Potential of a quantal response as a mechanism for oscillatory behavior: implications for our concepts of hormonal control mechanisms

This article describes the potential of a quantal (i.e., all-or-none) response as a model for understanding the interactions between endocrine, paracrine and autocrine hormones. We review the general features of continuous and discontinuous (i.e., oscillating) quantal models including the role of a threshold. In addition, we also describe a few of the many different biochemical mechanisms which may give rise to quantal behavior. One of the more attractive schemes involves the coordinate regulation of opposing biochemical pathways resulting from phosphorylation of hormone receptors and/or rate-limiting enzymes. At least one hormone receptor (i.e., that for insulin) and many rate-limiting enzymes which control the flow of metabolites through a variety of metabolic pathways can be phosphorylated at multiple sites by one or more protein kinases. Phosphorylation may enhance or inhibit the activities of these proteins depending on which sites are modified. Furthermore, since phosphorylation of some sites on a protein may enhance the ability of phosphoprotein phosphatases to dephosphorylate other sites responsible for biological activity of the protein, phosphorylation also has the potential to produce a discontinuous quantal response. Quantal response mechanisms may alter our notions of endocrine regulation. When a quantal response mechanism is applied to a simple negative feedback model similar to that which was originally postulated to explain the interactions between gonadotropin and steroid hormonal levels, the model can account for the oscillations in hormone levels even when the input is constant. Conversely, when a graded mechanism is applied to the same negative feedback model, the model will almost certainly result in constant hormone levels. Further, the model illustrates that small changes in rate constants and thresholds of response, amplification of hormonal signals, and degradation of intermediate regulators can produce large shifts in the output of the system. These may account for the variability in hormonal levels observed in some endocrine systems. Finally, the high sensitivity of the quantal response mechanism accounts for the data which suggest that gonadotropins may play permissive rather than causal roles in regulation of gonadal function. Since increasing evidence suggests that all cells of a given type may not be equal in terms of hormonal responsiveness, measurements of response in single cells over short time periods will be needed before the role of a quantal response can be determined and endocrine regulation will be fully understood.     

A concept of a general computer program for the iterative calculation of maximum likelihood estimators with application to qualitative dose response analyses

In this article we describe the construction of a general computer program for the iterative calculation of maximum likelihood estimators. The program is general in the sense that it allows the maximization of any given likelihood function. The user only has to write a subroutine LKLHD, in which the special likelihood function and their first and second derivatives will be calculated. This subroutine is an input parameter of the optimization program. This enables the user to employ one main program for the maximization of various likelihood functions. This advantage will be shown for the evaluation of qualitative dose response relationships (quantal assays: probit-, logit-analysis).     

Statistical models for low dose exposure

Extrapolation of health risks from high to low doses has received a considerable amount of attention in carcinogenic risk assessment over decades. Fitting statistical dose-response models to experimental data collected at high doses and use of the fitted model for estimating effects at low doses lead to quite different risk predictions. Dissatisfaction with this procedure was formulated both by toxicologists who saw a deficit of biological knowledge in the models as well as by risk modelers who saw the need of mechanistically-based stochastic modeling. This contribution summarizes the present status of low dose modeling and the determination of the shape of dose-response curves. We will address the controversial issues of the appropriateness of threshold models, the estimation of no observed adverse effect levels (NOAEL), and their relevance for low dose modeling. We will distinguish between quantal dose-response models for tumor incidence and models of the more informative age/time dependent tumor incidence. The multistage model and the two-stage model of clonal expansion are considered as dose-response models accounting for biological mechanisms. Problems of the identifiability of mechanisms are addressed, the relation between administered dose and effective target dose is illustrated by examples, and the recently proposed Benchmark Dose concept for risk assessment is presented with its consequences for mechanistic modeling and statistical estimation.     

