Fig 1.
Two- and three-dimensional cell domains and computational grids.
A. Two-dimensional domain and grid featuring 8,640 unique element nodes for spherical cell. B. Three-dimensional domain and grid featuring 10,324 nodes for spherical cell. Triangular grids optimized using Gmsh C Horizontal plane surface (x1-x2) used for demonstration of three-dimensional velocity flow fields. D Vertical plane surface (x1-x3) used for demonstration of three-dimensional velocity flow fields. All planes pass through midpoint of cell nucleus. Large arrows demonstrate the direction from which 3D results (presented on respective plane surface) will be viewed.
Table 1.
Computational model parameters assuming a base temperature of cytosolic fluid of approximately 37°C.
Fig 2.
Simulation results for two- and three-dimensional spherical cell domains.
A. Temperature profile across two-dimensional domain, with heated nuclear wall (38°C) and neutral cell membrane (37°C). B,C. Two-dimensional convection-induced horizontal (B; x1) and vertical (C; x2) velocity profiles demonstrating one major (left of nucleus) and one minor (right of nucleus) convective circulation structure characterized by central upwelling (red) and fountain-like downwelling (blue) around the outer cell wall. D. 2D velocity vectors with arrow length indicative of speed relative to maximum speed in domain. E,F. Equivalent velocity vectors on both vertical (E) and horizontal (F) planes in three-dimensional simulations. For clarity, vectors with a positive vertical (x3) component are shown in red, while those with a negative vertical component are shown in blue. The fountain-like structure of convective circulations is again clearly evidenced by large regions of upwelling in the center of the domain and the corresponding downwelling around the outer cell wall.
Fig 3.
Maximum upwelling (A) and downwelling (B) velocities in each respective direction from three-dimensional simulations with a range of hypothetical nuclear temperatures ranging from 37°C to 50°C. Intuitively, a higher temperature gradient between the local heat source and the outer cell membrane induced the largest convective velocities, reaching approximately 0.39 μm/s in the positive vertical direction (A).
Fig 4.
Péclet number (u*L/D) as a function of the temperature difference ΔT (Tmax−Tmin,°C) and the diffusion coefficient D (μm2/s), demonstrating regions in which Pe>1 and thus convection can theoretically dominate over diffusion.
Fig 5.
Simulated flow patterns within an 8-cell domain representative of a series of columnar epithelial cells, demonstrating the influence of: (A) increased nuclear heating (B), pseudo-stratification (C-E), altered shape of nucleus (F), altered location of nucleus (G) and uneven distribution of heating (H). Overlaid schematic provides a conceptual representation of the nuclear shape and temperature (brown ellipses), and the flow direction (black arrows).
Fig 6.
A. Immunofluorescence images of Bovine Pulmonary Artery Endothelial Cells (purchased from ThermoFisher Scientific) to provide a biologically realistic domain for application of the present model. Nuclei shown in blue are stained using DAPI, mitochondria in red (note clustering around cell nuclei) are stained using MitoTracker Red CMKRos, and cytoskeleton in green stained with Alexa Fluor 488 Phalloidin. B. Distribution of cell nuclei, mitochondria and the shape of the cell membranes (based on the distribution of the microtubules) extracted from the fluorescence image and used to develop a unique representative computational grid for each cell. Simulations are conducted with heating applied only in regions of mitochondrial clustering. The resulting flow field in terms of velocity vectors is overlaid on the original image, demonstrating the circulatory patterns hypothetically generated in this multi-cell domain. Note that the convective flows will typically be both within the x1-x2 plane of the image and also in the perpendicular x3 direction. These models assume no inter-cellular flow. However, cyclosis could promote movement of fluid, ions, and small molecules through gap junctions.