Sequence Of Divisions Research Articles

Video-assisted thoracoscopic lobectomy using a standardized three-port anterior approach - The Copenhagen experience.

Video-Assisted Thoracoscopic Surgery (VATS) lobectomy is now well established and performed all around the world. Formerly there was much debate about the feasibility of the technique in cancer surgery and proper lymph node handling. Although there is a lack of proper randomized studies, it is now generally accepted that the outcome of a VATS procedure is at least not inferior to a resection via a traditional thoracotomy. Several papers have concluded that there is no significant difference in survival rates and that there might even be a better outcome by VATS (1-3). A VATS lobectomy and even more a VATS anatomical segmentectomy is a challenging and technically demanding procedure to perform; and yet there is still no consensus about the basic principles in the technique. Different techniques have been described including the simultaneously stapled lobectomy (4), a VATS assisted operation with some rib spreading (5) and a true VATS lobectomy defined by no rib spreading along with anatomical hilar dissection and only monitor based vision rather than looking through the utility incision. The procedure is performed with up to 5 incisions and is even reported with a uniportal approach (6). Different lobe specific approaches have been reported (7) and a wide variation in instruments and camera positions is seen. At our institution we have a large experience with about 1,000 cases performed by a standardised three-port anterior approach with sequential division of the hilar structures, proper lymph node handling, no rib spreading and vision relying on the monitor only. This allows us to perform VATS lobectomies in the majority of the cases even if there are significant difficulties (8). We find that our standardized three-port anterior approach facilitates the VATS lobectomy, and it is our experience from visiting surgeons that our technique can easily be adapted by many surgeons, especially those who are used to an open anterior approach. The major advantages of the standardized anterior approach are: ❖ The mini-thoracotomy is placed directly over the hilum and the major pulmonary vessels. Easy to clamp the major vessels in case of major bleeding ❖ No need of changing the surgeons’ position or the place of the incision if a conversion is required ❖ The first structures to be transected are the major vessels ❖ The same approach to all lobes makes it easy to reproduce and learn ❖ The lung tissue only pushed backwards gently with peanuts and never grasped with forceps and therefore not torn apart ❖ Easy to teach as the surgeon and the assisting surgeon stand on the same side and use the same monitor. They do not work opposite to each other and therefore maybe against one and another. This facilitates a fluid learning process Indications for VATS lobectomy VATS lobectomy is commonly performed for selected peripherally located T1 or T2 tumours and usually reserved for patient where complications are not expected. We think that the advantages of a minimally invasive approach would also benefit cases that are more advanced and therefore the question in our daily clinically practice is: Are there any contraindications to perform the planned lobectomy as a VATS procedure? At present we find the following contraindications: ❖ T3 or T4 tumours. ❖ Tumours larger than 6 cm. ❖ Tumours visible in the bronchus by bronchoscopy within 2 cm of the origin of the lobe to be resected and where a possible Sleeve resection might be needed. ❖ Centrally placed tumours in the hilum and adherent to vessels. This means that patients with former Tuberculosis, previous cardiothoracic surgery and patients who have received preoperative chemo-radiotherapy are still considered as candidates for a VATS lobectomy. All our patients have a preoperative examination with lung function testing, PET/CT, bronchoscopy and EBUS/mediastinoscopy for preoperative staging (unless it is a peripheral placed T1 tumour on PET). With growing experience, we perform VATS lobectomy in the majority of the cases at our institution, even if they do present with co-morbidity. In the last few years, between 70% and 80% of all cancer lobectomies in our institution were performed by VATS and we now perform well over 200 VATS lobectomies and quite a few anatomical VATS segmentectomies each year (17 in 2011) with a very low conversion rate (2% in 2011).

Perfect powers generated by the twisted Fermat cubic

On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. It is shown that there are finitely many perfect powers in such a sequence whose first term is greater than $1$. Moreover, if the first term is divisible by $6$ and the generating point is triple another rational point then there are no perfect powers in the sequence except possibly an $l$th power for some $l$ dividing the order of $2$ in the first term.

Perfect powers in elliptic divisibility sequences

It is shown that there are finitely many perfect powers in an elliptic divisibility sequence whose first term is divisible by 2 or 3. For Mordell curves the same conclusion is shown to hold if the first term is greater than 1. Examples of Mordell curves and families of congruent number curves are given with corresponding elliptic divisibility sequences having no perfect power terms. The proofs combine primitive divisor results with modular methods for Diophantine equations.

ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS

AbstractIn this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.

