Nonlinear dynamics of cilia and flagella

Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.

Dynamic behaviour of rotary mechanical seals

This thesis covers both experimental and computer investigations into the dynamic behaviour of mechanical seals. The literature survey shows no investigations on the effect of vibration on mechanical seals of the type common in the various process industries. Typical seal designs are discussed. A form of Reynolds' equation has been developed that permits the calculation of stiffnesses and damping coefficients for the fluid film. The dynamics of the mechanical seal floating ring have been investigated using approximate formulae, and it has been shown that the floating ring will behave as a rigid body. Some elements, such as the radial damping due to the fluid film, are small and may be neglected. The equations of motion of the floating ring have been developed utilising the significant elements, and a solution technique described. The stiffness and damping coefficients of nitrile rubber o-rings have been obtained. These show a wide variation, with a constant stiffness up to 60 Hz. The importance of the effect of temperature on the properties is discussed. An unsuccessful test rig is described in the appendices. The dynamic behaviour of a mechanical seal has been investigated experimentally, including the effect of changes of speed, sealed pressure and seal geometry. The results, as expected, show that high vibration levels result in both high leakage and seal temperatures. Computer programs have been developed to solve Reynolds' Equation and the equations of motion. Two solution techniques for this latter program were developed, the unsuccesful technique is described in the appendices. Some stability problems were encountered, but despite these the solution shows good agreement with some of the experimental conditions. Possible reasons for the discrepancies are discussed. Various suggestions for future work in this field are given. These include the combining of the programs and more extensive experimental and computer modelling.

A molecular dynamics model of the atomic structure of dysprosium alumino-phosphate glass

Molecular dynamics (MD) has been used to identify the relative distribution of dysprosium in the phosphate glass DyAl0.30P3.05O9.62. The MD model has been compared directly with experimental data obtained from neutron diffraction to enable a detailed comparison beyond the total structure factor level. The MD simulation gives Dy ... Dy correlations at 3.80(5) and 6.40(5) angstrom with relative coordination numbers of 0.8(1) and 7.3(5), thus providing evidence of minority rare-earth clustering within these glasses. The nearest neighbour Dy-O peak occurs at 2.30 angstrom with each Dy atom having on average 5.8 nearest neighbour oxygen atoms. The MD simulation is consistent with the phosphate network model based on interlinked PO4 tetrahedra where the addition of network modifiers Dy3+ depolymerizes the phosphate network through the breakage of P-(O)-P bonds whilst leaving the tetrahedral units intact. The role of aluminium within the network has been taken into explicit account, and A1 is found to be predominantly (78 tetrahedrally coordinated. In fact all four A1 bonds are found to be to P (via an oxygen atom) with negligible amounts of Al-O-Dy bonds present. This provides an important insight into the role of Al additives in improving the mechanical properties of these glasses.

A decade of silicone hydrogel development:surface properties, mechanical properties, and ocular compatibility

Since the initial launch of silicone hydrogel lenses, there has been a considerable broadening in the range of available commercial material properties. The very mobile silicon–oxygen bonds convey distinctive surface and mechanical properties on silicone hydrogels, in which advantages of enhanced oxygen permeability, reduced protein deposition, and modest frictional interaction are balanced by increased lipid and elastic response. There are now some 15 silicone hydrogel material variants available to practitioners; arguably, the changes that have taken place have been strongly influenced by feedback based on clinical experience. Water content is one of the most influential properties, and the decade has seen a progressive rise from lotrafilcon-A (24%) to efrofilcon-A (74%). Moduli have decreased over the same period from 1.4 to 0.3 MPa, but not solely as a result of changes in water content. Surface properties do not correlate directly with water content, and ingenious approaches have been used to achieve desirable improvements (e.g., greater lubricity and lower contact angle hysteresis). This is demonstrated by comparing the hysteresis value of the earliest (lotrafilcon-A, >40°) and most recent (delefilcon-A, <10°) coated silicone hydrogels. Although wettability is important, it is not of itself a good predictor of ocular response because this involves a much wider range of physicochemical and biochemical factors. The interference of the lens with ocular dynamics is complex leading separately to tissue–material interactions involving anterior and posterior lens surfaces. The biochemical consequences of these interactions may hold the key to a greater understanding of ocular incompatibility and end of day discomfort.

The structure and dynamics of 2-dimensional fluids in swelling clays

The interlayer pores of swelling 2:1 clays provide an ideal 2-dimensional environment in which to study confined fluids. In this paper we discuss our understanding of the structure and dynamics of interlayer fluid species in expanded clays, based primarily on the outcome of recent molecular modelling and neutron scattering studies. Counterion solvation is compared with that measured in bulk solutions, and at a local level the cation-oxygen coordination is found to be remarkably similar in these two environments. However, for the monovalent ions the contribution to the first coordination shell from the clay surfaces increases with counterion radius. This gives rise to inner-sphere (surface) complexes in the case of potassium and caesium. In this context, the location of the negative clay surface charge (i.e. arising from octahedral or tetrahedral substitution) is also found to be of major importance. Divalent cations, such as calcium, eagerly solvate to form outer-sphere complexes. These complexes are able to pin adjacent clay layers together, and thereby prevent colloidal swelling. Confined water molecules form hydrogen bonds to each other and to the clays' surfaces. In this way their local environment relaxes to close to the bulk water structure within two molecular layers of the clay surface. Finally, we discuss the way in which the simple organic molecules methane, methanol and ethylene glycol behave in the interlayer region of hydrated clays. Quasi-elastic neutron scattering of isotopically labelled interlayer CH 3OD and (CH2OD)2 in deuterated clay allows us to measure the diffusion of the CH3- and CH2-groups in both clay and liquid environments. We find that in both the one-layer methanol solvates and the two-layer glycol solvates the diffusion of the most mobile organic molecules is close to that in the bulk solution.

Dynamics of pulsed flow in an elastic tube

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow in our attempt to specify the location of the haemorrhagic spot, which, if located accurately, could possibly be operated leading to an instant cure. The model we employ for the purpose is basically fluid mechanical in origin and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an artery or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations.

Complexity of classical dynamics of molecular systems. II. Finite statistical complexity of a water-Na+ system

The computational mechanics approach has been applied to the orientational behavior of water molecules in a molecular dynamics simulated water–Na + system. The distinctively different statistical complexity of water molecules in the bulk and in the first solvation shell of the ion is demonstrated. It is shown that the molecules undergo more complex orientational motion when surrounded by other water molecules compared to those constrained by the electric field of the ion. However the spatial coordinates of the oxygen atom shows the opposite complexity behavior in that complexity is higher for the solvation shell molecules. New information about the dynamics of water molecules in the solvation shell is provided that is additional to that given by traditional methods of analysis.

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Fluid dynamics and platelet deposition in a model arterial stenosis

The objective of this study was to gain further understanding and elucidation of the fluid dynamic factors and flow-induced mechanisms of the thrombogenic process of platelet deposition onto, and possible subsequent embolization from, the walls of an arterial stenosis. This has been accomplished by measurement of the axial dependence of platelet deposition within a modeled arterial stenosis for a transitional flow and a completely laminar flow field. The stenotic region of the model was collagen-coated to simulate a damaged endothelial lining of an artery. Fluid dynamics within a stenosis was studied using qualitative flow visualization, and was further compared to the in vitro platelet deposition studies. Normalized platelet density (NPD) measurements indicate decreased levels of NPD in the high shear throat region of the stenosis for a Reynolds number of 300 and a drastic increase in NPD at the throat for a Reynolds number of 175. This study provides further understanding of the flow dynamic effects on thrombus development within a stenosis. ^

Dynamics of the Disk-Pendulum Coupled System With Vertical Excitation

This paper investigates the static and dynamic characteristics of the semi-elliptical rocking disk on which a pendulum pinned. This coupled system’s response is also analyzed analytically and numerically when a vertical harmonic excitation is applied to the bottom of the rocking disk. Lagrange’s Equation is used to derive the motion equations of the disk-pendulum coupled system. The second derivative test for the system’s potential energy shows how the location of the pendulum’s pivotal point affects the number and stability of equilibria, and the change of location presents different bifurcation diagrams for different geometries of the rocking disk. For both vertically excited and unforced cases, the coupled system shows chaos easily, but the proper chosen parameters can still help the system reach and keep the steady state. For the steady state of the vertically excited rocking disk without a pendulum, the variation of the excitation’s amplitude and frequency result in the hysteresis for the amplitude of the response. When a pendulum is pinned on the rocking disk, three major categories of steady states are presently in the numerical way.

Role of Vinculin in Regulating Force-Sensitive Dynamics of Adherens Junctions During Collective Cell Migration

Dynamic processes such as morphogenesis and tissue patterning require the precise control of many cellular processes, especially cell migration. Historically, these processes are thought to be mediated by genetic and biochemical signaling pathways. However, recent advances have unraveled a previously unappreciated role of mechanical forces in regulating these homeostatic processes in of multicellular systems. In multicellular systems cells adhere to both deformable extracellular matrix (ECM) and other cells, which are sources of applied forces and means of mechanical support. Cells detect and respond to these mechanical signals through a poorly understood process called mechanotransduction, which can have profound effects on processes such as cell migration. These effects are largely mediated by the sub cellular structures that link cells to the ECM, called focal adhesions (FAs), or cells to other cells, termed adherens junctions (AJs).

Overall this thesis is comprised of my work on identifying a novel force dependent function of vinculin, a protein which resides in both FAs and AJs - in dynamic process of collective migration. Using a collective migration assay as a model for collective cell behavior and a fluorescence resonance energy transfer (FRET) based molecular tension sensor for vinculin I demonstrated a spatial gradient of tension across vinculin in the direction of migration. To define this novel force-dependent role of vinculin in collective migration I took advantage of previously established shRNA based vinculin knock down Marin-Darby Canine Kidney (MDCK) epithelial cells.

The first part of my thesis comprises of my work demonstrating the mechanosensitive role of vinculin at AJ’s in collectively migrating cells. Using vinculin knockdown cells and vinculin mutants, which specifically disrupt vinculin’s ability to bind actin (VinI997A) or disrupt its ability to localize to AJs without affecting its localization at FAs (VinY822F), I establish a role of force across vinculin in E-cadherin internalization and clipping. Furthermore by measuring E-cadherin dynamics using fluorescence recovery after bleaching (FRAP) analysis I show that vinculin inhibition affects the turnover of E-cadherin at AJs. Together these data reveal a novel mechanosensitive role of vinculin in E-cadherin internalization and turnover in a migrating cell layer, which is contrary to the previously identified role of vinculin in potentiating E-cadherin junctions in a static monolayer.

For the last part of my thesis I designed a novel tension sensor to probe tension across N-cadherin (NTS). N-cadherin plays a critical role in cardiomyocytes, vascular smooth muscle cells, neurons and neural crest cells. Similar to E-cadherin, N-cadherin is also believed to bear tension and play a role in mechanotransduction pathways. To identify the role of tension across N-cadherin I designed a novel FRET-based molecular tension sensor for N-cadherin. I tested the ability of NTS to sense molecular tension in vascular smooth muscle cells, cardiomyocytes and cancer cells. Finally in collaboration with the Horwitz lab we have been able to show a role of tension across N-cadherin in synaptogenesis of neurons.

A predictive computational fluid dynamics study of carotid artery

Abstract not available

Apicomplexans pulling the strings: manipulation of the host cell cytoskeleton dynamics

Invasive stages of apicomplexan parasites require a host cell to survive, proliferate and advance to the next life cycle stage. Once invasion is achieved, apicomplexans interact closely with the host cell cytoskeleton, but in many cases the different species have evolved distinct mechanisms and pathways to modulate the structural organization of cytoskeletal filaments. The host cell cytoskeleton is a complex network, largely, but not exclusively, composed of microtubules, actin microfilaments and intermediate filaments, all of which are modulated by associated proteins, and it is involved in diverse functions including maintenance of cell morphology and mechanical support, migration, signal transduction, nutrient uptake, membrane and organelle trafficking and cell division. The ability of apicomplexans to modulate the cytoskeleton to their own advantage is clearly beneficial. We here review different aspects of the interactions of apicomplexans with the three main cytoskeletal filament types, provide information on the currently known parasite effector proteins and respective host cell targets involved, and how these interactions modulate the host cell physiology. Some of these findings could provide novel targets that could be exploited for the development of preventive and/or therapeutic strategies.