Sparse Recovery of Positive Signals with Minimal Expansion

We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are crucial in applications, such as DNA microarrays and sensor networks, where dense measurements are not practically feasible. One possible construction uses the adjacency matrices of expander graphs, which often leads to recovery algorithms much more efficient than $\ell_1$ minimization. However, to date, constructions based on expanders have required very high expansion coefficients which can potentially make the construction of such graphs difficult and the size of the recoverable sets small. In this paper, we construct sparse measurement matrices for the recovery of non-negative vectors, using perturbations of the adjacency matrix of an expander graph with much smaller expansion coefficient. We present a necessary and sufficient condition for $\ell_1$ optimization to successfully recover the unknown vector and obtain expressions for the recovery threshold. For certain classes of measurement matrices, this necessary and sufficient condition is further equivalent to the existence of a "unique" vector in the constraint set, which opens the door to alternative algorithms to $\ell_1$ minimization. We further show that the minimal expansion we use is necessary for any graph for which sparse recovery is possible and that therefore our construction is tight. We finally present a novel recovery algorithm that exploits expansion and is much faster than $\ell_1$ optimization. Finally, we demonstrate through theoretical bounds, as well as simulation, that our method is robust to noise and approximate sparsity.Comment: 25 pages, submitted for publicatio

Chemical communication between synthetic and natural cells: a possible experimental design

The bottom-up construction of synthetic cells is one of the most intriguing and interesting research arenas in synthetic biology. Synthetic cells are built by encapsulating biomolecules inside lipid vesicles (liposomes), allowing the synthesis of one or more functional proteins. Thanks to the in situ synthesized proteins, synthetic cells become able to perform several biomolecular functions, which can be exploited for a large variety of applications. This paves the way to several advanced uses of synthetic cells in basic science and biotechnology, thanks to their versatility, modularity, biocompatibility, and programmability. In the previous WIVACE (2012) we presented the state-of-the-art of semi-synthetic minimal cell (SSMC) technology and introduced, for the first time, the idea of chemical communication between synthetic cells and natural cells. The development of a proper synthetic communication protocol should be seen as a tool for the nascent field of bio/chemical-based Information and Communication Technologies (bio-chem-ICTs) and ultimately aimed at building soft-wet-micro-robots. In this contribution (WIVACE, 2013) we present a blueprint for realizing this project, and show some preliminary experimental results. We firstly discuss how our research goal (based on the natural capabilities of biological systems to manipulate chemical signals) finds a proper place in the current scientific and technological contexts. Then, we shortly comment on the experimental approaches from the viewpoints of (i) synthetic cell construction, and (ii) bioengineering of microorganisms, providing up-to-date results from our laboratory. Finally, we shortly discuss how autopoiesis can be used as a theoretical framework for defining synthetic minimal life, minimal cognition, and as bridge between synthetic biology and artificial intelligence.Comment: In Proceedings Wivace 2013, arXiv:1309.712

Can graph-cutting improve microarray gene expression reconstructions?

Microarrays produce high-resolution image data that are, unfortunately, permeated with a great deal of “noise” that must be removed for precision purposes. This paper presents a technique for such a removal process. On completion of this non-trivial task, a new surface (devoid of gene spots) is subtracted from the original to render more precise gene expressions. The graph-cutting technique as implemented has the benefits that only the most appropriate pixels are replaced and these replacements are replicates rather than estimates. This means the influence of outliers and other artifacts are handled more appropriately (than in previous methods) as well as the variability of the final gene expressions being considerably reduced. Experiments are carried out to test the technique against commercial and previously researched reconstruction methods. Final results show that the graph-cutting inspired identification mechanism has a positive significant impact on reconstruction accuracy

State Complexity of Catenation Combined with Star and Reversal

This paper is a continuation of our research work on state complexity of combined operations. Motivated by applications, we study the state complexities of two particular combined operations: catenation combined with star and catenation combined with reversal. We show that the state complexities of both of these combined operations are considerably less than the compositions of the state complexities of their individual participating operations.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Emergence of switch-like behavior in a large family of simple biochemical networks

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the most elementary biochemical processes). We find that there exist reaction rate constants leading to bistability in ~90% of these GRN models, including several circuits that do not contain any of the TF cooperativity commonly associated with bistable systems, and the majority of which could only be identified as bistable through an original subnetwork-based analysis. A topological sorting of the two-gene family of networks based on the presence or absence of biochemical reactions reveals eleven minimal bistable networks (i.e., bistable networks that do not contain within them a smaller bistable subnetwork). The large number of previously unknown bistable network topologies suggests that the capacity for switch-like behavior in GRNs arises with relative ease and is not easily lost through network evolution. To highlight the relevance of the systematic application of CRNT to bistable network identification in real biological systems, we integrated publicly available protein-protein interaction, protein-DNA interaction, and gene expression data from Saccharomyces cerevisiae, and identified several GRNs predicted to behave in a bistable fashion.Comment: accepted to PLoS Computational Biolog