Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

The G-protein-coupled receptor kinases beta ARK1 and beta ARK2 are widely distributed at synapses in rat brain.

The beta-adrenergic receptor kinase (beta ARK) phosphorylates the agonist-occupied beta-adrenergic receptor to promote rapid receptor uncoupling from Gs, thereby attenuating adenylyl cyclase activity. Beta ARK-mediated receptor desensitization may reflect a general molecular mechanism operative on many G-protein-coupled receptor systems and, particularly, synaptic neurotransmitter receptors. Two distinct cDNAs encoding beta ARK isozymes were isolated from rat brain and sequenced. The regional and cellular distributions of these two gene products, termed beta ARK1 and beta ARK2, were determined in brain by in situ hybridization and by immunohistochemistry at the light and electron microscopic levels. The beta ARK isozymes were found to be expressed primarily in neurons distributed throughout the CNS. Ultrastructurally, beta ARK1 and beta ARK2 immunoreactivities were present both in association with postsynaptic densities and, presynaptically, with axon terminals. The beta ARK isozymes have a regional and subcellular distribution consistent with a general role in the desensitization of synaptic receptors.

Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Short-lived alpha-helical intermediates in the folding of beta-sheet proteins.

Several lines of evidence point strongly toward the importance of highly alpha-helical intermediates in the folding of all globular proteins, regardless of their native structure. However, experimental refolding studies demonstrate no observable alpha-helical intermediate during refolding of some beta-sheet proteins and have dampened enthusiasm for this model of protein folding. In this study, beta-sheet proteins were hypothesized to have potential to form amphiphilic helices at a period of <3.6 residues/turn that matches or exceeds the potential at 3.6 residues/turn. Hypothetically, such potential is the basis for an effective and unidirectional mechanism by which highly alpha-helical intermediates might be rapidly disassembled during folding and potentially accounts for the difficulty in detecting highly alpha-helical intermediates during the folding of some proteins. The presence of this potential was confirmed, indicating that a model entailing ubiquitous formation of alpha-helical intermediates during the folding of globular proteins predicts previously unrecognized features of primary structure. Further, the folding of fatty acid binding protein, a predominantly beta-sheet protein that exhibits no apparent highly alpha-helical intermediate during folding, was dramatically accelerated by 2,2,2-trifluoroethanol, a solvent that stabilizes alpha-helical structure. This observation suggests that formation of an alpha-helix can be a rate-limiting step during folding of a predominantly beta-sheet protein and further supports the role of highly alpha-helical intermediates in the folding of all globular proteins.

A prochelator activated by beta-secretase inhibits Abeta aggregation and suppresses copper-induced reactive oxygen species formation.

The intersection of the amyloid cascade hypothesis and the implication of metal ions in Alzheimer's disease progression has sparked an interest in using metal-binding compounds as potential therapeutic agents. In the present work, we describe a prochelator SWH that is enzymatically activated by beta-secretase to produce a high affinity copper chelator CP. Because beta-secretase is responsible for the amyloidogenic processing of the amyloid precursor protein, this prochelator strategy imparts disease specificity toward copper chelation not possible with general metal chelators. Furthermore, once activated, CP efficiently sequesters copper from amyloid-beta, prevents and disassembles copper-induced amyloid-beta aggregation, and diminishes copper-promoted reactive oxygen species formation.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Human uterine leiomyoma-derived fibroblasts stimulate uterine leiomyoma cell proliferation and collagen type I production, and activate RTKs and TGF beta receptor signaling in coculture.

BACKGROUND: Uterine leiomyomas (fibroids) are benign smooth muscle tumors that often contain an excessive extracellular matrix (ECM). In the present study, we investigated the interactions between human uterine leiomyoma (UtLM) cells and uterine leiomyoma-derived fibroblasts (FB), and their importance in cell growth and ECM protein production using a coculture system. RESULTS: We found enhanced cell proliferation, and elevated levels of ECM collagen type I and insulin-like growth factor-binding protein-3 after coculturing. There was also increased secretion of vascular endothelial growth factor, epidermal growth factor, fibroblast growth factor-2, and platelet derived growth factor A and B in the media of UtLM cells cocultured with FB. Protein arrays revealed increased phosphorylated receptor tyrosine kinases (RTKs) of the above growth factor ligands, and immunoblots showed elevated levels of the RTK downstream effector, phospho-mitogen activated protein kinase 44/42 in cocultured UtLM cells. There was also increased secretion of transforming growth factor-beta 1 and 3, and immunoprecipitated transforming growth factor-beta receptor I from cocultured UtLM cells showed elevated phosphoserine expression. The downstream effectors phospho-small mothers against decapentaplegic -2 and -3 protein (SMAD) levels were also increased in cocultured UtLM cells. However, none of the above effects were seen in normal myometrial cells cocultured with FB. The soluble factors released by tumor-derived fibroblasts and/or UtLM cells, and activation of the growth factor receptors and their pathways stimulated the proliferation of UtLM cells and enhanced the production of ECM proteins. CONCLUSIONS: These data support the importance of interactions between fibroid tumor cells and ECM fibroblasts in vivo, and the role of growth factors, and ECM proteins in the pathogenesis of uterine fibroids.

