A Ca2+^{2+} puff model based on integrodifferential equations

The calcium (Ca$^{2+}$) signalling system is important for many cellular processes within the human body. Signals are transmitted within the cell by releasing Ca$^{2+}$ from the endoplasmic reticulum (ER) into the cytosol via clusters of Ca$^{2+}$ channels. Mathematical models of Ca$^{2+}$ release via inositol 1,4,5-trisphosphate receptors (IP$_{3}$R) help with understanding underlying Ca$^{2+}$ dynamics but data-driven modelling of stochastic Ca$^{2+}$ release events, known as Ca$^{2+}$ puffs, is a difficult challenge. Parameterising Markov models for representing the IP$_{3}$R with steady-state single channel data obtained at fixed combinations of the ligands Ca$^{2+}$ and inositol-trisphosphate (IP$_{3}$) has previously been demonstrated to be insufficient. However, by extending an IP$_{3}$R model based on steady-state data with an integral term that incorporates the delayed response of the channel to varying Ca$^{2+}$ concentrations we succeed in generating realistic Ca$^{2+}$ puffs. By interpreting the integral term as a weighted average of Ca$^{2+}$ concentrations that extend over a time interval of length $\tau$ into the past we conclude that the IP$_{3}$R requires a certain amount of memory of past ligand concentrations.Comment: 31 pages, 8 figures, 1 tabl

Computational Explorations in Biomedicine: Unraveling Molecular Dynamics for Cancer, Drug Delivery, and Biomolecular Insights using LAMMPS Simulations

With the rapid advancement of computational techniques, Molecular Dynamics (MD) simulations have emerged as powerful tools in biomedical research, enabling in-depth investigations of biological systems at the atomic level. Among the diverse range of simulation software available, LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) has gained significant recognition for its versatility, scalability, and extensive range of functionalities. This literature review aims to provide a comprehensive overview of the utilization of LAMMPS in the field of biomedical applications. This review begins by outlining the fundamental principles of MD simulations and highlighting the unique features of LAMMPS that make it suitable for biomedical research. Subsequently, a survey of the literature is conducted to identify key studies that have employed LAMMPS in various biomedical contexts, such as protein folding, drug design, biomaterials, and cellular processes. The reviewed studies demonstrate the remarkable contributions of LAMMPS in understanding the behavior of biological macromolecules, investigating drug-protein interactions, elucidating the mechanical properties of biomaterials, and studying cellular processes at the molecular level. Additionally, this review explores the integration of LAMMPS with other computational tools and experimental techniques, showcasing its potential for synergistic investigations that bridge the gap between theory and experiment. Moreover, this review discusses the challenges and limitations associated with using LAMMPS in biomedical simulations, including the parameterization of force fields, system size limitations, and computational efficiency. Strategies employed by researchers to mitigate these challenges are presented, along with potential future directions for enhancing LAMMPS capabilities in the biomedical field.Comment: 39 pages- 10 figure