One Drop of Non-Determinism in a Random Deterministic Automaton

Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from n states to 2? states. In this article, we investigate this classical result in a probabilistic setting where we take a deterministic automaton with n states uniformly at random and add just one random transition. These automata are almost deterministic in the sense that only one state has a non-deterministic choice when reading an input letter. In our model each state has a fixed probability to be final. We prove that for any d ? 1, with non-negligible probability the minimal (deterministic) automaton of the language recognized by such an automaton has more than n^d states; as a byproduct, the expected size of its minimal automaton grows faster than any polynomial. Our result also holds when each state is final with some probability that depends on n, as long as it is not too close to 0 and 1, at distance at least ?(1/?n) to be precise, therefore allowing models with a sublinear number of final states in expectation

Modeling Chromosomes in Mouse to Explore the Function of Genes, Genomic Disorders, and Chromosomal Organization

One of the challenges of genomic research after the completion of the human genome project is to assign a function to all the genes and to understand their interactions and organizations. Among the various techniques, the emergence of chromosome engineering tools with the aim to manipulate large genomic regions in the mouse model offers a powerful way to accelerate the discovery of gene functions and provides more mouse models to study normal and pathological developmental processes associated with aneuploidy. The combination of gene targeting in ES cells, recombinase technology, and other techniques makes it possible to generate new chromosomes carrying specific and defined deletions, duplications, inversions, and translocations that are accelerating functional analysis. This review presents the current status of chromosome engineering techniques and discusses the different applications as well as the implication of these new techniques in future research to better understand the function of chromosomal organization and structures

Identification of the translocation breakpoints in the Ts65Dn and Ts1Cje mouse lines: relevance for modeling down syndrome

Down syndrome (DS) is the most frequent genetic disorder leading to intellectual disabilities and is caused by three copies of human chromosome 21. Mouse models are widely used to better understand the physiopathology in DS or to test new therapeutic approaches. The older and the most widely used mouse models are the trisomic Ts65Dn and the Ts1Cje mice. They display deficits similar to those observed in DS people, such as those in behavior and cognition or in neuronal abnormalities. The Ts65Dn model is currently used for further therapeutic assessment of candidate drugs. In both models, the trisomy was induced by reciprocal chromosomal translocations that were not further characterized. Using a comparative genomic approach, we have been able to locate precisely the translocation breakpoint in these two models and we took advantage of this finding to derive a new and more efficient Ts65Dn genotyping strategy. Furthermore, we found that the translocations introduce additional aneuploidy in both models, with a monosomy of seven genes in the most telomeric part of mouse chromosome 12 in the Ts1Cje and a trisomy of 60 centromeric genes on mouse chromosome 17 in the Ts65Dn. Finally, we report here the overexpression of the newly found aneuploid genes in the Ts65Dn heart and we discuss their potential impact on the validity of the DS model

Controlled Somatic and Germline Copy Number Variation in the Mouse Model

Changes in the number of chromosomes, but also variations in the copy number of chromosomal regions have been described in various pathological conditions, such as cancer and aneuploidy, but also in normal physiological condition. Our classical view of DNA replication and mitotic preservation of the chromosomal integrity is now challenged as new technologies allow us to observe such mosaic somatic changes in copy number affecting regions of chromosomes with various sizes. In order to go further in the understanding of copy number influence in normal condition we could take advantage of the novel strategy called Targeted Asymmetric Sister Chromatin Event of Recombination (TASCER) to induce recombination during the G2 phase so that we can generate deletions and duplications of regions of interest prior to mitosis. Using this approach in the mouse we could address the effects of copy number variation and segmental aneuploidy in daughter cells and allow us to explore somatic mosaics for large region of interest in the mouse

PloS one

Down syndrome (DS) results from one extra copy of human chromosome 21 and leads to several alterations including intellectual disabilities and locomotor defects. The transchromosomic Tc1 mouse model carrying an extra freely-segregating copy of human chromosome 21 was developed to better characterize the relation between genotype and phenotype in DS. The Tc1 mouse exhibits several locomotor and cognitive deficits related to DS. In this report we analyzed the contribution of the genetic dosage of 13 conserved mouse genes located between Abcg1 and U2af1, in the telomeric part of Hsa21. We used the Ms2Yah model carrying a deletion of the corresponding interval in the mouse genome to rescue gene dosage in the Tc1/Ms2Yah compound mice to determine how the different behavioral phenotypes are affected. We detected subtle changes with the Tc1/Ms2Yah mice performing better than the Tc1 individuals in the reversal paradigm of the Morris water maze. We also found that Tc1/Ms2Yah compound mutants performed better in the rotarod than the Tc1 mice. This data support the impact of genes from the Abcg1-U2af1 region as modifiers of Tc1-dependent memory and locomotor phenotypes. Our results emphasize the complex interactions between triplicated genes inducing DS features

