Crowding and Confinement Effects in Different Polymer Concentration

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

pubs.acs.org/Macromolecules

Crowding and Confinement Effects in Different Polymer Concentration Regimes and Their Roles in Regulating the Growth of Nanotubes Qiufen Zhang,† Lin Zhu,† Tianhao Hou,‡ Haojing Chang,† Qingwen Bai,† Jiang Zhao,*,‡ and Dehai Liang*,† †

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Beijing National Laboratory for Molecular Sciences, Department of Polymer Science and Engineering and the Key Laboratory of Polymer Chemistry and Physics of the Ministry of Education, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China ‡ Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China S Supporting Information *

ABSTRACT: Among numerous research studies focusing on macromolecular crowding and confinement, few are concerned with the medium at a broad range of concentrations, let alone the interplay between the crowding effect and confinement effect. In this work, we systematically studied the assembly of DNA tiles into nanotubes in polyethylene oxide (PEO) and polyacrylamide (PAM) media covering the concentration range of dilute, semidilute, and concentrated regimes. In light of the structure and kinetics of DNA assembly, both the PEO and PAM media can be divided into three regimes with increasing polymer concentration: the crowding regime, double-effect regime, and confinement regime. In the crowding regime, DNA tiles only form clusters because the assembly into a tube structure is hindered. In the double-effect regime, polymer chains form a transient network whose pore size is close to the diameter of DNA nanotubes. The confinement effect, together with the crowding effect, facilitates the assembly of DNA tiles into a tube structure. In the confinement regime, the length of DNA tubes decreases with polymer concentration, which can be quantitatively described by a scaling relationship. The borderlines of the three regimes are polymer-specific. The PEO medium enters the double-effect regime and confinement regime at concentrations much lower than the PAM medium, suggesting that the PEO medium exhibits stronger macromolecular crowding and confinement effects. We attribute it to the special hydrophilicity of PEO, which has the capability to couple with the lattice structure of a water network, leading to a decrease in thermal motion and hence a mutual stabilization.

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INTRODUCTION The cell interior is crowded with a high content (up to 400 g/ L) of macromolecules.1,2 The dense medium is able to modulate the structure and reaction rates of biomolecules such as proteins3−7 and nucleic acids.8−11 If the medium is inert to the solute biomolecules, the effects are attributed to macromolecular crowding and macromolecular confinement, both of which are excluded volume effects dominated by entropy.12,13 The former favors products with a more compact conformation, while the latter tends to befit the shape and size of products to that of the confinement volume.14−16 Recent studies show that the medium can also interact with the solute molecules via nonspecific interactions of enthalpic nature.17−20 Such enthalpic contributions can influence the excluded volume effect of macromolecular crowding and confinement depending on the propensity of those nonspecific interactions. Experimental and theoretical studies on macromolecular crowding and confinement are generally based on model systems in which synthetic polymers such as Ficoll, polyethylene oxide (PEO), or their mixtures are used as crowders © XXXX American Chemical Society

to learn their effect on enzyme reactions, protein stability, or DNA folding.21−23 However, the cell interior is much more complex. It contains different types of molecules, such as proteins, nucleic acids, and polysaccharides. Multiple noncovalent interactions between biomolecules blend the entropic and enthalpic contributions together. Besides, the molecules inside the cell are not uniformly distributed but with a volume ratio ranging from 5 to 40%, covering the dilute, semidilute, and concentrated regimes. It was reported that the thermodynamics and kinetics of protein folding inside cells were affected by the spatial heterogeneity of crowding.24−27 Ebbinghaus and Gruebele found that the folding free-energy landscape and local viscosity varied according to the microenvironments in the cellular landscape.25 Kozer et al. studied the effect of PEO at different concentrations on protein−protein association.28 They found that the association Received: February 4, 2019 Revised: April 15, 2019

