Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

Sublinear-Time Language Recognition and Decision by One-Dimensional Cellular Automata

After an apparent hiatus of roughly 30 years, we revisit a seemingly neglected subject in the theory of (one-dimensional) cellular automata: sublinear-time computation. The model considered is that of ACAs, which are language acceptors whose acceptance condition depends on the states of all cells in the automaton. We prove a time hierarchy theorem for sublinear-time ACA classes, analyze their intersection with the regular languages, and, finally, establish strict inclusions in the parallel computation classes $\mathsf{SC}$ and (uniform) $\mathsf{AC}$. As an addendum, we introduce and investigate the concept of a decider ACA (DACA) as a candidate for a decider counterpart to (acceptor) ACAs. We show the class of languages decidable in constant time by DACAs equals the locally testable languages, and we also determine $\Omega(\sqrt{n})$ as the (tight) time complexity threshold for DACAs up to which no advantage compared to constant time is possible.Comment: 16 pages, 2 figures, to appear at DLT 202

Loss of heterozygosity of TRIM3 in malignant gliomas

<p>Abstract</p> <p>Background</p> <p>Malignant gliomas are frequent primary brain tumors associated with poor prognosis and very limited response to conventional chemo- and radio-therapies. Besides sharing common growth features with other types of solid tumors, gliomas are highly invasive into adjacent brain tissue, which renders them particularly aggressive and their surgical resection inefficient. Therefore, insights into glioma formation are of fundamental interest in order to provide novel molecular targets for diagnostic purposes and potential anti-cancer drugs. Human <it>Tripartite motif protein 3 </it>(<it>TRIM3</it>) encodes a structural homolog of <it>Drosophila brain tumor </it>(<it>brat</it>) implicated in progenitor cell proliferation control and cancer stem cell suppression. <it>TRIM3 </it>is located within the loss of allelic heterozygosity (LOH) hotspot of chromosome segment 11p15.5, indicating a potential role in tumor suppression. ...</p> <p>Methods</p> <p>Here we analyze 70 primary human gliomas of all types and grades and report somatic deletion mapping as well as single nucleotide polymorphism analysis together with quantitative real-time PCR of chromosome segment 11p15.5.</p> <p>Results</p> <p>Our analysis identifies LOH in 17 cases (24%) of primary human glioma which defines a common 130 kb-wide interval within the <it>TRIM3 </it>locus as a minimal area of loss. We further detect altered genomic dosage of <it>TRIM3 </it>in two glioma cases with LOH at 11p15.5, indicating homozygous deletions of <it>TRIM3</it>.</p> <p>Conclusion</p> <p>Loss of heterozygosity of chromosome segment 11p15.5 in malignant gliomas suggests <it>TRIM3 </it>as a candidate brain tumor suppressor gene.</p

Long-Term Sphere Culture Cannot Maintain a High Ratio of Cancer Stem Cells: A Mathematical Model and Experiment

Acquiring abundant and high-purity cancer stem cells (CSCs) is an important prerequisite for CSC research. At present, researchers usually gain high-purity CSCs through flow cytometry sorting and expand them by short-term sphere culture. However, it is still uncertain whether we can amplify high-purity CSCs through long-term sphere culture. We have proposed a mathematical model using ordinary differential equations to derive the continuous variation of the CSC ratio in long-term sphere culture and estimated the model parameters based on a long-term sphere culture of MCF-7 stem cells. We found that the CSC ratio in long-term sphere culture presented as gradually decreased drift and might be stable at a lower level. Furthermore, we found that fitted model parameters could explain the main growth pattern of CSCs and differentiated cancer cells in long-term sphere culture

Differential roles of the Drosophila EMT-inducing transcription factors Snail and Serpent in driving primary tumour growth.

Several transcription factors have been identified that activate an epithelial-to-mesenchymal transition (EMT), which endows cells with the capacity to break through basement membranes and migrate away from their site of origin. A key program in development, in recent years it has been shown to be a crucial driver of tumour invasion and metastasis. However, several of these EMT-inducing transcription factors are often expressed long before the initiation of the invasion-metastasis cascade as well as in non-invasive tumours. Increasing evidence suggests that they may promote primary tumour growth, but their precise role in this process remains to be elucidated. To investigate this issue we have focused our studies on two Drosophila transcription factors, the classic EMT inducer Snail and the Drosophila orthologue of hGATAs4/6, Serpent, which drives an alternative mechanism of EMT; both Snail and GATA are specifically expressed in a number of human cancers, particularly at the invasive front and in metastasis. Thus, we recreated conditions of Snail and of Serpent high expression in the fly imaginal wing disc and analysed their effect. While either Snail or Serpent induced a profound loss of epithelial polarity and tissue organisation, Serpent but not Snail also induced an increase in the size of wing discs. Furthermore, the Serpent-induced tumour-like tissues were able to grow extensively when transplanted into the abdomen of adult hosts. We found the differences between Snail and Serpent to correlate with the genetic program they elicit; while activation of either results in an increase in the expression of Yorki target genes, Serpent additionally activates the Ras signalling pathway. These results provide insight into how transcription factors that induce EMT can also promote primary tumour growth, and how in some cases such as GATA factors a ‘multi hit’ effect may be achieved through the aberrant activation of just a single gene

dp53 Restrains Ectopic Neural Stem Cell Formation in the Drosophila Brain in a Non-Apoptotic Mechanism Involving Archipelago and Cyclin E

