Rapid Single-cell Measurement of Transient Transmembrane Water Flow under Osmotic Gradient

TL;DR

A new optical method called FIFIV allows real-time measurement of water flow through aquaporins in single cells, offering insights into their function and regulation.

Contribution

The paper introduces FIFIV, a novel optical technique for measuring transmembrane water flow in single cells with high spatiotemporal resolution.

Findings

FIFIV detects transmembrane water flow in single MDA-MB-231 breast cancer cells at speeds of 1 μm/s.

The method distinguishes between osmotic gradients using fluorescence signal peaks.

FIFIV achieves single-cell sensitivity and temporal resolution comparable to electrophysiological methods.

Abstract

Aquaporins (AQPs) are critical for transmembrane water transport in response to osmotic gradients, but their gating and regulatory mechanisms remain poorly understood. A central challenge is the lack of methods to measure water flow across AQPs from individual cells with the spatiotemporal resolution and sensitivity equivalent to patch-clamp recordings of ion fluxes—a limitation stemming from the electrically silent nature of water flow. Here, we present a novel optical technique—Flow-Induced Fluorescence Increase Velocimetry (FIFIV) based on Laser-Induced Fluorescence Photobleaching Anemometry (LIFPA)—that enables direct, real-time monitoring of cytoplasmic flow induced by transmembrane water transport under osmotic pressure gradients. Using small molecular fluorescent dyes to label cytoplasm in single adherent MDA-MB-231 breast cancer cells, we show detection of instantaneous extremely low transmembrane water flow signals on the order of 1 μm/s following localized hypotonic stimulation. This approach circumvents the limitations of traditional volume-based osmotic permeability assays, achieving single-cell sensitivity and temporal resolution comparable to electrophysiological measurements of ion flux. FIFIV potentially provides a new optical approach for probing transmembrane water-flow–induced intracellular dynamics, and a foundation for future investigations of AQP regulation and gating mechanisms in physiopathological studies and drug discovery.

A 1X PBS buffer droplet (∆c = 0) and DI water droplet (∆c≠0) is injected extracellularly on the left side of an adherent cell respectively. For ∆c = 0, fluorescence intensity decays exponentially. For ∆c≠0, however, there is a peak in the signal.

A 1X PBS buffer droplet (∆c = 0) and DI water droplet (∆c≠0) is injected extracellularly on the left side of an adherent cell respectively. For ∆c = 0, fluorescence intensity decays exponentially. For ∆c≠0, however, there is a peak in the signal.

Figures

Schematic in illustrating LIFPA principle. (a) Fluorescence decay process due to photobleaching when a dye solution flows through a laser beam. (b) The corresponding relation between the fluorescence intensity $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document}$ and the residence (or decay) time. (c) The concurrent relationship between flow velocity $\documentclass[12pt]{minimal} \usepackage

Principle and setup of the FIFIV system. a Schematic of transmembrane water flow induced by ∆c ≠ 0, generated by injection of a DI water droplet on the left side of a cell, while the right side remains exposed to the original isotonic medium. b Principle of FIFIV: Case 1 shows the baseline condition $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c=0$$\end{document}$ ; Case 2 illustrates the presence

Cell viability and uniformly labeled cell a Labeled cells with Calcein; b Fluorescence (arbitrary unit) profile across the top labeled cell. The figure indicates that the cells were alive and were uniformly labeled

Injection process of a fluorescein solution. a No fluorescence is visible when the injection starts at t = 0 s. The trace fluorescence seen is from the dye solution at the interface of the injection tip and the buffer solution. b At t = 0.1 s, the fluorescence becomes clearly visible, indicating that a small amount of dye solution has already flowed into the buffer solution. c At t = 0.2 s, the dye solution has been fully injected into the buffer solution. The subsequent images are similar to c. The scale bar is 30 μm

Boxplots summarizing statistical measurements of both the intracellular flow velocity $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document}$ and $\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{

Full text

Introduction

Transmembrane water transport across cell membranes is essential for maintaining homeostasis and regulating cellular function and volume (Hoffmann et al. 2009). Dysfunction of this process contributes to various diseases (Ibata et al. 2011; Yadav et al. 2020) and has been an active research topic for over a century (Ibata et al. 2011; Parisi et al. 2007). Aquaporins (AQPs), a family of water-selective channels discovered approximately 30 years ago(Agre 2004; Preston et al. 1992), are critical for osmotic balance and water homeostasis in organisms ranging from mammals to microbes and plants(Kortenoeven and Fenton 2014; Madeira et al. 2016). The primary function of AQPs is to facilitate rapid water movement across cytoplasmic membranes in response to osmotic shock(Stroka et al. 2014; Verkman et al. 2014), enabling biological processes, such as cell migration and blebbing(Huebert et al. 2010; Stroka et al. 2014). AQPs have also been implicated in pathologies including enhanced cancer cell migration during metastasis and Alzheimer’s disease(Bhattacharjee et al. 2024; Zeppenfeld et al. 2017), highlighting their translational potential as targets for diagnostic and therapeutic applications(Day et al. 2014; Ozu et al. 2022).

