Boundary induced phase transition with stochastic entrance and exit

We study an open-chain totally asymmetric exclusion process (TASEP) with stochastic gates present at the two boundaries. The gating dynamics has been modeled keeping the physical system of ion-channel gating in mind. These gates can randomly switch between an open state and a closed state. In the open state, the gates are highly permeable such that any particle arriving at the gate immediately passes through. In the closed state, a particle gets trapped at the gate and cannot pass through until the gate switches open again. We calculate the phase-diagram of the system and find important and non-trivial differences with the phase-diagram of a regular open-chain TASEP. In particular, depending on switching rates of the two gates, the system may or may not admit a maximal current phase. Our analytic calculation within mean-field theory captures the main qualitative features of our Monte Carlo simulation results. We also perform a refined mean-field calculation where the correlations at the boundaries are taken into account. This theory shows significantly better quantitative agreement with our simulation results

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4\pi$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.Comment: 6 pages, 4 figures, EPL forma

Integrative analysis of the inter-tumoral heterogeneity of triple-negative breast cancer.

Triple-negative breast cancers (TNBC) lack estrogen and progesterone receptors and HER2 amplification, and are resistant to therapies that target these receptors. Tumors from TNBC patients are heterogeneous based on genetic variations, tumor histology, and clinical outcomes. We used high throughput genomic data for TNBC patients (n = 137) from TCGA to characterize inter-tumor heterogeneity. Similarity network fusion (SNF)-based integrative clustering combining gene expression, miRNA expression, and copy number variation, revealed three distinct patient clusters. Integrating multiple types of data resulted in more distinct clusters than analyses with a single datatype. Whereas most TNBCs are classified by PAM50 as basal subtype, one of the clusters was enriched in the non-basal PAM50 subtypes, exhibited more aggressive clinical features and had a distinctive signature of oncogenic mutations, miRNAs and expressed genes. Our analyses provide a new classification scheme for TNBC based on multiple omics datasets and provide insight into molecular features that underlie TNBC heterogeneity

Non-monotonic behavior of timescales of passage in heterogeneous media: Dependence on the nature of barriers

Usually time of passage across a region may be expected to increase with the number of barriers along the path. Can this intuition fail depending on the special nature of the barrier? We study experimentally the transport of a robotic bug which navigates through a spatially patterned array of obstacles. Depending on the nature of the obstacles we call them either entropic or energetic barriers. For energetic barriers we find that the timescales of first passage vary non-monotonically with the number of barriers, while for entropic barriers first passage times increase monotonically. We perform an exact analytic calculation to derive closed form solutions for the mean first passage time for different theoretical models of diffusion. Our analytic results capture this counter-intuitive non-monotonic behaviour for energetic barriers. We also show non-monotonic effective diffusivity in the case of energetic barriers. Finally, using numerical simulations, we show this non-monotonic behaviour for energetic barriers continues to hold true for super-diffusive transport. These results may be relevant for timescales of intra-cellular biological processes

Asymptotic behaviour of convex and column-convex lattice polygons with fixed area and varying perimeter

We study the inflated phase of two dimensional lattice polygons, both convex and column-convex, with fixed area A and variable perimeter, when a weight \mu^t \exp[- Jb] is associated to a polygon with perimeter t and b bends. The mean perimeter is calculated as a function of the fugacity \mu and the bending rigidity J. In the limit \mu -> 0, the mean perimeter has the asymptotic behaviour \avg{t}/4 \sqrt{A} \simeq 1 - K(J)/(\ln \mu)^2 + O (\mu/ \ln \mu) . The constant K(J) is found to be the same for both types of polygons, suggesting that self-avoiding polygons should also exhibit the same asymptotic behaviour.Comment: 10 pages, 3 figure