Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we review a multiscale, i.e., from the molecular to the gross tumor scale, mathematical and computational "first-principle" approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We review the feasibility of this methodology that, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as a phenotype-diagnostic tool to predict collective and individual tumor cell invasion of surrounding tissue. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

MODELLING β2AR REGULATION

The β2 adrenergic receptor (β2AR) regulates smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory pathways that are stimulated during therapy and bring about tachyphylaxis, which is the loss of drug effects. Thus, an understanding of how the β2AR responds to various β-agonists is crucial to their rational use. Towards that end we have developed deterministic models that explore the mechanism of drug- induced β2AR regulation. These mathematical models can be classified into three classes; (i) Six quantitative models of SABA-induced G protein coupled receptor kinase (GRK)-mediated β2AR regulation; (ii) Three phenomenological models of salmeterol (a LABA)-induced GRK-mediated β2AR regulation; and (iii) One semi-quantitative, unified model of SABA-induced GRK-, protein kinase A (PKA)-, and phosphodiesterase (PDE)-mediated regulation of β2AR signalling. The various models were constrained with all or some of the following experimental data; (i) GRK-mediated β2AR phosphorylation in response to various LABAs/SABAs; (ii) dephosphorylation of the GRK site on the β2AR; (iii) β2AR internalisation; (iv) β2AR recycling; (v) β2AR desensitisation; (vi) β2AR resensitisation; (vii) PKA-mediated β2AR phosphorylation in response to a SABA; and (viii) LABA/SABA induced cAMP profile ± PDE inhibitors. The models of GRK-mediated β2AR regulation show that plasma membrane dephosphorylation and recycling of the phosphorylated β2AR are required to reconcile with the measured dephosphorylation kinetics. We further used a consensus model to predict the consequences of rapid pulsatile agonist stimulation and found that although resensitisation was rapid, the β2AR system retained the memory of prior stimuli and desensitised much more rapidly and strongly in response to subsequent stimuli. This could explain tachyphylaxis of SABAs over repeated use in rescue therapy of asthma patients. The LABA models show that the long action of salmeterol can be explained due to decreased stability of the arrestin/β2AR/salmeterol complex. This could explain long action of β-agonists used in maintenance therapy of asthma patients. Our consensus model of PKA/PDE/GRK-mediated β2AR regulation is being used to identify the dominant β2AR desensitisation pathways under different therapeutic regimens in human airway cells. In summary our models represent a significant advance towards understanding agonist-specific β2AR regulation that will aid in a more rational use of the β2AR agonists in the treatment of asthma.

Offline consolidation in implicit sequence learning

The goal of this study was to investigate offline memory consolidation with regard to general motor skill learning and implicit sequence-specific learning. We trained young adults on a serial reaction time task with a retention interval of either 24 hours (Experiment 1) or 1 week (Experiment 2) between two sessions. We manipulated sequence complexity (deterministic vs. probabilistic) and motor responses (unimanual or vs. bimanual). We found no evidence of offline memory consolidation for sequencespecific learning with either interval (in the sense of no deterioration over the interval but no further improvement either). However, we did find evidence of offline enhancement of general motor skill learning with both intervals, independent of kind of sequence or kind of response. These results suggest that general motor skill learning, but not sequence-specific learning, appears to be enhanced during offline intervals in implicit sequence learning.

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Detecting determinism with improved sensitivity in time series: Rank-based nonlinear predictability score

The rank-based nonlinear predictability score was recently introduced as a test for determinism in point processes. We here adapt this measure to time series sampled from time-continuous flows. We use noisy Lorenz signals to compare this approach against a classical amplitude-based nonlinear prediction error. Both measures show an almost identical robustness against Gaussian white noise. In contrast, when the amplitude distribution of the noise has a narrower central peak and heavier tails than the normal distribution, the rank-based nonlinear predictability score outperforms the amplitude-based nonlinear prediction error. For this type of noise, the nonlinear predictability score has a higher sensitivity for deterministic structure in noisy signals. It also yields a higher statistical power in a surrogate test of the null hypothesis of linear stochastic correlated signals. We show the high relevance of this improved performance in an application to electroencephalographic (EEG) recordings from epilepsy patients. Here the nonlinear predictability score again appears of higher sensitivity to nonrandomness. Importantly, it yields an improved contrast between signals recorded from brain areas where the first ictal EEG signal changes were detected (focal EEG signals) versus signals recorded from brain areas that were not involved at seizure onset (nonfocal EEG signals).