Reciprocal in vivo regulation of myocardial G protein-coupled receptor kinase expression by beta-adrenergic receptor stimulation and blockade.

BACKGROUND: Impaired myocardial beta-adrenergic receptor (betaAR) signaling, including desensitization and functional uncoupling, is a characteristic of congestive heart failure. A contributing mechanism for this impairment may involve enhanced myocardial beta-adrenergic receptor kinase (betaARK1) activity because levels of this betaAR-desensitizing G protein-coupled receptor kinase (GRK) are increased in heart failure. An hypothesis has emerged that increased sympathetic nervous system activity associated with heart failure might be the initial stimulus for betaAR signaling alterations, including desensitization. We have chronically treated mice with drugs that either activate or antagonize betaARs to study the dynamic relationship between betaAR activation and myocardial levels of betaARK1. METHODS AND RESULTS: Long-term in vivo stimulation of betaARs results in the impairment of cardiac +betaAR signaling and increases the level of expression (mRNA and protein) and activity of +betaARK1 but not that of GRK5, a second GRK abundantly expressed in the myocardium. Long-term beta-blocker treatment, including the use of carvedilol, improves myocardial betaAR signaling and reduces betaARK1 levels in a specific and dose-dependent manner. Identical results were obtained in vitro in cultured cells, demonstrating that the regulation of GRK expression is directly linked to betaAR signaling. CONCLUSIONS: This report demonstrates, for the first time, that betaAR stimulation can significantly increase the expression of betaARK1 , whereas beta-blockade decreases expression. This reciprocal regulation of betaARK1 documents a novel mechanism of ligand-induced betaAR regulation and provides important insights into the potential mechanisms responsible for the effectiveness of beta-blockers, such as carvedilol, in the treatment of heart failure.

In vivo ventricular gene delivery of a beta-adrenergic receptor kinase inhibitor to the failing heart reverses cardiac dysfunction.

BACKGROUND: Genetic manipulation to reverse molecular abnormalities associated with dysfunctional myocardium may provide novel treatment. This study aimed to determine the feasibility and functional consequences of in vivo beta-adrenergic receptor kinase (betaARK1) inhibition in a model of chronic left ventricular (LV) dysfunction after myocardial infarction (MI). METHODS AND RESULTS: Rabbits underwent ligation of the left circumflex (LCx) marginal artery and implantation of sonomicrometric crystals. Baseline cardiac physiology was studied 3 weeks after MI; 5x10(11) viral particles of adenovirus was percutaneously delivered through the LCx. Animals received transgenes encoding a peptide inhibitor of betaARK1 (Adeno-betaARKct) or an empty virus (EV) as control. One week after gene delivery, global LV and regional systolic function were measured again to assess gene treatment. Adeno-betaARKct delivery to the failing heart through the LCx resulted in chamber-specific expression of the betaARKct. Baseline in vivo LV systolic performance was improved in Adeno-betaARKct-treated animals compared with their individual pre-gene delivery values and compared with EV-treated rabbits. Total beta-AR density and betaARK1 levels were unchanged between treatment groups; however, beta-AR-stimulated adenylyl cyclase activity in the LV was significantly higher in Adeno-betaARKct-treated rabbits compared with EV-treated animals. CONCLUSIONS: In vivo delivery of Adeno-betaARKct is feasible in the infarcted/failing heart by coronary catheterization; expression of betaARKct results in marked reversal of ventricular dysfunction. Thus, inhibition of betaARK1 provides a novel treatment strategy for improving the cardiac performance of the post-MI heart.

Augmentation of cardiac contractility mediated by the human beta(3)-adrenergic receptor overexpressed in the hearts of transgenic mice.