To characterize AQP function and regulation, a rapid and direct measurement of transmembrane water flows at single cells with high sensitivity is essential. However, unlike ion channels—where ion flux can be quantified as an electric current via the patch-clamp technique— AQPs are electrically silent and water flow lacks an electrical signal(Erokhova et al. 2011; Ozu et al. 2022; Wan et al. 2004). As a result, no method currently matches the sensitivity of electrophysiology for measuring water transport under osmotic gradients applied near the cell surface. Instead, to characterize AQPs’ function and regulation, the rate of cell volume change is typically measured in response to an applied osmotic shock to cells to estimate transmembrane water permeability ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} ), a key metric for evaluating AQP function (Fenton et al. 2010; Madeira et al. 2016). Various methods have been developed to determine \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} by tracking cell volume changes or solute concentration shifts caused by the volume change during osmotic challenge (Madeira et al. 2016; Solenov et al. 2023; Verkman 2000). Some of these methods include two-dimensional (2-D) image analysis(Bettega et al. 1998; Fujiwara et al. 1999; Solenov et al. 2003), light scattering(Dobbs et al. 1998; Martins et al. 2013), bioelectrical impedance analysis(Farinas and Verkman 1996; Serra-Prat et al. 2019), digital holographic microscopy(Bélanger et al. 2019; Boss et al. 2013) and microfluidic-based methods(Heo et al. 2008; Jin and Verkman 2017). A more time-consuming approach, the expression of AQP on Xenopus oocyte membranes, has also been widely used to study AQPs’ function and regulation(Agre et al. 1993; Jo et al. 2015; Lin et al. 2023).

However, measuring cell volume change to determine Pm can be challenging(Ibata et al. 2011; Solenov et al. 2023; Verkman 2000), because it is not only slow but also difficult to measure the irregular volumes of attached cells, which are often deduced by measuring irregular 2-D cell membrane area that is also difficult to measure quickly and accurately(Fujiwara et al. 1999; Solenov et al. 2023), especially for adhered cells, whose height is required but equally difficult to determine. When testing adherent cells in suspension, the geometry is more spherical, but the assays are relatively less physiologically relevant for epithelial cells(Discher et al. 2005; Hoffman and Crocker 2009). Although assays based on water transport through a monolayer were developed, the measured Pm represents the combined contribution of two pathways: transcellular and paracellular. However, because AQPs mainly affect the transcellular pathway(Madeira et al. 2016; Verkman 2000), this method has difficulty in distinguishing Pm contributed by AQPs from paracellular pathway. In addition, Pm is often underestimated because of the slow mixing time (mixing artifacts)(Jin et al. 2015; Peckys et al. 2011; Solenov et al. 2023; Verkman 2000) in the measuring system, and a rapid injection of osmotic solution is required(Jin et al. 2015; Solenov et al. 2023). While these techniques have advanced our understanding of transmembrane water transport for characterizing AQPs’ function, they suffer from poor temporal resolution and sensitivity, and are limited by experimental artifacts and intrinsic challenges in measuring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} accurately (Solenov et al. 2023; Tradtrantip et al. 2017; Verkman et al. 2014).

Furthermore, in physiological contexts, cell volume does not always change significantly under an osmotic gradient. The extent of volume change may be limited by cellular volume-regulatory mechanism(Hoffmann et al. 2009; Larsen and Hoffmann 2016). For example, during water reabsorption across tight urinary epithelia—driven by a transepithelial osmotic gradient under antidiuretic hormone control—the cell volume in the collecting tubules of the rabbit kidney cortex increases by only ~ 2.3% during transcellular water flow(Strange and Spring 1987). Similarly, endothelial cells in microvessels experience a nearly steady osmotic gradient and flux from the lumen to the interstitium, as described by Starling’s law(Levick and Michel 2010; Truskey et al. 2004). In such cases, transcellular convection occurs without substantial changes in cell volume. Accurately measuring volume changes and plasma membrane surface area in these adhered cells is challenging and detecting transmembrane water transport signals requires new methodologies. Therefore, due to the lack of a suitable measuring technique, the roles and mechanisms of water transport in diseases remain poorly understood(Abulizi et al. 2023; Clapp & Martínez de la Escalera, 2006; Moon et al. 2022; Nagelhus and Ottersen 2013; Smith et al. 2023; Varricchio and Yool 2023), and a new sensitive measuring method with high spatiotemporal resolution is urgently needed to overcome the limitations of current transgenic animal models(Hub et al. 2010; Ozu et al. 2022; Solenov et al. 2023; Tradtrantip et al. 2017; Verkman 2000). On the other hand, single-cell analysis offers the advantage of revealing heterogeneity within the same population and its significant consequences for the health and function of the entire cell population(Cohen et al. 2008; Zare and Kim 2010).

Here, we show that a Flow-Induced Fluorescence Increase Velocimetry (FIFIV), which employs a small-molecule fluorescent dye rather than nanoparticles to probe cytoplasmic flow dynamics, can rapidly capture transient cytoplasmic flow signals triggered by a localized osmotic shock in single cells.

Cytoplasmic bulk flow velocity as a new variable for characterizing the permeability \documentclass[12pt]{minimal}

			\usepackage{amsmath}
			\usepackage{wasysym} 
			\usepackage{amsfonts} 
			\usepackage{amssymb} 
			\usepackage{amsbsy}
			\usepackage{mathrsfs}
			\usepackage{upgreek}
			\setlength{\oddsidemargin}{-69pt}
			\begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document}

Traditional methods for measuring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} by observing cell volume changes are based on the law of mass conservation in thermodynamics (Farinas and Verkman 1996; Sommer et al. 2007; Verkman 2000):

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\text{}\frac{\mathrm{d}{\mathrm{V}}_{\mathrm{c}}}{\mathrm{d}\mathrm{t}}\mathrm{\:\:=-P}}_{\mathrm{m}}{\mathrm{A}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{w}}\mathrm{[(}{\mathrm{c}}_{\mathrm{i}\mathrm{m}}-{\mathrm{c}}_{\mathrm{i}\mathrm{c}}\mathrm{)+}{{\upsigma\:}}_{\mathrm{p}}\mathrm{(}{\mathrm{c}}_{\mathrm{p}\mathrm{m}}-\text{}{\mathrm{c}}_{\mathrm{p}\mathrm{c}}\mathrm{)}+\frac{{\mathrm{p}}_{\mathrm{p}\mathrm{c}}-{\mathrm{p}}_{\mathrm{p}\mathrm{m}}}{\mathrm{RT}}\mathrm{]}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{V}}_{\mathrm{c}}$$\end{document} is the cell volume, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{t}$$\end{document} time, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} the osmotic water permeability coefficient of the cell membrane, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{V}}_{\mathrm{w}}$$\end{document} the partial molar volume of water, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} the membrane cross-sectional area across which water flows into or out of the cell; \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{c}}_{\mathrm{i}\mathrm{m}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{c}}_{\mathrm{i}\mathrm{c}}$$\end{document} are the osmolality of impermeant solutes on the medium and cytoplasm sides, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{c}}_{\mathrm{p}\mathrm{m}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{c}}_{\mathrm{p}\mathrm{c}}$$\end{document} the osmolality of permeant solutes on the medium and cytoplasm sides, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{{\upsigma\:}}_{\mathrm{p}}$$\end{document} the reflection coefficient of the permeant solutes, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{p}}_{\mathrm{p}\mathrm{m}}\:$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{p}}_{\mathrm{p}\mathrm{c}}$$\end{document} the hydrostatic pressures on the medium and cytoplasm sides, respectively. We assume that with the injection of DI water, no solutes are transported across cytoplasm membrane, thus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{{\upsigma\:}}_{\mathrm{p}}\mathrm{(}{\mathrm{c}}_{\mathrm{p}\mathrm{m}}-\text{}{\mathrm{c}}_{\mathrm{p}\mathrm{c}}\mathrm{)\:=\:0}$$\end{document} . Since the buffer solution in an imaging dish is normally more than 7 mm deep and over 1000 times thicker than the height of single cells, the injected DI water volume is small, and the cell volume change during the entire measurement process is also very small, we also assume that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{(\mathrm{p}}_{\mathrm{p}\mathrm{m}}-{\mathrm{p}}_{\mathrm{p}\mathrm{c}})=0$$\end{document} . Then, in the absence of hydrostatic pressure difference between the extracellular medium and cytoplasm, Eq. (1) becomes:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{\mathrm{d}{\mathrm{V}}_{\mathrm{c}}}{\mathrm{d}\mathrm{t}}\mathrm{=}-{\mathrm{P}}_{\mathrm{m}}{\mathrm{A}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{w}}\mathrm{(}{\mathrm{c}}_{\mathrm{i}\mathrm{m}}\mathrm{-}{\mathrm{c}}_{\mathrm{i}\mathrm{c}}\mathrm{)\:=}-{\mathrm{P}}_{\mathrm{m}}{\mathrm{A}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{w}}\varDelta\:\mathrm{c}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:\mathrm{c}={\mathrm{c}}_{\mathrm{i}\mathrm{m}}-{\mathrm{c}}_{\mathrm{i}\mathrm{c}}$$\end{document} is the osmotic pressure difference between the medium and cytoplasm at the local cell membrane surface, across which water flows under osmotic gradient. Equation 2 is the foundation for traditional methods to estimate the osmotic water permeability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} of cytoplasm membrane, where, for various given \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:\mathrm{c}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{\mathrm{d}{\mathrm{V}}_{\mathrm{c}}}{\mathrm{d}\mathrm{t}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} are measured, and then an averaged \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} is determined(Farinas and Verkman 1996; Kedem and Katchalsky 1958; Sommer et al. 2007). For adhered cells, which are more physiologically relevant, e.g. for epithelial cells, irregular geometry of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{V}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} are difficult to measure both rapidly and accurately.

In our new approach, from Eq. (2) we derived and found that the cytoplasmic bulk flow velocity can be described as:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}\mathrm{\:=\:}\frac{\mathrm{d}{\mathrm{V}}_{\mathrm{c}}\text{}}{{\mathrm{A}}_{\mathrm{c}}\mathrm{dt}}\mathrm{=}-{\mathrm{P}}_{\mathrm{m}}{\mathrm{V}}_{\mathrm{w}}\Delta\mathrm{c}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{\mathrm{d(}{\mathrm{V}}_{\mathrm{c}}\mathrm{/}{\mathrm{A}}_{\mathrm{c}}\mathrm{)\:}}{\mathrm{dt}}$$\end{document} is often called the rate of change in cell volume per unit of surface area or volumetric flux (Cussler 2009; Olbrich et al. 2000), and also local water flow velocity averaged on the local area \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} (Cussler 2009; R. Byron Bird, 2006). Here we see \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} as the flow velocity of the fluid-phase in cytoplasm (or velocity change from initial \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} = 0) caused by transmembrane water flow driven by injection of osmotic gradient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c$$\end{document} cross \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} extracellularly. According to Eq. (3), if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} can be measured instantaneously for a known \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c$$\end{document} , then, there is no longer a need to determine \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{A}}_{\mathrm{c}}$$\end{document} or wait for a measurable cell volume change to estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} . Notably, both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} share the same unit, suggesting that, in addition to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}},\:\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} could serve as a novel biophysical marker for characterizing AQPs’ function and regulation in response to rapid osmotic perturbations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c\ne\:0$$\end{document} , independent of volume change. In general, measuring \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} as an instantaneous quantity is significantly faster than tracking the cumulative change in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{V}}_{\mathrm{c}}$$\end{document} .

Cytoplasmic flows in large cells have been measured using nanoparticles (≥ 23 nm diameters) as tracers, whose volume is approximately ~ 10^5^ times larger than that of water molecules(Hebert et al. 2005; Keren et al. 2009). However, the 20–40 nm pores of the filamentous meshwork, combined with cytoplasmic organelles and crowders, limit particle mobility and compromise flow velocity measurements when using tracer particles(Luby-Phelps et al. 1986; Wirtz 2009). By contrast, small molecule fluorescent dyes enable more reliable detection of extremely low flow velocities (~ 1 μm/s) induced by osmotic shock, which is difficult to measure due to limited sensitivity of conventional velocimetry using particles as flow tracers. The extremely low intracellular flow velocity is predicted by Eq. (3) for a large membrane permeability coefficient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} = 0.1 mm/s (Verkman 2000) under a normal isotonic cell osmolality 300 mOsm gradient (Δc) generated by DI water as the hypotonic solution(Silverthorn 2016). Note, although the velocity is low, it could significantly and rapidly affect cell homeostasis because of small cell size.

Here, we show that FIFIV can rapidly capture transient cytoplasmic flow signals ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} ) triggered by a localized osmotic shock ∆c ≠ 0 in single cells. FIFIV is based on a Laser-Induced Fluorescence Photobleaching Anemometry (LIFPA), which offers high spatial and temporal resolution(Kuang et al. 2011; Kuang and Wang 2010; Zhao et al. 2016). Because LIFPA is also a relatively new technique, it is worth to introduce the principle of LIFPA first so that readers can better understand how FIFIV works.

Principle of LIFPA

We assume that (i) the decay rate of the concentration of fluorescent dye molecules is linearly proportional to their concentration, and (ii) the measured fluorescence intensity is linearly proportional to the dye concentration. Under these assumptions, photobleaching of fluorescent dyes under constant illumination intensity can be described by an exponential decay of the fluorescence intensity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{f}$$\end{document} with time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t$$\end{document} :

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{f}={I}_{0}{e}^{-t/\tau\:\:}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{0}$$\end{document} is the fluorescence intensity at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t=0\:$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\tau\:$$\end{document} is the photobleaching half-decay time, which is constant for a given dye and laser intensity. Consider the laser focal volume approximated as a small cube (Fig. 1), where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:A$$\end{document} is the cross-section area perpendicular to the flow direction, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:L$$\end{document} is the dimension along the flow, and the fluid velocity is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{U}_{c}$$\end{document} . A dye molecule entering the focal volume at position \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:x$$\end{document} remains inside for a residence time (Kuang et al. 2009)

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:t=x/{U}_{c}$$\end{document}

and thus bleaches according to

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{f}={I}_{0}{e}^{-x/{U}_{c}\tau\:}$$\end{document}

Fig. 1. Schematic in illustrating LIFPA principle. (a) Fluorescence decay process due to photobleaching when a dye solution flows through a laser beam. (b) The corresponding relation between the fluorescence intensity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} and the residence (or decay) time. (c) The concurrent relationship between flow velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:{U}_{c}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} described by Eq. (8). Note: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{t}_{1}<\:{t}_{2}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{U}_{c}\left({t}_{2}\right)$$\end{document} < \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{U}_{c}\left({t}_{1}\right)$$\end{document}

The total measured fluorescence collected by the detector is

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\begin{array}{cccc}&\:{I}_{fT}=KA{\int\:}_{0}^{L}{I}_{f}{\hspace{0.17em}}dx,&\:&\:\end{array}$$\end{document}

where K is a photoelectric conversion factor and is constant for a given optical system. Combining Eqs. (6) and (7) gives

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}=KA{I}_{0}{U}_{c}\tau\:(1-{e}^{-L/\left({U}_{c}\tau\:\right)})$$\end{document}

Differentiation shows

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{{dI}_{fT}}{d{U}_{c}}=KA{I}_{0}\tau\:[1-{e}^{-\frac{L}{\tau\:{U}_{c}}}\left(1+\frac{L}{\tau\:{U}_{c}}\text{}\right)]>0$$\end{document}

Equation (9) indicates that fluorescence intensity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} increases with the increase of flow velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{U}_{c}$$\end{document} when dye concentration is constant.

Therefore, for LIFPA, when molecules of a fluorescent solution with a constant dye concentration flow into a laser focal point, they start to bleach within the beam and their fluorescence intensity will continuously decay until they flow out of the focal point. This is because the fluorescence intensity is proportional to the unbleached dye concentration within the laser focal volume, which decrease with time during photobleaching. If the flow velocity is high as shown in the red line in Fig. 1a, the residence and bleaching times are short. Then the average fluorescence is relatively high as shown in the red dash lines in Fig. 1a and b. However, If the flow velocity is low as shown in the black line in Fig. 1a, the residence and bleaching times are long. Then the average fluorescence is relatively low as shown in the dash black lines in Fig. 1a with Eqs. (8) and 1b with Eq. (4). Figure 1(c) shows the relevant relation between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{U}_{c}$$\end{document} . This dependence of fluorescence on flow velocity forms the basis of LIFPA velocimetry, which, in turn, is the foundation of FIFIV.

Principle of FIFIV

When LIFPA is applied to intracellular flow, it becomes FIFIV. To apply FIFIV to measure transmembrane fluid (including water) flows under stimuli (e.g. osmotic pressure gradient), there should be an intracellular flow in cytoplasm. To generate a quasi-unidirectional flow in cytoplasm under osmotic pressure gradient, a DI water droplet is injected on one side of an adhered cell on an imaging dish. Figure 2a illustrates the generation of local cytoplasmic flow \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} under an imposed osmotic shock ∆c ≠ 0. The cell is initially equilibrated in an isotonic medium (e.g., 1× PBS buffer). A localized pulse injection of a hypotonic solution ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta\mathrm{c\:>\:0}$$\end{document} ; typically, a DI water droplet) near the left membrane establishes an instantaneous asymmetric osmotic gradient across the cell, while the right side remains exposed to near-isotonic conditions. This drives transient left-to-right transmembrane water flow, subsequently inducing a cytoplasmic flow. If FIFIV can rapidly detect the cytoplasmic velocity change \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} , then, according to Eq. (3), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{m}$$\end{document} can be determined in real time without requiring measurements of cell volume and surface area—parameters that are difficult to obtain rapidly for adherent cells with irregular geometry. Note that the “boundary” shown in the schematic of Fig. 2a represents only the initial local interface between the injected droplet and the extracellular buffer adjacent to the cell membrane, rather than a stable physical boundary. This initial interface is rapidly blurred by molecular diffusion. Figure 2a is therefore intended to illustrate the initial moment immediately following injection, before significant diffusion occurs. While this approach provides a simple and effective means to locally apply an osmotic shock in the present study for instantaneous measurement, it does not allow precise control or maintain the transient osmotic gradient.

