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Scale-free vertical tracking microscopy


The behavior and microscale processes associated with freely suspended organisms, along with sinking particles underlie key ecological processes in the ocean. Mechanistically studying such multiscale processes in the laboratory presents a considerable challenge for microscopy: how to measure single cells at microscale resolution, while allowing them to freely move hundreds of meters in the vertical direction? Here we present a solution in the form of a scale-free, vertical tracking microscope, based on a ‘hydrodynamic treadmill’ with no bounds for motion along the axis of gravity. Using this method to bridge spatial scales, we assembled a multiscale behavioral dataset of nonadherent planktonic cells and organisms. Furthermore, we demonstrate a ‘virtual-reality system for single cells’, wherein cell behavior directly controls its ambient environmental parameters, enabling quantitative behavioral assays. Our method and results exemplify a new paradigm of multiscale measurement, wherein one can observe and probe macroscale and ecologically relevant phenomena at microscale resolution. Beyond the marine context, we foresee that our method will allow biological measurements of cells and organisms in a suspended state by freeing them from the confines of the coverslip.

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Fig. 1: Scale-free vertical tracking microscopy using a hydrodynamic treadmill.
Fig. 2: Multiscale measurements of free-swimming behavior and flow fields of invertebrate larvae.
Fig. 3: Tracking single-celled protists.
Fig. 4: Multiscale behavioral measurements of P.miniata larvae.
Fig. 5: Diel migration at the scale of individual plankton.
Fig. 6: Scale-free tracking allows comparative multiscale analysis of gravity-biased behaviors across plankton species.

Data availability

The datasets generated during and/or analyzed during the current study are available in the manuscript or the Supplementary Information and are available from the corresponding author upon request.

Code availability

Data collection was performed using the tracking microscope described in the study. The microscope used custom firmware for controlling the stages written in C++ using open source Arduino libraries and custom subroutines. The software for GUI interactions and on-the-fly image analysis was written using the PyQt API in Python 3.6, using both open source libraries and custom subroutines. Both firmware and software codebases have been hosted at the following public repositories: and


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We thank C. Lowe and P. Bump for providing access to marine larvae and Hopkins Marine Station for access to laboratory space. We also thank the Puerto Rico Science Trust and Isla Magueyes Marine station for laboratory access. We thank E. Korkmazhan for technical assistance for an early version of the experiment. We thank R. Konte for making the drawings of marine larvae and organisms. We thank the Prakash laboratory members for fruitful discussions. D.K. was funded by a Bio-X Bowes Fellowship, H.L. was funded by a Bio-X SIGF Fellowship. A.G.L. was funded by a Simons Postdoctoral Fellowship in Marine Microbial Ecology. M.P. acknowledges support from NSF Career Award, Moore Foundation, HHMI Faculty Fellows program, NSF CCC (DBI-1548297) program and CZ BioHub Investigators program.

Author information

Authors and Affiliations



D.K. and M.P. designed the research. D.K., H.L., F.B., A.G.L., E.L. and M.P. designed the instrument. D.K., H.L., F.B., P.C., E.L. and A.G.L. built the setup. D.K., H.L., F.B., P.C., A.G.L. and M.P. performed experiments. D.K. and F.B. performed numerical simulations. D.K. performed analytical calculations. D.K., H.L. and F.B. wrote the control software. D.K., A.G.L. and M.P. analyzed the data. D.K., H.L., A.G.L. and M.P. wrote the manuscript.

Corresponding author

Correspondence to Manu Prakash.

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Competing interests

Portions of the technology described here are part of a US patent pending (US20190000044A1) to D.K and M.P.

Additional information

Peer review information Rita Strack was the primary editor on this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 CAD rendering of the scale-free vertical tracking microscope.

a, Fixed optics, moving stage configuration. This configuration gives flexibility in terms of designing the optics for the microscope and allows the addition of multiple cameras and optical paths. b, CAD rendering of the earlier design with fixed-stage and moving optics. This is more suitable for simple microscopy setups with a single camera.

