, we do not find any noteworthy results, so we excludethem from our discussion for the sake of brevity.

The energy of the interactions between the ssDNA andother components of the system are calculated using the pairinteraction feature of NAMD.34 We also estimate the entropiccontributions of counterions and water molecules, which loseentropy when they interact with, or bind to, the ssDNA. ANa+ counterion is defined as being bound to the DNA if itis within 7 Å (the Bjerrum length in water at 300 K) of aphosphate group. DNA-bound water molecules are defined asthose water molecules within 3 Å of the DNA. The 3 Å cut-off distance is somewhat arbitrary, although it could be con-sidered a distance at which water molecules strongly interactwith the DNA (e.g., through hydrogen bonds or electrostaticinteractions with phosphates). We note that the trends in thechange in the number of adsorbed water molecules with tem-perature, which are discussed in detail in the results section,are qualitatively similar with a 7 Å cutoff distance, suggestingthat these trends are independent of the cutoff distance (FigureS17 in the supplementary material). Details of the calculationof these estimates of the entropy are provided in Section S9(counterions) and Section S14 (water molecules) in the sup-plementary material.57

The uncertainty of the above quantities is calculated asthe standard deviation by block averaging with 10 blocks ina simulation. That is, the data were divided into 10 blocksof equal size, the average of each block was calculated, andthe standard deviation of the 10 averages is shown as theerror bars on all plots except for the free energy, wherethe Monte Carlo bootstrapping analysis described above isused.

III. RESULTS

A. Effect of surface chemistry on ssDNA structureand size at 300 K

First, we examine how the presence and chemistry of ahydrophilic or hydrophobic surface affect the conformationof the C16 ssDNA oligomer at 300 K.

In Figure 2, we show the free energy profile as a functionof Rg,DNA (i.e., the size of the ssDNA oligomer) for the C16

oligomer in bulk water and the OEG and OMe SAMs near(10 Å from the top of the SAMs). Qualitatively, the shape ofthe free energy profile is the same in bulk solution and nearthe hydrophilic or hydrophobic surfaces. For all three condi-tions (bulk, OEG, and OMe), the free energy minimum is be-tween 13 Å and 17 Å, and compacting the ssDNA to smallersizes (Rg,DNA < 13 Å) or extending the ssDNA to larger sizes(Rg,DNA > 17 Å) leads to an unfavorable increase in the freeenergy of several kcal/mol. The preferred values of Rg,DNA

(13–17 Å) are a reasonable range for an ssDNA hexadecamer.A semi-flexible polymer (i.e., the worm-like chain model,46

for which the radius of gyration is given by Eq. (17) ofRef. 47) with persistence length of 40 Å36 and a contourlength of 69 Å (i.e., 4.3 Å per base36) has a theoretical radiusof gyration of approximately 17 Å. Details of this calcula-tion are given in Section S4 in the supplementary material.57

There are small quantitative differences in the free energyprofile between OEG and OMe: the entire free energy pro-file for OEG, although qualitatively the same as that on OMe,is shifted to slightly smaller values of Rg,DNA relative to thefree energy profile for OMe. On the hydrophilic OEG surface,the free energy minimum is located at Rg,DNA = 13 Å whileon the hydrophobic OMe surface the free energy minimumis located at Rg,DNA = 17 Å. At the highest value of Rg,DNA

(∼23 Å), the value of the free energy on OEG is approxi-mately 0.5 kcal/mol higher than the corresponding value onOMe, indicating that larger ssDNA sizes are more unfavorableon OEG than on OMe. At the lowest value of Rg,DNA (∼9 Å),the free energy on OEG is approximately 2 kcal/mol lowerthan the corresponding value on OMe, indicating that smallerssDNA sizes are less unfavorable on OEG than on OMe.Overall, these observations indicate that slightly smaller

FIG. 2. Free energy as a function ssDNA size, Rg,DNA, for the C16 oligomerin bulk solution, 10 Å from the hydrophilic OEG surface, and 10 Å from thehydrophobic OMe surface. Error bars are calculated using the Monte Carlobootstrap procedure described in Sec. II.

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ssDNA sizes are favored on OEG relative to OMe. We nowdescribe various aspects of the ssDNA conformation to ex-plain the above trends in the free energy.

We first investigate the fraction of the total surface areaof the ssDNA that is associated with either the relatively hy-drophobic nucleobases or the hydrophilic phosphate back-bone to see if the ssDNA adopts conformations with vary-ing exposure of hydrophobic/hydrophilic regions dependingon surface chemistry and/or Rg,DNA. We note that the totalsurface area of the C16 ssDNA oligomer decreases with de-creasing Rg,DNA, as expected, and the total DNA surface areais not significantly affected by the presence or the chemistryof the surfaces (Figure S2 in the supplementary material).57

The surface area composition (i.e., the fraction of the totalsurface area that is composed of either phosphate backboneor nucleobases) is essentially independent of Rg,DNA, surfacepresence, and surface chemistry (Figure S2 in the supplemen-tary material).57 The absence of any major differences in sur-face composition of the DNA in bulk and near surfaces is con-sistent with the similar free energy profiles as a function ofRg,DNA (Figure 2) but does not suggest an explanation for whyslightly smaller conformations are favored on OEG comparedto OMe. To further explore the origin of the slightly smallerconformations that are favored near OEG, we now considerthe molecular-level interactions of the ssDNA with itself andwith other components in the system (i.e., the surfaces, water,and ions).

