Mechanisms and molecular regulation of mammalian tooth replacement

In most non-mammalian vertebrates, such as fish and reptiles, teeth are replaced continuously. However, tooth replacement in most mammals, including human, takes place only once and further renewal is apparently inhibited. It is not known how tooth replacement is genetically regulated, and little is known on the physiological mechanism and evolutionary reduction of tooth replacement in mammals. In this study I have attempted to address these questions. In a rare human condition cleidocranial dysplasia, caused by a mutation in a Runt domain transcription factor Runx2, tooth replacement is continued. Runx2 mutant mice were used to investigate the molecular mechanisms of Runx2 function. Microarray analysis from dissected embryonic day 14 Runx2 mutant and wild type dental mesenchymes revealed many downstream targets of Runx2, which were validated using in situ hybridization and tissue culture methods. Wnt signaling inhibitor Dkk1 was identified as a candidate target, and in tissue culture conditions it was shown that Dkk1 is induced by FGF4 and this induction is Runx2 dependent. These experiments demonstrated a connection between Runx2, FGF and Wnt signaling in tooth development and possibly also in tooth replacement. The role of Wnt signaling in tooth replacement was further investigated by using a transgenic mouse model where Wnt signaling mediator β-catenin is continuously stabilized in dental epithelium. This stabilization led to activated Wnt signaling and to the formation of multiple enamel knots. In vitro and transplantation experiments were performed to examine the process of extra tooth formation. We showed that new teeth were continuously generated and that new teeth form from pre-existing teeth. A morphodynamic activator-inhibitor model was used to simulate enamel knot formation. By increasing the intrinsic production rate of the activator (β-catenin), the multiple enamel knot phenotype was reproduced by computer simulations. It was thus concluded that β-catenin acts as an upstream activator of enamel knots, closely linking Wnt signaling to the regulation of tooth renewal. As mice do not normally replace teeth, we used other model animals to investigate the physiological and genetic mechanisms of tooth replacement. Sorex araneus, the common shrew was earlier reported to have non-functional tooth replacement in all antemolar tooth positions. We showed by histological and gene expression studies that there is tooth replacement only in one position, the premolar 4 and that the deciduous tooth is diminished in size and disappears during embryogenesis without becoming functional. The growth rates of deciduous and permanent premolar 4 were measured and it was shown by competence inference that the early initiation of the replacement tooth in relation to the developmental stage of the deciduous tooth led to the inhibition of deciduous tooth morphogenesis. It was concluded that the evolutionary loss of deciduous teeth may involve the early activation of replacement teeth, which in turn suppress their predecessors. Mustela putorius furo, the ferret, has a dentition that resembles that of the human as ferrets have teeth that belong to all four tooth families, and all the antemolar teeth are replaced once. To investigate the replacement mechanism, histological serial sections from different embryonic stages were analyzed. It was noticed that tooth replacement is a process which involves the growth and detachment of the dental lamina from the lingual cervical loop of the deciduous tooth. Detachment of the deciduous tooth leads to a free successional dental lamina, which grows deeper into the mesenchyme, and later buds the replacement tooth. A careful 3D analysis of serial histological sections was performed and it was shown that replacement teeth are initiated from the successional dental lamina and not from the epithelium of the deciduous tooth. The molecular regulation of tooth replacement was studied and it was shown by examination of expression patterns of candidate regulatory genes that BMP/Wnt inhibitor Sostdc1 was strongly expressed in the buccal aspect of the dental lamina, and in the intersection between the detaching deciduous tooth and the successional dental lamina, suggesting a role for Sostdc1 in the process of detachment. Shh was expressed in the enamel knot and in the inner enamel epithelium in both generations of teeth supporting the view that the morphogenesis of both generations of teeth is regulated by similar mechanisms. In summary, histological and molecular studies on different model animals and transgenic mouse models were used to investigate tooth replacement. This thesis work has significantly contributed to the knowledge on the physiological mechanisms and molecular regulation of tooth replacement and its evolutionary suppression in mammals.

A real-time algorithm for simulation of flexible objects and hyper-redundant manipulators

Flexible objects such as a rope or snake move in a way such that their axial length remains almost constant. To simulate the motion of such an object, one strategy is to discretize the object into large number of small rigid links connected by joints. However, the resulting discretised system is highly redundant and the joint rotations for a desired Cartesian motion of any point on the object cannot be solved uniquely. In this paper, we revisit an algorithm, based on the classical tractrix curve, to resolve the redundancy in such hyper-redundant systems. For a desired motion of the `head' of a link, the `tail' is moved along a tractrix, and recursively all links of the discretised objects are moved along different tractrix curves. The algorithm is illustrated by simulations of a moving snake, tying of knots with a rope and a solution of the inverse kinematics of a planar hyper-redundant manipulator. The simulations show that the tractrix based algorithm leads to a more `natural' motion since the motion is distributed uniformly along the entire object with the displacements diminishing from the `head' to the `tail'.

