Communication Cite This: J. Am. Chem. Soc. 2017, 139, 15588-15591
pubs.acs.org/JACS
Chemotaxis of Molecular Dyes in Polymer Gradients in Solution Rajarshi Guha,# Farzad Mohajerani,#,§ Matthew Collins,†,§ Subhadip Ghosh,† Ayusman Sen,*,† and Darrell Velegol*,# #
Department of Chemical Engineering, †Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *
nonequilibrium phenomenon (Figure 1B). Note that this observed dye migration is the opposite of expected Fickian diffusion of molecules to regions of low solute concentrations. We primarily used the spreading mode of chemotaxis, where the dye solution in buffer (typically 1 mM KCl) is entered through the middle channel and the polymer solution in buffer is entered through the side channels (Figure 1C). In all cases, the flow rate was maintained at 50 μL/h through each inlet using a syringe pump. Optical scanning was performed at a cutline near the end of the channel (∼38 mm from the inlet = ∼17 s residence time in the channel) with a laser scanning confocal microscope that scanned across the channel width, while focusing at the mid depth of the channel (∼20−25 μm). We measured the chemotactic shifts of dye molecules perpendicular to the direction of fluid movement. To do this, we evaluated normalized fluorescence intensity (I) across the channel and compared it with the control case, i.e., in absence of polymer (Supporting Information).18 The measured chemotactic shift of the dye (δ) is calculated by integrating the fluorescent intensity across the microchannel for the control and the experimental cases, and taking the difference (δ = ∫ Iexperimentdx − ∫ Icontroldx, see Supporting Information and Table S1). The molecule undergoing the chemotaxis was a dye molecule. We typically used 50 μM Rhodamine6G (Rh6G) as the probe dye for both spreading and focusing modes of chemotaxis. In gradients of 5 wt % Ficoll 400K (“K” represents kDa), Rh6G spreads with a typical “horn”-like pattern (Figure 1C). The maxima of the horn pattern lies near to the interface of mid and side channels, where the polymer concentration gradient is the highest. Note that the normalized blue curve generated from dye spreading to the side channels is the combined outcome of both Fickian diffusion as well as the chemotactic shift of the dye. This is in contrast to the normalized red curve, which is solely due to Fickian diffusion. Therefore, subtraction of the area under the red curve from the blue curve extracts out the chemotactic shift. Fickian diffusion and directed chemotaxis migration of the dye are independent of each other. The driving force of the former is the dye concentration gradient, and the driving force of the latter is polymer concentration gradient. However, both the Fickian diffusion and chemotaxis are equally affected by the diffusion coefficient of the dye. Chemotactic shift (δ) perpendicular to the fluid direction is closely related to the dye velocity (VD),
ABSTRACT: Chemotaxis provides a mechanism for directing the transport of molecules along chemical gradients. Here, we show the chemotactic migration of dye molecules in response to the gradients of several different neutral polymers. The magnitude of chemotactic response depends on the structure of the monomer, polymer molecular weight and concentration, and the nature of the solvent. The mechanism involves crossdiffusion up the polymer gradient, driven by favorable dye−polymer interaction. Modeling allows us to quantitatively evaluate the strength of the interaction and the effect of the various parameters that govern chemotaxis.
W
e report the phenomenon of molecular chemotaxis of dye in polymer gradients. Self-powered nano and microscale moving systems are currently of great interest due to potential applications in nanomachines, nanoscale assemblies, robotics, fluidics, and chemical/biochemical sensing.1,2 Recently discovered examples of molecular chemotaxis on surfaces3−6 suggest a method of directing molecular motion in low Reynolds number regimes where they typically undergo random Brownian diffusion. Directed motion is useful for molecular separations7 and nanoscale sensors8 while shedding light on transport in biological systems.9−13 To date, examples of molecular chemotaxis in solution have involved catalysis, where the catalyst is propelled up the substrate gradient.14,15 There are two thermodynamic driving forces for this chemotactic phenomenon in reactive systems: (a) the favorable interaction between the catalyst and the substrate, and (b) the energy released in the catalytic turnover of the substrate.16,17 Thus far, there has not been a method to separately evaluate the two contributing factors. Here, we show for a nonreacting system that simple binding interactions, primarily in the form of noncovalent hydrophobic interactions, can drive the directed motion of molecules. Through a combination of experiments and modeling, we evaluate the parameters governing molecular chemotaxis involving binding-unbinding alone. Our experiments are done in a microfluidic device. We used a three inlet−one outlet polydimethylsiloxane (PDMS) channel with typical dimensions (L × W × H) of 4 cm × 360 μm × 50 μm in order to study the dye chemotaxis in polymer gradients (Figure 1A). The interaction between a dye and a polymer can result in the collective movement of the dye molecules up a polymer concentration gradient. Strikingly, dye molecules that are initially distributed uniformly will eventually migrate toward areas of higher polymer concentration over time because of this © 2017 American Chemical Society
Received: August 17, 2017 Published: October 24, 2017 15588
DOI: 10.1021/jacs.7b08783 J. Am. Chem. Soc. 2017, 139, 15588−15591
Communication
Journal of the American Chemical Society
The equilibrium constant is defined on the basis of molar concentrations of D and P with the following form: Km = [DP]/([D][P]). In our experiments, we used [D] ≪ [P]. In the spreading mode, the total shift of Rh6G in 5 wt % Ficoll 400K gradients was 28.1 ± 4.1 μm. Almost a linear increase in chemotactic shift was observed between 0.5 and 5 wt % Ficoll 400K in a microfluidic channel (Figure 1D). This enhancement can be attributed to the increased concentration gradients of the polymer, and occurs despite a slightly increased solution viscosity at the higher polymer concentrations. The decrease in chemotactic shift above 5 wt % Ficoll 400K gradients is the result of a larger increase in viscosity. The viscosity (η) of solution doubles as the Ficoll wt % is increased from 5% (η = 2.2 cP) to 10% (η = 4.5 cP), decreasing both the Fickian diffusion and the cross-diffusion terms. In contrast, consistent with the absence of CD from the chemotaxis term in eq 1, varying Rh6G concentrations in the range of 25−100 μM did not change the chemotactic shift at 5 wt % Ficoll 400K gradient (Figure 1E). The system was modeled using the spatiotemporal diffusion equation across the channel in COMSOL Multiphysics (Figure 2 and Supporting Information). The flux of the dye (JD) in the
Figure 1. Chemotaxis of Rh6G dye in Ficoll 400K gradients in 3-inlet microfluidic channel. (A) Schematic of 3-inlet−1-outlet microfluidic channel used in spreading mode experiments where the dye enters from the mid channel. Typical flow rate (each inlet): 50 μL/h. The optical scan is performed at a cutline at 38 mm from channel entrance. (B) Dye enters from all three channel inlets at 50 μM concentration. A 5 wt % Ficoll 400K polymer enters from either the mid channel or the side channel inlets. Dye focuses or spreads to where polymer concentration is the highest. The continuous red lines are fitted to the blue experimental data. (C) Spreading mode of chemotaxis where dye enters from the mid channel inlet and polymer enters from two side channel inlets. The shift in normalized intensity (blue curve) is due to dye chemotaxis to the side channels. (D) Chemotactic shift (directed spreading mode) of 50 μM Rh6G increases with increase in Ficoll 400K concentrations between 0 and 5 wt %, and decreases thereafter due to a viscosity increase. (E) Different concentrations (25, 50, 75, and 100 μM) of Rh6G show similar chemotactic shifts in 5 wt % Ficoll 400K gradients. Note that the number of binding sites on the polymer is significantly larger than the number of dye molecules and, therefore, is not the limiting factor. For example, at 5 wt % Ficoll 400K (125 μM) concentration, there are ∼2900 monomeric binding sites (sucrose units) per molecule of Rh6G.
Figure 2. Modeling of chemotactic shifts of Rh6G in COMSOL using binding-unbinding theory for Rh6G−Ficoll system agrees with the experimental results. (A) The bell-shaped concentration profile illustrates only Fickian diffusion of the dye in the control case. (B) “Horns” appear in the concentration profile due to enhanced spreading of the dye caused by larger gradients imposed by Ficoll 400K. The binding-unbinding equilibrium constant (Km) is 2300 ± 350 L/mol for Rh6G-Ficoll 400K system. The blue dots represent experimental data and the red curve represents modeling.
presence of polymer was modeled incorporating the crossdiffusion coefficient of Rh6G dye in Ficoll (DXD) as follows: JD = −DD∇C D − DXD∇C P
Equation 3 was the model used in this work in order to calculate Km (Supporting Information), which was fitted using DXD = −DDKmCD/(1 + KmCP). This equation was obtained by setting JD,advection = VDCD and comparing the advective parts (second terms) of eqs 1 and 3. Dye diffusion in the polymer crowded environment was modeled using the expression DD = D0D Exp(−CP/C0P)20 where D0D is the diffusion coefficient of dye in the buffer, and C0P is a fitting parameter that depends on the molecular weight and viscosity of the polymer (crowding agent) (Supporting Information: modeling in COMSOL).20 We evaluated D0D and C0P from control experiments conducted in microfluidic channels. We also verified D0D values from fluorescence correlation spectroscopy (FCS) experiments (Supporting Information). Using this approach, good agreement between the experimental data for CD and the theoretical model was obtained, as shown in Figure 2A,B. Furthermore, we
which can be represented by the following expression derived from the work by Schurr et al.19 VD = −DD
∇C D Km + DD ∇C P CD 1 + K mC P
(1)
where DD is the Fickian diffusion coefficient of the dye, CD is the dye concentration,∇CD is the dye concentration gradient, Km is the measured equilibrium constant of dye−polymer binding−unbinding (eq 2), CP is the polymer concentration, and ∇CP is the polymer concentration gradient. The first term of eq 1 is the Fickian diffusion term and the second term is the cross-diffusion or chemotaxis term. The binding equation is Km
D + P ⇔ DP
(3)
(2) 15589
DOI: 10.1021/jacs.7b08783 J. Am. Chem. Soc. 2017, 139, 15588−15591
Communication
Journal of the American Chemical Society found increasing values of Km with increasing molecular weight of Ficoll (Table S2), which indicates overall enhancement of dye−polymer interaction with polymer molecular weight. Interestingly, we obtained similar values for Km, when normalized on the basis of number of monomeric sucrose units. The estimated dye−Ficoll equilibrium binding constant per monomer basis, Kmonomer ∼ 1.8 L mol−1 monomer−1. It is m reasonable that despite increase in polymer molecular weight, the per-monomer interaction would remain constant. The chemotactic shift of Rh6G was also studied using different molecular weights of the sucrose polymer (Ficoll) and polyethylene glycol (PEG) in order to assess the effects of polymer molecular weight, concentration, and nature of interaction (Figure 3). Larger chemotactic shifts in the case of Ficoll 400K can be attributed to larger concentration gradients produced with Ficoll 400K owing to its larger hydrodynamic radius. Thus, Ficoll 400K diffuses more slowly than Ficoll 70K and maintains a steeper gradient across the channel. In the microfluidic experiments, the concentration gradients are highest at the interface of the mid and side channels. As a result, Ficoll 400K has a “horn-like” elevated profile of the dye around that region (Figure 1C). In contrast, sucrose, the Ficoll monomer, cannot maintain a strong concentration gradient owing to its small size and fast diffusion. As a result, negligible chemotaxis of the dye is observed (Figure 3A). With increase in polymer molecular weight, as shown with Ficoll 20K, Ficoll 70K, and Ficoll 400K, the chemotactic shift increased at identical polymer concentration (Table S3a). Similarly, with PEG, the chemotactic shift of Rh6G increased monotonically in the range of 6K−20K and remained almost constant thereafter until 200K because of the viscosity increase (Figure 3B and Table S3b). In the case of PEGs, the chemotactic shifts increased monotonically with increasing concentrations between 0.1 wt % - 0.5 wt % as shown with PEG 200K (Figure 3C), due to higher polymer concentration gradients. To examine the role of hydrophobicity in dye−polymer interactions, we conducted experiments with a triblock copolymer of PEG and PPG (polypropylene glycol), abbreviated as PPP (PEG-PPG-PEG) 5.8K containing 70 wt % hydrophobic PPG. We compared the chemotactic shifts of Rh6G (hydrophobic) in 0.3 wt % hydrophilic PEG 6K and hydrophobic PPP 5.8K in a microchannel. Negligible chemotaxis was observed with PEG 6K, while significant chemotaxis was seen with PPP 5.8K (Figure 3D; Table S4a) due to enhanced hydrophobic dye−polymer interactions. For Rh6G dye and PPP 5.8K polymer, we found Kmonomer = m 7.71 ± 0.24 L mol−1 monomer−1, which is almost 4-fold higher than Ficoll. Therefore, even at low wt % (0.3%), PPP 5.8K is able to cause larger chemotaxis of Rh6G because of strong hydrophobic interactions when compared to 5 wt % Ficoll 400K. Additionally, hydrophobicity-enhanced chemotaxis can be correlated with the degree of methylation in the polymer (Table S4b). For example, 0.3 wt % PPP 2K containing only 10 wt % PEG units showed 3 fold higher chemotactic shift compared to 0.3 wt % PPP 2K containing 50 wt % PEG units. Adding salts to the aqueous medium enhanced the chemotactic shifts (Table S4c). This phenomenon is likely due to the enhancement of hydrophobic interaction by partially depleting the water layer adjacent to the polymer molecule.21,22 Changing the solvent from water to the more hydrophobic DMSO significantly suppressed the chemotactic shift of Rh6G toward the more hydrophilic Ficoll (Table S4d). A similar trend
Figure 3. Variation of Rh6G chemotaxis with different polymers molecular weights, polymers, and concentrations (wt %). (A) The chemotactic shift increases due to increase in Ficoll molecular weight at 5 wt % concentration. (B) The chemotactic shift increases for 0.3 wt % PEG gradients until 20K molecular weight and remains almost constant thereafter, primarily due to increase in viscosity. (C) Chemotactic shift increases linearly with increasing PEG 200K concentration between 0 and 0.5 wt %. (D) Negligible chemotactic shift of Rh6G toward 0.3 wt % hydrophilic PEG 6K in side channel (R) and large chemotactic shift of the same dye in the side channel (L) toward 0.3 wt % hydrophobic PPP 5.8K.
was observed in the case of the more hydrophobic PPP 5.8K (Table S4d). Chemotaxis of Rh6G became too small to measure when either DMSO or propylene carbonate was used because of stronger solvation.23,24 To probe the effect of hydrophobicity and charge, several xanthene dyes were investigated for chemotaxis with 5 wt % Ficoll 400K and 0.3 wt % PPP 5.8K gradients (Figure 4A−D and Table S5a,b). The chemotactic shift correlates with an empirical chemotaxis index (C.I.). The C.I., obtained from the dye’s structure, is the sum of the number of alkyl groups and the net positive charge (Figure 4B). Because chemotaxis depends on both the interaction and diffusion coefficients of the dye, we normalized the C.I. by multiplying by Ddye/DRh6G to account for different diffusivities. The extent of chemotaxis of xanthene dyes increased with increasing normalized C.I. (Figure 4C,D and Table S5a,b). In summary, we report the phenomenon of molecular chemotaxis of dye in polymer gradients in solution, due to primarily hydrophobic interactions. Rh6G and other dye molecules move toward higher concentration of polymers, thereby lowering the overall chemical potential of the system. The chemotactic shift of the dye is dependent on the hydrophobic nature of the polymer, the size and concentration gradient of the polymer, and the hydrophobic nature of the solvent. Our experiments show that the structure of the monomeric unit is critical to the observation of chemotaxis and affects the binding−unbinding equilibrium constant. The chemotactic propensity of different dyes that undergo chemotaxis was correlated to a normalized C.I., which combines the relative contributions of hydrophobic attraction and chargeinduced attraction/repulsion. In general, all molecules will chemotax up a gradient of an attractant, depending on the interaction and concentration gradients. The chemotaxis 15590
DOI: 10.1021/jacs.7b08783 J. Am. Chem. Soc. 2017, 139, 15588−15591
Journal of the American Chemical Society
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ACKNOWLEDGMENTS This work was supported by the Penn State MRSEC, Center for Nanoscale Science (NSF DMR-1420620). This work was also sponsored under NSF CBET-1603716.
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Figure 4. Chemotactic shift of different xanthene dyes is correlated to hydrophobic and charge-induced interactions through the “Chemotaxis Index” (C.I.). (A,B) General structure of xanthene dyes and the corresponding C.I. Normalized C.I. = C.I. × Ddye/DRh6G, which compensates for different diffusion coefficients of the dyes. (C) Chemotactic shift increases with increasing normalized C.I. in 5 wt % Ficoll 400K gradients due to increase in hydrophobic interaction and net positive charge of the dye. (D) Chemotactic shift rapidly increases with increasing normalized C.I. in hydrophobic 0.3 wt % PPP 5.8K gradients owing to increase in hydrophobic interaction and net positive charge of the dye.
mechanism often gives transport rates several times that of diffusion. This fact, combined with directional transport, can make chemotaxis a valuable strategy for transport over longer distances (see SI, Figure S4). Chemotaxis is of direct relevance to numerous binding events occurring in biological systems.25,26 In sensing and detection applications, chemotaxis can significantly speed up the migration of the analyte to the detector.8
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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/jacs.7b08783. Microfluidic channel fabrication, calculation of chemotaxis, dye chemotaxis values under different conditions, modeling details, and comparison of chemotaxis versus diffusion (PDF)
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REFERENCES
(1) Sánchez, S.; Soler, L.; Katuri, J. Angew. Chem., Int. Ed. 2015, 54, 1414−1444. (2) Li, J.; Rozen, I.; Wang, J. ACS Nano 2016, 10, 5619−5634. (3) Chang, T.; Rozkiewicz, D. I.; Ravoo, B. J.; Meijer, E. W.; Reinhoudt, D. N. Nano Lett. 2007, 7, 978−980. (4) Perl, A.; Gomez-Casado, A.; Thompson, D.; Dam, H. H.; Jonkheijm, P.; Reinhoudt, D. N.; Huskens, J. Nat. Chem. 2011, 3, 317−322. (5) Zhang, C.; Sitt, A.; Koo, H.-J.; Waynant, K. V.; Hess, H.; Pate, B. D.; Braun, P. V. J. Am. Chem. Soc. 2015, 137, 5066−5073. (6) Burgos, P.; Zhang, Z.; Golestanian, R.; Leggett, G. J.; Geoghegan, M. ACS Nano 2009, 3, 3235−3243. (7) Dey, K. K.; Das, S.; Poyton, M. F.; Sengupta, S.; Butler, P. J.; Cremer, P. S.; Sen, A. ACS Nano 2014, 8, 11941−11949. (8) Sitt, A.; Hess, H. Nano Lett. 2015, 15, 3341−3350. (9) Spolar, R. S.; Ha, J. H.; Record, M. T. Proc. Natl. Acad. Sci. U. S. A. 1989, 86, 8382−8385. (10) Xing, B.; Yu, C.-W.; Chow, K.-H.; Ho, P.-L.; Fu, D.; Xu, B. J. Am. Chem. Soc. 2002, 124, 14846−14847. (11) Kim, C. U.; Lew, W.; Williams, M. A.; Liu, H.; Zhang, L.; Swaminathan, S.; Bischofberger, N.; Chen, M. S.; Mendel, D. B.; Tai, C. Y.; Laver, W. G.; Stevens, R. C. J. Am. Chem. Soc. 1997, 119, 681− 690. (12) Skehel, J. J.; Bayley, P. M.; Brown, E. B.; Martin, S. R.; Waterfield, M. D.; White, J. M.; Wilson, I. A.; Wiley, D. C. Proc. Natl. Acad. Sci. U. S. A. 1982, 79, 968−972. (13) Fink, A. L. Physiol. Rev. 1999, 79, 425−449. (14) Sengupta, S.; Dey, K. K.; Muddana, H. S.; Tabouillot, T.; Ibele, M. E.; Butler, P. J.; Sen, A. J. Am. Chem. Soc. 2013, 135, 1406−1414. (15) Dey, K. K.; Sen, A. J. Am. Chem. Soc. 2017, 139, 7666−7676. (16) Astumian, R. D. Science 1997, 276, 917−922. (17) Butler, P. J.; Dey, K. K.; Sen, A. Cell. Mol. Bioeng. 2015, 8, 106− 118. (18) Dey, K. K.; Zhao, X.; Tansi, B. M.; Méndez-Ortiz, W. J.; Córdova-Figueroa, U. M.; Golestanian, R.; Sen, A. Nano Lett. 2015, 15, 8311−8315. (19) Schurr, J. M.; Fujimoto, B. S.; Huynh, L.; Chiu, D. T. A. J. Phys. Chem. B 2013, 117, 7626−7652. (20) Dauty, E.; Verkman, A. S. J. Mol. Recognit. 2004, 17, 441−447. (21) Back, J. F.; Oakenfull, D.; Smith, M. B. Biochemistry 1979, 18, 5191−5196. (22) Zhou, R.; Huang, X.; Margulis, C. J.; Berne, B. J. Science 2004, 305, 1605−1609. (23) Pedersen, C. J. J. Am. Chem. Soc. 1967, 89, 7017−7036. (24) Cram, D. J. Angew. Chem., Int. Ed. Engl. 1988, 27, 1009−1020. (25) Kirkman, H. N.; Gaetani, G. F. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 4343−4347. (26) Baeuerle, P. A.; Baltimore, D. Cell 1988, 53, 211−217.
AUTHOR INFORMATION
Corresponding Authors
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Ayusman Sen: 0000-0002-0556-9509 Author Contributions §
These authors contributed equally.
Notes
The authors declare no competing financial interest. 15591
DOI: 10.1021/jacs.7b08783 J. Am. Chem. Soc. 2017, 139, 15588−15591
