Comparative Study of Homotopy Analysis and Renormalization Group Methods on Rayleigh and Van der Pol Equations

A comparative study of the Homotopy Analysis method and an improved Renormalization Group method is presented in the context of the Rayleigh and the Van der Pol equations. Efficient approximate formulae as functions of the nonlinearity parameter $\varepsilon$ for the amplitudes $a(\varepsilon)$ of the limit cycles for both these oscillators are derived. The improvement in the Renormalization group analysis is achieved by invoking the idea of nonlinear time that should have significance in a nonlinear system. Good approximate plots of limit cycles of the concerned oscillators are also presented within this framework.Comment: 25 pages, 7 figures. Revised and upgraded: Differ Equ Dyn Syst, (26 July, 2015

Colonization behaviour of arbuscular mycorrhizal fungi and phosphorus uptake pattern of mycorrhizal sensitive upland paddy using hydroponics culture

Three upland rice cultivars namely Vandana, Brown Gora and Kalinga collected from the Central Rainfed Upland Rice Research Station (CRURRS), Hazaribag, Jharkhand of the Central Rice Research Institute, are mycorrhiza sensitive genotypes. Their affinity towards mycorrhizal colonization varied. The cv. Kalinga had the highest colonization followed by Vandana and Brown Gora. Variation of arbuscular mycorrhizal fungi affinity of the rice genotypes might be due to the variable demands of phosphorus nutrition of the different genotypes. To justify these variable demands of phosphorus among these three cultivars of rice, four different doses of phosphorus (5, 10, 15 and 20 ppm) were imposed to them in a system of hydroponics. Overall, among the three cultivars, the highest uptake efficiency (34% at 30 days, 57% at 45 days, 68% at 60days and 70% at 75 days interval) throughout the growth period was noticed in the cv. Brown Gora, followed by Kalinga and Vandana. The physiological demands of phosphorus of these cultivars were finally estimated as the contribution of uptake phosphorus to the total dry matter production of the plants with respect to available phosphorus. The overall results of these estimations gave the highest value in cv. Kalinga followed by the cv. Vandana and Brown Gora. Therefore, the cultivars Brown Gora and Kalinga could be recommended for the cultivation of the vast upland rain-fed areas of the country for higher yield and increased phosphorus use efficiency which could ultimately contribute significantly to the food grain production of the country

Golgi localization and dynamics of hyaluronan binding protein 1 (HABP1/p32/C1QBP) during the cell cycle

Hyaluronan binding protein 1 (HABP1) is a negatively charged multifunctional mammalian protein with a unique structural fold. Despite the fact that HABP1 possesses mitochondrial localization signal, it has also been localized to other cellular compartments. Using indirect immunofluorescence, we examined the sub-cellular localization of HABP1 and its dynamics during mitosis. We wanted to determine whether it distributes in any distinctive manner after mitotic nuclear envelope disassembly or is dispersed randomly throughout the cell. Our results reveal the golgi localization of HABP1 and demonstrate its complete dispersion throughout the cell during mitosis. This distinctive distribution pattern of HABP1 during mitosis resembles its ligand hyaluronan, suggesting that in concert with each other the two molecules play critical roles in this dynamic process

Towards targeted combinatorial therapy design for the treatment of castration-resistant prostate cancer

BACKGROUND: Prostate cancer is one of the most prevalent cancers in males in the United States and amongst the leading causes of cancer related deaths. A particularly virulent form of this disease is castration-resistant prostate cancer (CRPC), where patients no longer respond to medical or surgical castration. CRPC is a complex, multifaceted and heterogeneous malady with limited standard treatment options. RESULTS: The growth and progression of prostate cancer is a complicated process that involves multiple pathways. The signaling network comprising the integral constituents of the signature pathways involved in the development and progression of prostate cancer is modeled as a combinatorial circuit. The failures in the gene regulatory network that lead to cancer are abstracted as faults in the equivalent circuit and the Boolean circuit model is then used to design therapies tailored to counteract the effect of each molecular abnormality and to propose potentially efficacious combinatorial therapy regimens. Furthermore, stochastic computational modeling is utilized to identify potentially vulnerable components in the network that may serve as viable candidates for drug development. CONCLUSION: The results presented herein can aid in the design of scientifically well-grounded targeted therapies that can be employed for the treatment of prostate cancer patients

Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited

An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters

Optimal Constrained Stationary Intervention in Gene Regulatory Networks

A key objective of gene network modeling is to develop intervention strategies to alter regulatory dynamics in such a way as to reduce the likelihood of undesirable phenotypes. Optimal stationary intervention policies have been developed for gene regulation in the framework of probabilistic Boolean networks in a number of settings. To mitigate the possibility of detrimental side effects, for instance, in the treatment of cancer, it may be desirable to limit the expected number of treatments beneath some bound. This paper formulates a general constraint approach for optimal therapeutic intervention by suitably adapting the reward function and then applies this formulation to bound the expected number of treatments. A mutated mammalian cell cycle is considered as a case study