Temporal Changes in Randomness of Bird Communities across Central Europe

Many studies have examined whether communities are structured by random or deterministic processes, and both are likely to play a role, but relatively few studies have attempted to quantify the degree of randomness in species composition. We quantified, for the first time, the degree of randomness in forest bird communities based on an analysis of spatial autocorrelation in three regions of Germany. The compositional dissimilarity between pairs of forest patches was regressed against the distance between them. We then calculated the y-intercept of the curve, i.e. the ‘nugget’, which represents the compositional dissimilarity at zero spatial distance. We therefore assume, following similar work on plant communities, that this represents the degree of randomness in species composition. We then analysed how the degree of randomness in community composition varied over time and with forest management intensity, which we expected to reduce the importance of random processes by increasing the strength of environmental drivers. We found that a high portion of the bird community composition could be explained by chance (overall mean of 0.63), implying that most of the variation in local bird community composition is driven by stochastic processes. Forest management intensity did not consistently affect the mean degree of randomness in community composition, perhaps because the bird communities were relatively insensitive to management intensity. We found a high temporal variation in the degree of randomness, which may indicate temporal variation in assembly processes and in the importance of key environmental drivers. We conclude that the degree of randomness in community composition should be considered in bird community studies, and the high values we find may indicate that bird community composition is relatively hard to predict at the regional scale.

Progressive Image Denoising

Image denoising continues to be an active research topic. Although state-of-the-art denoising methods are numerically impressive and approch theoretical limits, they suffer from visible artifacts.While they produce acceptable results for natural images, human eyes are less forgiving when viewing synthetic images. At the same time, current methods are becoming more complex, making analysis, and implementation difficult. We propose image denoising as a simple physical process, which progressively reduces noise by deterministic annealing. The results of our implementation are numerically and visually excellent. We further demonstrate that our method is particularly suited for synthetic images. Finally, we offer a new perspective on image denoising using robust estimators.

Immunodeficiency in children starting antiretroviral therapy in low-, middle-, and high-income countries.

BACKGROUND The CD4 cell count or percent (CD4%) at the start of combination antiretroviral therapy (cART) is an important prognostic factor in children starting therapy and an important indicator of program performance. We describe trends and determinants of CD4 measures at cART initiation in children from low-, middle-, and high-income countries. METHODS We included children aged <16 years from clinics participating in a collaborative study spanning sub-Saharan Africa, Asia, Latin America, and the United States. Missing CD4 values at cART start were estimated through multiple imputation. Severe immunodeficiency was defined according to World Health Organization criteria. Analyses used generalized additive mixed models adjusted for age, country, and calendar year. RESULTS A total of 34,706 children from 9 low-income, 6 lower middle-income, 4 upper middle-income countries, and 1 high-income country (United States) were included; 20,624 children (59%) had severe immunodeficiency. In low-income countries, the estimated prevalence of children starting cART with severe immunodeficiency declined from 76% in 2004 to 63% in 2010. Corresponding figures for lower middle-income countries were from 77% to 66% and for upper middle-income countries from 75% to 58%. In the United States, the percentage decreased from 42% to 19% during the period 1996 to 2006. In low- and middle-income countries, infants and children aged 12-15 years had the highest prevalence of severe immunodeficiency at cART initiation. CONCLUSIONS Despite progress in most low- and middle-income countries, many children continue to start cART with severe immunodeficiency. Early diagnosis and treatment of HIV-infected children to prevent morbidity and mortality associated with immunodeficiency must remain a global public health priority.

