Exact ground and excited states of frustrated antiferromagnets on the CaV_4O_9 lattice

The experimental observation of a spin-gap in the antiferromagnetic spin-1/2 compound $CaV_4O_9$ has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.Comment: 13 pages, LaTeX, 4 figures, to appear in Phys. Rev.

Origins of Binary Gene Expression in Post-transcriptional Regulation by MicroRNAs

MicroRNA-mediated regulation of gene expression is characterised by some distinctive features that set it apart from unregulated and transcription factor-regulated gene expression. Recently, a mathematical model has been proposed to describe the dynamics of post-transcriptional regulation by microRNAs. The model explains the observations made in single cell experiments quite well. In this paper, we introduce some additional features into the model and consider two specific cases. In the first case, a non-cooperative positive feedback loop is included in the transcriptional regulation of the target gene expression. In the second case, a stochastic version of the original model is considered in which there are random transitions between the inactive and active expression states of the gene. In the first case we show that bistability is possible in a parameter regime, due to the presence of a non-linear protein decay term in the gene expression dynamics. In the second case, we derive the conditions for obtaining stochastic binary gene expression. We find that this type of gene expression is more favourable in the case of regulation by microRNAs as compared to the case of unregulated gene expression. The theoretical predictions relating to binary gene expression are experimentally testable.Comment: 10 Pages, 5 Figure

Exact ground and excited states of a t-J ladder doped with two holes

A two chain ladder model is considered described by the strong coupling $t-t^\prime-J-J^\prime$ Hamiltonian. For the case of two holes moving in a background of antiferromagnetically interacting spins, exact, analytical results are derived for the ground state energy and low-lying excitation spectrum. The ground state is a bound state of two holes with total spin S=0. The charge excitation is gapless and the spin excitation has a gap. The corresponding wavefunctions are also exactly determined. The bound hole pair is found to have symmetry of the d-wave type. In the limit of strong rung coupling, the model maps onto an effective hard core boson model which exhibits dominant superconducting pairing correlations.Comment: LaTeX, 15 pages, 5 PS figures, accepted in Journal of Physics: Condensed Matte

The p53-MDM2 network: from oscillations to apoptosis

The p53 protein is well-known for its tumour suppressor function. The p53-MDM2 negative feedback loop constitutes the core module of a network of regulatory interactions activated under cellular stress. In normal cells, the level of p53 proteins is kept low by MDM2, i.e. MDM2 negatively regulates the activity of p53. In the case of DNA damage,the p53-mediated pathways are activated leading to cell cycle arrest and repair of the DNA. If repair is not possible due to excessive damage, the p53-mediated apoptotic pathway is activated bringing about cell death. In this paper, we give an overview of our studies on the p53-MDM2 module and the associated pathways from a systems biology perspective. We discuss a number of key predictions, related to some specific aspects of cell cycle arrest and cell death, which could be tested in experiments