A new mouse model for the trisomy of the Abcg1-U2af1 region reveals the complexity of the combinatorial genetic code of down syndrome

Mental retardation in Down syndrome (DS), the most frequent trisomy in humans, varies from moderate to severe. Several studies both in human and based on mouse models identified some regions of human chromosome 21 (Hsa21) as linked to cognitive deficits. However, other intervals such as the telomeric region of Hsa21 may contribute to the DS phenotype but their role has not yet been investigated in detail. Here we show that the trisomy of the 12 genes, found in the 0.59 Mb (Abcg1-U2af1) Hsa21 sub-telomeric region, in mice (Ts1Yah) produced defects in novel object recognition, open-field and Y-maze tests, similar to other DS models, but induces an improvement of the hippocampal-dependent spatial memory in the Morris water maze along with enhanced and longer lasting long-term potentiation in vivo in the hippocampus. Overall, we demonstrate the contribution of the Abcg1-U2af1 genetic region to cognitive defect in working and short-term recognition memory in DS models. Increase in copy number of the Abcg1-U2af1 interval leads to an unexpected gain of cognitive function in spatial learning. Expression analysis pinpoints several genes, such as Ndufv3, Wdr4, Pknox1 and Cbs, as candidates whose overexpression in the hippocampus might facilitate learning and memory in Ts1Yah mice. Our work unravels the complexity of combinatorial genetic code modulating different aspect of mental retardation in DS patients. It establishes definitely the contribution of the Abcg1-U2af1 orthologous region to the DS etiology and suggests new modulatory pathways for learning and memor

DYRK1A, a Novel Determinant of the Methionine-Homocysteine Cycle in Different Mouse Models Overexpressing this Down-Syndrome-Associated Kinase

BACKGROUND:Hyperhomocysteinemia, characterized by increased plasma homocysteine level, is associated with an increased risk of atherosclerosis. On the contrary, patients with Down syndrome appear to be protected from the development of atherosclerosis. We previously found a deleterious effect of hyperhomocysteinemia on expression of DYRK1A, a Down-syndrome-associated kinase. As increased expression of DYRK1A and low plasma homocysteine level have been associated with Down syndrome, we aimed to analyze the effect of its over-expression on homocysteine metabolism in mice. METHODOLOGY/PRINCIPAL FINDINGS:Effects of DYRK1A over-expression were examined by biochemical analysis of methionine metabolites, real-time quantitative reverse-transcription polymerase chain reaction, and enzyme activities. We found that over-expression of Dyrk1a increased the hepatic NAD(P)H:quinone oxidoreductase and S-adenosylhomocysteine hydrolase activities, concomitant with decreased level of plasma homocysteine in three mice models overexpressing Dyrk1a. Moreover, these effects were abolished by treatment with harmine, the most potent and specific inhibitor of Dyrk1a. The increased NAD(P)H:quinone oxidoreductase and S-adenosylhomocysteine hydrolase activities were also found in lymphoblastoid cell lines from patients with Down syndrome. CONCLUSIONS/SIGNIFICANCE:Our results might give clues to understand the protective effect of Down syndrome against vascular defect through a decrease of homocysteine level by DYRK1A over-expression. They reveal a link between the Dyrk1a signaling pathway and the homocysteine cycle

Front Behav Neurosci

Cognitive impairment in Down syndrome (DS) has been linked to increased synaptic inhibition. The underlying mechanisms remain unknown, but memory deficits are rescued in DS mouse models by drugs targeting GABA receptors. Similarly, administration of epigallocatechin gallate (EGCG)-containing extracts rescues cognitive phenotypes in Ts65Dn mice, potentially through GABA pathway. Some developmental and cognitive alterations have been traced to increased expression of the serine-threonine kinase DYRK1A on Hsa21. To better understand excitation/inhibition balance in DS, we investigated the consequences of long-term (1-month) treatment with EGCG-containing extracts in adult mBACtgDyrk1a mice that overexpress Dyrk1a. Administration of POL60 rescued components of GABAergic and glutamatergic pathways in cortex and hippocampus but not cerebellum. An intermediate dose (60 mg/kg) of decaffeinated green tea extract (MGTE) acted on components of both GABAergic and glutamatergic pathways and rescued behavioral deficits as demonstrated on the alternating paradigm, but did not rescue protein level of GABA-synthesizing GAD67. These results indicate that excessive synaptic inhibition in people with DS may be attributable, in large part, to increased DYRK1A dosage. Thus, controlling the level of active DYRK1A is a clear issue for DS therapy. This study also defines a panel of synaptic markers for further characterization of DS treatments in murine models

The App-Runx1 Region Is Critical for Birth Defects and Electrocardiographic Dysfunctions Observed in a Down Syndrome Mouse Model

Down syndrome (DS) leads to complex phenotypes and is the main genetic cause of birth defects and heart diseases. The Ts65Dn DS mouse model is trisomic for the distal part of mouse chromosome 16 and displays similar features with post-natal lethality and cardiovascular defects. In order to better understand these defects, we defined electrocardiogram (ECG) with a precordial set-up, and we found conduction defects and modifications in wave shape, amplitudes, and durations in Ts65Dn mice. By using a genetic approach consisting of crossing Ts65Dn mice with Ms5Yah mice monosomic for the App-Runx1 genetic interval, we showed that the Ts65Dn viability and ECG were improved by this reduction of gene copy number. Whole-genome expression studies confirmed gene dosage effect in Ts65Dn, Ms5Yah, and Ts65Dn/Ms5Yah hearts and showed an overall perturbation of pathways connected to post-natal lethality (Coq7, Dyrk1a, F5, Gabpa, Hmgn1, Pde10a, Morc3, Slc5a3, and Vwf) and heart function (Tfb1m, Adam19, Slc8a1/Ncx1, and Rcan1). In addition cardiac connexins (Cx40, Cx43) and sodium channel sub-units (Scn5a, Scn1b, Scn10a) were found down-regulated in Ts65Dn atria with additional down-regulation of Cx40 in Ts65Dn ventricles and were likely contributing to conduction defects. All these data pinpoint new cardiac phenotypes in the Ts65Dn, mimicking aspects of human DS features and pathways altered in the mouse model. In addition they highlight the role of the App-Runx1 interval, including Sod1 and Tiam1, in the induction of post-natal lethality and of the cardiac conduction defects in Ts65Dn. These results might lead to new therapeutic strategies to improve the care of DS people

A new mouse model for the trisomy of the Abcg1–U2af1 region reveals the complexity of the combinatorial genetic code of down syndrome

Mental retardation in Down syndrome (DS), the most frequent trisomy in humans, varies from moderate to severe. Several studies both in human and based on mouse models identified some regions of human chromosome 21 (Hsa21) as linked to cognitive deficits. However, other intervals such as the telomeric region of Hsa21 may contribute to the DS phenotype but their role has not yet been investigated in detail. Here we show that the trisomy of the 12 genes, found in the 0.59 Mb (Abcg1–U2af1) Hsa21 sub-telomeric region, in mice (Ts1Yah) produced defects in novel object recognition, open-field and Y-maze tests, similar to other DS models, but induces an improvement of the hippocampal-dependent spatial memory in the Morris water maze along with enhanced and longer lasting long-term potentiation in vivo in the hippocampus. Overall, we demonstrate the contribution of the Abcg1–U2af1 genetic region to cognitive defect in working and short-term recognition memory in DS models. Increase in copy number of the Abcg1–U2af1 interval leads to an unexpected gain of cognitive function in spatial learning. Expression analysis pinpoints several genes, such as Ndufv3, Wdr4, Pknox1 and Cbs, as candidates whose overexpression in the hippocampus might facilitate learning and memory in Ts1Yah mice. Our work unravels the complexity of combinatorial genetic code modulating different aspect of mental retardation in DS patients. It establishes definitely the contribution of the Abcg1–U2af1 orthologous region to the DS etiology and suggests new modulatory pathways for learning and memory