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Integral finite surgeries on knots in S^3

Using the correction terms in Heegaard Floer homology, we prove that if a knot in S³ admits a positive integral T-, O-, or I-type surgery, it must have the same knot Floer homology as one of the knots given in our complete list, and the resulting manifold is orientation-preservingly homeomorphic to the p-surgery on the corresponding knot.

Three-dimensional superconformal field theory, Chern-Simons theory, and their correspondence

In this thesis, we discuss 3d-3d correspondence between Chern-Simons theory and three-dimensional N = 2 superconformal field theory. In the 3d-3d correspondence proposed by Dimofte-Gaiotto-Gukov information of abelian flat connection in Chern-Simons theory was not captured. However, considering M-theory configuration giving the 3d-3d correspondence and also other several developments, the abelian flat connection should be taken into account in 3d-3d correspondence. With help of the homological knot invariants, we construct 3d N = 2 theories on knot complement in 3-sphere for several simple knots. Previous theories obtained by Dimofte-Gaiotto-Gukov can be obtained by Higgsing of the full theories. We also discuss the importance of all flat connections in the 3d-3d correspondence by considering boundary conditions in 3d N = 2 theories and 3-manifold.

Topological strings, double affine Hecke algebras, and exceptional knot homology

In this thesis, we consider two main subjects: refined, composite invariants and exceptional knot homologies of torus knots. The main technical tools are double affine Hecke algebras ("DAHA") and various insights from topological string theory.

In particular, we define and study the composite DAHA-superpolynomials of torus knots, which depend on pairs of Young diagrams and generalize the composite HOMFLY-PT polynomials from the full HOMFLY-PT skein of the annulus. We also describe a rich structure of differentials that act on homological knot invariants for exceptional groups. These follow from the physics of BPS states and the adjacencies/spectra of singularities associated with Landau-Ginzburg potentials. At the end, we construct two DAHA-hyperpolynomials which are closely related to the Deligne-Gross exceptional series of root systems.

In addition to these main themes, we also provide new results connecting DAHA-Jones polynomials to quantum torus knot invariants for Cartan types A and D, as well as the first appearance of quantum E6 knot invariants in the literature.

Boat wakes and their influence on erosion in the Atlantic Intracoastal Waterway, North Carolina

Boat wakes in the Atlantic Intracoastal Waterway (AIWW) of North Carolina occur in environments not normally subjected to (wind) wave events, making sections of AIWW potentially vulnerable to extreme wave events generated by boat wakes. The Snow’s Cut area that links the Cape Fear River to the AIWW is an area identified by the Wilmington District of the U.S. Army Corps of Engineers as having significant erosion issues; it was hypothesized that this erosion could be being exacerbated by boat wakes. We compared the boat wakes for six combinations of boat length and speed with the top 5% wind events. We also computed the benthic shear stress associated with boat wakes and whether sediment would move (erode) under those conditions. Finally, we compared the transit time across Snow’s Cut for each speed. We focused on two size classes of V-hulled boats (7 and 16m) representative of AIWW traffic and on three boat speeds (3, 10 and 20 knots). We found that at 10 knots when the boat was plowing and not yet on plane, boat wake height and potential erosion was greatest. Wakes and forecast erosion were slightly mitigated at higher, planing speeds. Vessel speeds greater than 7 knots were forecast to generate wakes and sediment movement zones greatly exceeding that arising from natural wind events. We posit that vessels larger than 7m in length transiting Snow’s Cut (and likely many other fetch-restricted areas of the AIWW) frequently generate wakes of heights that result in sediment movement over large extents of the AIWW nearshore area, substantially in exceedance of natural wind wave events. If the speed, particularly of large V-hulled vessels (here represented by the 16m length class), were reduced to pre-plowing levels (~ 7 knots down from 20), transit times for Snow’s Cut would be increased approximately 10 minutes but based on our simulations would likely substantially reduce the creation of erosion-generating boat wakes. It is likely that boat wakes significantly exceed wind wave background for much of the AIWW and similar analyses may be useful in identifying management options.

Eigenmodes of lined flow ducts with rigid splices

This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure eigenmodes is given in terms of an azimuthal Fourier sum, with the Fourier coefficients given by a recurrence relation. Since this expression is derived using a Greens function method, the completeness of the expansion is guaranteed. A numerical procedure is described for solving this recurrence relation, which is found to converge exponentially with respect to number of Fourier terms used and is in practice quick to compute; this is then used to give several numerical examples for both uniform and sheared mean flow. An asymptotic expression is derived to directly calculate the pressure eigenmodes for thin splices. This asymptotic expression is shown to be quantitatively accurate for ducts with very thin splices of less than 1 % unlined area and qualitatively helpful for thicker splices of the order of 6 % unlined area. A thin splice is in some cases shown to increase the damping of certain acoustic modes. The influences of thin splices and thin boundary layers are compared and found to be of comparable magnitude for the parameters considered. Trapped modes at the splices are also identified and investigated. © 2011 Cambridge University Press.

The emergence of automated high-frequency flow cytometry: revealing temporal and spatial phytoplankton variability

Phytoplankton observation is the product of a number of trade-offs related to sampling processes, required level of diversity and size spectrum analysis capabilities of the techniques involved. Instruments combining the morphological and high-frequency analysis for phytoplankton cells are now available. This paper presents an application of the automated high-resolution flow cytometer Cytosub as a tool for analysing phytoplanktonic cells in their natural environment. High resolution data from a temporal study in the Bay of Marseille (analysis every 30 min over 1 month) and a spatial study in the Southern Indian Ocean (analysis every 5 min at 10 knots over 5 days) are presented to illustrate the capabilities and limitations of the instrument. Automated high-frequency flow cytometry revealed the spatial and temporal variability of phytoplankton in the size range 1−∼50 μm that could not be resolved otherwise. Due to some limitations (instrumental memory, volume analysed per sample), recorded counts could be statistically too low. By combining high-frequency consecutive samples, it is possible to decrease the counting error, following Poisson’s law, and to retain the main features of phytoplankton variability. With this technique, the analysis of phytoplankton variability combines adequate sampling frequency and effective monitoring of community changes.

High-speed knots in the hourglass shaped planetary nebula Hubble 12

We present a detailed kinematical analysis of the young compact hourglass-shaped planetary nebula Hb 12. We performed optical imaging and long-slit spectroscopy of Hb 12 using the Manchester echelle spectrometer with the 2.1-m San Pedro Mártir telescope. We reveal, for the first time, the presence of end caps (or knots) aligned with the bipolar lobes of the planetary nebula shell in a deep [NII] ?6584 image of Hb 12. We measured from our spectroscopy radial velocities of ~120kms-1 for these knots. We have derived the inclination angle of the hourglass-shaped nebular shell to be ~65° to the line of sight. It has been suggested that Hb 12's central star system is an eclipsing binary which would imply a binary inclination of at least 80°. However, if the central binary has been the major shaping influence on the nebula, then both nebula and binary would be expected to share a common inclination angle. Finally, we report the discovery of high-velocity knots with Hubble-type velocities, close to the core of Hb 12, observed in Ha and oriented in the same direction as the end caps. Very different velocities and kinematical ages were calculated for the outer and inner knots showing that they may originate from different outburst events.

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases.

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between knotted and unknotted regions. The increased curvature of knotted regions is expected to make them preferential substrates of type IIA topoisomerases because various earlier experiments have concluded that type IIA DNA topoisomerases preferentially interact with highly curved DNA regions. The supercoiling-induced tightening of DNA knots observed here shows that torsional tension in DNA may serve to expose DNA knots to the unknotting action of type IIA topoisomerases, and thus explains how these topoisomerases could maintain a low knotting equilibrium in vivo, even for long DNA molecules.

A Study On Vortex Knots

In this thesis an attempt is made to study vortex knots based on the work of Keener . It is seen that certain mistakes have been crept in to the details of this paper. We have chosen this study for an investigation as it is the first attempt to study vortex knots. Other works had given attention to this. In chapter 2 we have considered these corrections in detail. In chapter 3 we have tried a simple extension by introducing vorticity in the evolution of vortex knots. In chapter 4 we have introduced a stress tensor related to vorticity. Chapter 5 is the general conclusion.Knot theory is a branch of topology and has been developed as an independent branch of study. It has wide applications and vortex knot is one of them. As pointed out earlier, most of the studies in fluid dynamics exploits the analogy between vorticity and magnetic induction in the case of MHD. But vorticity is more general than magnetic induction and so it is essential to discuss the special properties of vortex knots, independent of MHD flows. This is what is being done in this thesis.

Characteristics of ABL during active and weak phases of monsoon

Understanding of the Atmospheric Boundary Layer (ABL) is imperative in the arena of the monsoon field. Here, the features of the ABL are studied employing Conserved Variable Analysis (CVA) using equivalent potential temperature and humidity. In addition, virtual potential temperature and wind are used during active and weak phases of monsoon. The analysis is carried out utilising the radiosonde observations during the monsoon months for two stations situated in the west coast of India. All these parameters show considerable variations during active and weak monsoon phases in both the stations. The core speed and core height vary with these epochs. The core speed is found to be more than 38 knots in the active monsoon phase around 1.2 km over Trivandrum and around 2 km over Mangalore. But during weak monsoon phase the core wind speed is decreased and core height is elevated over both stations. The wind direction shows an additional along shore component during weak monsoon period. The Convective Boundary Layer (CBL) height shows increase during weak monsoon phase over both stations due to less cloudiness and subsequent insolation. The CBL height during the southwest monsoon is more over Mangalore and is attributed by the orographic lifting in the windward side of the Western Ghats while the influence of the Ghats is less over Trivandrum.