To see if more favorable interactions within the ssDNAmolecule could explain the smaller conformations on OEG,we examine the number of intra-DNA hydrogen bonds andbase-base stacking. Although the frequency of intra-DNA hy-drogen bonds does slightly increase with decreasing Rg,DNA,which is reasonable because the hydrogen bonding donorsand acceptors are in closer proximity when the DNA issmaller, the presence and chemistry of the surfaces does notstrongly affect the number of these interactions (Figure 3(a)).Therefore, intra-DNA hydrogen bonds do not appear to ex-plain why smaller DNA conformations are favored on OEGcompared to OMe. Next, we consider base-base stacking,which is somewhat affected by the presence and chemistry ofthe surfaces for certain values of Rg,DNA (Figure 3(b)). At thelargest (Rg,DNA ≥ 21 Å) and smallest (Rg,DNA ≤ 11 Å) DNAsizes, the frequency of base-base stacking is unaffected bythe surfaces. However, at intermediate DNA sizes, the pres-ence and chemistry of the surfaces affect base-base stacking.At intermediate DNA sizes (13 Å ≤ Rg,DNA ≤ 17 Å), the ss-DNA shows the greatest amount of base-base stacking in bulksolution, which is consistent with the hypothesis set forth byMonserud et al. of a conformation of ssDNA where the rela-tively hydrophobic nucleobases are sequestered at the centerof a micelle-like globule to decrease their solvent exposure.15

Near OMe the frequency of base-base stacking is not signif-icantly different from bulk solution, which is somewhat sur-prising because one could expect that interactions betweenthe relatively hydrophobic nucleobases and the hydrophobicOMe surface would compete with base-base stacking. We pre-viously observed these nucleobase-OMe hydrophobic inter-actions (termed “face-on” interactions) in a study of shortssDNA oligomers near the OMe surface,28 and we discuss

the prevalence of these interactions for this longer ssDNAoligomer below (Figure 3(d)). Near OEG the frequency ofbase-base stacking is significantly reduced compared to bulksolution, possibly due to DNA-surface interactions, which wediscuss next (Figure 3(c)).

Regardless of the value of Rg,DNA, the ssDNA oligomerforms a larger number of hydrogen bonds with the OEG sur-face but a negligible number of hydrogen bonds with the OMesurface (Figure 3(c)), consistent with our previous study ofshort ssDNA oligomers.28 The polar OEG oligomers are ca-pable of forming hydrogen bonds with the DNA, whereasthe OMe oligomers are nonpolar and are therefore incapableof hydrogen bonding. We hypothesize that these DNA-OEGhydrogen bonds destabilize base-base stacking on the OEGsurface relative to bulk solution (Figure 3(b)). To quantifyhydrophobic DNA-surface interactions, we calculate the fre-quency of “face-on” states, wherein a nucleobase is close toand parallel to the surface. A nucleobase in a face-on confor-mation displaces a large number of water molecules from thesurface, which makes face-on states a reasonable proxy forhydrophobic interaction. Regardless of the value of Rg,DNA,we find that the DNA more frequently forms face-on interac-tions with the hydrophobic OMe surface than with the hy-drophilic OEG surface (Figure 3(d)), which is also consis-tent with our previous study of short ssDNA oligomers.28 Wenote that the ssDNA also forms a significant number of face-on interactions with the hydrophilic OEG surface because ofthe relatively large tolerances we employ in our geometricdefinition of a face-on state (4.5 Å surface distance and 45◦

between base and surface normal vectors). In contrast withDNA-surface hydrogen bonds, face-on interactions do notappear to destabilize base-base stacking relative to bulk(Figure 3(a)). It is interesting to note that Rg,DNA does not sig-nificantly affect these DNA-surface interactions. One reason-able expectation is that the ssDNA would form more face-oninteractions with the OMe surface when in extended confor-mations, which we do not observe. The absence of this find-ing is consistent with our observation that base-base stack-ing, which might be expected to compete with face-on inter-actions, is not affected by Rg,DNA near the OMe surface andis also consistent with our observation that the exposed hy-drophobic base surface area does not significantly increasewith increasing Rg,DNA. Although these DNA-surface inter-actions are of fundamental interest, they do not explain whyslightly smaller DNA conformations are favored on the OEGsurface.

