Integrins are a family of αβ heterodimeric transmembrane receptors. As an important class of adhesion receptors, integrins mediate cell adhesion, migration, and transformation through bidirectional signaling across the plasma membrane. Among the 24 different types of integrins, which are notorious for their capacity to recognize multiple ligands, the leukocyte integrin αMβ2 (Mac-1) is the most promiscuous member. In contrast to other integrins, Mac1 is unique with respect to its preference for cationic ligands. In this thesis, a new Mac-1 cationic ligand named pleiotrophin (PTN) is uncovered. PTN is an important cytokine and growth factor. Its activities in mitogenesis and angiogenesis have been extensively researched, but its function on immune cells was not widely explored. In this research, the cell biology and biochemical evidences show that PTN can regulate various Mac-1-expressing cells functions through the activation of the extracellular signal regulated kinases. Direct interactions between PTN and the αM I-domain, the major ligand-binding domain of Mac-1, has been shown using biolayer interferometry analyses and confirmed by solution NMR spectroscopy. The binding epitopes and the binding mechanism of PTN and αM I-domain interaction were further revealed by peptide array analysis and microscale thermophoresis. The data suggested that PTN’s thrombospondin type-1 repeat (TSR) domains and αM I-domain metal-ion-dependent adhesion site (MIDAS) are the major binding sites. In addition, this interaction followed a novel metal-ion independent binding mechanism which has not been found in other integrins. After a series of characterizations of αM I-domain using both experimental and computational methods, it showed that activated αM I-domain is significantly more dynamic than inactive αM I-domain, and the dynamics seem to modulate the effect of Mg2+ on its interactions with cationic ligands. To further explore the PTN induced Mac-1 structure rearrangement, intact Mac-1 was studied by negative stain electron microscopy. The results showed that the Mac-1 exhibited a very heterogeneous conformation distribution in detergents. In contrast, the Mac-1 adopted predominantly the bent conformation in phospholipid nanodisc condition. This Mac-1 nanodisc model provides a new platform for studying intact Mac-1 activation mechanism in a more physiologically relevant manner in the future.

This dissertation studies two outstanding microscale fluid mechanics problems: 1) mechanisms of gas production from the nanopores of shale; 2) enhanced mass flow rate in steady compressible gas flow through a micro-conduit.

The dissertation starts with a study of a volumetric expansion driven drainage flow of a viscous compressible fluid from a small capillary and channel in the low Mach number limit. An analysis based on the linearized compressible Navier-Stokes equations with no-slip condition shows that fluid drainage is controlled by the slow decay of the acoustic wave inside the capillary and the no-slip flow exhibits a slip-like mass flow rate. Numerical simulations are also carried out for drainage from a small capillary to a reservoir or a contraction of finite size. By allowing the density wave to escape the capillary, two wave leakage mechanisms are identified, which are dependent on the capillary length to radius ratio, reservoir size and acoustic Reynolds number. Empirical functions are generated for an effective diffusive coefficient which allows simple calculations of the drainage rate using a diffusion model without the presence of the reservoir or contraction.

In the second part of the dissertation, steady viscous compressible flow through a micro-conduit is studied using compressible Navier-Stokes equations with no-slip condition. The mathematical theory of Klainerman and Majda for low Mach number flow is employed to derive asymptotic equations in the limit of small Mach number. The overall flow, a combination of the Hagen-Poiseuille flow and a diffusive velocity shows a slip-like mass flow rate even through the overall velocity satisfies the no-slip condition. The result indicates that the classical formulation includes self-diffusion effect and it embeds the Extended Navier-Stokes equation theory (ENSE) without the need of introducing additional constitutive hypothesis or assuming slip on the boundary. Contrary to most ENSE publications, the predicted mass flow rate is still significantly below the measured data based on an extensive comparison with thirty-five experiments.