Matrix divisibility sequences

The plan for the paper is as follows: we shall first introduce the general notion of a matrix divisibility sequence indexed by a semigroup. Then we will see how a faithful representation of the semigroup by endomorphisms of an affine space gives rise to a matrix divisibility sequence, by considering the Jacobian matrices of the endomorphisms. We will show how most of the commonly known divisibility sequences (mentioned brie y above) arise as determinants of matrix divisibility sequences through interesting semigroups of endomorphisms of affine spaces, often associated to a representation of addition in an algebraic group. For example, Lucas sequences are associated to the 2 x 2 Borel group. We also construct the elliptic matrix divisibility sequence that underlies the usual elliptic divisibility sequences, and prove that it has primitive right matrix divisor classes.

The contribution of each anterior cruciate ligament bundle to the Lachman test

The clinical diagnosis of a partial tear of the anterior cruciate ligament (ACL) is still subject to debate. Little is known about the contribution of each ACL bundle during the Lachman test. We investigated this using six fresh-frozen cadaveric lower limbs. Screws were placed in the femora and tibiae as fixed landmarks for digitisation of the bone positions. The femur was secured horizontally in a clamp. A metal hook was screwed to the tibial tubercle and used to apply a load of 150N directed anteroposteriorly to the tibia to simulate the Lachman test. The knees then received constant axial compression and 3D knee kinematic data were collected by digitising the screw head positions in 30° flexion under each test condition. Measurements of tibial translation and rotation were made, first with the ACL intact, then after sequential cutting of the ACL bundles, and finally after complete division of the ACL. Two-way analysis of variance analysis was performed. During the Lachman test, in all knees and in all test conditions, lateral tibial translation exceeded that on the medial side. With an intact ACL, both anterior and lateral tibial landmarks translated significantly more than those on the medial side (p < 0.001). With sequential division of the ACL bundles, selective cutting of the posterolateral bundle (PLB) did not increase translation of any landmark compared with when the ACL remained intact. Cutting the anteromedial bundle (AMB) resulted in an increased anterior translation of all landmarks. Compared to the intact ACL, when the ACL was fully transected a significant increase in anterior translation of all landmarks occurred (p < 0.001). However, anterior tibial translation was almost identical after AMB or complete ACL division. We found that the AMB confers its most significant contribution to tibial translation during the Lachman test, whereas the PLB has a negligible effect on anterior translation. Section of the PLB had a greater effect on increasing the internal rotation of the tibia than the AMB. However, its contribution of a mean of 2.8° amplitude remains low. The clinical relevance of our investigation suggests that, based on anterior tibial translation only, one cannot distinguish between a full ACL and an isolated AMB tear. Isolated PLB tears cannot be detected solely by the Lachman test, as this bundle probably contributes more resistance to the pivot shift.

Primitive divisors of certain elliptic divisibility sequences

Let $P$ be a non-torsion point on the elliptic curve $E_{a}: y^{2}=x^{3}+ax$. We show that if $a$ is fourth-power-free and either $n>2$ is even or $n>1$ is odd with $x(P)<0$ or $x(P)$ a perfect square, then the $n$-th element of the elliptic divisibility sequence generated by $P$ always has a primitive divisor.

An integer factoring algorithm based on elliptic divisibility sequences

An integer factoring algorithm based on elliptic divisibility sequences

Some Monoapparitic Fourth Order Linear Divisibility Sequences

Abstract.A sequence of rational integers

The cell cycle

‘Dividing cells pass through a regular sequence of cell growth and division, known as the cell cycle’, according to a college textbook of biology published in 1983 [[1][1]], 5 years before the underlying principles of control were first laid bare during 1988, the annus mirabilis of cell cycle

The role of Pax6 in regulating the orientation and mode of cell division of progenitors in the mouse cerebral cortex

Successful brain development requires tight regulation of sequential symmetric and asymmetric cell division. Although Pax6 is known to exert multiple roles in the developing nervous system, its role in the regulation of cell division is unknown. Here, we demonstrate profound alterations in the orientation and mode of cell division in the cerebral cortex of mice deficient in Pax6 function (Pax6Sey/Sey) or after acute induced deletion of Pax6. Live imaging revealed an increase in non-vertical cellular cleavage planes, resulting in an increased number of progenitors with unequal inheritance of the apical membrane domain and adherens junctions in the absence of Pax6 function. This phenotype appears to be mediated by the direct Pax6 target Spag5, a microtubule-associated protein, reduced levels of which result in the replication of the Pax6 phenotype of altered cell division orientation. In addition, lack of Pax6 also results in premature delamination of progenitor cells from the apical surface due to an overall decrease in proteins mediating anchoring at the ventricular surface. Moreover, continuous long-term imaging in vitro revealed that Pax6-deficient progenitors generate daughter cells with asymmetric fates at higher frequencies. These data demonstrate a cell-autonomous role for Pax6 in regulating the mode of cell division independently of apicobasal polarity and cell-cell interactions. Taken together, our work reveals several direct effects that the transcription factor Pax6 has on the machinery that mediates the orientation and mode of cell division.

