Private information retrieval (PIR) allows a user to retrieve a desired message from a set of databases without revealing the identity of the desired message. The replicated databases scenario was considered by Sun and Jafar in [1], where N databases can store the same K messages completely. A PIR scheme was developed to achieve the optimal download cost given by 1In this work, we consider the problem of PIR from storage constrained databases. Each database has a storage capacity of µKL bits, where L is the size of each message in bits, and µ ∈ [1/N, 1] is the normalized storage. On one extreme, µ = 1 is the replicated databases case considered in [1]. On the other hand, when µ = 1/N , then in order to retrieve a message privately, the user has to download all the messages from the databases achieving a download cost of 1/K. We aim to characterize the optimal download cost versus storage trade-off for any storage capacity in the range µ ∈ [1/N, 1].In the storage constrained PIR problem, there are two key challenges: a) construction of communication efficient schemes through storage content design at each database that allow download efficient PIR; and b) characterizing the optimal download cost via information-theoretic lower bounds. The novel aspect of this work is to characterize the optimum download cost of PIR from uncoded storage constrained databases for any value of storage. In particular, for any (N, K), we show that the optimal trade-off between storage, µ, and the download cost, D(µ), is given by the lower convex hull of the N pairs t N

BackgroundXyloglucan (XyG) is a ubiquitous and fundamental polysaccharide of plant cell walls. Due to its structural complexity, XyG requires a combination of backbone-cleaving and sidechain-debranching enzymes for complete deconstruction into its component monosaccharides. The soil saprophyte Cellvibrio japonicus has emerged as a genetically tractable model system to study biomass saccharification, in part due to its innate capacity to utilize a wide range of plant polysaccharides for growth. Whereas the downstream debranching enzymes of the xyloglucan utilization system of C. japonicus have been functionally characterized, the requisite backbone-cleaving endo-xyloglucanases were unresolved.ResultsCombined bioinformatic and transcriptomic analyses implicated three glycoside hydrolase family 5 subfamily 4 (GH5_4) members, with distinct modular organization, as potential keystone endo-xyloglucanases in C. japonicus. Detailed biochemical and enzymatic characterization of the GH5_4 modules of all three recombinant proteins confirmed particularly high specificities for the XyG polysaccharide versus a panel of other cell wall glycans, including mixed-linkage beta-glucan and cellulose. Moreover, product analysis demonstrated that all three enzymes generated XyG oligosaccharides required for subsequent saccharification by known exo-glycosidases. Crystallographic analysis of GH5D, which was the only GH5_4 member specifically and highly upregulated during growth on XyG, in free, product-complex, and active-site affinity-labelled forms revealed the molecular basis for the exquisite XyG specificity among these GH5_4 enzymes. Strikingly, exhaustive reverse-genetic analysis of all three GH5_4 members and a previously biochemically characterized GH74 member failed to reveal a growth defect, thereby indicating functional compensation in vivo, both among members of this cohort and by other, yet unidentified, xyloglucanases in C. japonicus. Our systems-based analysis indicates distinct substrate-sensing (GH74, GH5E, GH5F) and attack-mounting (GH5D) functions for the endo-xyloglucanases characterized here.ConclusionsThrough a multi-faceted, molecular systems-based approach, this study provides a new insight into the saccharification pathway of xyloglucan utilization system of C. japonicus. The detailed structural–functional characterization of three distinct GH5_4 endo-xyloglucanases will inform future bioinformatic predictions across species, and provides new CAZymes with defined specificity that may be harnessed in industrial and other biotechnological applications.Electronic supplementary materialThe online version of this article (10.1186/s13068-018-1039-6) contains supplementary material, which is available to authorized users.

The heteropolysaccharide xyloglucan (XyG) comprises up to one‐quarter of the total carbohydrate content of terrestrial plant cell walls and, as such, represents a significant reservoir in the global carbon cycle. The complex composition of XyG requires a consortium of backbone‐cleaving endo‐xyloglucanases and side‐chain cleaving exo‐glycosidases for complete saccharification. The biochemical basis for XyG utilization by the model Gram‐negative soil saprophytic bacterium Cellvibrio japonicus is incompletely understood, despite the recent characterization of associated side‐chain cleaving exo‐glycosidases. We present a detailed functional and structural characterization of a multimodular enzyme encoded by gene locus CJA_2477. The CJA_2477 gene product comprises an N‐terminal glycoside hydrolase family 74 (GH74) endo‐xyloglucanase module in train with two carbohydrate‐binding modules (CBMs) from families 10 and 2 (CBM10 and CBM2). The GH74 catalytic domain generates Glc4‐based xylogluco‐oligosaccharide (XyGO) substrates for downstream enzymes through an endo‐dissociative mode of action. X‐ray crystallography of the GH74 module, alone and in complex with XyGO products spanning the entire active site, revealed a broad substrate‐binding cleft specifically adapted to XyG recognition, which is composed of two seven‐bladed propeller domains characteristic of the GH74 family. The appended CBM10 and CBM2 members notably did not bind XyG, nor other soluble polysaccharides, and instead were specific cellulose‐binding modules. Taken together, these data shed light on the first step of xyloglucan utilization by C. japonicus and expand the repertoire of GHs and CBMs for selective biomass analysis and utilization. Database Structural data have been deposited in the RCSB protein database under the Protein Data Bank codes: http://www.rcsb.org/pdb/search/structidSearch.do?structureId=5FKR, http://www.rcsb.org/pdb/search/structidSearch.do?structureId=5FKS, http://www.rcsb.org/pdb/search/structidSearch.do?structureId=5FKT and http://www.rcsb.org/pdb/search/structidSearch.do?structureId=5FKQ.