We study approximate string matching in connection with two string distance functions that are computable in linear time. The first function is based on the so-called $q$-grams. An algorithm is given for the associated string matching problem that finds the locally best approximate occurences of pattern $P$, $|P|=m$, in text $T$, $|T|=n$, in time $O(n\log (m-q))$. The occurences with distance $\leq k$ can be found in time $O(n\log k)$. The other distance function is based on finding maximal common substrings and allows a form of approximate string matching in time $O(n)$. Both distances give a lower bound for the edit distance (in the unit cost model), which leads to fast hybrid algorithms for the edit distance based string matching.
Circadian rhythms are endogenous 24-hour oscillations that regulate physiology, metabolism, sleep-wake cycles, and cellular homeostasis. Drosophila melanogaster, a genetically tractable model organism, has played a foundational role in uncovering the molecular mechanisms of circadian rhythms. The discovery of major clock genes, including period (per), timeless (tim), clock (clk), cycle (cyc), double time (dbt), and regulators such as Casein kinase 2 (CK2), emerged primarily from Drosophila research. CK2 operates as a critical post-translational regulator of PER protein phosphorylation, stability, nuclear entry, and degradation. Because PER dynamics dictate the timing and robustness of circadian rhythms in both flies and mammals, altered CK2 activity can profoundly impact rhythmic behaviour. CK2 dysregulation contributes not only to circadian disruption in Drosophila but also models broader pathological processes relevant to cancer, metabolic disease, neurodegeneration, and psychiatric disorders. This review synthesises CK2's molecular role in the Drosophila clock system, includes insights from computational modelling of CK2-PER dynamics, integrates tables throughout the text, and summarises the implications of dysregulated PER phosphorylation for human health.
Cellular adaptation to environmental changes relies on the dynamic remodeling of subcellular structures. Among these, sarcomere structures are fundamental to the organization and function of the cytoskeletal architecture. In muscle-type cells, sarcomeres exhibit ordered structures of consistent lengths, optimized for stable force generation. By contrast, nonmuscle-type cells display a higher degree of structural variability, with sarcomeres of varying lengths that contribute not only to force generation but also to adaptive remodeling upon environmental cues. While these differences in sarcomere structures have traditionally been attributed to the unique properties of specific proteins expressed in each cell type, the functional implications of such structural variability remain unclear. Here, we present a nonequilibrium physics framework to elucidate the role of sarcomere variability in cytoskeletal adaptation. Specifically, we demonstrate that the effective binding strength of sarcomere components can be evaluated by analyzing structural randomness using Shannon entropy. The increased entropy associated with the inherent randomness of sarcomere structures in nonmuscle-type cells lowers the energy barrier for cytoskeletal remodeling, enabling flexible adaptation to environmental demands. Meanwhile, the ordered sarcomere arrangements in muscle-type cells correspond to higher binding energies and more stable cytoskeletal configurations. Although structural disorder is often regarded as unfavorable in terms of stability, our study suggests that it plays a key role in enabling adaptive responses in cellular systems.
Keshav B. Patel, Wolfgang Bergmeier, Aaron L. Fogelson
Through experimental studies, many details of the pathway of integrin $α_{\rm IIb}β_3$ activation by ADP during the platelet aggregation process have been mapped out. ADP binds to two separate G protein coupled receptors on platelet surfaces, leading to alterations in the regulation of the small GTPase RAP1. We seek to (1) gain insights into the relative contributions of both pathways to RAP1-mediated integrin activation and to (2) predict wildtype and mutated cell behavior in response to a continuous range of external agonist concentrations. To this end, we develop a dynamical systems model detailing the action of each protein in the two pathways up to the regulation of RAP1. We perform a parameter estimation using flow cytometry data to determine a number of unknown rate constants. We then validate with already published data; in particular, the model confirmed the effect of impaired P2Y$_1$ receptor desensitization or reduced RASA3 expression on RAP1 activation. We then predict the effect of protein expression levels on integrin activation and show that components of the P2Y$_{12}$ pathway are critical to the regulation of integrin. This model aids in our understanding of interindividual variability in platelet response to ADP and therapeutic P2Y$_{12}$ inhibition. It also provides a more detailed view of platelet activation in the ongoing mathematical study of platelet aggregation.
We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at crosslinks to form a network. Assuming that the inter-crosslink distance is much shorter than the lengthscale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterising the cell rheology through the force-displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.
Zohreh Nouripour Sisakhti, Masoume Malmir, Masoumeh Bagheri Bisafar
et al.
AbstractIn the present study, a natural-based heterogeneous catalyst is synthesized. For this purpose, nano-hydroxyapatite (n-HA) is prepared, silica-modified and functionalized with phthalimide. Finally, Ag2+was immobilized onto n-HA/Si-PA-SC and reduced to Ag nanoparticles byBellis perennisflowers extract. n-HA/Si-PA-SC@Ag characterized by TGA, FTIR, SEM/EDX, XRD, TEM, BET and ICP-AES techniques. Moreover, metal–ligand interactions in n-HA/Si-PA-SC@Ag complex models were assessed to make a quantitative representation for the immobilization behavior of Ag NPs on the surface of n-HA/Si-PA-SC through quantum chemistry computations. Furthermore, the performance of n-HA/Si-PA-SC@Ag was studied in the nitroarene, methylene blue and congo red reductions. Finally, the recyclability study as well as Ag-leaching verified that, n-HA/Si-PA-SC@Ag was stable and reused-up to four times without losing its activity.