A mathematical model for the dynamics of happiness.

Positive psychology recognizes happiness as a construct comprising hedonic and eudaimonic well-being dimensions. Integrating these components and a set of theory-led assumptions, we propose a mathematical model, given by a system of nonlinear ordinary differential equations, to describe the dynamics of a person's happiness over time. The mathematical model offers insights into the role of emotions for happiness and why we struggle to attain sustainable happiness and tread the hedonic treadmill oscillating around a relative stable level of well-being. The model also indicates that lasting happiness may be achievable by developing constant eudaimonic emotions or human altruistic qualities that overcome the limits of the homeostatic hedonic system; in mathematical terms, this process is expressed as distinct dynamical bifurcations. This mathematical description is consistent with the idea that eudaimonic well-being is beyond the boundaries of hedonic homeostasis.

A Mathematical Model for the Effect of Low-Dose Radiation on the G2/M Transition.

We develop a mathematical model to study the immediate effect of low-dose radiation on the G2 checkpoint and the G2/M transition of the cell cycle via a radiation pathway (the ATM-Chk2 pathway) of an individual mammalian cell. The model consists of a system of nonlinear differential equations describing the dynamics of a network of regulatory proteins that play key roles in the G2/M transition, cell cycle oscillations, and the radiation pathway. We simulate the application of a single pulse of low-dose radiation at different intensities ([Formula: see text] 0-0.4 Gy) and times during the latter part of the G2-phase. We use bifurcation analysis to characterize the effect of radiation on the G2/M transition via the ATM-Chk2 pathway. We show that radiation between 0.1 and 0.3 Gy can delay the G2/M transition, and radiation higher than 0.3 Gy can fully activate the G2 checkpoint. Also, our results show that radiation can be low enough to neither delay the G2/M transition nor activate the G2 checkpoint ([Formula: see text] 0.1 Gy). Our model supports the idea that the cell response to radiation during G2-phase explains hyper-radiosensitivity and increased radioresistance (HRS/IRR) observed at low dose.

Using a model comparison approach to describe the assembly pathway for histone H1.

Histones H1 or linker histones are highly dynamic proteins that diffuse throughout the cell nucleus and associate with chromatin (DNA and associated proteins). This binding interaction of histone H1 with the chromatin is thought to regulate chromatin organization and DNA accessibility to transcription factors and has been proven to involve a kinetic process characterized by a population that associates weakly with chromatin and rapidly dissociates and another population that resides at a binding site for up to several minutes before dissociating. When considering differences between these two classes of interactions in a mathematical model for the purpose of describing and quantifying the dynamics of histone H1, it becomes apparent that there could be several assembly pathways that explain the kinetic data obtained in living cells. In this work, we model these different pathways using systems of reaction-diffusion equations and carry out a model comparison analysis using FRAP (fluorescence recovery after photobleaching) experimental data from different histone H1 variants to determine the most feasible mechanism to explain histone H1 binding to chromatin. The analysis favors four different chromatin assembly pathways for histone H1 which share common features and provide meaningful biological information on histone H1 dynamics. We show, using perturbation analysis, that the explicit consideration of high- and low-affinity associations of histone H1 with chromatin in the favored assembly pathways improves the interpretation of histone H1 experimental FRAP data. To illustrate the results, we use one of the favored models to assess the kinetic changes of histone H1 after core histone hyperacetylation, and conclude that this post-transcriptional modification does not affect significantly the transition of histone H1 from a weakly bound state to a tightly bound state.

Analysis of molecular diffusion by first-passage time variance identifies the size of confinement zones.

The diffusion of receptors within the two-dimensional environment of the plasma membrane is a complex process. Although certain components diffuse according to a random walk model (Brownian diffusion), an overwhelming body of work has found that membrane diffusion is nonideal (anomalous diffusion). One of the most powerful methods for studying membrane diffusion is single particle tracking (SPT), which records the trajectory of a label attached to a membrane component of interest. One of the outstanding problems in SPT is the analysis of data to identify the presence of heterogeneity. We have adapted a first-passage time (FPT) algorithm, originally developed for the interpretation of animal movement, for the analysis of SPT data. We discuss the general application of the FPT analysis to molecular diffusion, and use simulations to test the method against data containing known regions of confinement. We conclude that FPT can be used to identify the presence and size of confinement within trajectories of the receptor LFA-1, and these results are consistent with previous reports on the size of LFA-1 clusters. The analysis of trajectory data for cell surface receptors by FPT provides a robust method to determine the presence and size of confined regions of diffusion.

Core histone hyperacetylation impacts cooperative behavior and high-affinity binding of histone H1 to chromatin.

Linker histones stabilize higher order chromatin structures and limit access to proteins involved in DNA-dependent processes. Core histone acetylation is thought to modulate H1 binding. In the current study, we employed kinetic modeling of H1 recovery curves obtained during fluorescence recovery after photobleaching (FRAP) experiments to determine the impact of core histone acetylation on the different variants of H1. Following brief treatments with histone deacetylase inhibitor, most variants showed no change in H1 dynamics. A change in mobility was detected only when longer treatments were used to induce high levels of histone acetylation. This hyperacetylation imparted marked changes in the dynamics of low-affinity H1 population, while conferring variant-specific changes in the mobility of H1 molecules that were strongly bound. Both the C-terminal domain (CTD) and globular domain were responsible for this differential response to TSA. Furthermore, we found that neither the CTD nor the globular domain, by themselves, undergoes a change in kinetics following hyperacetylation. This led us to conclude that hyperacetylation of core histones affects the cooperative nature of low-affinity H1 binding, with some variants undergoing a predicted decrease of almost 2 orders of magnitude.

Molecular dynamics of histone H1.

The histone H1 family of nucleoproteins represents an important class of structural and architectural proteins that are responsible for maintaining and stabilizing higher-order chromatin structure. Essential for mammalian cell viability, they are responsible for gene-specific regulation of transcription and other DNA-dependent processes. In this review, we focus on the wealth of information gathered on the molecular kinetics of histone H1 molecules using novel imaging techniques, such as fluorescence recovery after photobleaching. These experiments have shed light on the effects of H1 phosphorylation and core histone acetylation in influencing chromatin structure and dynamics. We also delineate important concepts surrounding the C-terminal domain of H1, such as the intrinsic disorder hypothesis, and how it affects H1 function. Finally, we address the biochemical mechanisms behind low-affinity H1 binding.

Nucleoplasmic beta-actin exists in a dynamic equilibrium between low-mobility polymeric species and rapidly diffusing populations.

Beta-actin, once thought to be an exclusively cytoplasmic protein, is now known to have important functions within the nucleus. Nuclear beta-actin associates with and functions in chromatin remodeling complexes, ribonucleic acid polymerase complexes, and at least some ribonucleoproteins. Proteins involved in regulating actin polymerization are also found in the interphase nucleus. We define the dynamic properties of nuclear actin molecules using fluorescence recovery after photobleaching. Our results indicate that actin and actin-containing complexes are reduced in their mobility through the nucleoplasm diffusing at approximately 0.5 microm2 s(-1). We also observed that approximately 20% of the total nuclear actin pool has properties of polymeric actin that turns over rapidly. This pool could be detected in endogenous nuclear actin by using fluorescent polymeric actin binding proteins and was sensitive to drugs that alter actin polymerization. Our results validate previous reports of polymeric forms of nuclear actin observed in fixed specimens and reveal that these polymeric forms are very dynamic.

Using FRAP and mathematical modeling to determine the in vivo kinetics of nuclear proteins.

Fluorescence recovery after photobleaching (FRAP) has become a popular technique to investigate the behavior of proteins in living cells. Although the technique is relatively old, its application to studying endogenous intracellular proteins in living cells is relatively recent and is a consequence of the newly developed fluorescent protein-based living cell protein tags. This is particularly true for nuclear proteins, in which endogenous protein mobility has only recently been studied. Here we examine the experimental design and analysis of FRAP experiments. Mathematical modeling of FRAP data enables the experimentalist to extract information such as the association and dissociation constants, distribution of a protein between mobile and immobilized pools, and the effective diffusion coefficient of the molecule under study. As experimentalists begin to dissect the relative influence of protein domains within individual proteins, this approach will allow a quantitative assessment of the relative influences of different molecular interactions on the steady-state distribution and protein function in vivo.