Single-molecule experiments in biological physics: methods and applications

I review single-molecule experiments (SME) in biological physics. Recent technological developments have provided the tools to design and build scientific instruments of high enough sensitivity and precision to manipulate and visualize individual molecules and measure microscopic forces. Using SME it is possible to: manipulate molecules one at a time and measure distributions describing molecular properties; characterize the kinetics of biomolecular reactions and; detect molecular intermediates. SME provide the additional information about thermodynamics and kinetics of biomolecular processes. This complements information obtained in traditional bulk assays. In SME it is also possible to measure small energies and detect large Brownian deviations in biomolecular reactions, thereby offering new methods and systems to scrutinize the basic foundations of statistical mechanics. This review is written at a very introductory level emphasizing the importance of SME to scientists interested in knowing the common playground of ideas and the interdisciplinary topics accessible by these techniques. The review discusses SME from an experimental perspective, first exposing the most common experimental methodologies and later presenting various molecular systems where such techniques have been applied. I briefly discuss experimental techniques such as atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers (MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I then present several applications of SME to the study of nucleic acids (DNA, RNA and DNA condensation), proteins (protein-protein interactions, protein folding and molecular motors). Finally, I discuss applications of SME to the study of the nonequilibrium thermodynamics of small systems and the experimental verification of fluctuation theorems. I conclude with a discussion of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond. Matt

Behaviors and global dynamics of population models living in periodically fluctuating environments

Dans ce projet, nous étudions certaines classes d équations non-linéaires aux différences pour toutes les valeurs non-négatives admissibles de paramètres et de conditions initiales. Dans la première partie, nous présentons quelques définitions initiales et nécessaires de la stabilité dans la littérature des équations aux différences. Nous exprimons également plusieurs résultats connus et quelques théorèmes qui seront utiles dans notre recherche à la suite. Dans le deuxièllle chapitre, on étudie l'intervalle invariant, le caractère des sellli-cycles, la stabilité globale, et le "boundedness" de l'équation aux différences [Formule mathématique]. Dans la deuxième partie de ce travail, nous étudions la famille de modèles de la population, d'ordre supérieur, de l'équation logistique non-autonorne [Formule mathématique]. En particulier, le comporternent périodique, l'attractivité des solutions et la stabilité de solutions sont examinés en détail. Ce modèle représente les différentes croissances de population telles que la plupart des saumons et "spruce budworms" ayant assez de nourriture (feuillage). L'impact du caractère saisonnier , qui est indubitablenlent présent dans la croissance de la population, sur le comporternent des solutions (croissance de la population) est également envisagé. Enfin, nous présentons un modèle déterministe de l'infection par le VIH (virus d'immunodéficience hurnaine) en présence de la trithérapie. Puis la stabilité globale asymptotique de l'équilibre "disease-free" et l'équilibre endémique sont étudiés pour le modèle continu. En outre, le modèle est implicitement estimé par la méthode des différences finies, un système d'équations aux différences, afin de résoudre le système d 'IVP (problème aux valeurs initiales) . La dynamique du modèle estimé est complètement déterminée par une quantité de seuil R appelée le "basic reproduction number". Lorsque le nombre associé à la reproduction est inférieur à l'unité, le résultat indique que l'infection par le VIH peut être éliminée de la personne infectée. Un équilibre stable endémique existe lorsque le nombre associé à la reproduction est supérieur à l'unité (conduisant à la persistance et l'existence du VIH au sein de la personne infectée, puis de la communauté)

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

New developments in Functional and Fractional Differential Equations and in Lie Symmetry

Delay, difference, functional, fractional, and partial differential equations have many applications in science and engineering. In this Special Issue, 29 experts co-authored 10 papers dealing with these subjects. A summary of the main points of these papers follows:Several oscillation conditions for a first-order linear differential equation with non-monotone delay are established in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, whereas a sharp oscillation criterion using the notion of slowly varying functions is established in A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay. The approximation of a linear autonomous differential equation with a small delay is considered in Approximation of a Linear Autonomous Differential Equation with Small Delay; the model of infection diseases by Marchuk is studied in Around the Model of Infection Disease: The Cauchy Matrix and Its Properties. Exact solutions to fractional-order Fokker–Planck equations are presented in New Exact Solutions and Conservation Laws to the Fractional-Order Fokker–Planck Equations, and a spectral collocation approach to solving a class of time-fractional stochastic heat equations driven by Brownian motion is constructed in A Collocation Approach for Solving Time-Fractional Stochastic Heat Equation Driven by an Additive Noise. A finite difference approximation method for a space fractional convection-diffusion model with variable coefficients is proposed in Finite Difference Approximation Method for a Space Fractional Convection–Diffusion Equation with Variable Coefficients; existence results for a nonlinear fractional difference equation with delay and impulses are established in On Nonlinear Fractional Difference Equation with Delay and Impulses. A complete Noether symmetry analysis of a generalized coupled Lane–Emden–Klein–Gordon–Fock system with central symmetry is provided in Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays, and new soliton solutions of a fractional Jaulent soliton Miodek system via symmetry analysis are presented in New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis