On Integral Means for Fractional Calculus Operators of Multivalent Functions

2000 Mathematics Subject Classification: Primary 30C45, Secondary 26A33, 30C80Integral means inequalities are obtained for the fractional derivatives and the fractional integrals of multivalent functions. Relevant connections with various known integral means inequalities are also pointed out

Global parameter search reveals design principles of the mammalian circadian clock

Background: Virtually all living organisms have evolved a circadian (~24 hour) clock that controls physiological and behavioural processes with exquisite precision throughout the day/night cycle. The suprachiasmatic nucleus (SCN), which generates these ~24 h rhythms in mammals, consists of several thousand neurons. Each neuron contains a gene-regulatory network generating molecular oscillations, and the individual neuron oscillations are synchronised by intercellular coupling, presumably via neurotransmitters. Although this basic mechanism is currently accepted and has been recapitulated in mathematical models, several fundamental questions about the design principles of the SCN remain little understood. For example, a remarkable property of the SCN is that the phase of the SCN rhythm resets rapidly after a 'jet lag' type experiment, i.e. when the light/ dark (LD) cycle is abruptly advanced or delayed by several hours. Results: Here, we describe an extensive parameter optimization of a previously constructed simplified model of the SCN in order to further understand its design principles. By examining the top 50 solutions from the parameter optimization, we show that the neurotransmitters' role in generating the molecular circadian rhythms is extremely important. In addition, we show that when a neurotransmitter drives the rhythm of a system of coupled damped oscillators, it exhibits very robust synchronization and is much more easily entrained to light/dark cycles. We were also able to recreate in our simulations the fast rhythm resetting seen after a 'jet lag' type experiment. Conclusion: Our work shows that a careful exploration of parameter space for even an extremely simplified model of the mammalian clock can reveal unexpected behaviours and non-trivial predictions. Our results suggest that the neurotransmitter feedback loop plays a crucial role in the robustness and phase resetting properties of the mammalian clock, even at the single neuron level

Novel Mouse Xenograft Models Reveal a Critical Role of CD4+ T Cells in the Proliferation of EBV-Infected T and NK Cells

Epstein-Barr virus (EBV), a ubiquitous B-lymphotropic herpesvirus, ectopically infects T or NK cells to cause severe diseases of unknown pathogenesis, including chronic active EBV infection (CAEBV) and EBV-associated hemophagocytic lymphohistiocytosis (EBV-HLH). We developed xenograft models of CAEBV and EBV-HLH by transplanting patients' PBMC to immunodeficient mice of the NOD/Shi-scid/IL-2Rγnull strain. In these models, EBV-infected T, NK, or B cells proliferated systemically and reproduced histological characteristics of the two diseases. Analysis of the TCR repertoire expression revealed that identical predominant EBV-infected T-cell clones proliferated in patients and corresponding mice transplanted with their PBMC. Expression of the EBV nuclear antigen 1 (EBNA1), the latent membrane protein 1 (LMP1), and LMP2, but not EBNA2, in the engrafted cells is consistent with the latency II program of EBV gene expression known in CAEBV. High levels of human cytokines, including IL-8, IFN-γ, and RANTES, were detected in the peripheral blood of the model mice, mirroring hypercytokinemia characteristic to both CAEBV and EBV-HLH. Transplantation of individual immunophenotypic subsets isolated from patients' PBMC as well as that of various combinations of these subsets revealed a critical role of CD4+ T cells in the engraftment of EBV-infected T and NK cells. In accordance with this finding, in vivo depletion of CD4+ T cells by the administration of the OKT4 antibody following transplantation of PBMC prevented the engraftment of EBV-infected T and NK cells. This is the first report of animal models of CAEBV and EBV-HLH that are expected to be useful tools in the development of novel therapeutic strategies for the treatment of the diseases

Activation of AMPA Receptors in the Suprachiasmatic Nucleus Phase-Shifts the Mouse Circadian Clock In Vivo and In Vitro

The glutamatergic neurotransmission in the suprachiasmatic nucleus (SCN) plays a central role in the entrainment of the circadian rhythms to environmental light-dark cycles. Although the glutamatergic effect operating via NMDAR (N-methyl D-aspartate receptor) is well elucidated, much less is known about a role of AMPAR (α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptor) in circadian entrainment. Here we show that, in the mouse SCN, GluR2 and GluR4 AMPAR subtypes are abundantly expressed in the retinorecipient area. In vivo microinjection of AMPA in the SCN during the early subjective night phase-delays the behavioral rhythm. In the organotypic SCN slice culture, AMPA application induces phase-dependent phase-shifts of core-clock gene transcription rhythms. These data demonstrate that activation of AMPAR is capable of phase-shifting the circadian clock both in vivo and in vitro, and are consistent with the hypothesis that activation of AMPA receptors is a critical step in the transmission of photic information to the SCN

Integrative Gene Regulatory Network Analysis Reveals Light-Induced Regional Gene Expression Phase Shift Programs in the Mouse Suprachiasmatic Nucleus

We use the multigenic pattern of gene expression across suprachiasmatic nuclei (SCN) regions and time to understand the dynamics within the SCN in response to a circadian phase-resetting light pulse. Global gene expression studies of the SCN indicate that circadian functions like phase resetting are complex multigenic processes. While the molecular dynamics of phase resetting are not well understood, it is clear they involve a “functional gene expression program”, e.g., the coordinated behavior of functionally related genes in space and time. In the present study we selected a set of 89 of these functionally related genes in order to further understand this multigenic program. By use of high-throughput qPCR we studied 52 small samples taken by anatomically precise laser capture from within the core and shell SCN regions, and taken at time points with and without phase resetting light exposure. The results show striking regional differences in light response to be present in the mouse SCN. By using network-based analyses, we are able to establish a highly specific multigenic correlation between genes expressed in response to light at night and genes normally activated during the day. The light pulse triggers a complex and highly coordinated network of gene regulation. The largest differences marking neuroanatomical location are in transmitter receptors, and the largest time-dependent differences occur in clock-related genes. Nighttime phase resetting appears to recruit transcriptional regulatory processes normally active in the day. This program, or mechanism, causes the pattern of core region gene expression to transiently shift to become more like that of the shell region

Modeling Light Adaptation in Circadian Clock: Prediction of the Response That Stabilizes Entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature

How to Achieve Fast Entrainment? The Timescale to Synchronization

Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker