Nonlinear dynamics of nanobiophysics / / Slobodan Zdravković and Dalibor Chevizovich

• Record Nr.: UNISA996503463903316
• Autore: Zdravković Slobodan
• Pubbl/distr/stampa: Singapore : , : Springer, , [2023]; ©2023
• ISBN: 981-19-5323-6
• Descrizione fisica: 1 online resource (369 pages)
• Disciplina: 571.43
• Soggetti: Biomechanics; Nonlinear mechanics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Contents -- Introduction -- References -- The Insights into Richness of Nonlinear Schrödinger Equation -- 1 Introduction -- 2 Nonlinear Schrödinger Equation -- 2.1 Modulation Instability -- 2.2 Solitons -- 2.3 Breathers -- 2.4 Rogue Waves -- 3 Generalized NLSE -- 3.1 Higher-Order NLSE -- 3.2 Driven NLSE with Quadratic-Cubic Nonlinearity -- 4 Applications of Nonlinear Localized Waves in Biology -- 5 Conclusion -- References -- Nonlinear Dynamics of DNA Chain -- 1 DNA Dynamics -- 2 Resonance Mode and DNA Opening -- 3 Demodulated Standing Solitary Wave and DNA-RNA Transcription -- References -- Nonlinear Dynamics of DNA Chain with Long-Range Interactions -- 1 Introduction -- 2 Long-Range Interactions in Biological Systems -- 2.1 Long-Range Interactions of the Kac-Baker Type -- 2.2 Long-Range Interactions of the Power-Law Type -- 2.3 Physical Nature of Long-Range Interactions of the Power-Law Type -- 3 Long-Range Interactions in the HPB Model -- 3.1 Model Hamiltonian -- 3.2 Equations of Motions -- 3.3 Discrete Derivation Operator Technique -- 3.4 Soliton Solutions -- 4 Long-Range Interactions in the HPB Model with Damping Effect -- 4.1 Long-Range Hydrodynamical Damping Forces and Equations of Motions -- 4.2 Dissipative Soliton Solution -- 5 Conclusion -- References -- Trajectories of DNA Kinks -- 1 Kinks of Homogeneous DNA -- 2 Kink Trajectories in Homogeneous DNA -- 2.1 Kink Trajectories in the Case of Absence of External Field ; -- 2.2 Kink Trajectories in the Case of Constant External Field M0 -- 2.3 Kink Trajectories in the Case of Periodic External Field with Constant Frequency M( t ) = M0 cos(2Ωt) -- 2.4 Kink Trajectories in the Case of Periodic External Field with Slowly Varying Frequency M( t ) = M0 cos(Ωt - αt2 /2) -- 2.5 Kink Trajectories in the Case of on/off External Field -- 3 Kink Trajectories in Inhomogeneous DNA.; 3.1 Method of Concentrations -- 3.2 Method of Blocks and Its Application to Kinks of IFNA17 Gene -- 3.3 Kink Trajectories in the pBR322 Plasmid -- 4 Conclusions. Further Development and Perspectives of the Methods of Trajectories -- References -- Conformational B-A-Transition in the DNA Molecule Model -- References -- Soliton Excitations in a Twist-Opening Nonlinear DNA Model -- 1 Twist-Opening Nonlinear Model of DNA Double Helix -- 2 Dispersion Law -- 3 Continuum Approximation -- 4 Nonlinear Schrödinger Equation -- 5 Korteveg-de Vries Equation -- 6 Conclusion -- References -- Vibron Self-trapping in Quasi-One-Dimensional Biomolecules: Non-adiabatic Polaron Approach -- 1 Introduction -- 2 About Energy Processes Inside a Living Cell -- 2.1 Hydrolysis of Adenosine Triphosphate -- 3 Quasi-1D Biomolecules -- 3.1 Proteins: What Is Their Role in the Living Cell? -- 3.2 Proteins: What Is Their Basic Structure? -- 4 Intra-molecular Vibrational Excitation in Biomolecules: Quasi-Free Excitations or Polarons? -- 4.1 The Storage of the Energy Quanta in Biomolecules: Amide-I Mode -- 4.2 A Short Excursion to the Absorption Spectra of the Crystalline Acetanilide -- 4.3 Beyond Davydov Model -- 4.4 Further Investigations in the Framework of Non-adiabatic Polaron Theory -- 5 Theory of Exciton Self-trapped States: Non-adiabatic Polaron -- 5.1 Starting Hamiltonian -- 5.2 Classification of Self-trapped States and Criteria for Their Formation -- 5.3 Vibrons in Biomolecules -- 5.4 Theory of ST States of a Single Vibron Excitation in Quasi-1D Crystal Structure: Method of the Unitary Transformation -- 6 Results and the Discussion -- 7 Conclusion -- 8 Appendix -- 8.1 The Two Useful Relations -- 8.2 Some Important Operator Identities -- 8.3 Formulas of Lang-Firsov Unitary Transformation -- 8.4 The Mean Values of the Functions of Bose Operators -- References.; Quantum Correlation Effects in Biopolymer Structures -- 1 Introduction -- 2 Description of Quantum Correlations -- 2.1 Quantum Correlation Functions -- 2.2 Properties of the Quantum Correlation Functions -- 2.3 Quasi-Distribution Functions and Quantum Characteristic Functions -- 2.4 Non-classical Phenomena -- 2.5 Entanglement -- 3 Model Description of Quantum Correlations in Biomolecules -- 3.1 Quantum Mechanical Model of Protein Molecules -- 3.2 Influence of the Environment -- 3.3 Vibron Quantum Correlations -- 4 Conclusion -- References -- Nonlinear Dynamics of Microtubules -- 1 Introduction -- 2 Longitudinal Models for MT Dynamics -- 2.1 More General Procedure Within Longitudinal Models for MT Dynamics -- 2.2 Application of Morse Potential Energy -- 3 Angular Models for MT Dynamics -- 3.1 A Series Expansion Unknown Function Method Within the -Model for MT Dynamics -- 3.2 General Model for MT Dynamics -- Appendix -- References -- Calcium Signaling Along Actin Filaments in Stereocilia Controls Hair-Bundle Motility -- 1 Calcium Signaling -- 2 Polyelectrolyte Character of Actin Filaments -- 3 Models of Pulsatile Waves of Ca2+ Ions Along Actin Filaments -- 3.1 Electrochemical Model -- 3.2 The Model of F-Actin as a Nonlinear Transmission Line -- 4 Ca2+-Dependent Myosin-Based Hair-bundle Motility Adaptation -- 4.1 The Coupled Dynamics of Adaptation Motors and Transduction Channels of Stereocilia -- 5 Discussion and Conclusions -- References -- Theoretical Investigation of Interacting Molecular Motors -- 1 Introduction -- 2 Molecular Motors -- 3 Theoretical Approach (TASEP) ; -- 3.1 Boundary Conditions -- 3.2 Update Rules -- 3.3 Monte Carlo Simulations: Numerical Approach -- 3.4 Master Equation -- 3.5 Mathematical Framework -- 3.6 Mean-Field Approximation -- 4 Development of TASEP Models -- 5 Theoretical Model: TASEP with Interactions.; 5.1 Model Description -- 6 Conclusion -- References.