Fig. 2. Principle and setup of the FIFIV system. a Schematic of transmembrane water flow induced by ∆c ≠ 0, generated by injection of a DI water droplet on the left side of a cell, while the right side remains exposed to the original isotonic medium. b Principle of FIFIV: Case 1 shows the baseline condition \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c=0$$\end{document} ; Case 2 illustrates the presence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c\ne\:0$$\end{document} . c Schematic of experimental setup for measuring cytoplasmic velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{m}$$\end{document} . d Representative image showing the laser focal point (spot about 16 μm away from the left cell membrane surface) aligned within the cytoplasm of a single cell. The scale bar: 10 μm

The principle of using FIFIV to measure \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} is illustrated in Fig. 2b through two representative cases. In Case 1 ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c=0),\:$$\end{document} when a laser beam is focused within the quiescent cytoplasm of an adhered cell at rest, there is no bulk flow, dye molecules within the laser focal volume bleach continuously and the fluorescence signal \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} decays exponentially due to photobleaching (black curve).

In contrast, Case 2 depicts the response to an osmotic shock: as shown in Fig. 2a, a localized injection of a droplet of hypotonic solution (e.g., a DI-water droplet) on the left side of the cell establishes an osmotic shock ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c\ne\:0$$\end{document} ), causing a transmembrane water flow from left to right. Because the cytoplasm is effectively incompressible, this results in immediate cytoplasmic flow at the focal detection point. Unbleached dye nearby between the focal region and the left membrane is advected into the focal volume, replacing the bleached dye, disturbing the exponential decay and producing an immediate and transient rise (pulse) in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} . This analysis assumes a constant dye concentration outside the focal volume within cytoplasm over short timescales. Once osmotic equilibrium is reached, the flow ceases, resulting in a peak in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} , followed by another decay as shown in case 2 (red curve) in Fig. 2b.

The exponential decay of fluorescence in quiescent fluid results from a competition between two kinetic processes: the photochemical reaction and molecular diffusion due to Brownian motion within the detection volume. The photochemical reaction reduces the number of molecules capable of emitting fluorescence, while the diffusion of molecules from the surrounding area replenishes the pool of fluorescent molecules. The decay indicates that the rate of consumption exceeds the rate of fluorescence recovery for a given laser intensity and dye concentration. The average molecular diffusion velocity, which can be estimated using Brownian motion and the Stokes-Einstein equation, decreases over time(Li et al. 2010). However, if an additional convection velocity is present, it adds to the diffusion velocity, disturbing the exponential decay; this disturbance can be detected due to the high sensitivity of fluorescence spectroscopy. Given that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} falls within the low velocity range, FIFIV is well-suited for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} measurement.

Here, there is a time delay t_d_ between the moment of osmotic shock injection and the onset of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} increase (see later in Fig. 5a). t_d_ depends on the duration of injection and on factors such as AQP expression, gating, and regulation. The higher the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} , the smaller the t_d_. In FIFIV, if the osmotic gradient persists, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} will also decrease because water flows into the cytoplasm, eventually diluting the dye concentration. The key distinction between LIFPA and FIFIV is that LIFPA maintains a constant dye concentration, whereas FIFIV involves time-dependent changes in dye concentration after sufficient time when cell volume has changed significantly. Therefore, FIFIV is best applied over short measurement times for current injection method, before the diluted dye redistributes to the detection region. For this reason, before performing another measurement on the same cell, one must wait until the dye is diffused uniformly within the cytoplasm.

Materials and Methods

Setup

The FIFIV system was a custom-built instrument, and a schematic of the setup is shown in Fig. 2c. We integrated FIFIV system with a Nikon C2 confocal microscope. A cube diode laser with a wavelength of 405 nm from Coherent was used to excite a labeled cell and generate the intracellular FIFIV fluorescence signal. The laser was launched to the microscope port. The laser beam was directed into the microscope port and expanded to 5 mm in diameter using a beam expander before entering a 60X oil-immersion objective with numerical aperture (NA) of 1.4, achieving near-diffraction-limited spatial resolution of ~ 200 nm laterally and 500–600 nm axially. The laser power was modulated to remain below 10 µW at the entrance of the microscope using a function generator AFG3102 (Tektronix) at 100 kHz and a pulse width of 190 ns. A dichroic mirror (Chrome technology) was used for epifluorescence microscopy applications. A PInano XYZ P-545.3C7 Piezo stage (Physik Instrumente) with 1 nm resolution was mounted on the microscope to precisely manipulate and align the laser focus and cell position. For these experiments, the focal point was inside the cell and positioned 16 μm away from the left cell membrane as shown in Fig. 2d.

A beamsplitter reflected 20% of the signal to a CCD camera and transmitted 80% to a photodetector was installed to ensure a high signal-to-noise ratio for the detector. A collection lens was used to focus the signal to a multimode optical fiber, with a 10-µm diameter core, which acted as a pinhole to enhance spatial resolution. A band-pass filter, matching the emission wavelength of the fluorescent dye (Calcein AM 450), was placed in front of the fiber inlet to transmit the fluorescence signal from the dye while filtering out scattered laser light and other potential noise. A five-axis (5-D) stage was used to align the fiber inlet precisely with the focused signal. The fiber was connected to a photodetector. To achieve high sensitivity, the fluorescence signal was measured using an ultra-low-noise single-photon detection module (id100-MMF50, Becker & Hickl Inc.). The detector output was recorded on a computer through an analog-to-digital (A/D) converter (USB-6259, NI). LabVIEW software was used for data acquisition at a sampling rate of 5 Hz.

Materials and Sample Preparation

The epithelial breast cancer cell line MDA-MB-231, which predominantly expresses AQP1, AQP3, and AQP5(Ahmad et al. 2020; Stroka et al. 2014) was used for the FIFIV measurement of cytoplasmic flows to detect the transmembrane water flows driven by ∆c ≠ 0. MDA-MB-231 diameter in suspension is in the range of 16–21 μm (but differ when adherend) (Boussommier-Calleja et al. 2019; Keshavarz Motamed et al. 2024). All cells were cultured in a CO_2_ incubator (Sanyo) maintained at 37 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ C$$\end{document} . The cells were initially cultured following the manufacturer’s standard protocol using culture medium from Sigma-Aldrich. They were then transferred to an imaging dish (35 mm diameter, 12 mm height; IBIDI) and cultured for more than one day before testing to ensure firm adhesion to the substrate. The dish was precoated with collagen (Corning) prior to seeding to enhance cell attachment and growth.

The cytoplasm of live cells was labeled with the small fluorescent dye Calcein AM 450 (Invitrogen) via passive diffusion, following the manufacturer’s instructions. The dye is cylindrical, with a length of approximately 1.5 nm and a radius of 0.37 nm (data provided by Invitrogen). It has a maximum absorption wavelength near 400 nm, which aligns well with the 405 nm excitation wavelength of our laser. The final dye concentration in the working solution was 1 µM, used for labeling the cells. Calcein AM 450 was selected not only for transmembrane water-flow measurements but also for monitoring cell viability. After loading the dye, the cells in the dish were incubated for 45 min at 37 °C before testing. The labeled cells were then washed three times with 1× PBS buffer (Corning) and the dish containing the labeled, adherent cells was filled with approximately 2 mL of 1× PBS buffer, preparing it for experiments involving osmotic-shock injection. Note that Calcein AM 450 molecules are too large to pass through AQPs, and osmotic gradients cannot drive their transmembrane transport. Therefore, Calcein AM 450 fluorescence cannot be used to directly measure water flow across AQPs.

FIFIV determines cytoplasmic flow by measuring the fluorescence signal within the labeled cytoplasm. To ensure that changes in fluorescence intensity are caused by cytoplasmic flow, cells must be uniformly labeled with the fluorescent dye, so that any local variations in dye concentration do not produce fluctuations greater than those generated by flow induced by the osmotic gradient. After the labeled cells were incubated for 45 min, the cells in the imaging dish were examined under the microscope before experimentation to assess both cell viability and dye distribution within the cytoplasm. Calcein Violet AM can penetrate the nuclear membrane, allowing uniform dye distribution throughout the cytoplasm and nucleoplasm (Hulikova and Swietach 2016; Thermo Fisher Scientific. CellTrace Calcein Violet AM). Figure 3a shows the fluorescence image of the labeled cells, and Nikon Elements software was used to obtain the radial fluorescence-intensity profile across a single cell, as shown in Fig. 3b. The variation of fluorescence intensity was less than 4%. These results confirm that the cells were uniformly labeled.

Fig. 3. Cell viability and uniformly labeled cell a Labeled cells with Calcein; b Fluorescence (arbitrary unit) profile across the top labeled cell. The figure indicates that the cells were alive and were uniformly labeled

In addition, nuclocytoplasmic transport of small molecules (smaller than 20 kDa) proceeds passively and freely through nuclear pore complexes(Paine et al. 1975; Ribbeck and Görlich 2001). Because water molecular weight is only about 18 Da, there should be no barrier for water to transport through the nuclear envelope of cells. Cells may also express aquaporins on nuclear envelope(Yamazato et al. 2018), which could facilitate the rapid movement of water into the nucleus, thereby contributing to the FIFIV signal. Together, these characteristics make FIFIV straightforward to implement.

Microinjection and Detection

An Eppendorf microinjection system was mounted on the microscope for manipulating and injecting deionized (DI) water to generate a hypotonic gradient ∆c ≠ 0 that drives transcellular water flow across the cell plasma membrane. A CellTram Oil microinjector was used to manually inject DI water droplet for FIFIV measurement. At the tip of the CellTram Oil, there was a quartz capillary filled with DI water, with inner and outer diameters of 20 μm and 90 μm, respectively. During FIFIV measurements, the DI water droplet was injected in close proximity to the cell, while the instantaneous flow-velocity signal was continuously monitored. This approach minimizes the mixing time required for DI water to reach the cell membrane and reduces experimental artifacts.

The relative position of the capillary tip with respect to an adhered cell in the dish was precisely controlled by a 3-D PiezoXpert module and a InjectMan NI 2 controller, which provide a positioning resolution of 1 μm. These controllers were operated in conjunction with the motorized PInano stage. The injection tip was positioned approximately 30 μm from the left side of the cell membrane and 20 μm above the bottom surface of the adhered cell. The relative position of the DI water injection tip, the cell and laser focus point is illustrated in Fig. 2a. A CCD camera was used to monitor the alignment of the cell, the laser focal point, and the injection tip under the microscope. The cell volume was approximately estimated by measuring the 2-D surface area of the cells.

To evaluate the injection time of DI water, we used a fluorescent dye solution to visualize the dynamic process of the injection and estimate the injection time. DI water was replaced by a fluorescein solution at 10 µM in the injection tip, and the injection volume was 160 nL. Recording was started with a camera operating at 10 frames per second prior to injection. Figure 4 shows three images in sequence with a time interval of 0.1 s. Figure 4a is the time starting to inject, where there was almost no fluorescence, except the weak background noise from the tip. In Fig. 4b, only a little fluorescence stronger than that in Fig. 4a was visible, indicating the dynamic process of injection of the dye from the tip. Fluorescence intensity reached nearly its maximum in Fig. 4c, and after 0,2 s, no significant change in fluorescence was observed before the start of decay of the fluorescence because of the dye diffusion. The injection was almost achieved during Fig. 4b and c. Therefore, Fig. 4 indicates that the injection time was estimated to be about 0.2 s.

Fig. 4. Injection process of a fluorescein solution. a No fluorescence is visible when the injection starts at t = 0 s. The trace fluorescence seen is from the dye solution at the interface of the injection tip and the buffer solution. b At t = 0.1 s, the fluorescence becomes clearly visible, indicating that a small amount of dye solution has already flowed into the buffer solution. c At t = 0.2 s, the dye solution has been fully injected into the buffer solution. The subsequent images are similar to c. The scale bar is 30 μm

Results and Discussion

There is Pulse Increase in Fluorescence in Response to a Pulse Injection of the Osmotic Gradient Based on FIFIV

The capability of FIFIV to measure cytoplasmic flows induced by transmembrane flows following a pulse injection of ∆c ≠ 0 is given in Fig. 5, where the laser was activated at about 20 s. To confirm that the observed signal arises exclusively from ∆c ≠ 0, two control experiments were performed. In the first control, no water was injected at all, resulting in an expected exponential decay of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} (green curve). In the second, 100 nL of 1X PBS buffer was injected, creating an isotonic solution with ∆c = 0, which also produced a simple exponential decay (blue curve in Fig. 5a) as anticipated. In both control cases, no transmembrane water flow or cell volume change was observed during the measurement.

In contrast, when 100 nL DI water was injected, the medium on the left side of the cell became hypotonic locally, generating a transmembrane flow. Within about 1 s, the exponential decay was disturbed, and the signal began to increase from 54,000 to local peak of 62,000 after about 6 s. The increase is about 14.8%, followed by a faster decay and then a quasi-exponential decay again, as the transmembrane flow ceased once osmotic equilibrium was reached through both water flow into cell and diffusion of the droplet with the buffer (red curve, Fig. 5a). The area under the red pulse peak correlates with the total transmembrane water flux induced by ∆c ≠ 0 at the single cell level. Therefore, the local increase in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} within the pulse is consistent with the imposed osmotic perturbation. Similar pulse response curves to that in Fig. 5a under injection of osmotic gradient have been observed for more than 20 cells.

Fig. 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} time series and cell images. a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} response under three conditions: no injection (green); injection of an isotonic solution ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:c=0,\:$$\end{document} blue); and injection of a hypotonic solution ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:-\varDelta\:c>0,\:$$\end{document} red) near the cell surface. In the hypotonic case red (curve), the exponential decay of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} is immediately disrupted after the injection, producing a pulse signal corresponding to intracellular flow induced by transmembrane water flow across the cell membrane. b Image of the cell before hypotonic injection. c Image of the same cell 3 min after injection. Cell volume was increased by approximately 6.4% following the injection, confirming the transmembrane water flow. The ruler in b and c marks the cell position. Scale bar: 10 μm

Although fluorescence quenching is often applied in cell shrinking assays(Hamann et al. 2002; Kitchen et al. 2020), the signal increase observed in Fig. 5a cannot be attributed to the decrease in dye concentration resulting from the increased cell volume. This conclusion is supported by our observation that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} in cytoplasmic images increases with dye concentration in the range of 0.2–2 µM following incubation, and the working dye concentration here was approximately 1 µM. Moreover, cell volume changes were nearly negligible during the first 2 s, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} had already begun to rise. The slower cell volume increase occurs because, unlike suspension cells where the entire membrane experiences ∆c ≠ 0 uniformly, adhered cells respond to localized hypotonic stimulation (DI water droplet is only on one side), resulting in gradual swelling. The vertical line in Fig. 5a marks the start of the injection. The corresponding cell volume increase 3 min after injection is shown in Fig. 5b and c, where the area analysis indicates a volume increase of about 6.4%, assuming cell height remained unchanged.

Figure 5a could also be used to estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} . After reaching its maximum, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} is expected to gradually decrease. However, when water flows into the cell and reaches the focal point, the local dye concentration decreases, causing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} to decline more rapidly than it would if the dye concentration remained constant. The flow velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} can be approximated as the ratio of the distance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:L$$\end{document} between the focal point and the membrane on the injection side in Fig. 2d to the time interval \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:t$$\end{document} between the start of the injection and the moment when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} starts to sharply decrease after the peak, i.e. the time taken for water to travel from the membrane surface to the focal point. Assuming water reaches the focal point from the surface at the time when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} decays sharply than that before injection of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta\mathrm{c}\ne\:0$$\end{document} , the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} can be estimated as.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}=\varDelta\:L/\varDelta\:t$$\end{document}

In current case, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:L$$\end{document} is 16 μm as shown in Fig. 2d, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\varDelta\:t$$\end{document} is 8.2 s as indicated in Fig, 5a. For the red curve in Fig. 5a, from Eq. (10), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} is estimated to be approximately 1.95 μm/s. Using Eq. (3) and assuming ∆c = 300 mOsm(Silverthorn 2016), the corresponding \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} is estimated to be ~ 0.0361 cm/s, which is about 60% higher than the reported value of 0.0225 cm/s for the same cell line(Satooka and Hara-Chikuma 2016).

Twenty cells were measured to assess the statistical properties of FIFIV, and the results are summarized in Fig. 6, which reports the mean values and relative standard deviations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} . The average values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} were 2.07 μm s⁻¹ and 0.0383 cm s⁻¹, respectively. The relative standard deviation of both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}\:$$\end{document} was the same of 26.8% because of their linear relationship.

This level of variability reflects combined technical and biological sources typical of single-cell biophysical assays. Several factors may contribute to the observed variability. First, the osmotic pressure gradient generated by manually local injection in a dish is not precisely controlled or maintained. Additional sources of variation include cell-to-cell heterogeneity, uncertainties in the positioning of the laser focal spot and injection tip, and the irregular geometry of adherent cells (which is, however, more pathophysiological relevant for epithelial cells). Variability may also arise from differences in assay timing (within approximately 12 h) following cell incubation and labeling, as well as from manual determination of the injection onset and the arrival time of water at the detection volume. Many of these sources of variability could be reduced in future studies by implementing a microfluidic platform, together with automated control systems and software-based data acquisition and analysis.

Fig. 6. Boxplots summarizing statistical measurements of both the intracellular flow velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}\:\mathrm{P}}_{\mathrm{m}}$$\end{document} obtained from 20 cells. For each boxplot, the box represents the interquartile range (IQR) with the central line indicating the median, and the whiskers showing the full data range. The red dot denotes the mean value, and the red error bar represents ± 1 standard deviation (SD). For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{U}}_{\mathrm{c}}$$\end{document} the mean velocity was 2.07 μm/s, with an SD of 0.55 μm/s, corresponding to a relative standard deviation (RSD) of 26.8%. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\mathrm{P}}_{\mathrm{m}}$$\end{document} measurements are presented using the same statistical representation. The mean permeability was 0.0383 cm/s, with an SD of 0.01026 cm/s, yielding an RSD of 26.8%

There is pulse fluorescence response to injection of osmotic gradient even though the cell volume change is not significant

In physiology, the endothelial cells of microvessels experience a nearly steady osmotic pressure difference and a continuous flux of water from the lumen toward the interstitium, as described by Starling’s law (Levick and Michel 2010; Truskey et al., 2004). During water reabsorption across tight urinary epithelia—driven by a transepithelial osmotic pressure gradient under the regulation of antidiuretic hormone—the cell volume in the collecting tubules of the rabbit kidney cortex increases only modestly (by approximately 2.3%) during transcellular water flow (Strange and Spring 1987). This may indicate that there could be transcellular flows without measurable cell volume change.

Because FIFIV is highly sensitive to flow dynamics, it can also detect the flow changes induced by a rapid injection of ∆c ≠ 0 even when cell volume changes are not measurable, as shown in Fig. 7. To facilitate cells to reach a quasi-saturated volume, we used a larger injection droplet of DI water this time. Fourteen seconds after the laser beam was switched on and focused inside the cell, 160 nL of DI water was injected as shown by the vertical line in Fig. 7a. An immediate rise in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} was observed within around 1 s, indicating the onset of the transmembrane and cytoplasmic flows generated by the imposed ∆c ≠ 0. A comparison of Fig. 7d (before injection) and Fig. 7e (3 min after the first injection, sufficiently long to reach osmotic equilibrium and uniform dye concentration) shows an about 12% increase in cell volume. Two minutes later, another 160 nL of DI water was injected, resulting in another \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} increase, as shown in Fig. 7b. However, by 3 min post-injection, the cell volume in Fig. 7f had increased by only 2% compared to that in Fig. 7e. A third injection of 160 nL of DI water conducted 2 min later, still produced a clear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} rise as shown in Fig. 7c, despite the already elevated cell volume compared to Fig. 7d. Notably, almost no additional volume change was detected in Fig. 7g relative to that in Fig. 7f, suggesting that the cell volume had reached a temporarily quasi-steady state. The signal increase in Fig. 7c may result from a flow behavior analogous to the transcellular flow in endothelial cells in capillaries, where water enters the cell from one side and exits from the other, or from a volume regulation mechanism. Further study is needed to understand the reason. The reduced signal amplitudes in Fig. 7b and c compared to that in Fig. 7a are attributed to photobleaching and dilution of the fluorescent dye in the cytoplasm due to volume increase. Figure 7 shows FIFIV could potentially measure transcellular flows as well.

Fig. 7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} time series and images of a single cell subjected to multiple DI water injections. a-c \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{I}_{fT}$$\end{document} responses to the first, second, and third injections of 160 nL DI water, respectively, showing pulse signals induced by ∆c ≠ 0. d: Image of the cell before the first injection. e-g Bright-field images of the same cell 3 min after the first, second, and third injections, respectively. While clear pulse signals were observed for each injection, the cell volume exhibited almost no additional change after the third injection. This suggests the involvement of a volume-regulation mechanism that limits cell swell further and may allow water to flow out of the cell from the opposite side. Scale bar: 10 μm

Conclusion

In conclusion, while transmembrane water flow driven by osmotic gradients lacks electrical signals, the resultant cytoplasmic flow generates a measurable fluorescence signal. Leveraging fluorescence spectroscopy, FIFIV detects instantaneous changes in transmembrane water transport and the induced cytoplasmic flows with high temporal resolution, eliminating the need for measurements of slow volume change. This work establishes FIFIV as a new optical approach for probing transmembrane water-flow–induced intracellular dynamics, providing a foundation for future investigations of AQP regulation and gating mechanisms. FIFIV could be applied to characterize AQPs’ function and regulation at a single cell level by comparing cells with and without siRNA knockdown of AQPs or by applying AQP modulators under osmotic shock—analogous to how patch-clamp techniques are used to study ion flux through ion channels under a membrane voltage. FIFIV requires no genetic modification and may be directly applied to human epithelial cells in adhered conditions, offering physiological relevance and potential compatibility with high-throughput drug screening and in vitro studies. In addition, FIFIV has the potential to quantify transcellular water transport across microvascular endothelia.