Two variants on T2DM susceptible gene HHEX are associated with CRC risk in a Chinese population

Increasing amounts of evidence has demonstrated that T2DM (Type 2 Diabetes Mellitus) patients have increased susceptibility to CRC (colorectal cancer). As HHEX is a recognized susceptibility gene in T2DM, this work was focused on two SNPs in HHEX, rs1111875 and rs7923837, to study their association with CRC. T2DM patients without CRC (T2DM-only, n=300), T2DM with CRC (T2DM/CRC, n=135), cancer-free controls (Control, n=570), and CRC without T2DM (CRC-only, n=642) cases were enrolled. DNA samples were extracted from the peripheral blood leukocytes of the patients and sequenced by direct sequencing. The χ(2) test was used to compare categorical data. We found that in T2DM patients, rs1111875 but not the rs7923837 in HHEX gene was associated with the occurrence of CRC (p= 0.006). for rs1111875, TC/CC patients had an increased risk of CRC (p=0.019, OR=1.592, 95%CI=1.046-2.423). Moreover, our results also indicated that the two variants of HEEX gene could be risk factors for CRC in general population, independent on T2DM (p< 0.001 for rs1111875, p=0.001 for rs7923837). For rs1111875, increased risk of CRC was observed in TC or TC/CC than CC individuals (p<0.001, OR= 1.780, 95%CI= 1.385-2.287; p<0.001, OR= 1.695, 95%CI= 1.335-2.152). For rs7923837, increased CRC risk was observed in AG, GG, and AG/GG than AA individuals (p< 0.001, OR= 1.520, 95%CI= 1.200-1.924; p=0.036, OR= 1.739, 95%CI= 0.989-3.058; p< 0.001, OR= 1.540, 95%CI= 1.225-1.936). This finding highlights the potentially functional alteration with HHEX rs1111875 and rs7923837 polymorphisms may increase CRC susceptibility. Risk effects and the functional impact of these polymorphisms need further validation

PERMANENCE AND UNIVERSAL CLASSIFICATION OF DISCRETE-TIME COMPETITIVE SYSTEMS VIA THE CARRYING SIMPLEX

We study the permanence and impermanence for discrete-time Kolmogorov systems admitting a carrying simplex. Sufficient conditions to guarantee permanence and impermanence are provided based on the existence of a carrying simplex. Particularly, for low-dimensional systems, permanence and impermanence can be determined by boundary fixed points. For a class of competitive systems whose fixed points are determined by linear equations, there always exists a carrying simplex. We provide a universal classification via the equivalence relation relative to local dynamics of boundary fixed points for the three-dimensional systems by the index formula on the carrying simplex. There are a total of 33 stable equivalence classes which are described in terms of inequalities on parameters, and we present the phase portraits on their carrying simplices. Moreover, every orbit converges to some fixed point in classes 1-25 and 33; there is always a heteroclinic cycle in class 27; Neimark-Sacker bifurcations may occur in classes 26-31 but cannot occur in class 32. Based on our permanence criteria and the equivalence classification, we obtain the specific conditions on parameters for permanence and impermanence. Only systems in classes 29,31,33 and those in class 27 with a repelling heteroclinic cycle are permanent. Applications to discrete population models including the Leslie-Gower models, Atkinson-Allen models and Ricker models are given.Peer reviewe

On the dynamics of multi-species Ricker models admitting a carrying simplex

We study the dynamics of the Ricker model (map) T. It is known that under mild conditions, T admits a carrying simplex , which is a globally attracting invariant hypersurface of codimension one. We define an equivalence relation relative to local stability of fixed points on the boundary of Σ on the space of all 3D Ricker models admitting carrying simplices. There are a total of 33 stable equivalence classes. We list them in terms of simple inequalities on the parameters, and draw each one's phase portrait on Σ. Classes 1-18 have trivial dynamics, i.e. every orbit converges to some fixed point. Each map from classes 19-25 admits a unique positive fixed point with index -1, and Neimark-Sacker bifurcations do not occur in these 7 classes. In classes 26-33, there exists a unique positive fixed point with index 1. Within each of classes 26 to 31, there do exist Neimark-Sacker bifurcations, while in class 32 Neimark-Sacker bifurcations can not occur. Whether there is a Neimark-Sacker bifurcation in class 33 or not is still an open problem. Class 29 can admit Chenciner bifurcations, so two isolated closed invariant curves can coexist on the carrying simplex in this class. Each map in class 27 admits a heteroclinic cycle, i.e. a cyclic arrangement of saddle fixed points and heteroclinic connections. As the growth rate increases the carrying simplex will break, and chaos can occur for large growth rate. We also numerically show that the 4D Ricker map can admit a carrying simplex containing a chaotic attractor, which is found in competitive mappings for the first time.Peer reviewe

(2E)-2-[2-(4-Chloro­phen­yl)hydrazin-1-yl­idene]-4,4,4-trifluoro-3-oxobutanal

The title compound, C10H6ClF3N2O2, was synthesized by coupling 4-dimethyl­amino-1,1,1-trifluoro­but-3-en-2-one with 4-chloro­benzene­diazo­nium chloride. It crystallizes with two mol­ecules in the asymmetric unit, which form two similar centrosymmetric dimers via hydrogen bonds. Extensive electron delocalization and intra­molecular N—H⋯O hydrogen bonds are responsible for a planar conformation of the mol­ecules (maximum deviations = 0.010 and −0.015 Å for the two molecules). In addition to hydrogen bonds, π–π stacking inter­actions with centroid–centroid distances of 3.604 (2) and 3.583 (2) Å contribute to the stability of the crystal structure