We now consider interactions between the DNA andwater. DNA-water interactions, quantified by the number ofDNA-water hydrogen bonds divided by the number of oxy-gen and nitrogen atoms in the DNA molecule, do not show anobvious trend with Rg,DNA (Figure 3(e)). The average num-ber of DNA-water hydrogen bonds is largest in bulk becausethe presence of a surface necessarily decreases the number ofwater molecules near the DNA molecule compared to bulksolution (Figure S3 in the supplementary material).57 The av-erage number of DNA-water hydrogen bonds is lowest nearthe OEG surface because some DNA-water hydrogen bondsare replaced by DNA-surface hydrogen bonds (Figure 3(c)),and because the OEG surface, by interacting strongly with

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FIG. 3. Molecular-level interactions of the C16 ssDNA oligomer as a function of Rg,DNA in bulk solution, 10 Å from the hydrophilic OEG surface, and 10 Åfrom the hydrophobic OMe surface. (a) The frequency of intra-DNA hydrogen bonds. (b) The frequency of base-base stacking. (c) The frequency of DNA-surface hydrogen bonds. (d) The frequency of face-on conformations, which facilitate hydrophobic interactions. (e) The number of DNA-water hydrogen bonds,normalized to the number of hydrogen bonding partners on the ssDNA. (f) The fraction of the total number of Na+ counterions that are bound to the DNA. Acounterion is defined as being bound to the DNA if it is within 7 Å (the Bjerrum length in water at 300 K) of a phosphate group on the DNA. Error bars are thestandard deviation calculated by block averaging over 10 blocks.

the DNA through hydrogen bonding, displaces some watermolecules from near the DNA (Figure S3 in the supplemen-tary material).57 The average number of DNA-water hydrogenbonds when the DNA is near the OMe surface is intermedi-ate between bulk and OEG because the OMe surface does notform hydrogen bonds with the DNA but, simply by its pres-ence, reduces the number of water molecules near the DNA.Overall, water-DNA interactions do not suggest an obviousexplanation for the slightly smaller conformations of DNA onOEG compared to OMe.

Next, we examine DNA-ion interactions, which are quan-tified by the number of DNA-bound counterions. A Na+

counterion is defined as being “bound” to the DNA if it is

within 7 Å (the Bjerrum length in water at 300 K) of a neg-atively charged phosphate. Both in bulk and on the two sur-faces, we observe an increase in the fraction of DNA-boundcounterions as Rg,DNA decreases, indicating that more com-pact DNA conformations have increased interactions withcounterions (Figure 3(f)). This finding can be rationalizedby considering that at lower Rg,DNA the negatively chargedphosphate groups are closer together, and the greater den-sity of negative charge (per volume) attracts a greaternumber of counterions (i.e., cooperative binding of the coun-terions by the phosphates). We note that the fraction of DNA-bound counterions is essentially the same near both OEGand OMe at all values of Rg,DNA but is considerably lower

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for the DNA in bulk. The reason for this difference is thegreater concentration of counterions in the simulations ofsurface-containing systems, which is due to the smaller totalamount of water in the surface-containing systems (∼7500water molecules) relative to the bulk systems (∼15 000 wa-ter molecules). The difference in counterion concentration be-tween bulk and surface-containing systems is due to the sim-ulation set-up rather than a physical expectation one shouldhave in experimental measurements. Regardless of the dif-ference in the absolute fraction of bound counterions be-tween bulk and the two surfaces, the relative increase in thefraction of DNA-bound counterions with decreasing Rg,DNA

is essentially the same in bulk and near the two SAMs,which is relevant to the following discussion of the energeticand entropic contributions to the free energy as a functionof Rg,DNA.

To better understand the significance of increasing DNA-counterion interactions with decreasing Rg,DNA, and of theother molecular-level interactions of DNA discussed above,we now examine the energetics of the interactions of DNAwith the other components in the systems. In Figure 4 wepresent the energy of interactions between the C16 ssDNAoligomer and other components in the systems (i.e., water,counterions, and the hydrophilic OEG or hydrophobic OMesurfaces) as a function of DNA size. The energies have beenshifted vertically so that the energy for largest Rg,DNA is zerokcal/mol, which allows us to visualize the effect of decreasingDNA size on the interaction energies. First, in Figure 4(a), we

present the total interactions of DNA with everything else inthe system (water, counterions, and surface). We emphasizethat this is not the total potential energy of the entire system.We do not include a discussion of the total potential energyof these systems because, as is common in biological simula-tions, the value and fluctuations of the total potential energyare largely dictated by the relatively large volume of water.As such, it is difficult to discern any effect of Rg,DNA or sur-face chemistry on the total potential energy (Figure S4 in thesupplementary material).57 In bulk and near both surfaces, thetotal DNA interaction energy decreases substantially (i.e., be-comes more energetically favorable) with decreasing Rg,DNA

(Figure 4(a)). The large decrease in the total DNA interac-tion energy with decreasing Rg,DNA is primarily due to thedecrease in the DNA-ion interaction energy that occurs inbulk and on both surfaces (Figure 4(b)). The large decrease inthe DNA-ion interaction energy is reasonable given that thefraction of bound counterions increases as Rg,DNA decreases(Figure 3(f)): the closer proximity of the ions to the DNAleads to stronger DNA-ion energetic interaction. We note thatthe absolute values of DNA-ion interaction energy are less fa-vorable in bulk solution, where the fraction of bound counte-rions is lower, and more favorable for the ssDNA near the sur-faces, where the fraction of bound counterions is higher, butthe change in the DNA-ion interaction energy, and the changein the fraction of bound counterions, relative to the largestssDNA conformations (Figure 3(f)) is the same for bulk andboth surfaces.

FIG. 4. Energetic interactions between the C16 ssDNA oligomer and (a) everything in the system (water, counterions, and surface), (b) Na+ counterions, (c)water molecules, and (d) the OEG or OMe surface as a function of Rg,DNA in bulk solution, 10 Å from the hydrophilic OEG surface, and 10 Å from thehydrophobic OMe surface. Error bars are the standard deviation calculated by block averaging over 10 blocks. Energies are shifted vertically such that theenergy is zero at Rg,DNA = 23 Å.

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Another contribution to the total DNA interaction en-ergy is the DNA-water interaction energy (Figure 4(c)). Thechange in the DNA-water interaction energy with Rg,DNA ismuch smaller than the change in the DNA-ion interactionenergy (Figure 4(b)), and the error bars for bulk and bothsurfaces overlap, making it difficult to distinguish any dif-ferences. However, the remaining contribution to the totalDNA interaction energy, the DNA-surface interaction energy,shows clear surface-dependent effects (Figure 4(d)). As thesize of the DNA decreases, the interactions with OMe do notchange significantly, but the interactions with the hydrophilicOEG surface become much more favorable. The increasedfavorability of DNA-OEG interaction energy with decreas-ing Rg,DNA suggests an energetic motivation for the slightlysmaller ssDNA sizes that are favored on OEG compared toOMe (Figure 2). We hypothesize that the higher charge den-sity of the DNA at lower Rg,DNA increases DNA-OEG interac-tions in the same way that the more compact DNA moleculebinds a greater number of counterions (Figure 3(f)). Addi-tionally, it may be the higher charge density of the DNA-counterion complex, rather than just the DNA itself, that in-creases DNA-surface interactions with the polar OEG surface,since the energetic interaction of the DNA-bound counterionswith the OEG surface becomes more favorable as Rg,DNA de-creases (Figure S5 in the supplementary material).57 Whilethe energetic interactions could favor small ssDNA size, onealso needs to take into account the entropic penalty of con-fining the counterions near the ssDNA. DNA-bound coun-terions have reduced translational entropy, and because thechange in the fraction of DNA-bound counterions with de-creasing Rg,DNA is similar in bulk and near both surfaces, theentropic penalty of confining additional ions near the DNA atsmaller Rg,DNA is similar in bulk, near OEG, and near OMe(Figure S6 and Section S9 in the supplementary material fordetails of this calculation).57 This loss of counterion transla-tional entropy appears to be compensated by favorable ener-getic interactions between the DNA-bound counterions andthe polar OEG surface, but not compensated by the negligibleinteractions between counterions and the non-polar OMe sur-

face (Figure S5 in the supplementary material).57 Overall, in-creasing energetic interactions of the ssDNA and DNA-boundcounterions with the OEG surface with decreasing Rg,DNA

provide a plausible explanation for the slightly smaller con-formations of the ssDNA on the hydrophilic OEG surface rel-ative to the hydrophobic OMe surface.

B. Effect of temperature on ssDNA structure,energetics, and size

We now discuss the temperature-dependence of the struc-ture, size, and interactions of the C16 ssDNA oligomer, whichwe obtained using temperature-replica exchange moleculardynamics.

We present aspects of the molecular-level structure andinteractions as a function of temperature and Rg,DNA. As tem-perature increases, the fraction of total DNA surface areathat is phosphate backbone decreases (Figures S7(a) for bulk,S8(a) for OEG, and S9(a) for OMe in the supplementarymaterial) and the fraction of surface area that is nucleobaseslightly increases (Figures S7(b), S8(b), and S9(b) in the sup-plementary material).57 We note that the trend of decreasingnucleobase surface area with decreasing Rg,DNA for the ss-DNA in bulk at 300 K (Figure S2(b) in the supplementarymaterial)57 is also observed at most of the other tempera-tures, which indicates that some micelle-like behavior (i.e.,sequestering of the nucleobases) may also be present at thesetemperatures. The reduction in the phosphate backbone ex-posure with increasing temperature is complemented by thecorresponding increase in the nucleobase exposure. The causeof the slight increase in the nucleobase surface area appearsto be a decrease in base-base stacking with increasing tem-perature (Figure 5(a) for bulk and Figures S8(c) and S9(c)in the supplementary material)57 that was expected becauseof previous experimental observations.48 Along with the de-crease in base-base stacking with increasing temperature(Figure 5(a)), the prevalence of face-on interactions with thehydrophobic OMe surface increases slightly with temperaturefor the most extended ssDNA conformations (Figure 5(b)).

FIG. 5. Effect of temperature on several structural characteristics of the C16 ssDNA oligomer as a function of the ssDNA size (Rg,DNA). The effect of increasingtemperature from 273 K to 373 K is indicated by the color of the lines changing from blue to red, by an increase in line thickness, and by the directionof the arrows. (a) Frequency of base-base stacking in bulk solution, which is also representative of the behavior near OEG and OMe (shown in figures inthe supplementary material).57 (b) Frequency of face-on conformations with the hydrophobic OMe surface, which increases slightly with temperature for theextended ssDNA conformations (Rg,DNA ≥ 19 Å). (c) Number of DNA-water hydrogen bonds, normalized to the number of hydrogen bonding partners on thessDNA in bulk solution, which is representative of the behavior near OEG and OMe. Error bars are the standard deviation calculated by block averaging over10 blocks.

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This finding is interesting because it could indicate strongerhydrophobic interactions of the ssDNA with a hydrophobicsurface at increased temperature, but we must note that, be-cause of the constant-volume simulations we have used andbecause the hydrophobic effect is temperature- and pressure-dependent,49, 50 it is difficult to draw conclusions about hy-drophobic interactions in constant-pressure conditions. DNA-water hydrogen bonds decrease with increasing temperature(Figure 5(c)), which is reasonable given that increasing tem-perature increases the translational and rotational motion ofwater molecules, making it more entropically favorable to in-crease the mobility of water molecules by breaking DNA-water hydrogen bonds.

Next, we consider the interaction energy of the ssDNAwith other components in the system. Figure 6 shows the en-ergetic interactions of the DNA near OEG, which are repre-sentative of the temperature-dependence of these interactionsin bulk and near OMe, which are shown in Figures S10 andS11 in the supplementary material,57 with the exception ofthe DNA-surface interaction energy as discussed below. Wenote that Figure 6 shows the absolute values of the energy,unlike Figure 4 which shows the energy relative to the largestvalue of Rg,DNA. The total interaction energy of the ssDNAwith everything else in the system (Eall-DNA) does not changesignificantly with increasing temperature, although there isa very slight upward trend with increasing temperature

(Figure 6(a)), which is expected because the increasing im-portance of entropy with increasing temperature should gen-erally allow the system to sample states with less favorableenergetic interactions.

The DNA-ion interaction energy becomes slightlymore favorable with increasing temperature (Eions-DNA,Figure 6(b)), while the DNA-water interaction energy be-comes less favorable with increasing temperature (Ewater-DNA,Figure 6(c)). The reason for these two changes is the balanceof the energetic and entropic contributions of the counterionsand water molecules. First considering the energetic contribu-tions, the counterions each bear a positive charge and there-fore have a much stronger electrostatic drive to interact withthe negatively charged phosphate backbone than the polar-but-uncharged water molecules do. Therefore, each individ-ual counterion has a more favorable energetic interaction withthe DNA than each individual water molecule (Figure S12 inthe supplementary material).57 Next considering the entropiccontributions, both water and counterions lose a considerableamount of translational entropy when they are near the DNA,but water molecules also lose rotational and vibrational en-tropy when they are adsorbed to the DNA. Consequently, theentropic cost of confining water molecules near the DNA ishigher than the cost of confining counterions near the DNA,and furthermore this entropic cost increases with tempera-ture by a greater extent for the water molecules than for the

FIG. 6. Effect of temperature on energetic interactions of the C16 ssDNA oligomer 10 Å from the hydrophilic OEG surface, which is representative of thebehavior in bulk and near the hydrophobic OMe surface, as a function of the ssDNA size (Rg,DNA). The effect of increasing temperature from 273 K to 373 K isindicated by the color of the lines changing from blue to red, by increasing thickness of the lines, and by the direction of the arrows. The energetic interactionsare between the C16 ssDNA oligomer and (a) everything in the system (water, counterions, and surface), (b) Na+ counterions, (c) water molecules, and (d) theOEG or OMe surface. Error bars are the standard deviation calculated by block averaging over 10 blocks.

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counterions (Figures S13 and S14, and Section S14 in thesupplementary material for details of this calculation).57 Thedecrease in water-DNA energetic interactions and the in-crease in the importance of water entropy with increasingtemperature are also suggested by the decreasing numberof DNA-water hydrogen bonds with increasing temperature(Figure 5(c)). Overall, the counterions have a stronger ener-getic motivation and a smaller entropic penalty for interact-ing with the DNA than the water molecules do, and conse-quently the increasing importance of entropy with increasingtemperature decreases DNA-water interactions while increas-ing DNA-ion interactions.

Near OEG, the DNA-surface interaction energy(Esurface-DNA, Figure 6(d)) becomes less favorable withincreasing temperature, likely for the same reasons that thewater-DNA interaction energy becomes less favorable withincreasing temperature, which is that dominant entropiccontributions at higher temperatures steer the system towardstates with higher entropy, and less favorable energy. Thereduction in DNA-surface interactions with increasingtemperature is not evident in the number of DNA-surface hy-drogen bonds (Figure S15 in the supplementary material),57

possibly because of the imprecise nature of the geometricdefinition of hydrogen bonds that we have used. Near OMe,the DNA-surface interaction energy becomes slightly morefavorable with increasing temperature (Figure S11 in thesupplementary material),57 which may be connected withthe slight increase in the number of face-on conformations(i.e., hydrophobic interactions) between the relatively hy-drophobic nucleobases and the hydrophobic OMe surfacewith increasing temperature (Figure 5(b)).