Accumulating evidence suggests that tumor-initiating stem cells or cancer stem cells (CSCs) possibly originating from normal stem cells may be the root cause of certain malignancies. How stem cell homeostasis is impaired in tumor tissues is not well understood, although certain tumor suppressors have been implicated. In this study, we use the Drosophila neural stem cells (NSCs) called neuroblasts as a model to study this process. Loss-of-function of Numb, a key cell fate determinant with well-conserved mammalian counterparts, leads to the formation of ectopic neuroblasts and a tumor phenotype in the larval brain. Overexpression of the Drosophila tumor suppressor p53 (dp53) was able to suppress ectopic neuroblast formation caused by numb loss-of-function. This occurred in a non-apoptotic manner and was independent of Dacapo, the fly counterpart of the well-characterized mammalian p53 target p21 involved in cellular senescence. The observation that dp53 affected Edu incorporation into neuroblasts led us to test the hypothesis that dp53 acts through regulation of factors involved in cell cycle progression. Our results show that the inhibitory effect of dp53 on ectopic neuroblast formation was mediated largely through its regulation of Cyclin E (Cyc E). Overexpression of Cyc E was able to abrogate dp53′s ability to rescue numb loss-of-function phenotypes. Increasing Cyc E levels by attenuating Archipelago (Ago), a recently identified transcriptional target of dp53 and a negative regulator of Cyc E, had similar effects. Conversely, reducing Cyc E activity by overexpressing Ago blocked ectopic neuroblast formation in numb mutant. Our results reveal an intimate connection between cell cycle progression and NSC self-renewal vs. differentiation control, and indicate that p53-mediated regulation of ectopic NSC self-renewal through the Ago/Cyc E axis becomes particularly important when NSC homeostasis is perturbed as in numb loss-of-function condition. This has important clinical implications

γCOP Is Required for Apical Protein Secretion and Epithelial Morphogenesis in Drosophila melanogaster

Background: There is increasing evidence that tissue-specific modifications of basic cellular functions play an important role in development and disease. To identify the functions of COPI coatomer-mediated membrane trafficking in Drosophila development, we were aiming to create loss-of-function mutations in the γCOP gene, which encodes a subunit of the COPI coatomer complex. Principal Findings: We found that γCOP is essential for the viability of the Drosophila embryo. In the absence of zygotic γCOP activity, embryos die late in embryogenesis and display pronounced defects in morphogenesis of the embryonic epidermis and of tracheal tubes. The coordinated cell rearrangements and cell shape changes during tracheal tube morphogenesis critically depend on apical secretion of certain proteins. Investigation of tracheal morphogenesis in γCOP loss-of-function mutants revealed that several key proteins required for tracheal morphogenesis are not properly secreted into the apical lumen. As a consequence, γCOP mutants show defects in cell rearrangements during branch elongation, in tube dilation, as well as in tube fusion. We present genetic evidence that a specific subset of the tracheal defects in γCOP mutants is due to the reduced secretion of the Zona Pellucida protein Piopio. Thus, we identified a critical target protein of COPI-dependent secretion in epithelial tube morphogenesis. Conclusions/Significance: These studies highlight the role of COPI coatomer-mediated vesicle trafficking in both general and tissue-specific secretion in a multicellular organism. Although COPI coatomer is generally required for protein secretion, we show that the phenotypic effect of γCOP mutations is surprisingly specific. Importantly, we attribute a distinct aspect of the γCOP phenotype to the effect on a specific key target protein

Drosophila neuroblasts retain the daughter centrosome

During asymmetric mitosis, both in male Drosophila germline stem cells and in mouse embryo neural progenitors, the mother centrosome is retained by the self-renewed cell; hence suggesting that mother centrosome inheritance might contribute to stemness. We test this hypothesis in Drosophila neuroblasts (NBs) tracing photo converted centrioles and a daughter-centriole-specific marker generated by cloning the Drosophila homologue of human Centrobin. Here we show that upon asymmetric mitosis, the mother centrosome is inherited by the differentiating daughter cell. Our results demonstrate maturation-dependent centrosome fate in Drosophila NBs and that the stemness properties of these cells are not linked to mother centrosome inheritance

Spt6 is a maintenance factor for centromeric CENP-A

Replication and transcription of genomic DNA requires partial disassembly of nucleosomes to allow progression of polymerases. This presents both an opportunity to remodel the underlying chromatin and a danger of losing epigenetic information. Centromeric transcription is required for stable incorporation of the centromere-specific histone dCENP-A in M/G1 phase, which depends on the eviction of previously deposited H3/H3.3-placeholder nucleosomes. Here we demonstrate that the histone chaperone and transcription elongation factor Spt6 spatially and temporarily coincides with centromeric transcription and prevents the loss of old CENP-A nucleosomes in both Drosophila and human cells. Spt6 binds directly to dCENP-A and dCENP-A mutants carrying phosphomimetic residues alleviate this association. Retention of phosphomimetic dCENP-A mutants is reduced relative to wildtype, while non-phosphorylatable dCENP-A retention is increased and accumulates at the centromere. We conclude that Spt6 acts as a conserved CENP-A maintenance factor that ensures long-term stability of epigenetic centromere identity during transcription-mediated chromatin remodeling