Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

Analytical Studies on Diffusion and lntermittency in Chaotic Maps

The study of simple chaotic maps for non-equilibrium processes in statistical physics has been one of the central themes in the theory of chaotic dynamical systems. Recently, many works have been carried out on deterministic diffusion in spatially extended one-dimensional maps This can be related to real physical systems such as Josephson junctions in the presence of microwave radiation and parametrically driven oscillators. Transport due to chaos is an important problem in Hamiltonian dynamics also. A recent approach is to evaluate the exact diffusion coefficient in terms of the periodic orbits of the system in the form of cycle expansions. But the fact is that the chaotic motion in such spatially extended maps has two complementary aspects- - diffusion and interrnittency. These are related to the time evolution of the probability density function which is approximately Gaussian by central limit theorem. It is noticed that the characteristic function method introduced by Fujisaka and his co-workers is a very powerful tool for analysing both these aspects of chaotic motion. The theory based on characteristic function actually provides a thermodynamic formalism for chaotic systems It can be applied to other types of chaos-induced diffusion also, such as the one arising in statistics of trajectory separation. It was noted that there is a close connection between cycle expansion technique and characteristic function method. It was found that this connection can be exploited to enhance the applicability of the cycle expansion technique. In this way, we found that cycle expansion can be used to analyse the probability density function in chaotic maps. In our research studies we have successfully applied the characteristic function method and cycle expansion technique for analysing some chaotic maps. We introduced in this connection, two classes of chaotic maps with variable shape by generalizing two types of maps well known in literature.

Characterization and Pathogenicity of Vibrio cholerae and Vibrio vulnificus from Marine environments