A

DOI: 10.1021/acs.macromol.9b00240 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules rate was accelerated in the semidilute solution due to the depletion effect. But in the dilute and concentrated regimes, it was slowed down because of the repulsion force. The concentrated polymer solution is also likely to confine the aggregate into an anisotropic structure,29 which fits the “tube” model proposed by Edwards and Doi.30 Both the confinement and crowding effects become stronger with increasing polymer concentration. However, the interplay between these two excluded volume effects at varying polymer concentrations has not been clarified. The understanding of macromolecular crowding and confinement at the cellular level still depends on appropriate model systems that can quantitatively differentiate an entropic contribution from an enthalpic contribution and a crowding effect from a confinement effect. In this work, we chose PEO and PAM as the crowders and systematically study the macromolecular crowding and confinement effects on the growth of DNA nanotubes in polymer media at concentrations ranging from dilute to concentrated regimes. It was reported that PEO, a commonly used inert crowder, exhibited certain nonspecific interactions with proteins,31−33 which was different from PAM. Unlike proteins, DNA has a relatively simpler structure, and its assembly process is readily determined. Moreover, it is more viable to differentiate a macromolecular crowding effect from a confinement effect since the latter will be more severe as DNA nanotubes grow longer or as the polymer concentration is elevated. Scaling theory is applied to quantitatively describe the relationship between the polymer concentration and degree of confinement. Results show that the effect of a polymer medium can be divided into three regimes with increasing concentration: the crowding regime, double-effect regime, and confinement regime. The borderlines of the regimes are polymer-specific. Scaling exponents show that the confinement effect of PEO is much stronger than that of PAM in regulating the growth of DNA nanotubes.

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Scheme 1. Sequence of DNA Tiles and the Assembly Process

mL and 0 to 24 mg/mL, respectively. The DNA-polymer mixtures were kept at 4 °C before use. Growth of DNA Nanotubes in a Polymer Solution. The DNA-polymer mixture was heated at 95 °C for 5 min to denature all the DNA strands, followed by an annealing process to 45 °C at a 1 °C/min cooling rate. The annealing process allowed the DNA strands to form tiles. The growth of tiles into a DNA nanotube was triggered when the mixture solution was quenched to 25 °C in a sample reservoir built on a glass slide. The moment of quenching was set as the zero time point. The growth of DNA nanotubes was monitored for 40 min by a laboratory-built total internal reflection fluorescence microscope (TIRFM), which was equipped with an electronmultiplying charge-coupled device camera (Andor DV887 EMCCD). The shortest exposure time was 0.1 s. The excitation laser beam (Melles Griot, USA, 532 nm) hits the sample surface from the bottom of the slides, and the images are collected through an oilimmersion objective lens (100×, numerical aperture = 1.45). The images were analyzed by ImageJ software. To prevent sample adsorption, the microscope slides were pretreated by γ-MPS to introduce a double bond on the surface, followed by polymerization of AM monomers to form a PAM layer. Viscosity of PEO and PAM. The viscosities of PAM and PEO solutions in 1× TAE buffer at different concentrations were determined by an Anton Paar Physica MCR 301 rheometer (Anton Paar GmbH, Austria) at 25.0 °C. The double gap (DG 26.7), cone plate (CP50−1), or parallel plate (PP25) was used depending on the viscosity range. For each sample, the apparent viscosity at a shear rate ranging from 0.1 to 1000 s−1 was measured. Each measurement was repeated at least three times. The zero-shear-rate viscosity (η0) was obtained by the extrapolation method using the Carreau−Yasuda I model.35 The plots of specific viscosity ηsp = (η0/ηbuffer − 1) as a function of concentration (c) were drawn for both PAM and PEO. The overlap concentration c* and the entanglement concentration ce were determined by fitting the plots with different power law equations ηsp = bcK with “b” and “K” being constants. Image Process. The images were analyzed using the “analyze particle” function in ImageJ software. The DNA assemblies were treated as irregular particles whose sizes were characterized by a statistical Feret diameter. For an irregular object, the Feret diameter is the distance between parallel tangents on opposite sides of the object. The averaged value over all orientations is named the statistical Feret diameter, denoted as dF in this work. dFmin describes the shortest Feret diameter of the object. The contour of each assembly in the field was determined by an intensity profile. The dF and dFmin of the assembled structures or nanotubes were obtained from the software. Typically, 20 to 100 particles were analyzed, and the standard errors were calculated. The trajectory of each assembly was acquired with the Mtrack2 plugin in ImageJ software. The mean squared displacement (MSD) was calculated according to ⟨Δr(τ)2⟩ = ⟨|r(t + τ) − r(t)|2⟩, where r is the position in the xy plane, and τ is the time interval. The velocity−