Having described the effect of temperature on themolecular-level structure and interactions of the ssDNA C16

oligomer, we now shift our focus to the effect of temperatureon the free energy as a function of Rg,DNA at varying tem-peratures in bulk solution and near the OEG and OMe sur-faces in Figure 7. Qualitatively, since the free energy profileis essentially the same shape irrespective of the temperature,increasing the temperature does not drastically change free

energy landscape. Clearly, as expected, increasing the tem-perature generally flattens the free energy profile. Interest-ingly, the amount by which the free energy changes is dif-ferent for bulk, OEG, and OMe, and within each of the threecases the amount of the change is different for the compactconformations (Rg,DNA < 16 Å) and the extended conforma-tions (Rg,DNA > 16 Å). Qualitatively, as temperature increasesthe free energy profile decreases more for the compact con-formations than for the extended conformations regardless ofthe presence or chemistry of the surfaces, a difference that wenow quantify and investigate in greater detail.

To compare the behavior of the compact and extendedconformations for ssDNA C16 oligomer, in Figure 8 wepresent the free energy difference between the free energy at16 Å (roughly the minimum free energy in all three cases:bulk, OEG and OMe) and (i) the most extended DNA confor-mation (∼23 Å, �Flarge, Figure 8(a)) and (ii) the most com-pact DNA conformation (∼9 Å, �Fsmall, Figure 8(b)). Thepoints on the free energy landscape between which we cal-culate this difference are shown schematically in Figure 7(a).The free energy difference between the intermediate (16 Å)and the extended (23 Å) conformations (�Flarge) decreasesonly slightly with temperature, and remains close to a valueof 6 kcal/mol in bulk and on both surfaces (Figure 8(a)). Incontrast, the free energy difference between the inter-mediate (16 Å) and the compact (9 Å) conformations(�Fsmall) decreases significantly with increasing temperature(Figure 8(b)). In bulk solution, �Fsmall decreases from ap-proximately 6 kcal/mol to approximately 4 kcal/mol, whileon both surfaces �Fsmall decreases by a greater amount thanin bulk from approximately 8 kcal/mol to approximately 4kcal/mol as temperature increases from 273 K to 373 K. Wespeculate that the latter trend, the larger decrease in �Fsmall

on the surfaces compared to bulk solution, may be related tosteric hindrance between the ssDNA and the surfaces, whicharises because the ssDNA is held near the surfaces (10 Å cen-ter of mass distance). When the ssDNA is in an extendedconformation, it assumes an anisotropic, rod-like conforma-tion parallel to the surface in the xy-plane. As the size of the

FIG. 7. Effect of temperature on the free energy as a function of DNA size (Rg,DNA) for the C16 ssDNA oligomer (a) in bulk solution, (b) 10 Å from thehydrophilic OEG surface, and (c) 10 Å from the hydrophobic OMe surface. The effect of increasing temperature is indicated by the color of the lines changingfrom blue to red and by increasing thickness of the lines, and by the direction of the arrows in (b) and (c). The arrows in (a) indicate values of free energy forwhich the free energy difference is plotted in Figure 8. �Fsmall is the free energy change from intermediate (16 Å) to small (9 Å) values of Rg,DNA, and �Flarge

is the free energy change from intermediate to large (23 Å) values of Rg,DNA. Error bars are calculating using the Monte Carlo bootstrap procedure described inSec. II.

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FIG. 8. Effect of temperature on changes in free energy (a) and (b) and num-ber of water molecules within 3 Å of the ssDNA (c) and (d). The changes arebetween intermediate (16 Å) and large (23 Å) values of Rg,DNA (a) and (c) andbetween intermediate (16 Å) and small (9 Å) values of Rg,DNA (b) and (d).�F indicates a free energy difference, while �Water indicates a differencein the number of DNA-bound water molecules (i.e., those water moleculeswithin 3 Å of the ssDNA). The subscript “large” indicates that the differ-ence is between intermediate (16 Å) and large (23 Å) values of Rg,DNA, whilethe subscript “small” indicates that the difference is between intermediate(16 Å) and small (9 Å) values of Rg,DNA. The number of DNA-bound watermolecules at intermediate Rg,DNA (16 Å) is estimated as the average of thenumber of water molecules in the neighboring umbrella sampling windows(i.e., Rg,DNA = 15 Å and 17 Å). The error bars are calculated as the root sumof the squares of the constituent uncertainties.

ssDNA decreases, the ssDNA contracts in the xy-plane toform a globular conformation. To accommodate this contrac-tion in the xy-plane, it is reasonable that the ssDNA would bedriven to expand in the z-direction to assume a more isotropicglobular conformation. Expanding in the z-direction might,for example, help alleviate electrostatic repulsion betweenphosphates. However, because the ssDNA is held near the sur-face, this expansion in the z-direction is impeded by sterichindrance from the surface, whereas in bulk solution there isno such impediment. Increasing the temperature apparentlyreduces the drive for the ssDNA to expand in the z-direction(e.g., by reducing electrostatic repulsion within the ssDNA byneutralizing the negative charge of the phosphates through in-creased ssDNA-counterion interactions, Figure 6(b)), whichreduces the effect of ssDNA-surface steric hindrance. Conse-quently, there is a greater reduction in �Fsmall with increasingtemperature near the surfaces than in bulk solution.

