Seasonal Rhythms of Neuronal Activity in the Human Biological Clock: A Mathematical Model

The mammalian suprachiasmatic nucleus (SCN) is implicated in the temporal organization of circadian and seasonal processes. Photic information may have a synchronizing effect on the endogenous clock of the SCN by inducing periodic changes in the functional activity of specific groups of neurons. The present study was performed to analyze the annual profiles of the arginine vasopressin (AVP)- and vasoactive intestinal polypeptide (VIP)-producing neurons in the human SCN. The populations of AVP- and VIP-expressing neurons in the SCN showed marked annual rhythms with an asymmetrical, bimodal waveform. Time series analysis indicated that these annual cycles in peptidergic activity could be described by a statistical model consisting of multiple-harmonic regression and ARMA components. The annual AVP cycle was adequately described by a two-harmonic model and a third-order autoregressive noise component, whereas the properties of the VIP cycle were best characterized by a two-harmonic model and a first-order autoregressive noise component. The models of both annual cycles reached a maximum in September–October and a minimum in May–June, and their estimated amplitudes, relative to the annual mean, were similar in size. These findings indicate that the biosynthesis of vasopressin and VIP in the human SCN exhibits an annual rhythmicity, and that the temporal organization of these processes is mainly controlled by environmental lighting conditions.     

The Baseline Cosinus Function: A Periodic Regression Model for Biological Rhythms

A periodic regression model, named the Baseline Cosinus Function (BCF), was designed to fit biological rhythms that show temporal deviations (peaks) above or below an otherwise relatively stable baseline. The BCF model has four parameters only, namely, baseline, peak-height, acrophase, and peak-width. BCF-regressions to daily rhythms in urinary 6-sulphatoxymelatonin (aMT6s), hypothalamic glutamate concentration, and body temperature of hamsters are compared to fits of single (SCF) and complex cosine functions (CCF; using the fundamental and the first harmonic). Goodness of fit statistics show that BCF-regressions to aMT6s-profiles of 36 hamsters resulted in lower residual errors than both SCF and CCF regressions, in particular when rhythms were determined under long photoperiod (n = 18) with relatively short nocturnal peaks (? 2 = 316.6, 142.7 and 74.5 for SCF, CCF and BCF, respectively). For aMT6s rhythms obtained from hamsters in short photoperiod (n = 18) with prolonged nocturnal peaks, goodness of fit was equivalent in CCF and BCF regressions (? 2 = 326.3, 107.0 and 101.4, for SCF, CCF, BCF, respectively), while BCF requires one parameter less than CCF. BCF-fits to daily patterns of hypothalamic glutamate and body temperature demonstrate that this model may be applied to various data types and has particular advantages when rhythms are sharply peaked, and when an independent estimate of peak-width, i.e., the total duration of a rise above the baseline, is desired.     

The Baseline Cosinus Function: A Periodic Regression Model for Biological Rhythms

Abstract

Both tryptophan oxygenase and tyrosine aminotransferase of rat liver show diurnal variations in the inducibility by quinolinic acid. The maxima of effectiveness of quinolinic acid precede the maxima of normal enzyme activity. In the case of tyrosine aminotransferase, the induction kinetics and the dose response curve were also greatly depending on the time of day. No rhythmicity could be detected in the activities of 3‐hydroxyanthranilate oxygenase and ornithine aminotransferase.     

A Mathematical Model of the Human Menstrual Cycle

A mathematical model for the hormonal interactions of the human menstrual cycle is presented. The feedback effects of estrogen on the release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) are considered, including a mechanism describing the midcycle LH peak. Computer simulation with this model yields results which are periodic and in good agreement with physiological data.     

A Periodically-Forced Mathematical Model for the Seasonal Dynamics of Malaria in Mosquitoes

We describe and analyze a periodically-forced difference equation model for malaria in mosquitoes that captures the effects of seasonality and allows the mosquitoes to feed on a heterogeneous population of hosts. We numerically show the existence of a unique globally asymptotically stable periodic orbit and calculate periodic orbits of field-measurable quantities that measure malaria transmission. We integrate this model with an individual-based stochastic simulation model for malaria in humans to compare the effects of insecticide-treated nets (ITNs) and indoor residual spraying (IRS) in reducing malaria transmission, prevalence, and incidence. We show that ITNs are more effective than IRS in reducing transmission and prevalence though IRS would achieve its maximal effects within 2 years while ITNs would need two mass distribution campaigns over several years to do so. Furthermore, the combination of both interventions is more effective than either intervention alone. However, although these interventions reduce transmission and prevalence, they can lead to increased clinical malaria; and all three malaria indicators return to preintervention levels within 3 years after the interventions are withdrawn.     

