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Learning algebra concepts, particularly those involving functions, is crucial yet challenging in mathematics education. Research suggests that collaborative learning, where students work in small teams to solve math problems, can support conceptual learning. However, collaborative problem solving (CPS) is complex and requires students’ social and cognitive skills for success. This study investigates the impacts of guided facilitation on supporting CPS in mathematics tasks during small-team collaboration. Using epistemic network analysis and sequential pattern mining, we analyzed chat logs from student teams and human facilitators and compared the interactions in facilitated and unfacilitated teams. Results indicated that near-peer facilitation effectively promoted constructive behaviors like multiple turns of social negotiation, while reducing inappropriate communications. Different facilitation strategies, such as encouraging students to respond to each other or clarify their statements, elicited targeted CPS behaviors, possibly leading to improved team performance. Findings have practical implications for facilitating CPS in mathematics classrooms. 

Stretched-exponential protein refolding kinetics, first observed decades ago, were attributed to a nonnative ensemble of structures with parallel, non-interconverting folding pathways. However, the structural origin of the large energy barriers preventing interconversion between these folding pathways is unknown. Here, we combine simulations with limited proteolysis (LiP) and cross-linking (XL) mass spectrometry (MS) to study the protein phosphoglycerate kinase (PGK). Simulations recapitulate its stretched-exponential folding kinetics and reveal that misfolded states involving changes of entanglement underlie this behavior: either formation of a nonnative, noncovalent lasso entanglement or failure to form a native entanglement. These misfolded states act as kinetic traps, requiring extensive unfolding to escape, which results in a distribution of free energy barriers and pathway partitioning. Using LiP-MS and XL-MS, we propose heterogeneous structural ensembles consistent with these data that represent the potential long-lived misfolded states PGK populates. This structural and energetic heterogeneity creates a hierarchy of refolding timescales, explaining stretched-exponential kinetics. 

One-third of protein domains in the CATH database contain a recently discovered tertiary topological motif: non-covalent lasso entanglements, in which a segment of the protein backbone forms a loop closed by non-covalent interactions between residues and is threaded one or more times by the N- or C-terminal backbone segment. Unknown is how frequently this structural motif appears across the proteomes of organisms. And the correlation of these motifs with various classes of protein function and biological processes have not been quantified. Here, using a combination of protein crystal structures, AlphaFold2 predictions, and Gene Ontology terms we show that in E. coli, S. cerevisiae and H. sapiens that 71%, 52% and 49% of globular proteins contain one-or-more non-covalent lasso entanglements in their native fold, and that some of these are highly complex with multiple threading events. Further, proteins containing these tertiary motifs are consistently enriched in certain functions and biological processes across these organisms and depleted in others, strongly indicating an influence of evolutionary selection pressures acting positively and negatively on the distribution of these motifs. Together, these results demonstrate that non-covalent lasso entanglements are widespread and indicate they may be extensively utilized for protein function and subcellular processes, thus impacting phenotype. 

This paper explores the differences between two types of natural language conversations between a student and pedagogical agent(s). Both types of conversations were created for formative assessment purposes. The first type is conversation-based assessment created via knowledge engineering which requires a large amount of human effort. The second type, which is less costly to produce, uses prompt engineering for LLMs based on Evidence-Centered design to create these conversations and glean evidence about students¿½f knowledge, skills and abilities. The current work compares linguistic features of the artificial agent(s) discourse moves in natural language conversations created by the two methodologies. Results indicate that more complex conversations are created by the prompt engineering method which may be more adaptive than the knowledge engineering approach. However, the affordances of prompt engi-neered, LLM generated conversation-based assessment may create more challenges for scoring than the original knowledge engineered conversations. Limitations and implications are dis-cussed. 

Abstract Some misfolded protein conformations can bypass proteostasis machinery and remain soluble in vivo. This is an unexpected observation, as cellular quality control mechanisms should remove misfolded proteins. Three questions, then, are: how do long-lived, soluble, misfolded proteins bypass proteostasis? How widespread are such misfolded states? And how long do they persist? We address these questions using coarse-grain molecular dynamics simulations of the synthesis, termination, and post-translational dynamics of a representative set of cytosolic E. coli proteins. We predict that half of proteins exhibit misfolded subpopulations that bypass molecular chaperones, avoid aggregation, and will not be rapidly degraded, with some misfolded states persisting for months or longer. The surface properties of these misfolded states are native-like, suggesting they will remain soluble, while self-entanglements make them long-lived kinetic traps. In terms of function, we predict that one-third of proteins can misfold into soluble less-functional states. For the heavily entangled protein glycerol-3-phosphate dehydrogenase, limited-proteolysis mass spectrometry experiments interrogating misfolded conformations of the protein are consistent with the structural changes predicted by our simulations. These results therefore provide an explanation for how proteins can misfold into soluble conformations with reduced functionality that can bypass proteostasis, and indicate, unexpectedly, this may be a wide-spread phenomenon.