Formation of atypical podosomes in extravillous trophoblasts regulates extracellular matrix degradation

Throughout pregnancy the cytotrophoblast, the stem cell of the placenta, gives rise to the differentiated forms of trophoblasts. The two main cell lineages are the syncytiotrophoblast and the invading extravillous trophoblast. A successful pregnancy requires extravillous trophoblasts to migrate and invade through the decidua and then remodel the maternal spiral arteries. Many invasive cells use specialised cellular structures called invadopodia or podosomes in order to degrade extracellular matrix. Despite being highly invasive cells, the presence of invadapodia or podosomes has not previously been investigated in trophoblasts. In this study these structures have been identified and characterised in extravillous trophoblasts. The role of specialised invasive structures in trophoblasts in the degradation of the extracellular matrix was compared with well characterised podosomes and invadopodia in other invasive cells and the trophoblast specific structures were characterised by using a sensitive matrix degradation assay which enabled visualisation of the structures and their dynamics. We show trophoblasts form actin rich protrusive structures which have the ability to degrade the extracellular matrix during invasion. The degradation ability and dynamics of the structures closely resemble podosomes, but have unique characteristics that have not previously been described in other cell types. The composition of these structures does not conform to the classic podosome structure, with no distinct ring of plaque proteins such as paxillin or vinculin. In addition, trophoblast podosomes protrude more deeply into the extracellular matrix than established podosomes, resembling invadopodia in this regard. We also show several significant pathways such as Src kinase, MAPK kinase and PKC along with MMP-2 and 9 as key regulators of extracellular matrix degradation activity in trophoblasts, while podosome activity was regulated by the rigidity of the extracellular matrix.

Liquid crystalline elastomers: the relationship between macroscopic behaviour and the level of backbone anisotropy

Nematic monodomain liquid crystalline elastomers have been prepared through in situ cross-linking of an acrylate based side-chain liquid crystalline polymer in a magnetic field. At the nematic–isotropic transition, the sample is found to undergo an anisotropic shape change. There is found to be an increase in dimensions perpendicular — and a decrease parallel — to the director, this is consistent with alignment of the polymer backbone parallel to the direction of mesogen alignment in the nematic state. From a quantitative investigation of this behaviour, we estimate the level of backbone anisotropy for the elastomer. As second measure of the backbone anisotropy, the monodomain sample was physically extended. We have investigated, in particular, the situation where a monodomain sample is deformed with the angle between the director and the extension direction approaching 90°. The behaviour on extension of these acrylate samples is related to alternative theoretical interpretations and the backbone anisotropy determined. Comparison of the chain anisotropy derived from these two approaches and the value obtained from previous small-angle neutron scattering measurements on deuterium labelled mixtures of the same polymer shows that some level of chain anisotropy is retained in the isotropic or more strictly weakly paranematic state of the elastomer. The origin and implications of this behaviour are discussed.

Orientation effects in monodomain nematic liquid crystalline polysiloxane elastomers

A series of monodomain liquid crystalline (LC) elastomers based on a polysiloxane were synthesised. These elastomers were prepared either with one or two cross-linking agents in the presence of a mechanical field. By using the real-time X-ray facility at the University of Reading (AXIS), we have shown that the nematic order parameter 〈P2 〉 is dependent on both the extension λ value and the degree of cross-linking. We have also shown that the monodomain elastomers, exhibiting permanent alignment and 〈P2 〉 values of about 0.5, can be prepared by using only one cross-linking agent making the synthesis of these monodomain LC elastomers much more simple and cost effective than that proposed by Küpfer.

Memory effects in liquid crystal elastomers

Free-standing monodomain liquid crystal elastomer samples are shown to have a complete memory of the orientational configuration at the time of cross-linking. This memory is demonstrated through samples in which the parent polymer system is first aligned in a magnetic field prior to cross-linking. These films show reversible nematic-isotropic phase transitions and x-ray scattering patterns characteristic of nematic phases. The liquid crystal elastomer films exhibit a remarkable memory effect, in that the sample may be held at temperatures well above the nematic-isotropic transition for extended periods ( > 2 weeks), but on cooling into the liquid crystal phase region, both the original director alignment and the degree of preferred orientation are recovered. It is demonstrated that these novel memory effects are equilibrium in nature. The origins of this phenomena in terms of coupling between the mesogenic side-chains and the polymer network are discussed.

The effect of the spacer length on the nature of coupling in side chain liquid crystals polymers and elastomers

Side chain liquid crystal polymers and elastomers exhibit a rich phase behaviour which arises from the antagonistic influences of the entropically disordered polymer chain configuration and the long range orientational ordering of the mesogenic units. This competition arises since the natural macroscopic phase separation is inhibited by the inherent chemical connectivity of the system. At the heart of this connectivity is the spacer link and we consider here its influence on the phase behaviour. In particular we consider a series of elastomers in which the number of alkyl units in the spacer is systematically varied from 2 to 6. The lengthening of the coupling spacer is accompanied by an alternation of the sign of coupling between the polymer chain and the mesogenic unit. These results demonstrate the dominating influence of the so-called hinge effect in determining the phase behaviour. In addition to the alternation of the sign there is some decrease in the magnitude of the coupling with increasing spacer length.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

Coupling and memory in liquid crystal elastomers

The polymer backbone of a side-chain liquid crystal polymer exhibits an anisotropic shape due to the coupling of the liquid crystal orientational order of the mesogenic side-chains to the backbone. The magnitude and sign of this coupling may be controlled by chemical design. The introduction of chemical cross-links in to such a system provides both a memory of the anisotropic organisation and a mechanism by which the microscopic anisotropy can be realised at a macroscopic level. We show how this anisotropic network structure yields new phenomena when electric or mechanical fields are applied.

Side-chain liquid crystalline elastomers: the relationship between the orientational ordering of the polymer backbone and the length of the coupling chain

The influence of cross-linking on the phase behaviour of a series of side-chain liquid crystalline elastomers has been studied. For samples cross-linked in the temperature range corresponding to the nematic phase, the phase transition was shifted compared to that observed when an identical sample was cross-linked in the isotropic phase. This shift represented a stabilisation of the nematic phase in the former case, in line with theoretical expectations. By utilising a novel, slow cross-linking method, which allows the polymer backbone to take up an equilibrium conformation prior to network formation, it proved possible to monitor the shifts in phase transition temperature as a function of the length of the methylene chain coupling the mesogenic units to the polymer backbone. The results obtained are related to the backbone anisotropy and indicate that the level of orientational order of the polymer in the nematic phase backbone increases with a reduction in the length of the coupling chain.

Spectrum of a Feinberg-Zee random hopping matrix

This paper provides a new proof of a theorem of Chandler-Wilde, Chonchaiya, and Lindner that the spectra of a certain class of infinite, random, tridiagonal matrices contain the unit disc almost surely. It also obtains an analogous result for a more general class of random matrices whose spectra contain a hole around the origin. The presence of the hole forces substantial changes to the analysis.

Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.