Peripheral chondrosarcoma progression is associated with increased type X collagen and vascularisation

Endochondral bone formation requires a cartilage template, known as the growth plate, and vascular invasion, bringing osteoblasts and osteoclasts. Endochondral chondrocytes undergo sequences of cell division, matrix secretion, cell hypertrophy, apoptosis, and matrix calcification/mineralisation. In this study, two critical steps of endochondral bone formation, the deposition of collagen X-rich matrix and blood vessel attraction/invasion, were investigated by immunohistochemistry. Fourteen multiple osteochondromas and six secondary peripheral chondrosarcomas occurring in patients with multiple osteochondromas were studied and compared to epiphyseal growth plate samples. Mutation analysis showed all studied patients (expect one) to harbour a germ-line mutations in either EXT1 or EXT2. Here, we described that homozygous mutations in EXT1/EXT2, which are causative for osteochondroma formation, are likely to affect terminal chondrocyte differentiation and vascularisation in the osteocartilaginous interface. Contrastingly, terminal chondrocyte differentiation and vascularisation seem to be unaffected in secondary peripheral chondrosarcoma. In addition, osteochondromas with high vascular density displayed a higher proliferation rate. A similar apoptotic rate was observed in osteochondromas and secondary peripheral chondrosarcomas. Recently, it has been shown that cells with functional EXT1 and EXT2 are outnumbering EXT1/EXT2 mutated cells in secondary peripheral chondrosarcomas. This might explain the increased type X collagen production and blood vessel attraction in these malignant tumours.

Organ aging and susceptibility to cancer may be related to the geometry of the stem cell niche

Telomere loss at each cell replication limits the proliferative capacity of normal cells, including adult stem cells. Entering replicative senescence protects dividing cells from neoplastic transformation, but also contributes to aging of the tissue. Recent experiments have shown that intestinal mouse stem cells divide symmetrically, at random make decisions to remain stem cells or to differentiate, and gradually lose telomeric DNA. A cell's decision whether to differentiate or to remain a stem cell depends on the local cellular and chemical environment and thus tissue architecture is expected to play role in cell proliferation dynamics. To take into account the structure of the stem cell niche in determining its proliferative potential and susceptibility to cancer, a theoretical model is introduced and the niche proliferative potential is quantified for different architectures. The niche proliferative potential is quantitatively related to the proliferative potential of the individual stem cells for different structural classes of the stem cell niche. Stem cells at the periphery of a niche are under pressure to divide and to differentiate, as well as to maintain the stem cell niche boundary, and thus the geometry of the stem cell niche is expected to play a role in determining the stem cell division sequence and differentiation. Smaller surface-to-volume ratio is associated with higher susceptibility to cancer, higher tissue renewal capacity, and decreased aging rate. Several testable experimental predictions are discussed, as well the presence of stochastic effects.

Protecting Children From Toxicants

Protecting Children From Toxicants

Self-organizing systems based on morphogenesis principles

Morphogenesis is the process that gives shapes to organisms from an embryonic stage through a sequence of cell divisions. Starting from a simple embryonic cell, the controlled division and transformation of the cells into different types leads to the creation of a complex organism. The growth of complex organisms is completely autonomic and is one of the best examples of self-organizing systems found in nature. In comparison, the computing infrastructure in current data centers is more static and requires significant human intervention in order to take on the form that is desired. However, emerging technology such as virtualization of servers and networks enables an architecture where distributed computer systems can take different forms using the concept of morphogenesis. Using this vision, all machines in a virtualized data center initially start with a single software image and, using a distributed scheme, adopt a structure in which different images take on the roles of a database server, a web server, a load balancer, a firewall, or a caching proxy in topologies whose structures form on their own. In this paper, we present a novel architecture of a virtualized data center that self-organizes using the principles of morphogenesis.

Elliptic nets and elliptic curves

An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P_1, ..., P_n are points on E defined over K. To this information we associate an n-dimensional array of values in K satisfying a nonlinear recurrence relation. Arrays satisfying this relation are called elliptic nets. We demonstrate an explicit bijection between the set of elliptic nets and the set of elliptic curves with specified points. We also obtain Laurentness/integrality results for elliptic nets.

