Painlev\'e Analysis, Prelle-Singer Approach, Symmetries and Integrability of Damped H\'enon-Heiles System

We consider a modified damped version of H\'enon-Heiles system and investigate its integrability. By extending the Painlev\'e analysis of ordinary differential equations we find that the modified H\'enon-Heiles system possesses the Painlev\'e property for three distinct parametric restrictions. For each of the identified cases, we construct two independent integrals of motion using the well known Prelle-Singer method. We then derive a set of nontrivial non-point symmetries for each of the identified integrable cases of the modified H\'enon-Heiles system. We infer that the modified H\'enon-Heiles system is integrable for three distinct parametric restrictions. Exact solutions are given explicitly for two integrable cases.Comment: Accepted for publication in Journal of Mathematical Physic

Post-harvest soil nutrient prediction in hybrid castor (Ricinus communis l.) Cropping sequence using a multivariate analysis technique

In the era of precision agriculture, the fertilizer prescription based on the soil fertility status is much required.  Analyzing the soil after each crop is necessary for fertilizer recommendation and developing an alternative technique to forecast the soil available nutrient value rather than analyzing the soil. Multiple linear regression (MLR) equation was developed using filed experiment data to predict the soil available nutrient in castor cropping sequence. The post-harvest soil available nutrient was considered as the dependent variable and the initially available soil nutrient values, fertilizer added, yield and nutrient uptake of castor as an independent variable. In general, the post-harvest soil nutrient model's prediction accuracy was notable and had a coefficient of determination of less than 0.90. By calculating the RMSE (root means square error), R2 value, the ratio performance to deviation (RPD) and, RE (relative error) the performance of the MLR model was confirmed.Using the validated model, post-harvest soil available nutrients were predicted and compared with laboratory tested soil available nutreints. It turned out that the established model is more precisely effective and equally precise. Fertilizer recommendation could be made to subsequent crop after hybrid castor using the predicted soil available nutrients

Characterization of manganese superoxide dismutase from a marine cyanobacterium Leptolyngbya valderiana BDU20041

Abstract Background Cyanobacteria are recognized as the primordial organisms to grace the earth with molecular oxygen ~3.5 billion years ago as a result of their oxygenic photosynthesis. This laid a selection pressure for the evolution of antioxidative defense mechanisms to alleviate the toxic effect of active oxygen species (AOS) in cyanobacteria. Superoxide dismutases (SODs) are metalloenzymes that are the first arsenal in defense mechanism against oxidative stress followed by an array of antioxidative system. Unlike other living organisms, cyanobacteria possess multiple isoforms of SOD. Hence, an attempt was made to demonstrate the oxidative stress tolerance ability of marine cyanobacterium, Leptolyngbya valderiana BDU 20041 and to PCR amplify and sequence the SOD gene, the central enzyme for alleviating stress. Result L. valderiana BDU 20041, a filamentous, non-heterocystous marine cyanobacterium showed tolerance to the tested dye (C.I. Acid Black 1) which is evident by increased in biomass (i.e.) chlorophyll a. The other noticeable change was the total ROS production by culture dosed with dye compared to the control cultures. This prolonged incubation showed sustenance, implying that cyanobacteria maintain their antioxidant levels. The third significant feature was a two-fold increase in SOD activity of dye treated L. valderiana BDU20041 suggesting the role of SOD in alleviating oxidative stress via Asada-Halliwell pathway. Hence, the organism was PCR amplified for SOD gene resulting in an amplicon of 550 bp. The sequence analysis illustrated the presence of first three residues involved in motif; active site residues at H4, 58 and D141 along with highly conserved Mn specific residues. The isolated gene shared 63.8% homology with MnSOD of bacteria confirmed it as Mn isoform. This is the hitherto report on SOD gene from marine cyanobacterium, L. valderiana BDU20041 of Indian subcontinent. Conclusion Generation of Reactive Oxygen Species (ROS) coupled with induction of SOD by marine cyanobacterium, L. valderiana BDU20041 was responsible for alleviating stress caused by an azo dye, C. I. Acid Black 1. The partial SOD gene has been sequenced and based on the active site, motif and metal specific residues; it has been identified as Mn metalloform. </jats:sec

Comparative analysis of cyanobacterial superoxide dismutases to discriminate canonical forms

<p>Abstract</p> <p>Background</p> <p>Superoxide dismutases (SOD) are ubiquitous metalloenzymes that catalyze the disproportion of superoxide to peroxide and molecular oxygen through alternate oxidation and reduction of their metal ions. In general, SODs are classified into four forms by their catalytic metals namely; FeSOD, MnSOD, Cu/ZnSOD and NiSOD. In addition, a cambialistic form that uses Fe/Mn in its active site also exists. Cyanobacteria, the oxygen evolving photosynthetic prokaryotes, produce reactive oxygen species that can damage cellular components leading to cell death. Thus, the co-evolution of an antioxidant system was necessary for the survival of photosynthetic organisms with SOD as the initial enzyme evolved to alleviate the toxic effect. Cyanobacteria represent the first oxygenic photoautotrophs and their SOD sequences available in the databases lack clear annotation. Hence, the present study focuses on structure and sequence pattern of subsets of cyanobacterial superoxide dismutases.</p> <p>Result</p> <p>The sequence conservation and structural analysis of Fe (<it>Thermosynechococcus elongatus </it>BP1) and MnSOD (<it>Anabaena </it>sp. PCC7120) reveal the sharing of N and C terminal domains. At the C terminal domain, the metal binding motif in cyanoprokaryotes is DVWEHAYY while it is D-X-[WF]-E-H-[STA]-[FY]-[FY] in other pro- and eukaryotes. The cyanobacterial FeSOD differs from MnSOD at least in three ways <it>viz</it>. (i) FeSOD has a metal specific signature F184X₃A188Q189_.......T280_......F/Y303 while, in Mn it is R184X₃G188G189_......G280......W303, (ii) aspartate ligand forms a hydrogen bond from the active site with the outer sphere residue of W243 in Fe where as it is Q262 in MnSOD; and (iii) two unique lysine residues at positions 201 and 255 with a photosynthetic role, found only in FeSOD. Further, most of the cyanobacterial Mn metalloforms have a specific transmembrane hydrophobic pocket that distinguishes FeSOD from Mn isoform. Cyanobacterial Cu/ZnSOD has a copper domain and two different signatures G-F-H-[ILV]-H-x-[NGT]-[GPDA]-[SQK]-C and G-[GA]-G-G-[AEG]-R-[FIL]-[AG]-C-G, while Ni isoform has an nickel containing SOD domain containing a Ni-hook HCDGPCVYDPA.</p> <p>Conclusion</p> <p>The present analysis unravels the ambiguity among cyanobacterial SOD isoforms. NiSOD is the only SOD found in lower forms; whereas, Fe and Mn occupy the higher orders of cyanobacteria. In conclusion, cyanobacteria harbor either Ni alone or a combination of Fe and Ni or Fe and Mn as their catalytic active metal while Cu/Zn is rare.</p