EXPERIMENTAL SECTION

Materials. Single-stranded oligonucleotides (purity, >99%) with known sequences were purchased from Invitrogen Biotech (Shanghai, China). Polyacrylamide (PAM, Mw = 5.1 × 106 g/mol, Rg = 101 nm), high-molecular-weight polyethylene oxide (PEO, Mw = 1.1 × 106 g/ mol, Rg = 71 nm), and low-molecular-weight polyethylene oxide (Mw = 4.0 × 103 g/mol, Rg = 4 nm) were purchased from Sigma-Aldrich (St. Louis, U.S.A.). The molecular weight and size were determined by laser light scattering (LLS). Acrylamide (AM), Tris(hydroxymethyl) aminomethane (Tris base), ethylenediamine tetra acetic acid (EDTA), and 3-(trimethoxysilyl)propyl methacrylate (γMPS) were purchased from Sigma-Aldrich (St. Louis, USA) and used as received. HAc, Mg(Ac)2, and NaCl were purchased from Beijing Chemical Reagent Company (Beijing, China) and used as received. Preparation of the DNA-Polymer Mixture. The protocols for the assembly of DNA nanotubes can be found elsewhere.34 Briefly, the five DNA strands with known sequences are able to form a rectangular tile of 4 × 2 × 14.3 nm. Four to ten of such tiles further assemble into a tube structure with a diameter ranging from 7 to 20 nm (Scheme 1). The fifth strand in Scheme 1 was labeled by a fluorophore, Alexa 532, for online observation of the assembly process by microscopy. The DNA strands were initially dissolved and stored in 1× TE buffer (10 mM Tris-acetate, 1 mM EDTA, pH 8.3), while PAM or PEO was dissolved in Milli-Q water. DNA strands and a known amount of PAM or PEO solution were mixed together. TAE buffer (10×; 400 mM Tris base, 200 mM HAc, 20 mM EDTA, 125 mM Mg(Ac)2, pH 8.3) and Milli-Q water were used to dilute the mixture. The final mixture solution contained 100 nM of each DNA strand in 1× TAE buffer, with 2% strand 5 being labeled with Alex 532. The concentrations of PAM and PEO ranged from 0 to 30 mg/ B

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Macromolecules velocity autocorrelation function, Cv(τ) = ⟨v(t)·v(t + τ)⟩/⟨v(t)2⟩, in which v(t) represents the instantaneous velocity vector at time t, was also calculated.

which again demonstrates that PEO behaves differently in water compared with PAM. Concentration Effect on the Growth of DNA Nanotubes. The growth of DNA nanotubes in PEO or PAM media was monitored by fluorescence microscopy. To unify the macromolecular crowding and confinement effects of different polymer media, we use c/c* to denote the concentration. Figure 2 compares the growth of DNA assemblies in PEO

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RESULTS AND DISCUSSION c* and ce Values of PAM and PEO. The overlap concentration c* and entanglement concentration ce are two critical values that divide the polymer solution into dilute, semidilute, and concentrated regimes. In each regime, the power law scaling relationship between the specific viscosity of the polymer solution and its concentration is different. In a good solvent, the theoretical exponents are 1, 2, and 14/3 at concentrations below c*, in between c* and ce, and above ce, respectively.36 On the basis of this principle, we determined the c* and ce values of PAM and PEO from the plots of specific viscosity versus concentration (Figure 1). Table 2 compares

Figure 1. Concentration dependence of the specific viscosity for PAM (open circle) and PEO (open inverted triangle) in 1× TAE buffer at 25.0 °C. Figure 2. (A−G) Microscopy images showing the growth of DNA nanotubes in PEO media of varying concentrations as denoted by c/ c*.

the critical values of PAM and PEO. The Mw of PAM is about 5 times larger than that of PEO, corresponding to a factor of 3 in terms of degree of polymerization (N). However, the c* value of PAM, as determined by viscosity, is much larger than PEO. It is known that c* is proportional to N−0.76 in a good solvent.36 The lower c* value for PEO, which has a shorter chain than PAM, suggests that the behavior of PEO in water is different from that of PAM in water. The c* value can also be estimated from LLS results by the equation Mw/(4πNARg3/ 3).37 The calculated values for PAM and PEO are 2.0 and 1.2 mg/mL, respectively. It is known that the c* value determined by LLS is lower than that determined by specific viscosity.38 However, the trend remains. Same as c*, ce is also proportional to N−0.76 in a good solvent.36 The ce values of PAM and PEO are close, as determined from the specific viscosity (Table 1),

media at varying concentrations. Similar results are obtained in PAM media (Figure S1). DNA tiles quickly aggregate into clusters at c/c* = 0 (Figure 2A), and a tube structure is formed with time when c/c* exceeds 1 (Figure 2C). As the crowder concentration further increases, the tube shape matures with truncated length (Figure 2D−G). To quantitatively describe the process, we use the Feret diameter (dF), minimum Feret diameter (dFmin), and their ratio (dF/dFmin) to characterize the size and anisotropy of the DNA assemblies at the final stage. In both PEO and PAM media, dF, which represents the average assembly diameter, decreases at the studied c/c* range (Figure 3A,C). The dFmin also shows a diminishing trend with c/c*, but it reaches a