SOME FOURTH-ORDER LINEAR DIVISIBILITY SEQUENCES

We extend the Lucas–Lehmer theory for second-order divisibility sequences to a large class of fourth-order sequences, with appropriate laws of apparition and of repetition. Examples are provided by the numbers of perfect matchings, or of spanning trees, in families of graphs, and by the numbers of points on elliptic curves over finite fields. Whether there are fourth-order divisibility sequences not covered by our theory is an open question.

The Arabidopsis RWP-RK Protein RKD4 Triggers Gene Expression and Pattern Formation in Early Embryogenesis

Morphogenesis of seed plants commences with highly stereotypical cell division sequences in early embryogenesis [1, 2]. Although a small number of transcription factors and a mitogen-activated protein (MAP) kinase cascade have been implicated in this process [3-8], pattern formation in early embryogenesis remains poorly understood. We show here that the Arabidopsis RKD4, a member of the RWP-RK motif-containing putative transcription factors [9], is required for this process. Loss-of-function rkd4 mutants were defective in zygotic cell elongation, as well as subsequent cell division patterns. As expected from this mutant phenotype, RKD4 was transcribed preferentially in early embryos. RKD4 possessed functional characteristics of transcription factors and was able to ectopically induce early embryo-specific genes when overexpressed in seedlings. Strikingly, induced overexpression of RKD4 primed somatic cells for embryogenesis independently of external growth regulators. These results reveal that RKD4 is a novel key regulator of the earliest stage of plant development.

Microtubule configurations and nuclear DNA synthesis during initiation of suspensor-bearing embryos from Brassica napus cv. Topas microspores

In the new Brassica napus microspore culture system, wherein embryos with suspensors are formed, ab initio mimics zygotic embryogenesis. The system provides a powerful in vitro tool for studying the diverse developmental processes that take place during early stages of plant embryogenesis. Here, we studied in this new culture system both the temporal and spatial distribution of nuclear DNA synthesis places and the organization of the microtubular (MT) cytoskeleton, which were visualized with a refined whole mount immunolocalization technology and 3D confocal laser scanning microscopy. A ‘mild’ heat stress induced microspores to elongate, to rearrange their MT cytoskeleton and to re-enter the cell cycle and perform a predictable sequence of divisions. These events led to the formation of a filamentous suspensor-like structure, of which the distal tip cell gave rise to the embryo proper. Cells of the developing pro-embryo characterized endoplasmic (EMTs) and cortical microtubules (CMTs) in various configurations in the successive stages of the cell cycle. However, the most prominent changes in MT configurations and nuclear DNA replication concerned the first sporophytic division occurring within microspores and the apical cell of the pro-embryo. Microspore embryogenesis was preceded by pre-prophase band formation and DNA synthesis. The apical cell of the pro-embryo exhibited a random organization of CMTs and, in relation to this, isotropic expansion occurred, mimicking the development of the apical cell of the zygotic situation. Moreover, the apical cell entered the S phase shortly before it divided transversally at the stage that the suspensor was 3–8 celled.

Effect of life history on microRNA expression during C. elegans development

Animals have evolved mechanisms to ensure the robustness of developmental outcomes to changing environments. MicroRNA expression may contribute to developmental robustness because microRNAs are key post-transcriptional regulators of developmental gene expression and can affect the expression of multiple target genes. Caenorhabditis elegans provides an excellent model to study developmental responses to environmental conditions. In favorable environments, C. elegans larvae develop rapidly and continuously through four larval stages. In contrast, in unfavorable conditions, larval development may be interrupted at either of two diapause stages: The L1 diapause occurs when embryos hatch in the absence of food, and the dauer diapause occurs after the second larval stage in response to environmental stimuli encountered during the first two larval stages. Dauer larvae are stress resistant and long lived, permitting survival in harsh conditions. When environmental conditions improve, dauer larvae re-enter development, and progress through two post-dauer larval stages to adulthood. Strikingly, all of these life history options (whether continuous or interrupted) involve an identical pattern and sequence of cell division and cell fates. To identify microRNAs with potential functions in buffering development in the context of C. elegans life history options, we used multiplex real-time PCR to assess the expression of 107 microRNAs throughout development in both continuous and interrupted life histories. We identified 17 microRNAs whose developmental profile of expression is affected by dauer life history and/or L1 diapause, compared to continuous development. Hence these microRNAs could function to regulate gene expression programs appropriate for different life history options in the developing worm.