The genus Vibrioof the family Vibrionaceae are Gram negative, oxidasepositive, rod- or curved- rodshaped facultative anaerobes, widespread in marine and estuarine environments. Vibrio species are opportunistic human pathogens responsible for diarrhoeal disease, gastroenteritis, septicaemia and wound infections and are also pathogens of aquatic organisms, causing infections to crustaceans, bivalves and fishes. In the present study, marine environmental samples like seafood and water and sediment samples from aquafarms and mangroves were screened for the presence of Vibrio species. Of the134 isolates obtained from the various samples, 45 were segregated to the genus Vibrio on the basis of phenotypic characterization.like Gram staining, oxidase test, MoF test and salinity tolerance. Partial 16S rDNA sequence analysis was utilized for species level identification of the isolates and the strains were identified as V. cholerae(N=21), V. vulnificus(N=18), V. parahaemolyticus(N=3), V. alginolyticus (N=2) and V. azureus (N=1). The genetic relatedness and variations among the 45 Vibrio isolates were elucidated based on 16S rDNA sequences. Phenotypic characterization of the isolates was based on their response to 12 biochemical tests namely Voges-Proskauers’s (VP test), arginine dihydrolase , tolerance to 3% NaCl test, ONPG test that detects β-galactosidase activity, and tests for utilization of citrate, ornithine, mannitol, arabinose, sucrose, glucose, salicin and cellobiose. The isolates exhibited diverse biochemical patterns, some specific for the species and others indicative of their environmental source.Antibiogram for the isolates was determined subsequent to testing their susceptibility to 12 antibiotics by the disc diffusion method. Varying degrees of resistance to gentamycin (2.22%), ampicillin(62.22%), nalidixic acid (4.44%), vancomycin (86.66), cefixime (17.77%), rifampicin (20%), tetracycline (42.22%) and chloramphenicol (2.22%) was exhibited. All the isolates were susceptible to streptomycin, co-trimoxazole, trimethoprim and azithromycin. Isolates from all the three marine environments exhibited multiple antibiotic resistance, with high MAR index value. The molecular typing methods such as ERIC PCR and BOX PCR revealed intraspecies relatedness and genetic heterogeneity within the environmental isolatesof V. cholerae and V. vulnificus. The 21 strains of V. choleraewere serogroupedas non O1/ non O139 by screening for the presence O1rfb and O139 rfb marker genes by PCR. The virulence/virulence associated genes namely ctxA, ctxB, ace, VPI, hlyA, ompU, rtxA, toxR, zot, nagst, tcpA, nin and nanwere screened in V. cholerae and V. vulnificusstrains.The V. vulnificusstrains were also screened for three species specific genes viz., cps, vvhand viu. In V. cholerae strains, the virulence associated genes like VPI, hlyA, rtxA, ompU and toxR were confirmed by PCR. All the isolates, except for strain BTOS6, harbored at least one or a combination of the tested genes and V. choleraestrain BTPR5 isolated from prawn hosted the highest number of virulence associated genes. Among the V. vulnificusstrains, only 3 virulence genes, VPI, toxR and cps, were confirmed out of the 16 tested and only 7 of the isolates had these genes in one or more combinations. Strain BTPS6 from aquafarm and strain BTVE4 from mangrove samples yielded positive amplification for the three genes. The toxRgene from 9 strains of V. choleraeand 3 strains of V. vulnificus were cloned and sequenced for phylogenetic analysis based on nucleotide and the amino acid sequences. Multiple sequence alignment of the nucleotide sequences and amino acid sequences of the environmental strains of V. choleraerevealed that the toxRgene in the environmental strains are 100% homologous to themselves and to the V. choleraetoxR gene sequence available in the Genbank database. The 3 strains of V. vulnificus displayed high nucleotide and amino acid sequence similarity among themselves and to the sequences of V. cholerae and V. harveyi obtained from the GenBank database, but exhibited only 72% homology to the sequences of its close relative V. vulnificus. Structure prediction of the ToxR protein of Vibrio cholerae strain BTMA5 was by PHYRE2 software. The deduced amino acid sequence showed maximum resemblance with the structure of DNA-binding domain of response regulator2 from Escherichia coli k-12 Template based homology modelling in PHYRE2 successfully modelled the predicted protein and its secondary structure based on protein data bank (PDB) template c3zq7A. The pathogenicity studies were performed using the nematode Caenorhabditiselegansas a model system. The assessment of pathogenicity of environmental strain of V. choleraewas conducted with E. coli strain OP50 as the food source in control plates, environmental V. cholerae strain BTOS6, negative for all tested virulence genes, to check for the suitability of Vibrio sp. as a food source for the nematode;V. cholerae Co 366 ElTor, a clinical pathogenic strain and V. cholerae strain BTPR5 from seafood (Prawn) and positive for the tested virulence genes like VPI, hlyA, ompU,rtxA and toxR. It was found that V. cholerae strain BTOS6 could serve as a food source in place of E. coli strain OP50 but behavioral aberrations like sluggish movement and lawn avoidance and morphological abnormalities like pharyngeal and intestinal distensions and bagging were exhibited by the worms fed on V. cholerae Co 366 ElTor strain and environmental BTPR5 indicating their pathogenicity to the nematode. Assessment of pathogenicity of the environmental strains of V. vulnificus was performed with V. vulnificus strain BTPS6 which tested positive for 3 virulence genes, namely, cps, toxRand VPI, and V. vulnificus strain BTMM7 that did not possess any of the tested virulence genes. A reduction was observed in the life span of worms fed on environmental strain of V. vulnificusBTMM7 rather than on the ordinary laboratory food source, E. coli OP50. Behavioral abnormalities like sluggish movement, lawn avoidance and bagging were also observed in the worms fed with strain BTPS6, but the pharynx and the intestine were intact. The presence of multi drug resistant environmental Vibrio strainsthat constitute a major reservoir of diverse virulence genes are to be dealt with caution as they play a decisive role in pathogenicity and horizontal gene transfer in the marine environments.

Differential induction, isolation, physicochemical and molecular characterization of temperate phages of environmental Vibrio cholerae as evidence of phage mediated Horizontal Gene Transfer

The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.