Table 1. Physicochemical Parameters of PAM and PEO polymer

Mw (g/mol)

N

Rg (nm)

c* (mg/mL)

ce (mg/mL)

c*a (mg/mL)

PAM PEO

5.1 × 106 1.1 × 106

6.7 × 104 2.4 × 104

101 71

2.7 1.7

12 12

2.0 1.2

a

Calculated from Mw/(4πNARg3/3). C

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Figure 3. Concentration (c/c*) dependence of (A, C) dF and dFmin as well as (B, D) dF/dFmin of the assembled DNA structures in (A, B) PEO and (C, D) PAM. The c/c* range is divided into three regimes as indicated by different background colors. The dotted vertical lines in each panel indicate the corresponding locations of c* and ce.

Figure 4. Microscopic imaging showing the movement of assembled structures with time in PEO media at (A1−A5) 0.7c*, (B1−B5) 2.1c*, (C1− C5) 5.7c*, and (D1−D5) 8.5c*. The last two panels in each row show the trajectory of the assemblies together with the enlargement of the selected area.

minimum value and then remains constant afterward. The dFmin describes the shortest diameter of the structures, and its minimum value at a high c/c* region denotes the diameter of the DNA nanotubes. The dF/dFmin thus represents the aspect ratio of the DNA assembly. As dFmin reaches the minimum value and remains stable, the dF/dFmin also indicates the change of tube length since the diameter is constant. The dF/ dFmin shows a similar trend with c/c* in both PEO and PAM solutions. It slowly increases at an early stage followed by a shoot-up and then declines afterward (Figure 3B,D). Therefore, we propose a division of the c/c* range into three regimes underpinned by changes in dFmin, dF, and dF/dFmin in PEO and PAM media. In a low-concentration regime represented by an indigo background in Figure 3, both dFmin

and dF decrease sharply, and dF/dFmin increases slightly with c/c*, suggesting that the crowder at higher concentrations prevents DNA assemblies from growing larger, yet it facilitates the formation of anisotropic structures. The intermediate regime, indicated by the light yellow background in Figure 3, is characterized by a slower decreasing tendency in dF, a soar in dF/dFmin, and dFmin reaching its minimum. In fact, DNA tiles start to assemble into fine nanotubes in this narrow concentration regime. In the third regime, a further increase in polymer concentration leads to a monotonic reduction in the length of DNA tubes, as indicated by the decrease in dF and dF/dFmin (Figure 3). The regime borderlines in PEO and PAM are quite different, and they do not necessarily conform with c* and ce indicated in D

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Figure 5. (A) Averaged mean squared displacement (MSD) and (B) velocity−velocity autocorrelation function Cv(τ) of DNA assemblies versus time interval in PEO solution at different concentrations. The fitted power law exponents for MSD and Cv (0.1 s) are annotated on the corresponding figures.

MSD and Cv(τ) exhibit a broad distribution (Figures S2 and S3). It is understandable considering that the DNA assemblies are heterogeneous in size, shape, and motion. However, the averaged MSD and Cv(τ) show a strong dependence on polymer concentration (Figure 5). The MSD curves are fitted with the general diffusion equation MSD = 4Dτα, with D and α being the diffusion coefficient and exponent, respectively. Results show that the power law exponent monotonously decreases from 0.88 at 0.7c* to 0.15 at 8.5c*, suggesting that the motion of DNA assemblies in a polymer solution is subdiffusive and becomes heavier with increasing polymer concentration. The diffusion coefficient correspondingly decreases from 0.25 μm2/s at 0.7c* to 0.001 μm2/s at 8.5c*. The Cv values are negative at 0.1 s (Figure 5B), indicating successive steps moving in opposite directions as a result of movement under restricted conditions. The negative Cv (0.1 s) value reaches −0.31 at 8.5c*, which agrees with the reptation behavior of DNA tubes confined in the entangled PEO network. Together, the increasingly subdiffusive and anticorrelation behavior suggests that the confinement effect becomes stronger at higher polymer concentrations, in agreement with the findings in other reports.39−41 Mechanism of Crowding and Confinement. Taking the above results into consideration, we brought up a proposed identification of three regimes of macromolecular crowding and confinement in light of DNA tile assembly. These regimes are related with but different from those separated by c* and ce. In the first regime, DNA tiles form irregular clusters whose size decreases with increasing medium concentration. No effective network is formed as the upper limit is much lower than ce (Figure 3). Therefore, the behavior of DNA tiles is affected dominantly by the macromolecular crowding effect in this regime. On the one hand, the surrounding polymer chains generate a depletion force that facilitates the formation of DNA clusters in the size of micrometers. This interaction is nondirectional, and it does not promote the formation of regular DNA tubes. On the other hand, the viscous medium brings a significant reduction to the tile diffusion rate, thus hindering its assembly (Figure 1).42−44 The macromolecular crowding effect, which favors the product with compact conformation, also limits the size growth of DNA tiles. All these effects become stronger with increasing crowder concentration. Because the hindrance weighs more than the depletion effect, the size of the DNA assemblies sharply decreases. Since all these changes in DNA assembly behavior

Figure 3 by red vertical dotted lines. The DNA tiles start to form nanotubes in the PEO solution at a concentration slightly above c* (1.2c*) (Figure 3A,B), while the counterpart in the PAM solution is postponed to 3.4c* (Figure 3C,D). Similarly, the reduction of tube length occurs at 2.1c* in the PEO solution, which is far below ce (7.1c*), while the corresponding value in the PAM solution is 4.8c*, close to ce (4.2c*). These values suggest that PEO exhibits a much stronger effect than PAM in regulating the assembly of DNA tiles. The PEO medium facilitates the formation of DNA tubes at concentrations slightly above c*, while it hinders the growth of tubes at concentrations far below ce. No effective network is even formed in PEO under such conditions. Concentration Effect on the Kinetics of DNA Assembly. To further reveal the effect of the polymer medium in different c/c* regimes, we analyzed the movement trajectories of DNA assemblies in the PEO solution. In the dilute regime at c/c* < 1, polymer chains exist as isolated random coils, and the irregular DNA assemblies can move, rotate, and reshape freely in the polymer solution (Figure 4A and Movie S1). The trajectory of the mass center covers a range of about 2 μm for a large particle, with that for the smaller ones covering beyond 5 μm (Figure 4A6). In the intermediate regime, for example, at c/c* = 2.1, polymer chains start to overlap and interpenetrate with each other, which significantly hinders the movement of DNA particles, as indicated in Figure 4B6. Small DNA nanotubes can move further, while the larger ones can only move and rotate in a restricted area, adjusting their direction so that the smaller ones can link to one of their ends (Figure 4B and Movie S2). In the third regime at c/c* = 5.7 (above ce), long and fine DNA nanotubes are formed but are confined in a polymer medium. Their rotations are prohibited, and only axial movement at a small scale is allowed (Figure 4C). A short nanotube is able to migrate about 3 μm and connect onto a branch of the existing large DNA tube via an end−end linkage (Figure 4C and Movie S3). At even higher concentrations, such as 8.5c*, only short DNA nanotubes with a uniform length are observed. All nanotubes are confined in the polymer medium with only reptation along the axis occurring in a much smaller scale (Figure 4D and Movie S4). To further reveal the crowding and confinement effects on the diffusion of the assembled structures, we calculated the mean squared displacement (MSD) and velocity−velocity autocorrelation function (Cv(τ)) with time interval for all the trajectories at each polymer concentration in Figure 4. Both E

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Figure 6. (A) Growth curve of DNA nanotubes in the confining regime of PEO solution and (B) the dependence of Lm/L0 on c/c*.

crowder, the confinement regime also exists, but the concentration is above 50 mg/mL (2c*), corresponding to an about 5% volume ratio (Figure S4). This result indicates that topological restriction is the nature of confinement in a polymer medium. Such “soft” confinement allows the existence of structures whose diameters are much larger than the pore size, which is different from the hard confinement generated by, for example, cell nuclei,48,49 nanopores,50 and droplets.51 To quantitatively describe the confinement effect of a PEO medium on the growth of DNA nanotubes, we analyzed the time dependence of the tube length (L) at each concentration in this regime. The curves are shown in Figure 6A. All the curves can be fitted by an exponential growth equation

in this regime can be explained solely by the macromolecular crowding effect, we name it the crowding regime. In the narrow intermediate regime, the structure of DNA assemblies undergoes a transition from irregular clusters to nanotubes. The polymer concentration is above c* but below or close to ce (Figure 3). The overlap of polymer chains results in a highly dynamic transient network, and the depletion effect is negligible.45 However, the topological constraint still generates a strong confinement effect on the growth of DNA tiles. The mesh size ξ of the network can be estimated by ξ = Rg(c/c*)−0.76.36,46 With known Rg and c* values in Table 1, the calculated ξ values of PEO and PAM media in this regime range from 40 to 55 nm and 30 to 40 nm, respectively. The diameter of the DNA nanotube is about 7−20 nm,34 about half the mesh size of the polymer network. Therefore, the topological constraint prevents DNA tiles from forming large clusters. Instead, these tiles tend to assemble into nanotubes as designed. In this regime, macromolecular confinement starts to play a role, and it is the main driving force for the formation of nanotubes. Since both crowding and confinement affect the growth of DNA nanotubes, we name this regime the doubleeffect regime. In the third regime, the length of DNA nanotubes decreases with increasing polymer concentration, which can be attributed to the confinement effect. This regime is thus named as the confinement regime. The lower limit of the confinement regime is different for PAM and PEO. In PAM, the whole regime is above ce. An effective stable network cross-linked by chain entanglements is formed at this point. The mesh size is calculated to be 30 to 17 nm in the 4.8c* to 10.8c* range, close to or lower than the diameter of DNA nanotubes. As the mesh size decreases with concentration, the growth of DNA nanotubes is hindered until it is fully prohibited. Similar results are also observed in the PEO medium. However, only the upper portion (>7.1c*) of the regime is above ce, indicating that the transient PEO network shows a similar effect on nanotube growth as the stable network formed by PAM does. The reptation model, which was proposed by de Gennes to describe the dynamics of a chain in a concentrated polymer medium,47 can be applied to explain the confinement of the PEO network. The constraint on reptation is caused by a collective topological restriction from many neighboring chains that are not necessarily entangled. The dynamics of DNA nanotubes in this regime also fits the reptation model (Figure 4 and Movie S4); thus, the tubes endure similar constraints but with higher strength because of their much larger diameters. When PEO with a low molecular weight (Mw = 4.0 × 103 g/ mol), which is difficult to form entanglements, is used as the

i i t yy L = Lmjjjj1 − expjjj− zzzzzzz (1) k τ {{ k with Lm being the equilibrium length under confinement and τ being the characteristic growth time. Lm is smaller with increasing PEO concentration (Table 2). This is apprehensive since the mesh size decreases and the

Table 2. Mesh Size of PEO Medium and Length of DNA Nanotubes c/c* ξ (nm) Lm (μm)

4.2 24 2.0

5.7 19 1.7

8.5 14 1.6

14.1 9 1.1

medium viscosity increases with the concentration. The linear fitting of log10(Lm/L0) to log10(c/c*) is shown in Figure 6B, which yields Lm /L0 ∝ (c /c*)−0.46

(2)

with L0 being the length of DNA tiles and Lm/L0 being the aggregation number Nm. It is known that the concentration dependence of the mesh size follows (ξ/Rg) ∝ (c/c*)−0.76. Combining this relationship with eq 2, we obtain Lm /L0 ∝ (ξ /R g)0.6

that is ξ /R g ∝ Nm1.67

The exponent in the PEO medium is 1.67, much larger than the value (0.56) in the PAM medium,29 indicating that the length of the DNA nanotube (Nm) is smaller in the PEO medium with a mesh size ξ/Rg same as that in the PAM F

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support this conclusion. We attribute it to the special hydrophilicity of PEO that derives from its capability to couple with the lattice structure of the water network, leading to a decrease in thermal motion and hence a mutual stabilization. Many life-related structures, such as filaments, microtubules, and mitotic spindles, are fibers or tubes, and they are located in a medium with multiple components at different concentrations. In fact, the crowding regime, double-effect regime, and confinement regime could exist simultaneously but at different cellular locations. The components, even in the same region, also change with time and so does their concentration, which results in a transition of one regime into another. Therefore, the dynamic behaviors of these life structures are effectively regulated by the macromolecular crowding and confinement effects even in the absence of nonspecific interactions. Dysregulation of the environment could result in irregular growth of fibers or tubes, such as disease-related amyloids.

medium. The confinement effect of PEO is therefore stronger than PAM. Difference between PEO and PAM. Results on the lowmolecular-weight PEO show that the borderlines for the DNA tiles to form tubes (2.0c*) and the growth of tubes being hindered (12c*) are similar to those in high-molecular-weight PEO (Figure S4), suggesting that the molecular weight difference between PEO and PAM is not predominant. We attribute the strong crowding and confinement effects of PEO to its hydrophilicity. Even though both PAM and PEO can be dissolved readily in water in common experimental conditions, it is reported that water is a poor solvent for polyacrylamide from a thermodynamic viewpoint.52 This is probably correlated with the strong intra- and interchain hydrogen bonding and dipole−dipole interactions in PAM, while the hydrogen bonding between polymer chains and water molecules is dominant in PEO.53 As a result, a monomer unit of PEO can carry more water molecules than that of PAM, with the numbers being 2.4 and 1.9, respectively.54 Besides, it is reported that PEO is able to fit in the lattice structure of the water network, leading to a coupling that results in a decrease in thermal motion and hence a mutual stabilization.55 The block copolymers of PEO-b-PAM form associates in water, which further confirmed that PEO−water and PAM−water interactions are stemmed from different mechanisms.56−58 The hydrophilic nature and coupling of PEO with the water structure render the polymer chain a sheath of water layer, which increases the effective chain diameter. This accounts for lower c* and ce in water. In the double-effect regime, the mesh size (40−56 nm) of PEO is larger than that (30−40 nm) of PAM in regulating DNA tiles into tube structures. It is reasonable considering that PEO carries a thicker water layer, probably a few nanometers in thickness. In the confinement regime, a transient network is formed. Since the coupling suppresses the thermal motion of chains and stabilizes the network, together with the highly thick network strands, the PEO medium therefore shows an enhanced confinement effect.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00240. Microscopy images showing the growth of DNA nanotubes in PAM media of varying concentrations denoted by c/c*; individual mean squared displacement and the velocity−velocity autocorrelation function versus the time interval and their average at different concentrations; microscopy images showing the growth of DNA nanotubes in low-molecular-weight PEO solution of varying concentrations (PDF) Polymer chains existing as isolated random coils and irregular DNA assemblies moving, rotating, and reshaping freely in the polymer solution (AVI) Small DNA nanotubes moving further and larger ones only moving and rotating in a restricted area (AVI) Short nanotubes migrating and connecting onto branches of the existing large DNA tube (AVI) All nanotubes confined in the polymer medium with only reptation along the axis occurring in a much smaller scale (AVI)

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CONCLUSIONS The effect of the polymer medium on the assembly and growth of DNA nanotubes can be divided into three regimes with increasing polymer concentration: the crowding regime, double-effect regime, and confinement regime. In the crowding regime, no effective network is formed. The DNA tiles can only form clusters because the assembly is hindered by typical macromolecular crowding effects. In the double-effect regime, the polymer chains form a transient network with the pore size close to that of the DNA nanotubes. The macromolecular confinement effect starts to play a role in regulating the assembly of DNA tiles into a tube structure, together with the aforementioned crowding effect. As the polymer concentration further increases, the confinement becomes dominant. In the confinement regime, the DNA tiles form shorter tubes in more concentrated polymer solutions, which can be quantitatively described by a scaling relationship. The borderlines of the three regimes are polymer-specific, and they do not agree with c* and ce that separate the polymer solution into dilute, semidilute, and concentrated regions. The PEO medium enters the double-effect regime and confinement regime earlier than PAM, suggesting that the PEO medium possesses stronger macromolecular crowding and confinement effects. It even hinders the growth of DNA clusters without forming an effective network. The scaling exponents also

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.L.). *E-mail: [email protected] (J.Z.). ORCID

Jiang Zhao: 0000-0001-7788-2708 Dehai Liang: 0000-0003-4246-050X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support for this work from the National Natural Science Foundation of China (nos. 21774002 and 21574002) and Beijing Natural Science Foundation (no. 2171001) is gratefully acknowledged. G

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DOI: 10.1021/acs.macromol.9b00240 Macromolecules XXXX, XXX, XXX−XXX