Optimizing the human learnability of abstract network representations.

Precisely how humans process relational patterns of information in knowledge, language, music, and society is not well understood. Prior work in the field of statistical learning has demonstrated that humans process such information by building internal models of the underlying network structure. However, these mental maps are often inaccurate due to limitations in human information processing. The existence of such limitations raises clear questions: Given a target network that one wishes for a human to learn, what network should one present to the human? Should one simply present the target network as-is, or should one emphasize certain parts of the network to proactively mitigate expected errors in learning? To investigate these questions, we study the optimization of network learnability in a computational model of human learning. Evaluating an array of synthetic and real-world networks, we find that learnability is enhanced by reinforcing connections within modules or clusters. In contrast, when networks contain significant core-periphery structure, we find that learnability is best optimized by reinforcing peripheral edges between low-degree nodes. Overall, our findings suggest that the accuracy of human network learning can be systematically enhanced by targeted emphasis and de-emphasis of prescribed sectors of information.

Architecture and evolution of semantic networks in mathematics texts.

Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here, we study the topological structure of semantic networks reflecting mathematical concepts and their relations in college-level linear algebra texts. We hypothesize that these networks will exhibit structural order, reflecting the logical sequence of topics that ensures accessibility. We find that the networks exhibit strong core-periphery architecture, where a dense core of concepts presented early is complemented with a sparse periphery presented evenly throughout the exposition; the latter is composed of many small modules each reflecting more narrow domains. Using tools from applied topology, we find that the expositional evolution of the semantic networks produces and subsequently fills knowledge gaps, and that the density of these gaps tracks negatively with community ratings of each textbook. Broadly, our study lays the groundwork for future efforts developing optimal design principles for textbook exposition and teaching in a classroom setting.

Structural and Functional Influence of the Glycine-Rich Loop G302GGGY on the Catalytic Tyrosine of Histone Deacetylase 8.

Histone deacetylase 8 (HDAC8) catalyzes the hydrolysis of acetyl-l-lysine to yield products l-lysine and acetate through a mechanism in which a nucleophilic water molecule is activated by a histidine general base and a catalytic metal ion (Zn2+ or Fe2+). Acetyl-l-lysine also requires activation by metal coordination and a hydrogen bond with catalytic tyrosine Y306, which also functions in transition state stabilization. Interestingly, Y306 is located in the conserved glycine-rich loop G302GGGY. The potential flexibility afforded by the tetraglycine segment may facilitate induced-fit conformational changes in Y306 between "in" and "out" positions, as observed in related deacetylases. To probe the catalytic importance of the glycine-rich loop in HDAC8, we rigidified this loop by preparing the G302A, G303A, G304A, and G305A mutants and measured their steady state kinetics and determined their X-ray crystal structures. Substantial losses of catalytic efficiency are observed (10-500-fold based on kcat/KM), particularly for G304A HDAC8 and G305A HDAC8. These mutants also exhibit the greatest structural changes for catalytic tyrosine Y306 (1.3-1.7 Å shifts of the phenolic hydroxyl group). Molecular dynamics simulations further indicate that G304 and G305 undergo pronounced structural changes as residue 306 undergoes a transition between "in" and "out" conformations. Thus, the G304A and G305A substitutions likely compromise the position and conformational changes of Y306 required for substrate activation and transition state stabilization. The G302A and G303A substitutions have less severe catalytic consequences, and these substitutions may influence an internal channel through which product acetate is believed to exit.

Biochemical and structural characterization of HDAC8 mutants associated with Cornelia de Lange syndrome spectrum disorders.

Cornelia de Lange Syndrome (CdLS) spectrum disorders are characterized by multiple organ system congenital anomalies that result from mutations in genes encoding core cohesin proteins SMC1A, SMC3, and RAD21, or proteins that regulate cohesin function such as NIPBL and HDAC8. HDAC8 is the Zn(2+)-dependent SMC3 deacetylase required for cohesin recycling during the cell cycle, and 17 different HDAC8 mutants have been identified to date in children diagnosed with CdLS. As part of our continuing studies focusing on aberrant HDAC8 function in CdLS, we now report the preparation and biophysical evaluation of five human HDAC8 mutants: P91L, G117E, H180R, D233G, and G304R. Additionally, the double mutants D233G-Y306F and P91L-Y306F were prepared to enable cocrystallization of intact enzyme-substrate complexes. X-ray crystal structures of G117E, P91L-Y306F, and D233G-Y306F HDAC8 mutants reveal that each CdLS mutation causes structural changes that compromise catalysis and/or thermostability. For example, the D233G mutation disrupts the D233-K202-S276 hydrogen bond network, which stabilizes key tertiary structure interactions, thereby significantly compromising thermostability. Molecular dynamics simulations of H180R and G304R HDAC8 mutants suggest that the bulky arginine side chain of each mutant protrudes into the substrate binding site and also causes active site residue Y306 to fluctuate away from the position required for substrate activation and catalysis. Significantly, the catalytic activities of most mutants can be partially or fully rescued by the activator N-(phenylcarbamothioyl)-benzamide, suggesting that HDAC8 activators may serve as possible leads in the therapeutic management of CdLS.