BACKGROUND: Stimulation of beta(1)- and beta(2)-adrenergic receptors (ARs) in the heart results in positive inotropy. In contrast, it has been reported that the beta(3)AR is also expressed in the human heart and that its stimulation leads to negative inotropic effects. METHODS AND RESULTS: To better understand the role of beta(3)ARs in cardiac function, we generated transgenic mice with cardiac-specific overexpression of 330 fmol/mg protein of the human beta(3)AR (TGbeta(3) mice). Hemodynamic characterization was performed by cardiac catheterization in closed-chest anesthetized mice, by pressure-volume-loop analysis, and by echocardiography in conscious mice. After propranolol blockade of endogenous beta(1)- and beta(2)ARs, isoproterenol resulted in an increase in contractility in the TGbeta(3) mice (30%), with no effect in wild-type mice. Similarly, stimulation with the selective human beta(3)AR agonist L-755,507 significantly increased contractility in the TGbeta(3) mice (160%), with no effect in wild-type mice, as determined by hemodynamic measurements and by end-systolic pressure-volume relations. The underlying mechanism of the positive inotropy incurred with L-755,507 in the TGbeta(3) mice was investigated in terms of beta(3)AR-G-protein coupling and adenylyl cyclase activation. Stimulation of cardiac membranes from TGbeta(3) mice with L-755,507 resulted in a pertussis toxin-insensitive 1.33-fold increase in [(35)S]GTPgammaS loading and a 1.6-fold increase in adenylyl cyclase activity. CONCLUSIONS: Cardiac overexpression of human beta(3)ARs results in positive inotropy only on stimulation with a beta(3)AR agonist. Overexpressed beta(3)ARs couple to G(s) and activate adenylyl cyclase on agonist stimulation.

In vivo inhibition of elevated myocardial beta-adrenergic receptor kinase activity in hybrid transgenic mice restores normal beta-adrenergic signaling and function.

BACKGROUND: The clinical syndrome of heart failure (HF) is characterized by an impaired cardiac beta-adrenergic receptor (betaAR) system, which is critical in the regulation of myocardial function. Expression of the betaAR kinase (betaARK1), which phosphorylates and uncouples betaARs, is elevated in human HF; this likely contributes to the abnormal betaAR responsiveness that occurs with beta-agonist administration. We previously showed that transgenic mice with increased myocardial betaARK1 expression had impaired cardiac function in vivo and that inhibiting endogenous betaARK1 activity in the heart led to enhanced myocardial function. METHODS AND RESULTS: We created hybrid transgenic mice with cardiac-specific concomitant overexpression of both betaARK1 and an inhibitor of betaARK1 activity to study the feasibility and functional consequences of the inhibition of elevated betaARK1 activity similar to that present in human HF. Transgenic mice with myocardial overexpression of betaARK1 (3 to 5-fold) have a blunted in vivo contractile response to isoproterenol when compared with non-transgenic control mice. In the hybrid transgenic mice, although myocardial betaARK1 levels remained elevated due to transgene expression, in vitro betaARK1 activity returned to control levels and the percentage of betaARs in the high-affinity state increased to normal wild-type levels. Furthermore, the in vivo left ventricular contractile response to betaAR stimulation was restored to normal in the hybrid double-transgenic mice. CONCLUSIONS: Novel hybrid transgenic mice can be created with concomitant cardiac-specific overexpression of 2 independent transgenes with opposing actions. Elevated myocardial betaARK1 in transgenic mouse hearts (to levels seen in human HF) can be inhibited in vivo by a peptide that can prevent agonist-stimulated desensitization of cardiac betaARs. This may represent a novel strategy to improve myocardial function in the setting of compromised heart function.

Level of beta-adrenergic receptor kinase 1 inhibition determines degree of cardiac dysfunction after chronic pressure overload-induced heart failure.

BACKGROUND: Heart failure is characterized by abnormalities in beta-adrenergic receptor (betaAR) signaling, including increased level of myocardial betaAR kinase 1 (betaARK1). Our previous studies have shown that inhibition of betaARK1 with the use of the Gbetagamma sequestering peptide of betaARK1 (betaARKct) can prevent cardiac dysfunction in models of heart failure. Because inhibition of betaARK activity is pivotal for amelioration of cardiac dysfunction, we investigated whether the level of betaARK1 inhibition correlates with the degree of heart failure. METHODS AND RESULTS: Transgenic (TG) mice with varying degrees of cardiac-specific expression of betaARKct peptide underwent transverse aortic constriction (TAC) for 12 weeks. Cardiac function was assessed by serial echocardiography in conscious mice, and the level of myocardial betaARKct protein was quantified at termination of the study. TG mice showed a positive linear relationship between the level of betaARKct protein expression and fractional shortening at 12 weeks after TAC. TG mice with low betaARKct expression developed severe heart failure, whereas mice with high betaARKct expression showed significantly less cardiac deterioration than wild-type (WT) mice. Importantly, mice with a high level of betaARKct expression had preserved isoproterenol-stimulated adenylyl cyclase activity and normal betaAR densities in the cardiac membranes. In contrast, mice with low expression of the transgene had marked abnormalities in betaAR function, similar to the WT mice. CONCLUSIONS: These data show that the level of betaARK1 inhibition determines the degree to which cardiac function can be preserved in response to pressure overload and has important therapeutic implications when betaARK1 inhibition is considered as a molecular target.