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Vertex transitive graphs G with chi(D)(G) > chi(G) and small automorphism group
No full textFor a graph G and a positive integer k, a vertex labelling f : V (G) -> {1, 2,...,k} is said to be k-distinguishing if no non-trivial automorphism of G preserves the sets f(-1) (i) for each i epsilon {1,...,k}. The distinguishing chromatic number of a graph G, denoted chi(D)(G), is defined as the minimum k such that there is a k-distinguishing labelling of V (G) which is also a proper coloring of the vertices of G. In this paper, we prove the following theorem: Given k epsilon N, there exists an infinite sequence of vertex-transitive graphs G(i) = (V-i, E-i) such that 1. chi(D)(G(i)) > chi(G(i)) > k, 2. vertical bar Aut(G(i))vertical bar < 2k vertical bar V-i vertical bar, where Aut(G(i)) denotes the full automorphism group of G(i). In particular, this answers a question posed by the first and second authors of this paper
Diffusion caused by two noises-active and thermal
No full textThe diffusion of colloids inside an active system-e.g. within a living cell or the dynamics of active particles itself (e.g. self-propelled particles) can be modeled through overdamped Langevin equation which contains an additional noise term apart from the usual white Gaussian noise, originating from the thermal environment. The second noise is referred to as `active noise' as it arises from activity such as chemical reactions. The probability distribution function (PDF or the propagator) in space-time along with moments provides essential information for understanding their dynamical behavior. Here we employ the phase-space path integral method to obtain the propagator, thereby moments and PDF for some possible models for such noise. At first, we discuss the diffusion of a free particle driven by active noise. We consider four different possible models for active noise, to capture the possible traits of such systems. We show that the PDF for systems driven by noises other than Gaussian noise largely deviates from normal distribution at short to intermediate time scales as a manifestation of out-of-equilibrium state, albeit converges to Gaussian distribution after a long time as a consequence of the central limit theorem. We extend our work to the case of a particle trapped in a harmonic potential and show that the system attains steady state at long time limit. Also, at short time scales, the nature of distribution is different for different noises, e.g. for particle driven by dichotomous noise, the probability is mostly concentrated near the boundaries whereas a long exponential tail is observed for a particle driven by Poissonian white noise
Lysozyme elicits pain during nerve injury by neuronal Toll-like receptor 4 activation and has therapeutic potential in neuropathic pain
No full textThe role of neuronal Toll-like receptor 4 (TLR4) in nerve injury is being pursued actively. However, the endogenous activation of neuronal TLR4 during neuroinflammation, in absence of the participation of glial TLR4, remains elusive. Here, we identified lysozyme as an endogenous activator of neuronal TLR4 signaling during nerve injury. Upon nerve injury, enhanced expression of lysozyme promoted neuronal hyperexcitability and neuropathic pain. Injections of lysozyme in healthy rats increased their mechanical and thermal pain sensitivity. Likewise, infusion of spinal cord slices with lysozyme increased neuronal excitability typical of neuropathic pain. Our results also showed that lysozyme activated excitability of both A delta- and C-fibers. Thus, in addition to the discovery of lysozyme as an endogenous ligand for regulating neuronal TLR4 signaling, this study also lays the foundation of our understanding of its role in nervous system pathologies, providing multiple avenues for treating neuroinflammation
UvrA and UvrC subunits of the Mycobacterium tuberculosis UvrABC excinuclease interact independently of UvrB and DNA
No full textThe UvrABC excinuclease plays a vital role in bacterial nucleotide excision repair. While UvrA and UvrB subunits associate to form a UvrA(2)B(2) complex, interaction between UvrA and UvrC has not been demonstrated or quantified in any bacterial species. Here, using Mycobacterium tuberculosis UvrA (MtUvrA), UvrB (MtUvrB) and UvrC (MtUvrC) subunits, we show that MtUvrA binds to MtUvrB and equally well to MtUvrC with submicromolar affinity. Furthermore, MtUvrA forms a complex with MtUvrC both in vivo and in vitro, independently of DNA and UvrB. Collectively, these findings reveal new insights into the pairwise relationships between the subunits of the UvrABC incision complex
Protective effects of syringic acid, resveratrol and their combination against isoprenaline administered cardiotoxicity in wistar rats
No full textObjective: To evaluate the cardio-protection of syringic acid (SA) in combination with resveratrol (RV) in isoproterenol (ISO) induced myocardial infarcted (MI) rats. Methods: Groups of all rats were subjected oral pre-treatment at the beginning of the study with SA (50 mg/kg), RV (50 mg/kg) and combination (COMB) of SA (25 mg/kg) and RV (25 mg/kg) along with gallic acid (GA) (50 mg/kg) for 30 days. After sacrification, homogenate of heart tissue along with serum were utilized for further biochemical investigations. The effects on creatine kinase (CK), aspartate transaminase (AST), alanine transaminase (ALT) and gamma glutamyl transferase (GGT) were studied in serum and heart tissues. Glutathione-s-transferase (GST), glutathione peroxidase (GPX) and reduced glutathione (GSH), membrane bound enzymes and electrolytes were tested in heart tissues. Body weights and heart weights were also observed along with high sensitivity C-reactive protein (hs-CRP), uric acid and total protein content (TPC) in serum. Results: CK, AST, ALT and GGT levels in serum were augmented significantly while these enzymes are decreased in cardiac tissue samples of ISO-treated rats. GST, GPX, GSH, Na+/K+, Mg2+, Ca2+ ATPases, K+ ions were significantly decreased while Na+ and Ca2+ ions were increased in the heart tissues of ISO-injected rats. Loss and gain of body and heart weights were noticed significantly in rats having ISO administration. ISO group showed significant increase in hs-CRP and Uric acid while significant decrease in TPC. All of actions of ISO were ameliorated by COMB. Conclusions: COMB suppressed ISO induced MI in rats and exhibited cardio-protection
Genetic architecture of subcortical brain structures in 38,851 individuals
No full textSubcortical brain structures are integral to motion, consciousness, emotions and learning. We identified common genetic variation related to the volumes of the nucleus accumbens, amygdala, brainstem, caudate nucleus, globus pallidus, putamen and thalamus, using genome-wide association analyses in almost 40,000 individuals from CHARGE, ENIGMA and UK Biobank. We show that variability in subcortical volumes is heritable, and identify 48 significantly associated loci (40 novel at the time of analysis). Annotation of these loci by utilizing gene expression, methylation and neuropathological data identified 199 genes putatively implicated in neurodevelopment, synaptic signaling, axonal transport, apoptosis, inflammation/infection and susceptibility to neurological disorders. This set of genes is significantly enriched for Drosophila orthologs associated with neurodevelopmental phenotypes, suggesting evolutionarily conserved mechanisms. Our findings uncover novel biology and potential drug targets underlying brain development and disease
Solution of the problem of propagation of water waves over a pair of asymmetrical rectangular trenches
No full textThe problem of propagation of obliquely incident surface water waves over a pair of asymmetrical rectangular trenches in a channel of finite depth is examined for its solution. The mathematical problem is handled for its numerical solution with the aid of a system of singular integral equations of first kind. The resulting integral equations are solved numerically by using suitably designed polynomial approximations of the unknown functions. System of linear algebraic equations is obtained by utilizing the zeros of Chebyshev polynomial of first kind as collocation points and hence the occurrence of ill-conditioned matrix is avoided. The effectiveness of the pair of trenches is studied by analyzing the physical quantities namely the reflection and transmission coefficients. As a special limiting case, the results for a single trench problem are derived and are found to be in excellent agreement with the results available in the literature. The effect of various parameters are analyzed through different graphs for a pair of asymmetrical trenches. The energy balance relation is derived and used to check the accuracy of numerical results