A Logical Descriptor for Regular Languages via Stone Duality

In this paper we introduce a class of descriptors for regular languages arising from an application of the Stone duality between finite Boolean algebras and finite sets. These descriptors, called classical fortresses, are object specified in classical propositional logic and capable to accept exactly regular languages. To prove this, we show that the languages accepted by classical fortresses and deterministic finite automata coincide. Classical fortresses, besides being propositional descriptors for regular languages, also turn out to be an efficient tool for providing alternative and intuitive proofs for the closure properties of regular languages.

A Randomized, Controlled Trial of an Aerosolized Vaccine against Measles.

Background Aerosolized vaccine can be used as a needle-free method of immunization against measles, a disease that remains a major cause of illness and death. Data on the immunogenicity of aerosolized vaccine against measles in children are inconsistent. Methods We conducted an open-label noninferiority trial involving children 9.0 to 11.9 months of age in India who were eligible to receive a first dose of measles vaccine. Children were randomly assigned to receive a single dose of vaccine by means of either aerosol inhalation or a subcutaneous injection. The primary end points were seropositivity for antibodies against measles and adverse events 91 days after vaccination. The noninferiority margin was 5 percentage points. Results A total of 1001 children were assigned to receive aerosolized vaccine, and 1003 children were assigned to receive subcutaneous vaccine; 1956 of all the children (97.6%) were followed to day 91, but outcome data were missing for 331 children because of thawed specimens. In the per-protocol population, data on 1560 of 2004 children (77.8%) could be evaluated. At day 91, a total of 662 of 775 children (85.4%; 95% confidence interval [CI], 82.5 to 88.0) in the aerosol group, as compared with 743 of 785 children (94.6%; 95% CI, 92.7 to 96.1) in the subcutaneous group, were seropositive, a difference of -9.2 percentage points (95% CI, -12.2 to -6.3). Findings were similar in the full-analysis set (673 of 788 children in the aerosol group [85.4%] and 754 of 796 children in the subcutaneous group [94.7%] were seropositive at day 91, a difference of -9.3 percentage points [95% CI, -12.3 to -6.4]) and after multiple imputation of missing results. No serious adverse events were attributable to measles vaccination. Adverse-event profiles were similar in the two groups. Conclusions Aerosolized vaccine against measles was immunogenic, but, at the prespecified margin, the aerosolized vaccine was inferior to the subcutaneous vaccine with respect to the rate of seropositivity. (Funded by the Bill and Melinda Gates Foundation; Measles Aerosol Vaccine Project Clinical Trials Registry-India number, CTRI/2009/091/000673 .).

Twenty questions with noise: Bayes optimal policies for entropy loss

We consider the problem of twenty questions with noisy answers, in which we seek to find a target by repeatedly choosing a set, asking an oracle whether the target lies in this set, and obtaining an answer corrupted by noise. Starting with a prior distribution on the target's location, we seek to minimize the expected entropy of the posterior distribution. We formulate this problem as a dynamic program and show that any policy optimizing the one-step expected reduction in entropy is also optimal over the full horizon. Two such Bayes optimal policies are presented: one generalizes the probabilistic bisection policy due to Horstein and the other asks a deterministic set of questions. We study the structural properties of the latter, and illustrate its use in a computer vision application.

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Poorly Associated With Vertebral Strength

Trabecular bone score (TBS) rests on the textural analysis of DXA to reflect the decay in trabecular structure characterising osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible as prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly due to an unrealistic set-up and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings was used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation (“full vertebra”), 2) via the classical endplate embedding (“vertebral body”) or 3) via a ball joint to induce anterior wedge failure (“vertebral section”). HR-pQCT scans acquired prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (Fexp) and apparent failure stress (σexp) was assessed and their relative contribution to a multi-linear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with Fexp and σexp, except for the “vertebral body” case (r2 = 0.396, p = 0.028). Aside from the “vertebra section” set-up where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing set-up, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk.