Transient Pulse Formation in Jasmonate Signaling Pathway

The jasmonate (JA) signaling pathway in plants is activated as defense response to a number of stresses like attacks by pests or pathogens and wounding by animals. Some recent experiments provide significant new knowledge on the molecular detail and connectivity of the pathway. The pathway has two major components in the form of feedback loops, one negative and the other positive. We construct a minimal mathematical model, incorporating the feedback loops, to study the dynamics of the JA signaling pathway. The model exhibits transient gene expression activity in the form of JA pulses in agreement with experimental observations. The dependence of the pulse amplitude, duration and peak time on the key parameters of the model is determined computationally. The deterministic and stochastic aspects of the pathway dynamics are investigated using both the full mathematical model as well as a reduced version of it. We also compare the mechanism of pulse formation with the known mechanisms of pulse generation in some bacterial and viral systems

Functional characteristics of a double positive feedback loop coupled with autorepression

We study the functional characteristics of a two-gene motif consisting of a double positive feedback loop and an autoregulatory negative feedback loop. The motif appears in the gene regulatory network controlling the functional activity of pancreatic $\beta$-cells. The model exhibits bistability and hysteresis in appropriate parameter regions. The two stable steady states correspond to low (OFF state) and high (ON state) protein levels respectively. Using a deterministic approach, we show that the region of bistability increases in extent when the copy number of one of the genes is reduced from two to one. The negative feedback loop has the effect of reducing the size of the bistable region. Loss of a gene copy, brought about by mutations, hampers the normal functioning of the $\beta$-cells giving rise to the genetic disorder, maturity-onset diabetes of the young (MODY). The diabetic phenotype makes its appearance when a sizable fraction of the $\beta$-cells is in the OFF state. Using stochastic simulation techniques, we show that, on reduction of the gene copy number, there is a transition from the monostable ON to the ON state in the bistable region of the parameter space. Fluctuations in the protein levels, arising due to the stochastic nature of gene expression, can give rise to transitions between the ON and OFF states. We show that as the strength of autorepression increases, the ON$\to$OFF state transitions become less probable whereas the reverse transitions are more probable. The implications of the results in the context of the occurrence of MODY are pointed out..Comment: 9 pages 14 figure

Emergent Bistability : Effects of Additive and Multiplicative Noise

Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been proposed which involves only positive feedback and no cooperativity in the regulation. An additional positive feedback loop is effectively generated due to the inhibition of cellular growth by the synthesized proteins. The mechanism, demonstrated for a synthetic circuit, may be prevalent in natural systems also as some recent experimental results appear to suggest. In this paper, we study the effects of additive and multiplicative noise on the dynamics governing emergent bistability. The calculational scheme employed is based on the Langevin and Fokker-Planck formalisms. The steady state probability distributions of protein levels and the mean first passage times are computed for different noise strengths and system parameters. In the region of bistability, the bimodal probability distribution is shown to be a linear combination of a lognormal and a Gaussian distribution. The variances of the individual distributions and the relative weights of the distributions are further calculated for varying noise strengths and system parameters. The experimental relevance of the model results is also pointed out.Comment: 16 pages, 11 figures, version accepted for publication in Eur. Phys. J.

Reaction diffusion processes on random and scale-free networks

We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.Comment: 8 pages, 7 figure

Prototypical quadruplet for few-shot class incremental learning

Many modern computer vision algorithms suffer from two major bottlenecks: scarcity of data and learning new tasks incrementally. While training the model with new batches of data the model looses it's ability to classify the previous data judiciously which is termed as catastrophic forgetting. Conventional methods have tried to mitigate catastrophic forgetting of the previously learned data while the training at the current session has been compromised. The state-of-the-art generative replay based approaches use complicated structures such as generative adversarial network (GAN) to deal with catastrophic forgetting. Additionally, training a GAN with few samples may lead to instability. In this work, we present a novel method to deal with these two major hurdles. Our method identifies a better embedding space with an improved contrasting loss to make classification more robust. Moreover, our approach is able to retain previously acquired knowledge in the embedding space even when trained with new classes. We update previous session class prototypes while training in such a way that it is able to represent the true class mean. This is of prime importance as our classification rule is based on the nearest class mean classification strategy. We have demonstrated our results by showing that the embedding space remains intact after training the model with new classes. We showed that our method preformed better than the existing state-of-the-art algorithms in terms of accuracy across different sessions

Generalized zero-shot learning using generated proxy unseen samples and entropy separation

The recent generative model-driven Generalized Zero-shot Learning (GZSL) techniques overcome the prevailing issue of the model bias towards the seen classes by synthesizing the visual samples of the unseen classes through leveraging the corresponding semantic prototypes. Although such approaches significantly improve the GZSL performance due to data augmentation, they violate the principal assumption of GZSL regarding the unavailability of semantic information of unseen classes during training. In this work, we propose to use a generative model (GAN) for synthesizing the visual proxy samples while strictly adhering to the standard assumptions of the GZSL. The aforementioned proxy samples are generated by exploring the early training regime of the GAN. We hypothesize that such proxy samples can effectively be used to characterize the average entropy of the label distribution of the samples from the unseen classes. Further, we train a classifier on the visual samples from the seen classes and proxy samples using entropy separation criterion such that an average entropy of the label distribution is low and high, respectively, for the visual samples from the seen classes and the proxy samples. Such entropy separation criterion generalizes well during testing where the samples from the unseen classes exhibit higher entropy than the entropy of the samples from the seen classes. Subsequently, low and high entropy samples are classified using supervised learning and ZSL rather than GZSL. We show the superiority of the proposed method by experimenting on AWA1, CUB, HMDB51, and UCF101 datasets