Single-Polymer Dynamics in Steady Shear Flow

Abstract

The conformational dynamics of individual, flexible polymers in steady shear flow were directly observed by the use of video fluorescence microscopy. The probability distribution for the molecular extension was determined as a function of shear rate, ␥, for two different polymer relaxation times, . In contrast to the behavior in pure elongational flow, the average polymer extension in shear flow does not display a sharp coil-stretch transition. Large, aperiodic temporal fluctuations were observed, consistent with end-over-end tumbling of the molecule. The rate of these fluctuations (relative to the relaxation rate) increased as the Weissenberg number, ␥, was increased.The dynamics of flexible polymers in shear is of great practical interest because this type of flow occurs whenever a fluid flows past a surface. Macroscopic, non-Newtonian rheological properties of polymer solutions, such as flow-dependent viscosities and normal stresses, result from microscopic stresses that arise when polymeric molecules are stretched and affect the solvent motion. Thus, much effort has been directed at predicting the molecular dynamics of polymers in shear flows (1-5). However, it has been difficult to rigorously test these predictions because the dynamics of a polymer molecule in shear have not been observed directly. Experimental efforts have mainly focused on measuring bulk rheological properties or on measuring the scattering of light or neutrons by polymer solutions (6 -10). Here we describe how single-molecule imaging techniques (11) can be used to study the configurations of polymers in shear flow so that the detailed molecular predictions of theories can be tested.It has long been recognized that the amount of distortion of a molecule is strongly dependent on the nature of the flow (4, 5). In general, any planar flow of the form v ជ ϭ v x x ϩ v y ŷ may be represented as a linear superposition of a rotational flow with a vorticity ϭ [(‫ץ‬v y / ‫ץ‬x) Ϫ (‫ץ‬v x /‫ץ‬y)]/2 and an elongational flow with a strain rate ϭ [(‫ץ‬v y /‫ץ‬x) ϩ (‫ץ‬v x /‫ץ‬y)]/2. In a pure elongational flow ( ϭ 0) one expects large deformations of a polymer, whereas in a pure rotational flow ( ϭ 0) one expects only rotation and not deformation (4,5).Most practical flows consist of a mixture of both rotational and elongational components, and the resulting polymer deformation depends on the relative magnitudes of and . In general, the response is not necessarily a linear superposition of the responses to each component. In a simple shear flow (v y ϭ 0 and v x ϭ ␥y, where ␥ ϭ dv x /dy is the shear rate) the magnitude of the elongational and rotational components are equal ( ϭ ) (Fig. 1A). In this case, it has been suggested that the polymer will not attain a stable, strongly stretched state (4, 5). In fact, large fluctuations in the extension due to an end-over-end tumbling of the molecule have been observed in some simulations (3). These fluctuations presumably occur because the stretched state is destabilized by the rotational component of the sh...

The effects of shear flow on protein structure and function

“…It was found that, at relatively high shear rates, the sharp coil-stretch transitions of DNA chains observed in pure elongation flow was absent in shear flow. 16,21 Individual chains in steady shear flow rather showed large, aperiodic temporal fluctuations in conformation, consistent with what had been predicted in theory. 84 In addition, stretching of DNA chains in shear flow occurred at a strain value \50 (%10 1 ), 16 which is several orders of magnitude lower than the %10 5 critical strain value observed for poly-L-lysine 55 as well as folded proteins.…”

“…It is modeled as a linear superposition of rotational flow with vorticity x, and elongational flow with strain rate _ c ¼ @v x @y . 16 In the rotational component of the flow field, protein molecules experience whole body rotation with no hydrodynamic shear strain, hence maintain their structural integrity. However, protein molecules are subjected to stretching events when oriented in the extensional flow field.…”

“…conformational dynamics of DNA chains in both elongation 21 and shear 16 flows. The elongation and shear flow experiments were performed in a microfabricated flow cell and between two parallel glass plates ($50 lm gap), respectively, at very low shear rates ranging from 0.05 to 4.0 s 21 .…”

“…13 Proteins have been shown to exhibit conformational dynamics in shear flow. [14][15][16][17] Protein solutions are exposed to shear stresses during bioprocessing steps as a result of centrifugation, fractionation, pumping, and ultrafiltration. 13,18,19 Similarly, the shipping and handling of biotherapeutics and protein based bioprocessing reagents such as monoclonal antibodies, hormones, cytokines, and enzymes can result in significant agitation.…”

Using extensional flow to reveal diverse aggregation landscapes for three IgG1 molecules

“…Whether shear alone or an initial extensional flow event prior to shear is required to induce WFL aggregation remains to be seen. The latter scenario could cause a localized unfolding of a protein molecule (e.g., as seen for von Willebrand factor (Lippok et al, 2016) and for BSA in our previous study (Dobson et al, 2017), which may then be susceptible to “tumbling” events under shear flow in the capillary (Smith, Babcock, & Chu, 1999) and rapid self‐association in a concentration and time‐dependent manner.…”