Extended Data Fig. 2 Design space for scale-free vertical tracking using a “hydrodynamic treadmill”: Effect of stage and fluid dynamics.

a, When an object accelerates vertically to achieve a maximum velocity uobj over a behavioral timescale τobj, its motion is compensated by the stage. b, Left, velocity time traces of the object (green dotted line), stage (blue solid line) and fluid (cyan dash-dotted line), showing the viscous delay (τvisc) between stage and fluid movements. Tracking success can be quantified by the difference (Δτ) between two sets of time-scales, one related to the object (τobj+τFOV) and the other related to the stage plus fluid system (τstage+τvisc), where τFOV=LFOV/uobj and LFOV is the optical field-of-view (FOV) size. (b) Right, successful tracking is when the object’s movements can be compensated so that its distance from the center of the optical FOV (red dashed line) never exceeds half the FOV size (solid red line). c, Plots of Δτ with respect to the chamber width (W) and object speed (uobj) for τobj = 0 (instantaneous velocity changes). The tracking limits (zero-crossing of Δτ) are shown for different behavioral timescales τobj (solid, dashed and dot-dashed contour lines). Symbols (mean) and whiskers (standard deviation) correspond to various organisms (see Supplementary Table 1) which were successfully tracked for chamber widths of 3.2,3.5 and 4 mm.

Extended Data Fig. 3 Design space for scale-free vertical tracking using a “hydrodynamic treadmill”: Effect of transient fluid shear and chamber curvature.

a, Rotational stage acceleration leads to a non-uniform velocity profile, which at the scale of the object is locally a simple shear flow. This shear flow (with shear rate \(\dot \gamma\)), can be decomposed into an extensional and vortical component, both of which perturb the object’s equilibrium orientation, in opposing directions. A gravitactic effect, due to a displaced center-of-mass and center-of-buoyancy, stabilizes the orientation and aligns it with gravity over a timescale τgrav. A balance of these two effects is quantified by the ratio of time-scales τshear|min/τgrav, where τshear|min is the inverse of the maximum possible shear rate during a chamber acceleration. b, Plot of τshear|min/τgrav with respect to stage acceleration and the gravitactic moment arm relative to object size. There is a broad region where the object orientation is highly stable (\(\tau _{shear|min}/\tau _{grav} \gg 1\)), implying that tracking has a negligible effect on orientation. The upper bound for stage acceleration is set by imposing the condition \(\tau _{shear|min}/\tau _{grav} > 100\) (solid red curve), and the lower bound is set by the condition Δτ>0 in Extended Data Fig. 2c (cross-over contours shown for τobj = 0, 2, 4). c, Top, tracking a linear motion using a circular chamber implies that, for a non-zero vertical tracking error (Δz), there is a radial drift induced in the object’s motion. Bottom, this drift velocity is given by udrift(t)/uobjz/R(t), where R(t) is the radial position of the object at time t. d, Ratio of radial drift velocity to object’s speed plotted as a function of the radius of the fluidic chamber center-line ((Ri+Ro)/2) and the vertical tracking error, showing the cross-over (red solid line) where the ratio exceeds 1%.

Supplementary information

Supplementary Information

Supplementary Note, Supplementary Discussion, Supplementary Video Captions 1–6, Supplementary Figs. 1–17 and Supplementary Tables 1–5.

Reporting Summary

Supplementary Video 1

Overview of the scale-free vertical tracking microscopy method.

Supplementary Video 2

A comparative study of marine invertebrate larvae behavior.

Supplementary Video 3

Tracking unicellular plankton.

Supplementary Video 4

Multiscale tracking of freely swimming P. miniata (bat star) larvae reveal behavioral transitions that regulate depth and enable feeding.

Supplementary Video 5

Diel behavior of polychaete larvae measured at the scale of individual organisms.

Supplementary Video 6

Measuring of behavior of plankton in depth-patterned virtual environments: Volvox colony response to depth-dependent changes in light intensity.

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Krishnamurthy, D., Li, H., Benoit du Rey, F. et al. Scale-free vertical tracking microscopy. Nat Methods 17, 1040–1051 (2020).

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