While there is a qualitative downward trend in �Fsmall

with increasing temperature both in bulk and near the sur-faces (Figure 8(b)), there is essentially no change in �Flarge

with increasing temperature (Figure 8(a)). The reason for thedifference in the temperature dependence of the compact andextended conformations appears to be differences in entropiccontributions by water molecules that are adsorbed to theDNA in different ssDNA conformations. As temperature in-creases, the translational, rotational, and vibrational entropy

of water molecules becomes increasingly important, but wa-ter molecules that are adsorbed to the DNA (e.g., through hy-drogen bonds) have substantially reduced entropy.51 There-fore, DNA conformations that adsorb a greater number ofwater molecules will be more entropically unfavorable. Torelate this idea to the difference in the free energy changebetween the intermediate and extreme (most compact, mostextended) values of Rg,DNA, we quantify the change in thenumber of DNA-bound water molecules from the intermedi-ate to the extreme conformations as a function of temperature(Figures 8(c) and 8(d)), and we also estimate the entropic costof confining these water molecules near the DNA (Figure S16in the supplementary material).57 The quantities shown inFigures 8(c) and 8(d) are the number of water moleculesthat are adsorbed to or displaced from the DNA during achange in DNA conformation. For the change from interme-diate (16 Å) to extended (23 Å) conformations (�Waterlarge),additional water molecules adsorb to the ssDNA, as expected,and the number of additional adsorbed water molecules (ap-proximately 12) is essentially independent of temperature(Figure 8(c)). However, the entropic cost of confining eachof these water molecules near the ssDNA increases as tem-perature increases (i.e., both �S and T�S for the process oftransferring a single water molecule from bulk water into thevicinity of the ssDNA become increasingly negative with in-creasing temperature, see Section S14 in the supplementarymaterial).57 Therefore, although �Waterlarge is essentially in-dependent of temperature, the total entropic cost associatedwith �Waterlarge becomes increasingly unfavorable with in-creasing temperature. This increasingly unfavorable loss ofwater entropy with increasing temperature helps explain whythe free energy cost of increasing the ssDNA size (�Flarge)does not significantly decrease with increasing temperature.Simplistically, we might expect increasing the temperature toflatten the entire ssDNA conformation free energy landscapeuniformly (i.e., the increasing importance of entropy with in-creasing temperature would allow the system to sample allvalues of Rg,DNA, large and small, more easily). However, theincreasing entropy loss of the DNA-bound water moleculeswith increasing temperature, which makes it less likely forthe system to sample the large ssDNA conformations wherea greater number of water molecules are bound to the ss-DNA, counters the increasing influence of entropy on otherdegrees of freedom with increasing temperature, which wouldotherwise make it more likely for the system to sample anyvalue of Rg,DNA, including the large values, at higher temper-atures. Therefore, it appears that �Flarge does not change sig-nificantly with increasing temperature because of this balanceof entropic contributions from water molecules and from allother sources.

For the change from intermediate (16 Å) to compact(9 Å) conformations (�Watersmall), water molecules are dis-placed from the ssDNA oligomer, as expected, and thenumber of displaced water molecules increases with in-creasing temperature (Figure 8(d)). At the highest tempera-ture shown here (373 K), approximately 5 additional watermolecules are displaced compared to the lowest temperature(273 K). Because the entropic cost of confining a single watermolecule near the DNA increases with increasing temperature

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(Section S14 in the supplementary material), the release ofwater molecules becomes increasingly entropically favorablewith increasing temperature (Figure S16(a) in the supple-mentary material), which is consistent with the decreasingfree energy cost of forming a compact ssDNA conformation(�Fsmall, Figure 8(b)).57

Additional contributions to the relative changes in �Flarge

and �Fsmall with increasing temperature include (i) the in-creasing entropic unfavorability of highly extended ssDNAconformations, which could cause the decrease in �Flarge withincreasing temperature to be smaller, and (ii) the reduction inbase-base stacking with increasing temperature, which couldmake it easier for the ssDNA oligomer to assume a globularconformation and could thereby allow �Fsmall to decrease bya greater extent.

IV. CONCLUSION

We used atomistic molecular dynamics simulations, com-bined with umbrella sampling and temperature-replica ex-change to enhance conformational sampling, to study the con-formations and interactions of a ssDNA oligomer consist-ing of 16 cytosine nucleotides (C16) in bulk solution, near amodel hydrophilic oligo(ethylene glycol) (OEG) surface, andnear a model hydrophobic oligo(methylene) (OMe) surface.We calculated the free energy as a function of ssDNA size,Rg,DNA. Then, as a function of Rg,DNA, surface presence andchemistry, and temperature, we quantified the molecular-levelstructure (e.g., surface area composition), interactions (e.g.,DNA-surface hydrogen bonds), and energetics of the ssDNAoligomer.

Although the free energy as a function of Rg,DNA isonly weakly affected by surface presence and chemistry,slightly smaller ssDNA conformations are favored on the hy-drophilic OEG surface relative to the hydrophobic OMe sur-face. More compact ssDNA conformations concentrate thenegative charge of the DNA in a smaller spatial region, whichincreases the favorable electrostatic interactions between thessDNA, Na+ counterions, and the polar OEG surface. The in-crease in ssDNA-OEG and DNA-bound counterion-OEG in-teractions appears to be the energetic driving force for theslightly smaller conformations favored by the OEG surface.

The ssDNA surface composition (i.e., the relative expo-sure of hydrophobic nucleobase and hydrophilic phosphatebackbone), which shows some evidence for a micellar con-formation in bulk solution (i.e., sequestration of the relativelyhydrophobic nucleobases), is not significantly affected by thepresence of either the hydrophilic or the hydrophobic surface.DNA self-interactions (i.e., intra-DNA hydrogen bonds andbase-base stacking) are only weakly affected by the two sur-faces, although it appears that hydrogen bonds between thessDNA and the hydrophilic OEG surface may disrupt base-base stacking.

Increasing the temperature has qualitatively similar ef-fects in bulk solution and near both the hydrophilic OEG sur-face and the hydrophobic OMe surface. Increasing tempera-ture decreases base-base stacking and slightly increases theamount of exposed nucleobase surface area. The increase inthe exposure of the relatively hydrophobic nucleobases could

lead to increased hydrophobic interactions at higher temper-atures, although we note limitations in this interpretation inthe discussion of limitations next. DNA-water interactions de-crease with increasing temperature due to entropic effects.Interestingly, DNA-counterion interactions actually increasewith increasing temperature because of the greater electro-static interaction of counterions with DNA relative to wa-ter with DNA and because of the greater entropic cost ofconfining water molecules near the DNA relative to that ofcounterions. Finally, while increasing temperature flattens theentire free energy landscape as a function of Rg,DNA, morecompact ssDNA conformations see a greater reduction inthe free energy than do more extended ssDNA conforma-tions. The reason for this is the entropically favorable releaseof DNA-bound water molecules, which we find increaseswith increasing temperature for the more compact ssDNAconformations.

Lastly, we note the limitations to the simulation approachwe have used and future directions for this work. One, wehave only studied the behavior of the ssDNA when it is held at10 Å from the two surfaces. The reason for this was the greatlyincreased computational expense of simulating additional sur-face separation distances. Constructing a two-dimensionalfree energy landscape of DNA conformation and surface dis-tance would be a valuable future direction that could revealhow DNA adsorption and conformation are related. However,obtaining sufficient sampling for such a 2D free energy land-scape would be computationally costly and would likely re-quire the use of methods that improve the computational effi-ciency of replica exchange molecular dynamics.52, 53 Two, theuse of temperature-replica exchange subjects the biomolec-ular force fields to conditions for which they have not beenrigorously tested. For example, the TIP3P water model doesnot reproduce phase behavior of water,54 and the Amber forcefields are parameterized at ambient conditions (i.e., 300 K andatmospheric pressure).31 As such, the force fields likely do notaccurately describe the behavior of ssDNA at elevated tem-peratures. However, it seems reasonable that the force fieldfor ssDNA will still serve as a qualitative model of an am-phiphilic polyelectrolyte even at high temperatures, and in anycase the purpose of the high-temperature replicas is primarilyto accelerate conformational sampling in the low-temperaturereplicas where the force fields are more reliable. Three, thetemperature-replica exchange simulations were conducted atconstant volume, so the pressure increases with tempera-ture. We used constant volume conditions rather than con-stant pressure conditions because the high-temperature repli-cas would require a greatly increased volume to maintainconstant atmospheric pressure (i.e., water would vaporize atthe highest temperatures employed in the temperature-replicaexchange protocol at atmospheric pressure). The large dif-ferences in system volume and phase could make it diffi-cult to successfully exchange between high-temperature repli-cas. However, because the replicas at very high temperatures(>373 K) are intended only as a means to increase con-formation sampling in the lower-temperature replicas, ratherthan as a means to sample the actual behavior of the ss-DNA at the highest temperatures, the use of constant vol-ume conditions seems reasonable. Nonetheless, because the

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155103-14 R. M. Elder and A. Jayaraman J. Chem. Phys. 140, 155103 (2014)

hydrophobic effect is both temperature- and pressure-dependent,48, 49 care must be taken in comparing our resultsat elevated temperatures and correspondingly elevated pres-sures with experimental or simulation results obtained at at-mospheric pressure. Four, these simulations contained onlyneutralizing counterions (i.e., an added salt concentration ofzero), which is dissimilar from typical experimental measure-ments where a finite concentration of salt is used. In futuresimulation studies of DNA-surface interactions, we will em-ploy finite salt concentrations to avoid some of the known de-ficiencies of zero salt conditions.55, 56 Despite this limitation,our findings are still applicable to understanding the behav-ior ssDNA and other polyelectrolytes in low salt conditions.Finally, this study is an extension of our previous work onshort ssDNA oligomers near surfaces,28 and to connect theseworks with various applications involving double-strandedDNA near surfaces, our future work will include studies ofthe stability of dsDNA near surfaces of various chemistries.

ACKNOWLEDGMENTS

This research was partially supported by the NationalScience Foundation Award No. DMR-1206894. The authorsalso thank the National Science Foundation for supercomput-ing time through Teragrid/XSEDE (grant TG-MCB100140).This work also used the Janus supercomputer, which is sup-ported by the National Science Foundation (Award No. CNS-0821794) and the University of Colorado Boulder. The Janussupercomputer is a joint effort of the University of ColoradoBoulder, the University of Colorado Denver and the NationalCenter for Atmospheric Research.

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