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

What's past is prologue: FRAP keeps delivering 50 years later

Fluorescence recovery after photobleaching (FRAP) has emerged as one of the most widely utilized techniques to quantify binding and diffusion kinetics of biomolecules in biophysics. Since its inception in the mid-1970s, FRAP has been used to address an enormous array of questions including the characteristic features of lipid rafts, how cells regulate the viscosity of their cytoplasm, and the dynamics of biomolecules inside condensates formed by liquid-liquid phase separation. In this perspective, I briefly summarize the history of the field and discuss why FRAP has proven to be so incredibly versatile and popular. Next, I provide an overview of the extensive body of knowledge that has emerged on best practices for quantitative FRAP data analysis, followed by some recent examples of biological lessons learned using this powerful approach. Finally, I touch on new directions and opportunities for biophysicists to contribute to the continued development of this still-relevant research tool.

A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19

The COVID-19 pandemic has ravaged global health and national economies worldwide. Testing and isolation are effective control strategies to mitigate the transmission of COVID-19, especially in the early stage of the disease outbreak. In this paper, we develop a deterministic model to investigate the impact of testing and compliance with isolation on the transmission of COVID-19. We derive the control reproduction number R C , which gives the threshold for disease elimination or prevalence. Using data from New York State in the early stage of the disease outbreak, we estimate R C = 7.989 . Both elasticity and sensitivity analyses show that testing and compliance with isolation are significant in reducing R C and disease prevalence. Simulation reveals that only high testing volume combined with a large proportion of individuals complying with isolation have great impact on mitigating the transmission. The testing starting date is also crucial: the earlier testing is implemented, the more impact it has on reducing the infection. The results obtained here would also be helpful in developing guidelines of early control strategies for pandemics similar to COVID-19.

Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic. We are especially interested in two current topics: effect of vaccination and the universally observed oscillations in infections. We use a nonlinear Susceptible, Infected, & Immune model incorporating a dynamic transmission rate and vaccination policy. The US data provides a starting point for analyzing stability, bifurcations and dynamics in general. Further parametric analysis reveals a saddle-node bifurcation under imperfect vaccination leading to the occurrence of sustained epidemic equilibria. This work points to the tremendous value of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of vaccination, and frequency, phase, and amplitude of transmission rate on the persistent dynamic behavior of the disease.

Inferences from FRAP data are model dependent: A subdiffusive analysis

Fluorescence recovery after photobleaching (FRAP) is a widely used biological experiment to study the kinetics of molecules that react and move randomly. Since the development of FRAP in the 1970s, many reaction-diffusion models have been used to interpret FRAP data. However, intracellular molecules are widely observed to move by anomalous subdiffusion instead of normal diffusion. In this article, we extend a popular reaction-diffusion model of FRAP to the case of subdiffusion modeled by a fractional diffusion equation. By analyzing this reaction-subdiffusion model, we show that FRAP data are consistent with both diffusive and subdiffusive motion in many scenarios. We illustrate this general result by fitting our model to FRAP data from glucocorticoid receptors in a cell nucleus. We further show that the assumed model of molecular motion (normal diffusion or subdiffusion) strongly impacts the biological parameter values inferred from a given experimentally observed FRAP curve. We additionally analyze our model in three simplified parameter regimes and discuss parameter identifiability for varying subdiffusion exponents.

Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems

Mathematical models are critical to understand the spread of pathogens in a population and evaluate the effectiveness of non-pharmaceutical interventions (NPIs). A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence ( I P P ) or the epidemic final size ( E F S ). While most of them optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the I P P and the E F S , while minimizing the intervention's side effects. In this work, based on a new characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets in terms of herd immunity), we study how to minimize the E F S while keeping the I P P controlled at any time. A procedure is proposed to tailor NPIs by separating transient from stationary control objectives: the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.

Iron-Induced Oxidative Stress in Human Diseases

Iron is responsible for the regulation of several cell functions. However, iron ions are catalytic and dangerous for cells, so the cells sequester such redox-active irons in the transport and storage proteins. In systemic iron overload and local pathological conditions, redox-active iron increases in the human body and induces oxidative stress through the formation of reactive oxygen species. Non-transferrin bound iron is a candidate for the redox-active iron in extracellular space. Cells take iron by the uptake machinery such as transferrin receptor and divalent metal transporter 1. These irons are delivered to places where they are needed by poly(rC)-binding proteins 1/2 and excess irons are stored in ferritin or released out of the cell by ferroportin 1. We can imagine transit iron pool in the cell from iron import to the export. Since the iron in the transit pool is another candidate for the redox-active iron, the size of the pool may be kept minimally. When a large amount of iron enters cells and overflows the capacity of iron binding proteins, the iron behaves as a redox-active iron in the cell. This review focuses on redox-active iron in extracellular and intracellular spaces through a biophysical and chemical point of view.

Recent Advances in Fluorescence Recovery after Photobleaching for Decoupling Transport and Kinetics of Biomacromolecules in Cellular Physiology

Among the new molecular tools available to scientists and engineers, some of the most useful include fluorescently tagged biomolecules. Tools, such as green fluorescence protein (GFP), have been applied to perform semi-quantitative studies on biological signal transduction and cellular structural dynamics involved in the physiology of healthy and disease states. Such studies focus on drug pharmacokinetics, receptor-mediated endocytosis, nuclear mechanobiology, viral infections, and cancer metastasis. In 1976, fluorescence recovery after photobleaching (FRAP), which involves the monitoring of fluorescence emission recovery within a photobleached spot, was developed. FRAP allowed investigators to probe two-dimensional (2D) diffusion of fluorescently-labelled biomolecules. Since then, FRAP has been refined through the advancements of optics, charged-coupled-device (CCD) cameras, confocal microscopes, and molecular probes. FRAP is now a highly quantitative tool used for transport and kinetic studies in the cytosol, organelles, and membrane of a cell. In this work, the authors intend to provide a review of recent advances in FRAP. The authors include epifluorescence spot FRAP, total internal reflection (TIR)/FRAP, and confocal microscope-based FRAP. The underlying mathematical models are also described. Finally, our understanding of coupled transport and kinetics as determined by FRAP will be discussed and the potential for future advances suggested.

Stochastic modelling of bird flocks: accounting for the cohesiveness of collective motion

Collective behaviour can be difficult to discern because it is not limited to animal aggregations such as flocks of birds and schools of fish wherein individuals spontaneously move in the same way despite the absence of leadership. Insect swarms are, for example, a form of collective behaviour, albeit one lacking the global order seen in bird flocks and fish schools. Their collective behaviour is evident in their emergent macroscopic properties. These properties are predicted by close relatives of Okubo's 1986 [Adv. Biophys. 22, 1-94. (doi:10.1016/0065-227X(86)90003-1)] stochastic model. Here, we argue that Okubo's stochastic model also encapsulates the cohesiveness mechanism at play in bird flocks, namely the fact that birds within a flock behave on average as if they are trapped in an elastic potential well. That is, each bird effectively behaves as if it is bound to the flock by a force that on average increases linearly as the distance from the flock centre increases. We uncover this key, but until now overlooked, feature of flocking in empirical data. This gives us a means of identifying what makes a given system collective. We show how the model can be extended to account for intrinsic velocity correlations and differentiated social relationships.

An optogenetic method for interrogating YAP1 and TAZ nuclear-cytoplasmic shuttling

The shuttling of transcription factors and transcriptional regulators into and out of the nucleus is central to the regulation of many biological processes. Here we describe a new method for studying the rates of nuclear entry and exit of transcriptional regulators. A photo-responsive LOV (light-oxygen-voltage) domain from Avena sativa is used to sequester fluorescently labelled transcriptional regulators YAP1 and TAZ (also known as WWTR1) on the surface of mitochondria and to reversibly release them upon blue light illumination. After dissociation, fluorescent signals from the mitochondria, cytoplasm and nucleus are extracted by a bespoke app and used to generate rates of nuclear entry and exit. Using this method, we demonstrate that phosphorylation of YAP1 on canonical sites enhances its rate of nuclear export. Moreover, we provide evidence that, despite high intercellular variability, YAP1 import and export rates correlate within the same cell. By simultaneously releasing YAP1 and TAZ from sequestration, we show that their rates of entry and exit are correlated. Furthermore, combining the optogenetic release of YAP1 with lattice light-sheet microscopy reveals high heterogeneity of YAP1 dynamics within different cytoplasmic regions, demonstrating the utility and versatility of our tool to study protein dynamics. This article has an associated First Person interview with Anna M. Dowbaj, joint first author of the paper.