Quantitative mapping of dynamic 3D transport in growing cells via volumetric spatio-temporal image correlation spectroscopy (vSTICS)

Abstract

Quantitatively mapping three-dimensional (3D) flow, diffusion, and particle density in crowded living cells remains challenging because most dynamic optical microscopy measurements are effectively planar and existing analysis methods struggle with dense, noisy volumetric data. We introduce volumetric spatio-temporal image correlation spectroscopy (vSTICS), a framework that recovers voxel-resolved flow, diffusion coefficients, and particle densities from 3D fluorescence time series. Growing Camellia japonica pollen tubes were imaged with field-synthesis lattice light-sheet microscopy, and localized 3D spatio-temporal correlation analysis was applied to overlapping volumetric samples to generate maps of velocity, diffusion, and density. Validation with synthetic flow-diffusion simulations showed accurate recovery of seeded transport parameters, including velocities near $3$ $μ$m s$^{-1}$ and diffusion near $10^{-3}$ $μ$m$^2$ s$^{-1}$. Fluorescent microsphere experiments verified particle number and point spread function readouts and measured diffusion coefficients of $0.3 \pm 0.1$ $μ$m$^2$ s$^{-1}$ in gel, consistent with imaging-FCS measurements of $0.5 \pm 0.2$ $μ$m$^2$ s$^{-1}$. Applied to mitochondria in pollen tubes, vSTICS resolved a bidirectional reverse-fountain pattern with slower anterograde transport ($0.1$-$1$ $μ$m s$^{-1}$) and faster retrograde motion peaking near $3$ $μ$m s$^{-1}$, plus a retrograde corridor about $2$ $μ$m wide. Density and diffusion maps indicated a denser, more advective core and higher peripheral diffusion. High-density sub-diffraction vesicle mapping produced similar velocity landscapes with about ten-fold higher particle densities. These results establish vSTICS as a practical method for quantitative 3D mapping of intracellular transport and refines the reverse-fountain model by revealing asymmetric, predominantly transverse circulation.

Figures (7)

• Figure 1: Overview of volumetric STICS (vSTICS).(A) A 4D image sequence, $i(x,y,z,t)$, is sampled with overlapping regions of interest (ROIs) that are shifted through the volume. (B) For each local ROI$(x,y,z,t)$, fluorescence fluctuations are analyzed over a finite time window. (C) The spatio-temporal autocorrelation function, $r(\xi,\eta,\phi,\tau)$, is computed for a sequence of lag times $\tau$, producing a correlation peak that evolves with transport. (D) At each lag, the correlation function is fit with an asymmetric 3D Gaussian model, $g(\xi,\eta,\phi,\tau)$. (E) The fitted Gaussian parameters summarize transport: the peak position $(\mu_{\xi},\mu_{\eta},\mu_{\phi})$ shifts with $\tau$ and yields the local velocity, while the fitted amplitude $g(0,0,0,\tau)$ reports density and diffusion. In particular, the zero-lag amplitude is inversely proportional to the average number of particles in the sampling volume, and its decay with $\tau$ reflects diffusive motion. (F--H) Repeating this analysis over all overlapping ROIs generates volumetric maps of flow (F), diffusion (G), and density (H).
• Figure 2: Simulation benchmark for vSTICS.(A) A volumetric image time series is simulated with an asymmetric Gaussian PSF with $\omega_{xy} = 1.5$ pix and $\omega_{z} = 5$ pix. The image size is $128^{3} \ \text{pix}^{3}$ with a pixel size of 0.1 $\mu\text{m}$ for 128 time points, with an imaging time of 10 ms per volume. (B) The 3D normalized intensity fluctuation autocorrelation function at $\tau=0$, shown in a 3D view, as well as XY and XZ projections. A symmetric ROI size of 32 pix, with a ROI shift of 4 pix. (C) The 3D density map of the volumetric time series at $\tau=1$ (top) with its corresponding density histogram (bottom) indicating both mean fitted value and seeded density. (D) The 3D diffusion map of the volumetric time series at $\tau=1$ (top) with its corresponding diffusion histogram (bottom) indicating both mean fitted value and seeded diffusion coefficient. A TOI window of 5 frames was used. (E) The 3D vector flow field of the volumetric time series at $\tau=1$ (top) with its corresponding velocity histogram (bottom) indicating both mean fitted value and seeded velocity in each Cartesian direction.
• Figure 3: Fluorosphere calibration samples for experimental vSTICS validation.(A) A 3D intensity stack of stationary fluorospheres of radius 50 nm, embedded in agarose with a field of view of 55 $\times$ 55 $\mu\text{m}^{2}$ (left) with its corresponding volumetric normalized autocorrelation function (middle) and its symmetric Gaussian fit (right). (B) A 3D time series intensity stack of fluoropsheres of radius 50 nm in 0.3 $\%$ Gelrite mixture, with a field of view of 55 $\times$ 55 $\mu\text{m}^{2}$ (left) with its corresponding volumetric normalized autocorrelation function at $\tau = 1$ (middle) and the corresponding decay of the correlation amplitude $g(\vec{0)}$ as a function of time lag $\tau$, fit with a single component 3D diffusion model (right).
• Figure 4: In vitro fertilization and mitochondrial labelling of Camellia japonica pollen tubes.(A)Camellia japonica flower with pollen shown in yellow. (B) A bright field image of fertilized pollen grains grown on germination media (Section \ref{['Methods']}) 3 hours post deposition. (C) Lattice light-sheet image of a single pollen tube grown in a custom sample holder 2 hours post deposition, labeled with MitoTracker Green, and $xy$ projection shown in (D). Region near the growing tip highlighted in the black box is shown in (E), with a bottom surface perspective of the tube (left), and the sagittal plane of the tube (right).
• Figure 5: Biological benchmark for vSTICS using mitochondrial labelling of Camellia japonica pollen tubes.(A) A volumetric time series of the pollen tube, displayed with the sagittal plane relative to the growth axis (left), with discrete centroids of the $\text{ROIs}$ displayed in red, with parameters $\text{ROI}_{xy} = 64 \ \text{pix}$, $\text{ROI}_{z} = 16 \ \text{pix}$, $\text{ROI Shift}_{xy} = 5 \ \text{pix}$, $\text{ROI Shift}_{z} = 2 \ \text{pix}$, $\text{TOI} = 5 \ \text{frames}$, $\text{TOI Shift} = 1 \ \text{frame}$. (B) Volumetric density mapping of the growing pollen tube at the first $\text{TOI}$ (top) with the density histogram averaged over all $\text{TOIs}$ with a Gaussian fit. (C) Volumetric diffusion mapping of the growing pollen tube at the first $\text{TOI}$ (top) with the diffusion histogram (top) averaged over all $\text{TOIs}$ with generalized extreme value (GEV) fit with an average $D = 0.15\ \mu\text{m}^{2}\,\text{s}^{-1}$. The inset show the decay of the ACF amplitude fit with a 3D diffusion model. (D) Velocity flow field at the first $\text{TOI}$ superimposed on a volumetric rendering of the pollen tube (top). The corresponding normalized histogram of the velocity measured in each orthogonal direction, with a bimodal Gaussian fit for components $v_{x}$ and $v_{y}$, and a Gaussian fit for $v_{z}$.