scholarly journals Parameter estimation in fluorescence recovery after photobleaching: quantitative analysis of protein binding reactions and diffusion

2021 ◽  
Vol 83 (1) ◽  
Author(s):  
Daniel E. Williamson ◽  
Erik Sahai ◽  
Robert P. Jenkins ◽  
Reuben D. O’Dea ◽  
John R. King
Keyword(s):  
Fluorescence Recovery After Photobleaching ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Fluorescence Recovery ◽  
Model Parameters ◽  
Biological Parameters ◽  
Curve Approximation ◽  
Experimental Parameters ◽  
And Diffusion

AbstractFluorescence recovery after photobleaching (FRAP) is a common experimental method for investigating rates of molecular redistribution in biological systems. Many mathematical models of FRAP have been developed, the purpose of which is usually the estimation of certain biological parameters such as the diffusivity and chemical reaction rates of a protein, this being accomplished by fitting the model to experimental data. In this article, we consider a two species reaction–diffusion FRAP model. Using asymptotic analysis, we derive new FRAP recovery curve approximation formulae, and formally re-derive existing ones. On the basis of these formulae, invoking the concept of Fisher information, we predict, in terms of biological and experimental parameters, sufficient conditions to ensure that the values all model parameters can be estimated from data. We verify our predictions with extensive computational simulations. We also use computational methods to investigate cases in which some or all biological parameters are theoretically inestimable. In these cases, we propose methods which can be used to extract the maximum possible amount of information from the FRAP data.

Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200003 ◽  
Author(s):  
Robert A. Van Gorder
Keyword(s):  
Autonomous Systems ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Time Dependent ◽  
Model Parameters ◽  
Time Varying ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Dependent Model ◽  
Spatio Temporal

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

scholarly journals Analysis of Wave Solutions of an Adhenovirus-Tumor Cell System

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Baba Issa Camara ◽  
Houda Mokrani
Keyword(s):  
Gene Therapy ◽  
Tumor Cell ◽  
Management Strategy ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Theoretical Implication ◽  
Cell System ◽  
Model Parameters ◽  
Wave Solutions ◽  
Existence Of Periodic Solutions

We discuss biological background and mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reaction-diffusion system, we model interactions between gliom cells and viruses. We establish some sufficient conditions on model parameters which guarantee the permanence of the system and the existence of periodic solutions. Our study has experimental and theoretical implication in the perspective management strategy of therapy.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Conditions for the local and global asymptotic stability of the time–fractional Degn–Harrison system

2020 ◽  
Vol 21 (7-8) ◽  
pp. 749-759
Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linearization Method ◽  
Direct Lyapunov Method ◽  
Fractional Systems ◽  
Reaction Diffusion Model ◽  
Theoretical Results

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.

scholarly journals Improved Model of Fluorescence Recovery Expands the Application of Multiphoton Fluorescence Recovery after Photobleaching in Vivo

2009 ◽  
Vol 96 (12) ◽  
pp. 5082-5094 ◽  
Author(s):  
Kelley D. Sullivan ◽  
William H. Sipprell ◽  
Edward B. Brown ◽  
Edward B. Brown
Keyword(s):  
Fluorescence Recovery After Photobleaching ◽  
Fluorescence Recovery ◽  
Improved Model

scholarly journals Rotational dynamics of colloidal spheres probed with fluorescence recovery after photobleaching

2004 ◽  
Vol 120 (9) ◽  
pp. 4517-4529 ◽  
Author(s):  
M. P. Lettinga ◽  
G. H. Koenderink ◽  
B. W. M. Kuipers ◽  
E. Bessels ◽  
A. P. Philipse
Keyword(s):  
Fluorescence Recovery After Photobleaching ◽  
Rotational Dynamics ◽  
Fluorescence Recovery ◽  
Colloidal Spheres

scholarly journals Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Guichen Lu
Keyword(s):  
Reaction Diffusion ◽  
Complete Characterization ◽  
Propagation Model ◽  
Transition Theory ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Biological Parameters ◽  
Dynamical Transition ◽  
Attractor Bifurcation

We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.

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