Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Continuous KAOS, ASM, and Formal Control System Design Across the Continuous/Discrete Modeling Interface: A Simple Train Stopping Application

A very simple model for train stopping is used as a vehicle for investigating how the development of a control system, initially designed in the continuous domain and subsequently discretized, can be captured within a formal development process compatible with standard model based refinement methodologies. Starting with a formalized requirements analysis using KAOS, an abstract model of the continuous system is created in the ASM formalism. This requires extensions of the KAOS and ASM formalisms, capable of dealing with quantities evolving continuously over real time, which are developed. After considering how the continuous system, described as a continuous control system in the state space framework, can be discretized, a discrete control system is created in the state space framework. This is re-expressed in the ASM formalism. The rigorous results on the relationship between continuous and discrete control system models that are needed to establish provable properties of the discretization, then become the ingredients of a retrenchment between continuous and discrete ASM models, and are thus fully integrated into th

Lysine-Specific Demethylase 1 (LSD1/KDM1A) Contributes to Colorectal Tumorigenesis via Activation of the Wnt/Β-Catenin Pathway by Down-Regulating Dickkopf-1 (DKK1)

<div><p>We collected paired samples of tumor and adjacent normal colorectal tissues from 22 patients with colorectal carcinoma to compare the differences in the expression of lysine specific demethylase 1 (LSD1) in these two tissues. The results showed that in 19 paired samples (86.4%), LSD1 is more highly expressed in tumor tissue than in normal tissue. To explore the role of LSD1 in colorectal tumorigenesis, we used somatic cell gene targeting to generate an LSD1 knockout (KO) HCT 116 human colorectal cancer cell line as a research model. The analysis of phenotypic changes showed that LSD1 KO colorectal cancer cells are less tumorigenic, both in vivo and in vitro. The differential expression analysis of the cells by mRNA sequencing (RNA-Seq) yielded 2,663 differentially expressed genes, and 28 of these genes had highly significant differences (Q <0.01). We then selected the 4 colorectal cancer-related genes ADM, DKK1, HAS3 and SMURF2 for quantitative real-time PCR verification. The results showed that the differences in the expression of ADM, DKK1 and HAS3 were consistent with those measured using the RNA-Seq data. As DKK1 was the gene with the most significant differential expression, we analyzed the key proteins of the DKK1-related Wnt/β-catenin signaling pathway and found that, after knocking out LSD1, the amount of free β-catenin translocated to the nucleus was significantly reduced and that the transcription of the signaling pathway target gene c-Myc was down-regulated. Our studies show that LSD1 activates the Wnt/β-catenin signaling pathway by down-regulating the pathway antagonist DKK1, which may be one of the mechanisms leading to colorectal tumorigenesis.</p></div

Re-expression of LSD1 in the KO cell restored the phenotype.

<p>(A) Proliferation assays. (B) Plate colony formation. (C) Soft agar colony formation.</p

Expression differences of LSD1 between tumor and adjacent normal colorectal tissues.

<p>GAPDH was used as an internal control. #1∼#22, paired tissue samples 1∼22.</p

A diagram of the Wnt/β-catenin signaling pathway.

<p>We propose that LSD1 down-regulates the Wnt/β-catenin signaling pathway antagonist, DKK1, and that this down-regulation causes free β-catenin to avoid degradation and accumulate in the cytoplasm. The free β-catenin then translocated to the nucleus, activates the transcription of the signaling pathway target gene c-Myc, and finally leads to the aberrant proliferation of cells and tumorigenesis.</p

Generation of the LSD1 KO colorectal cancer cell line.

<p>(A) Selection of colorectal cancer cell lines. (B) Diagram of the targeting strategy. The endogenous LSD1 locus is shown, along with the AAV targeting vector and the targeted allele before and after Cre-mediated recombination. PCR primers P1∼P10 were described in Materials and Methods. Three STOP codons TGA were added at the end of the left HA to ensure premature termination of the transcript. L-ITR and R-ITR, left and right inverted terminal repeats, respectively; HA, homology arm; TK, TK promoter; Neo, neomycin resistance gene; polyA, polyadenylation signal. (C) Identification of LSD1 null cell lines by genomic PCR. PCR detected the WT and targeted alleles from the indicated cells using genomic DNA as template. Two independent clones for the KO are shown. The lower row with the band designated “WT” indicates that the lower band was amplified from wild-type allele. The upper row with the band designated “KO” shows that the upper band was amplified from the allele with part of exon 7 of the LSD1 knocked out and LoxP inserted. (D) Confirmation of LSD1 null cell lines by Western blot analysis. β-actin was used as an internal control.</p