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Viscophobic turning dictates microalgae transport in viscosity gradients

Nature Physics volume 17, pages 926–930 (2021)Cite this article

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Abstract

Gradients in fluid viscosity characterize microbiomes ranging from mucus layers on marine organisms1 and human viscera2,3 to biofilms4. Although such environments are widely recognized for their protective effects against pathogens and their ability to influence cell motility2,5, the physical mechanisms regulating cell transport in viscosity gradients remain elusive6,7,8, primarily due to a lack of quantitative observations. Through microfluidic experiments, we directly observe the transport of model biflagellated microalgae (Chlamydomonas reinhardtii) in controlled viscosity gradients. We show that despite their locally reduced swimming speed, the expected cell accumulation in the viscous region9,10 is stifled by a viscophobic turning motility. This deterministic cell rotation—consistent with a flagellar thrust imbalance11,12—reorients the swimmers down the gradient, causing their accumulation in the low-viscosity zones for sufficiently strong gradients. Corroborated by Langevin simulations and a three-point force model of cell propulsion, our results illustrate how the competition between viscophobic turning and viscous slowdown ultimately dictates the fate of population-scale microbial transport in viscosity gradients.

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Fig. 1: Viscosity gradient strength regulates dispersal of swimming microalgae.
Fig. 2: Coupling of swimming kinematics to viscosity gradient induces viscophobic turning.
Fig. 3: Simulations illustrate the competition between viscophobic drift and viscous slowdown driving cell accumulation.

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Data availability

Data files used during the current study are publicly available at https://doi.org/10.7910/DVN/QXI6X1. Source data are provided with this paper.

Code availability

The algorithms and simulation codes are described in the Methods and Supplementary Information. Code to reproduce the analysis reported is publicly available at https://doi.org/10.7910/DVN/QXI6X1.

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Acknowledgements

We thank G. J. Elfring for helpful discussions and R. J. Henshaw for comments on the manuscript. This work was funded by NSF awards CAREER-1554095 and CBET-1701392 to J.S.G.

Author information

Author notes

  1. These authors contributed equally: Michael R. Stehnach, Nicolas Waisbord.

Authors and Affiliations

  1. Department of Mechanical Engineering, Tufts University, Medford, MA, USA

    Michael R. Stehnach, Nicolas Waisbord, Derek M. Walkama & Jeffrey S. Guasto

  2. Department of Physics and Astronomy, Tufts University, Medford, MA, USA

    Derek M. Walkama

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  1. Michael R. Stehnach
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Contributions

M.R.S., N.W. and J.S.G. designed the research. M.R.S. and N.W. performed experiments, and M.R.S., N.W. and D.M.W. analysed experimental data. All authors contributed to simulations and theoretical analyses and wrote the paper.

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Correspondence to Jeffrey S. Guasto.

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Peer review information Nature Physics thanks Arnold Mathijssen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Time evolution of the viscosity profile.

Transient diffusion of the PEO molecules results in a viscosity profile that evolves from a near step function to a smooth monotonic profile. Swimming cell assays are analyzed in the time range 30≤t≤90 min, when the gradient evolves more slowly, and the profile is approximately linear in the center of the channel. The slope of the viscosity profile is quantified by fitting a line to the five central points in the channel. The reported viscosity gradient, ∇η, is the average slope of the viscosity profiles from 30-90 min (Extended Data Table 1).

Source data

Extended Data Fig. 2 Spatially resolved microrheology quantifies the viscosity profile in a microfluidic device.

a, The mean square displacement (MSD) of tracer particles in different locations across the microfluidic viscosity gradient device at time, t = 10 min ( ∇ η = 3.4 × 10−3 cP ⋅ μm−1; see also Extended Data Fig. 1). Solid lines are linear fits to the MSDs. b, The slopes of the tracer particle MSDs in a are used to determine the spatially resolved viscosity profile, η(x), across 11 bins of the microchannel width using Stokes-Einstein relation (Supplementary Section 2.2). Shaded region (smaller than the markers) represents the propagation of uncertainty from the error of the fit in a.

Source data

Extended Data Fig. 3 Control experiments show negligible chemotaxis and chemokinetic effects for wild-type C. reinhardtii in PEO gradients.

a,b, Viscotaxis assays reveal the local, measured cell density (a) and mean swimming speed (b) remain spatially uniform for small viscosity gradients. Base PEO concentrations of 0.05% in viscous media inlet (∇η = 0.46 × 10−3 cP ⋅ μm−1; N=3; right) are comparable to the control experiment with no viscosity gradient (∇η = 0 cP ⋅ μm−1; N=4; left, repeated from Fig. 1h,i). For these control experiments, the base PEO concentration (0.05%) is nearly the same order of magnitude as the maximum gradient (0.82%), yet has no appreciable effect on the local viscosity. Thus, the lack of discernible cell accumulation and the lack of statistically significant spatial variations in swimming speed indicate that PEO likely does not act as a chemoattractant nor does it have any chemokinetic effect on C. reinhardtii. The shaded areas represent the standard error.

