Mahashweta Basu

Fixed-energy sandpiles belong generically to directed percolation.

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.

CSF proteomics of secondary phase spinal cord injury in human subjects: perturbed molecular pathways post injury.

Recovery of sensory and motor functions following traumatic spinal cord injury (SCI) is dependent on injury severity. Here we identified 49 proteins from cerebrospinal fluid (CSF) of SCI patients, eight of which were differentially abundant among two severity groups of SCI. It was observed that the abundance profiles of these proteins change over a time period of days to months post SCI. Statistical analysis revealed that these proteins take part in several molecular pathways including DNA repair, protein phosphorylation, tRNA transcription, iron transport, mRNA metabolism, immune response and lipid and ATP catabolism. These pathways reflect a set of mechanisms that the system may adopt to cope up with the assault depending on the injury severity, thus leading to observed physiological responses. Apart from putting forward a picture of the molecular scenario at the injury site in a human study, this finding further delineates consequent pathways and molecules that may be altered by external intervention to restrict neural degeneration.

Asymmetric simple exclusion process on a Cayley tree

We study the asymmetric exclusion process on a regular Cayley tree with arbitrary co-ordination number. In this model particles can enter the system only at the parent site and exit from any of the sites at the last level. In the bulk they move downward to one of the unoccupied neighbours chosen randomly. We show that the steady state current that flows from one level to the next is independent of the exit rate, and increases monotonically with the entry rate and the co-ordination number. Unlike the TASEP, the model has only one phase and the density profile shows no boundary layers.

Comparison of Modules of Wild Type and Mutant Huntingtin and TP53 Protein Interaction Networks: Implications in Biological Processes and Functions

Disease-causing mutations usually change the interacting partners of mutant proteins. In this article, we propose that the biological consequences of mutation are directly related to the alteration of corresponding protein protein interaction networks (PPIN). Mutation of Huntingtin (HTT) which causes Huntingtons disease (HD) and mutations to TP53 which is associated with different cancers are studied as two example cases. We construct the PPIN of wild type and mutant proteins separately and identify the structural modules of each of the networks. The functional role of these modules are then assessed by Gene Ontology (GO) enrichment analysis for biological processes (BPs). We find that a large number of significantly enriched () GO terms in mutant PPIN were absent in the wild type PPIN indicating the gain of BPs due to mutation. Similarly some of the GO terms enriched in wild type PPIN cease to exist in the modules of mutant PPIN, representing the loss. GO terms common in modules of mutant and wild type networks indicate both loss and gain of BPs. We further assign relevant biological function(s) to each module by classifying the enriched GO terms associated with it. It turns out that most of these biological functions in HTT networks are already known to be altered in HD and those of TP53 networks are altered in cancers. We argue that gain of BPs, and the corresponding biological functions, are due to new interacting partners acquired by mutant proteins. The methodology we adopt here could be applied to genetic diseases where mutations alter the ability of the protein to interact with other proteins.

Modules of human micro-RNA co-target network

Human micro RNAs (miRNAs) target about 90% of the coding genes and form a complex regulatory network. We study the community structure of the miRNA co-target network considering miRNAs as the nodes which are connected by weighted links. The weight of link that connects a pair of miRNAs denote the total number of common transcripts targeted by that pair. We argue that the network consists of about 74 modules, quite similar to the components (or clusters) obtained earlier [Online J Bioinformatics, 10,280], indicating that the components of the miRNA co-target network are self organized in a way to maximize the modularity.

Distribution of microRNA co-targets exhibit universality across a wide class of species

MicroRNAs (miRNAs) are small non-coding RNAs which regulate gene expression by binding to the UTR of the corresponding messenger RNAs. We construct miRNA co-target networks for a wide class of species (22 in total) using a target prediction database, MicroCosm Targets. For each species, miRNA pairs having one or more common target genes are connected and the number of co-targets are assigned as the weight of these links. We show that the link-weight distributions of all the species collapse remarkably onto each other when scaled suitably —the scale-factor turns out to be a measure of complexity of the species. A simple model, where targets are chosen randomly by miRNAs, could provide the correct scaling function and suggest that the increase of species complexity is related to the increase of the fraction of genes typically targeted by their miRNAs.

A novel approach to discontinuous bond percolation transition

We introduce a bond percolation procedure on a D-dimensional lattice where two neighbouring sites are connected by N channels, each operated by valves at both ends. Out of a total of N, randomly chosen n valves are open at every site. A bond is said to connect two sites if there is at least one channel between them, which has open valves at both ends. We show analytically that in all spatial dimensions, this system undergoes a discontinuous percolation transition in the N→∞ limit when crosses a threshold. It must be emphasized that, in contrast to the ordinary percolation models, here the transition occurs even in one-dimensional systems, albeit discontinuously. We also show that a special kind of discontinuous percolation occurs only in one dimension when N depends on the system size.

Universality splitting in distribution of number of miRNA co-targets.

In a recent work (Basu et al., in EPL 105:28007, 2014) it was pointed out that the link-weight distribution of microRNA co-target network of a wide class of species are universal up to scaling. The number cell types, widely accepted as a measure of complexity, turns out to be proportional to these scale-factor. In this article we discuss additional universal features of these networks and show that, this universality splits if one considers distribution of number of common targets of three or more number of microRNAs. These distributions for different species can be collapsed onto two distinct set of universal functions, revealing the fact that the species which appeared in early evolution have different complexity measure compared to those appeared late.

Two-dimensional random walk in a bounded domain

In a recent letter Ciftci and Cakmak (EPL, 87 (2009) 60003) showed that the two-dimensional random walk in a bounded domain, where walkers which cross the boundary return to a base curve near the origin with deterministic rules, can produce regular patterns. Our numerical calculations suggest that the cumulative probability distribution function of the returning walkers along the base curve is a Devils staircase, which can be explained from the mapping of these walks to a non-linear stochastic map. The non-trivial probability distribution function (PDF) is a universal feature of CCRW characterized by the fractal dimension d=1.75(0) of the curve which bounds this distribution.