Our results suggest that the proteins identified in this study may be associated with the unique function of periodontal ligament cells in maintaining periodontal tissue homeostasis, thus providing a comprehensive reference for understanding and investigating in greater detail the molecular mechanisms of periodontal ligament cells involved in periodontal regeneration.

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The Monin-Obukhov similarity theory (MOST) is widely used for the surface turbulence flux-gradient relations in modeling and data analysis. Here we quantify multiscale turbulence processes by applying our newly developed analysis technique to large-eddy simulation data, and find that in the unstable surface layer, large convective eddies (with the scaling of boundary layer depth) and local free convection exist in addition to small eddies. An empirical MOST function (considering the last two processes only) is found to underestimate the surface friction velocity and heat flux both by about 30%. Much better results can be obtained using a function that explicitly considers all three processes. Generally, the nondimensional wind shear exhibits larger scatter and deviates more from the MOST than the temperature gradient. Based on these results, we propose the revised Sorbjan (1986, https://doi.org/10.1007/BF00120989) function (with coefficients determined from this study) for wind shear and MOST function for temperature gradient, for estimating surface fluxes in the unstable surface layer. The three-dimensional multiscale analysis method we develop in this study is of general nature and can be of interest for problems of three-dimensional multiscale process description in other disciplines.In this section, we will first present briefly the OPD technique and its extension to three dimensions (see Method S1 in the supporting information for details). The standard MOST and previous efforts to improve the flux-gradient relations for the unstable condition will be described as well. Finally, we will describe how the data used in this study are obtained via large-eddy simulation.