Source data

Extended Data Fig. 4 Mean square displacements of tracer particles for viscosity measurements in bulk fluid.

Microrheology quantifies the viscosity of PEO solutions in M1 media at various concentrations. The slopes of linear fits (solid lines) to the mean square displacements (MSDs; markers) yield the tracer particle diffusion coefficients, which are used to determine the viscosity of the solution via the Stokes-Einstein relation (Supplementary Section 2.1). Measured viscosities are listed in Extended Data Table 2.

Source data

Extended Data Fig. 5 Measurement of mean square displacement (MSD) of wild-type C. reinhardtii in uniform viscosity to determine rotational diffusion coefficient.

Mean square displacements of C. reinhardtii were measured in 0.996 cP ( ≈ 1,800 trajectories) and 4.48 cP ( ≈ 10,700 trajectories) bulk viscosities. The resulting MSDs were fitted using an analytical result for a persistent random walk52,53, \(\langle \Delta {r}^{2}\rangle =0.5\ {V}^{2}/{D}_{r}^{2}(2{D}_{r}t+\exp (-2{D}_{r}t)-1)\), where the ensemble averaged cell swimming speeds, V, are known independently (74.7 μm/s and 22.7 μm/s, respectively), and the rotational diffusion coefficient, Dr, is the lone fitting parameter. The resulting rotational diffusion coefficients were Dr = 0.070 s−1 and 0.068 s−1. As a sensitivity analysis, varying the fit window from 10 s to 20 s resulted in Dr = 0.071 ± 0.006 s−1 and 0.068 ± 0.001 s−1 for 0.996 cP and 4.48 cP, respectively, where the error is the standard deviation of the resulting rotational diffusion coefficients.

Source data

Extended Data Fig. 6 Time evolution of swimming cell orientation distribution in a viscosity gradient.

a-c, In the absence of a viscosity gradient or viscophobic turning, an initially random uniform distribution of cell swimming orientations remains random, as illustrated across experiments, Langevin simulations, and a Fokker-Plank (FP) model, respectively. d-f, In contrast, in the presence of a viscosity gradient or orientation dependent viscophobic turning rate, the orientation of cells readily condenses in the down-gradient direction. Experimentally measured cell swimming trajectories were sub-sampled from the central portion (400μm≤x≤600μm) of the microfluidic gradient generating channel with a uniform orientation distribution p(θ∣t) at t = 0 for ∇ η = 0 cP ⋅ μm−1 (a; control, ≈ 1, 170 trajectories) and for ∇ η = 7.2 × 10−3 cP ⋅ μm−1 (d; ≈ 1,330 trajectories). Peaks in a at ≈ 6 s are due to cell collisions with microchannel walls. Langevin simulations in the absence (b) and presence (e) of viscophobic turning (\({\omega }_{visc}=0.07\ {{\rm{s}}}^{-1},\Delta V/{V}_{\max }=0.776\)) show quantitative agreement with experiments having matching conditions (Extended Data Fig. 7 and Fig. 3a,b) in a and d, respectively. A one-dimensional Fokker-Planck model of the cell swimming orientation distribution (Supplementary Section 5.3) likewise captures the time evolution of the conditional probability density for the control (c) and corresponding maximum viscosity gradient conditions (f; Fig. 3b).

Source data

Extended Data Fig. 7 Comparison of cell density profile due to (viscous) slowdown and Langevin simulations incorporating viscophobic turning.

Langevin simulations enable independent exploration of the parameters ΔV/Vmax and ωvisc, and include an empirical wall scattering boundary condition (Supplementary Section 5.1). Cell density profiles, ρ(x), are shown for fixed ΔV/Vmax and a range of turning rate amplitudes (solid lines). The resulting density profiles are compared to a theoretical distribution, ρ0, for cells with spatially varying swimming speed in the absence of viscophobic turning (black dashed curve; Supplementary Section 4.1).

Source data

Extended Data Table 1 Measured viscosity gradients for viscotaxis experiments
Full size table
Extended Data Table 2 Viscosity of bulk PEO solutions
Full size table
Extended Data Table 3 Measured transient viscosity gradient for viscotaxis experiments
Full size table

Supplementary information

Supplementary Information

Supplementary Sections 1–7, Figs. 1–4 and references.

Reporting Summary

Supplementary Video 1

Wild-type C. reinhardtii swimming in a uniform viscosity environment (∇η = 0 cP μm−1). Microfluidic channel containing M1 media only (×10 objective; 30 fps; real-time playback).

Supplementary Video 2

Wild-type C. reinhardtii swimming in a microfluidic viscosity gradient (∇η = 7.2 × 10−3 cP μm−1). Initially stratified microfluidic channel contained 0.82% (w/v) PEO in M1 media on left and M1 media on right (×10 objective; 30 fps; real-time playback).

Source data

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Source Data Extended Data Fig. 1

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Stehnach, M.R., Waisbord, N., Walkama, D.M. et al. Viscophobic turning dictates microalgae transport in viscosity gradients. Nat. Phys. 17, 926–930 (2021). https://doi.org/10.1038/s41567-021-01247-7

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