Theoretical model of confined thermoviscous flows for artificial cytoplasmic streaming

Abstract

Recent experiments in cell biology have probed the impact of artificially-induced intracellular flows in the spatiotemporal organisation of cells and organisms. In these experiments, mild dynamical heating (a few kelvins) via focused infrared light from a laser leads to long-range, thermoviscous flows of the cytoplasm inside a cell. To extend future use of this method in cell biology, popularised as focused-light-induced cytoplasmic streaming (FLUCS), new quantitative models are needed to link the external light forcing to the produced flows and transport. Here, we present a fully analytical, theoretical model describing the fluid flow induced by the dynamical laser stimulus at all length scales (both near the scan path of the laser beam and in the far field) in two-dimensional confinement. We model the effect of the focused light as a small, local temperature change in the fluid, which causes a small change in both the density and the viscosity of the fluid locally. In turn, this results in a locally compressible fluid flow. We analytically solve for the instantaneous flow field induced by the translation of a heat spot of arbitrary time-dependent amplitude along a scan path of arbitrary length. We show that the leading-order instantaneous flow field results from the thermal expansion of the fluid and is independent of the thermal viscosity coefficient. This leadingorder velocity field is proportional to the thermal expansion coefficient and the magnitude of the temperature perturbation, with far-field behaviour typically dominated by a source or sink flow and proportional to the rate of change of the heat-spot amplitude. In contrast, and in agreement with experimental measurements, the net displacement of a material point due to a full scan of the heat spot is quadratic in the heat-spot amplitude, as it results from the interplay of thermal expansion and thermal viscosity changes. The corresponding average velocity of material points over a scan is a hydrodynamic source dipole in the far field, with direction dependent on the relative importance of thermal expansion and thermal viscosity changes. Our quantitative findings show excellent agreement with recent experimental results and will enable the design of new controlled experiments to establish the physiological role of physical transport processes inside cells.