A Plastic Clock: How Circadian Rhythms Respond to Environmental Cues in Drosophila

Circadian clocks synchronize the physiology and behavior of most animals with the day to night cycle. A fundamental property of the molecular pacemakers generating circadian rhythms is their self-sustained nature: they keep oscillating even under constant conditions, with a period close to, but not exactly, 24 h. However, circadian pacemakers have to be sensitive to environmental cues to be beneficial. They need to be reset every day to keep a proper phase relationship with the day to night cycle, and they have to be able to adjust to seasonal changes in day length and temperature. Here, we review our current knowledge of the molecular and neural mechanisms contributing to the plasticity of Drosophila circadian rhythms, which are proving to be remarkably sophisticated and complex.     

The Photosynthesis and Cell Shape Rhythms can be Naturally Uncoupled from the Biological Clock in Euglena gracilis

A naturally occurring population of Euglena (Klebs Strain Z)cells, with unusual biological clock properties, has been isolated.The photosynthesis reactions, which are usually controlled bythe biological clock, are uncoupled from the clock in the newpopulation. The rate of oxygen evolution is influenced predominantlyby the environmental growth parameters instead of the biologicalclock. In addition, the rhythm in cellular shape has a differenttiming from the control population and can be temporarily uncoupledfrom the clock by lowering the light intensity used for growth Key words: Biological clock, photosynthesis, Euglena     

Circadian Rhythms in NEUROSPORA CRASSA: Interactions between Clock Mutations

Mutations at four loci in Neurospora crassa that alter the period of the circadian rhythm have been used to construct a series of double mutant strains in order to detect interactions between these mutations. Strains carrying mutations at three of these loci have altered periods on minimal media: prd-1, several alleles at the olir (oligomycin resistance) locus and four alleles at the frq locus. A mutation at the fourth locus, cel, which results in a defect in fatty acid synthesis, also leads to lengthening of the period when the medium is supplemented with linoleic acid (18:2). The cel mutation was crossed into strains carrying the frq, prd-1 and olir mutations, and the periods of the double mutant strains with and without 18:2 supplementation were determined. In addition, data from the literature for other combinations of loci and/or chemical effects on the period have been reanalyzed.--It was found that both prd-1 and olir are epistatic to the effects of 18:2 on cel; in the series of cel frq double mutant strains, the period-lengthening effect of 18:2 is inversely proportional to the period of the frq parent, indicating an interaction between frq and cel; period effects reported in the literature can be described as changes by a fixed ratio or percentage of the period rather than by a fixed number of hours, and the data, therefore, can support a multiplicative as well as an additive model.--Several biochemical interpretations of these interactions are discussed, based on simple chemical kinetics, enzyme inhibition kinetics and the control of flux through metabolic pathways.     

A Mathematical Model of the Human Respiratory Control System

The respiratory system exhibits the properties of a control system of the regulator type. Equations describing this biological control system have been derived. Transient and steady-state solutions for various CO₂ and O₂ step input disturbances were obtained utilizing a digital computer and are compared with experimental results. The effectiveness of the respiratory system as a regulator is investigated. Further extensions of the model are suggested.     

A Mathematical Model towards Understanding the Mechanism of Neuronal Regulation of Wake-NREMS-REMS States

In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s) that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.     

Disposition of Mulberry Pollen in the Human Respiratory System: A Mathematical Model

Inhaled particle deposition sites must be identified to effectively treat human airway diseases. We have determined distribution patterns of a selected aeroallergen, mulberry pollen, among human extrathoracic (ET: i.e., oronasopharyngeal) regions and the lung. A predictive model validated by inhalation exposure data from human subjects was utilized. Deposition locations were primarily functions of (1) mulberry particle parameters (geometric size, 11–18 μm; shape, spherical; and density, 1.14 g cm^?3), and (2) mode of breathing. In the general population, two styles of inhalation are prevalent, normal augmentors (NAs) and mouth breathers (MBs). Their clinical definitions are based on intra-ET airflow divisions. For a NA-mode breathing sedentary (minute ventilation = V_E = 10 L min^?1) adult, 93% of inhaled mulberry pollen was removed by the ET compartment and 7% collected within the lung. For a MB, the respective deposition efficiencies were 75% and 25%. To apply the model, we used a daily springtime mulberry pollen concentration of 1748 grains m^?3 and an exposure time of 0.5 hour to calculate actual doses for the respiratory system. Under the stipulated conditions, a MB would inhale 524 pollen grains per day and 131 would be deposited in the lung; the value is 37 grains for a NA. Preliminary epidemiological results suggest 15% of the study population are MBs in whom such pollen deposits are likely contributors to airway disease.     

害虫生物防治的数学模型

文章讨论一类捕食者（天敌）具脉冲放养与食饵（害虫）具阶段结构时滞的捕食-食饵模型,得到了害虫灭绝周期解全局吸引的充分条件和害虫的密度可以控制在经济危害水平E（EIL）之下的脉冲存放周期．为现实的害虫管理提供一定的理论依据．