Letter pubs.acs.org/macroletters
Mobility Gradient Induces Cross-Streamline Migration of Semiflexible Polymers Dagmar Steinhauser,† Sarah Köster,‡ and Thomas Pfohl*,†,§ †
Max-Planck-Institut für Dynamik und Selbstorganisation, Bunsenstrasse 10, 37073 Göttingen, Germany “Institut für Röntgenphysik, CRC Nanospektroskopie und Röntgenbildgebung, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany § Chemie Departement, Universität Basel, Klingelbergstrasse 80, 4056 Basel, Switzerland ‡
ABSTRACT: Many aspects of modern material science and biology rely on the strategic manipulation and understanding of polymer dynamics in confining micro- and nanoflow. We directly observe and analyze nonequilibrium structural and dynamic properties of individual semiflexible actin filaments in pressure-driven microfluidic channel flow using fluorescence microscopy. Different conformational shapes, such as filaments fluctuating in an elongated manner, parabolically bent, as well as tumbling, are identified. With increasing flow velocity, a strong center-of-mass migration toward the channel walls is observed. This significant migration effect can be explained by a shear rate dependent spatial diffusivity due to a gradient in chain mobility of the semiflexible polymers. channel center is predicted by computer simulations for flexible polymers modeled by a bead−spring representation,12,17 for semiflexible polymers modeled by mesoscale hydrodynamic simulations,18−20 and for stiff polymers modeled as Brownian stiff rods.21−23 However, there is no experimental evidence for Brownian cross-streamline migration in straight channels so far. In this work, we use actin filaments with a persistence length Lp ≈ 13 μm24,25 as a model system to study the flow of semiflexible polymers in straight microchannels with a depth of h = (10 ± 1) μm and a width of d = (10 ± 2) μm, emulating an almost cylinder-like Poiseuille flow profile.26 Individual actin filaments are visualized by fluorescence microcopy. The microscope is focused to the center plane of the channel (see Figure 1a). All filaments having a predominantly sharp contour and therefore located in the focal plane ±0.5 μm are analyzed. Filaments located above or below of the focal plane are not considered in further analyses. The contour length of the actin filaments inside the dilute solution varies. For the analysis, the contour length of each actin filament is measured and all filaments with L = (8 ± 2) μm are included in the statistics. About 1000 filaments are analyzed for each velocity. All relevant length scales of the investigated system (h, d, L, Lp) have approximately the same numerical value. This chosen experimental system has several important advantages over, for example, possible DNA-based systems in the regime L ∼ Lp ∼ h. Due to the small persistence length of DNA, Lp ≈ 50 nm, it would be very challenging to accurately image individual DNA
ingle polymer dynamics in confining geometries and flows are of central importance in materials science, mechanical engineering, biology, and biotechnology. Shrinking fluidic devices to the micrometer and nanometer scale results in critical channel dimensions approaching macromolecular scales. To this end, many experiments have been performed to study the conformation and orientation of polymers in different flow fields.1−6 In particular, DNA molecules, which can be described as flexible polymers, have been investigated in different flow fields, including shear,1−3 elongational,4 oscillatory,5 mixed,6 and Poiseuille7 flow. However, less is known about the behavior of semiflexible polymers (where the contour length L and the persistence length Lp are of the same order (L ≈ Lp)) in channel and shear flow. Besides configurational and orientational dynamics, the positional distribution of polymers across the channel width is a point of great interest. Predictions from different theoretical and computational studies for polymers in straight microchannels are controversial, even in answering fundamental questions such as the direction of migration toward or away from walls.8−11 Generally, kinetic theories suggest two different sources for cross-streamline migration of polymers inside a straight channel. 9−12 First, near a wall, hydrodynamic interactions with the wall lead to migration away from the wall due to the broken symmetry. This is consistent with the increase of depletion layers near walls with increasing velocities, which was shown in computer simulations12,13 and in DNA experiments near a single wall.14 Second, Brownian migration10−12,15,16 is expected in inhomogeneous flow fields due to a coupling of a spatially varying diffusion of polymers to hydrodynamics. For Poiseuille flow, migration away from the
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© 2012 American Chemical Society
Received: January 31, 2012 Accepted: April 2, 2012 Published: April 10, 2012 541
dx.doi.org/10.1021/mz3000539 | ACS Macro Lett. 2012, 1, 541−545
ACS Macro Letters
Letter
Figure 1. (a) Schematic representation of flowing actin filaments inside microchannels. The filaments are observed in the focal plane and experience a parabolic flow profile. Typical contour conformations of actin filaments in flow: (b) elongated filament, (c) parabolically bent filament (U-form), and (d) tumbling filament.
Figure 2. (a) Orientational order parameter S plotted vs the center-ofmass position ycm for different velocities. (b) Center-of-mass probability distributions for different flow velocities. The plots show the distribution of filaments along the channel cross-section for a half channel with the channel center at ycm = 0 μm and the channel wall at ycm = 5.5 μm.
molecules at high flow rates. Moreover, the high charge density of DNA would lead to strong electrostatic interactions with channel walls. A pressure-driven flow with maximum velocities ranging from v0 = 0−2.4 mm/s is applied. The flow velocities and the parabolic flow profiles in the focal observation plane are determined using flow measurements of very short filaments (99%, from Cytoskeleton, Denver, U.S.A.) is polymerized in a 50 mM KCl buffer and stabilized by phalloidin.25 Labeled actin filaments are visualized by fluorescence microcopy using an Olympus BX61 microscope and a Plan Apochromat 100× oil immersion objective. To enable short exposure times (
