Viña del Mar University

Carbonic anhydrase isoforms I and II (hCA-I and hCA-II) are metalloenzymes involved in essential physiological processes and represent relevant therapeutic targets for disorders such as glaucoma and osteoporosis. Chalcones have emerged as promising scaffolds for carbonic anhydrase inhibition; however, their structure-activity relationships, particularly for non-sulfonamide derivatives, remain insufficiently explored from a computational point of view. In this study, a dataset of 118 chalcone derivatives has been analyzed by using a three-dimensional quantitative structure-activity relationship (3D-QSAR) modeling, which comprises Comparative Molecular Field Analysis (CoMFA) and Comparative Molecular Similarity Index Analysis (CoMSIA). The developed models exhibited strong internal consistency and predictive capability for both isoforms. For hCA-I, steric, electrostatic, hydrophobic, and hydrogen bond acceptor fields has been identified as key contributors to inhibitory activity, whereas for hCA-II, hydrogen bond donor features played a more prominent role. Molecular docking and molecular dynamics simulations have been employed as complementary approaches to analyze ligand-protein interactions and binding stability. In addition, quantum chemical descriptors, derived from density functional theory, that have been integrated with the 3D-QSAR analysis, reveal a consistent correspondence between contour map features and the distribution of frontier molecular orbitals and molecular electrostatic potential. Furthermore, ADME-based pharmacokinetic properties of the proposed compounds have been evaluated to assess their potential drug-likeness. Based on the integrated computational analysis, six new chalcone derivatives, with predicted inhibitory activity in the nanomolar range, are proposed. Overall, this study provides a consistent physicochemical framework for understanding the inhibitory activity of chalcone derivatives and highlights key molecular features that may guide the modulation of activity across hCA-I and hCA-II isoforms.

Research on the teaching and learning of linear algebra has been ongoing for several decades, but it has recently been renewed in the context of non-routine tasks and technological ecosystems, including artificial intelligence. This article analyzes two key transitions: (a) from school-level geometry and algebra to linear algebra, and (b) between different paradigms of linear algebra. We propose a fundamental situation in which the goal is to find the vertices of a polygon given its midpoints. This problem can be modelled using systems of linear equations that may have a unique solution, infinitely many, or none. The situation was divided into three tasks and implemented in three universities in the Valparaíso region that train prospective mathematics teachers. Thirty pre-service teachers participated. Data collected included audio recordings, screen captures, and written productions. The analysis was conducted using the categories of the Mathematical Working Space and the paradigms of linear algebra. Results show that most students were able to transition from geometry to linear algebra, mainly within the first paradigm. The mathematical work was predominantly semiotic and instrumental, but a gradual increase in discursive work was observed all along the didactical situation. Various digital tools were used—mainly GeoGebra and MatrixCalculator, with some use of Wolfram Alpha and ChatGPT—serving to both find algebraic solutions and validate them geometrically. The findings suggest that a long sequence of several open tasks involving domain changes and diverse technologies can support the introduction of linear algebra in teacher education.

Handgrip strength (HGS) has been considered as an indicator of muscle strength and overall physical fitness, with increasing relevance in sports science for talent identification and performance monitoring. However, no bibliometric study has been conducted to map the HGS research landscape in athletic contexts. A bibliometric analysis was conducted in the Web of Science Core Collection database, retrieving 229 publications. Typical bibliometric laws (i.e., Price’s, Bradford’s, Lotka’s, and Zipf’s) were employed to analyze publication trends, core journals, influential authors, country contributions, and keyword co-occurrences. Annual publications increased exponentially, especially after 2019, reaching 37 documents in 2024. The Journal of Strength and Conditioning Research and Journal of Sports Medicine and Physical Fitness were the most prominent journals. The United States and Spain led in productivity and impact. Key research themes included strength, performance, body composition, and physical fitness, with HGS demonstrating significant associations with sport tasks such as throwing, racquet sports, and weightlifting. HGS constitutes an accessible and valuable tool for assessing and predicting athletic performance, especially in sports requiring upper body strength and coordination. Future research should aim to expand database inclusion and address identified gaps, such as the relationship between HGS training and sport-specific outcomes.

We study periodic dynamics and error-threshold behavior in a delayed quasispecies model consisting of a master sequence (x0) and two mutant populations (x1,x2). The system, formulated as delay differential equations with time-periodic replication rates, yields new conditions for the existence and absence of T-periodic solutions. Using topological degree arguments, we show that when mutation probabilities (Qji) lie strictly between 0 and 1 and at least one fitness function (fj) is periodic, the system supports nontrivial positive periodic orbits, with or without backward mutations. This shows that fluctuating environments, such as circadian or treatment-induced cycles, can sustain oscillatory genotype distributions. Conversely, if mutations are strictly unidirectional and the master sequence is consistently dominated in fitness, no positive T-periodic orbit arises. In this regime, the master sequence decays monotonically to extinction without time delays, while time delays induce non-monotonic decay, recovering the classical error-threshold phenomenon and linking it to cancer-related quasispecies dynamics.

In this research, we present a generalized quasispecies model in which population growth is governed by an arbitrary nonlinear function incorporating time delays. We begin by demonstrating that, under the constant population constraint, the dynamics of the system with time delays remain confined to the invariant manifold for both forward and backward time evolution. Furthermore, we establish that in this modified quasispecies model, defined on a single-peak fitness landscape, in the presence of backward mutation and periodic fluctuations in replication rates and in replication probabilities, the concentration of the ith replicating species exhibits a periodic behavior in time independent of the magnitude of the time delays. Specifically, this concentration oscillates between the minimum and maximum values of the probabilities Q_ji associated with erroneous replication; that is, the probability that a mutated replicator of type j produces an offspring of type i. Moreover, under the presence of time delays and non-constant periodic fluctuations in replication rates, we show that if the probability that a mutated replicator of type j produces an offspring of type i remains constant across all replicators, then the unique positive periodic solution is necessarily a constant solution.