A Single Compartment Quantal Response Model with an Inspection Process

In a single compartment quantal response model, besides the input and release processes, an inspection process, assumed to be independent of the input and release processes, is considered. Each time when a release occurs, we assume the amount of release is randomly proportional to the amount present and the proportional rates form a sequence of independent and identically distributed random variables with support on [0, 1]. The input policy we consider is a modification of (s, S) input policy in the inventory model. More precisely, let 0 ≦s₂ ≦s₁ ≦s ≦ S, if after a release, the amount of the drug in subject's body is less than a level s₂ which is small enough, then there will be an input immediately with probability 1 — p and no more inputs thereafter with probability p, also there will be an input immediately if the dose level is in the interval [s₂, s₁). If the dose level is in the interval [s₁, s) there will be no input unless the inspector arrives. On the other hand, if the dose level is greater than or equal to s, then there will be no input. We consider a stochastic model as described above, and obtain the expressions for some quantities of interest. A Monte Carlo study has also been carried out to demonstrate some behaviors of our quantal response process.     

Fitting the linear-quadratic model using time of occurrence as the end-point for quantal response multifraction experiments

A statistical technique is given for fitting the linear-quadratic model to experimental quantal response multifraction data using the time of the response as the end-point. The analysis used is based on the Cox Proportional Hazards model. The technique is useful for late effects where the time of occurrence of the response is dose dependent. The technique is compared to logistic regression analysis and the advantages and disadvantages are discussed. Both methods are applied to a lung pneumonitis experiment and a kidney experiment.     

Cancer immunotherapy, mathematical modeling and optimal control

Clinical immunologists, among other problems, routinely face a question: what is the best time and dose for a certain therapeutic agent to be administered to the patient in order to decrease/eradicate the pathological condition? In cancer immunotherapies the therapeutic agent is something able to elicit an immune response against cancer. The immune response has its own dynamics that depends on the immunogenicity of the therapeutic agent and on the duration of the immune response. The question then is "how can we decide when and how much of the drug to inject so to have a prolonged and effective immune response to the cancer?". This question can be addressed in mathematical terms in two stages: first one construct a mathematical model describing the cancer-immune interaction and secondly one applies the theory of optimal control to determine when and to which extent to stimulate the immune system by means of an immunotherapeutic agent administered in discrete variable doses within the therapeutic period. The solution of this mathematical problem is described and discussed in this article. We show that the method employed can be applied to find the optimal protocol in a variety of clinical problems where the kinetics of the drug or treatment and its influence on the physiologic/pathologic functions have been described by a system of ordinary differential equations.     

Does the Duration and Time of Sleep Increase the Risk of Allergic Rhinitis? Results of the 6-Year Nationwide Korea Youth Risk Behavior Web-Based Survey

Allergic rhinitis (AR) is the most common chronic disorder in the pediatric population. Although several studies have investigated the correlation between AR and sleep-related issues, the association between the duration and time of sleep and AR has not been analyzed in long-term national data. This study investigated the relationship between sleep time and duration and AR risk in middle- and high-school students (adolescents aged 12–18). We analyzed national data from the Korea Youth Risk Behavior Web-based Survey by the Korea Centers for Disease Control and Prevention from 2007–2012. The sample size was 274,480, with an average response rate of 96.2%. Multivariate logistic regression analyses were conducted to determine the relationship between sleep and AR risk. Furthermore, to determine the best-fitted model among independent variables such as sleep duration, sleep time, and the combination of sleep duration and sleep time, we used Akaike Information Criteria (AIC) to compare models. A total of 43,337 boys and 41,665 girls reported a diagnosis of AR at baseline. The odds ratio increased with age and with higher education and economic status of the parents. Further, students in mid-sized and large cities had stronger relationships to AR than those in small cities. In both genders, AR was associated with depression and suicidal ideation. In the analysis of sleep duration and sleep time, the odds ratio increased in both genders when sleep duration was <7 hours, and when the time of sleep was later than 24∶00 hours. Our results indicate an association between sleep time and duration and AR. This study is the first to focus on the relationship between sleep duration and time and AR in national survey data collected over 6 years.     

Dose–response relationship from longitudinal data with response‐dependent dose modification using likelihood methods

In some clinical trials or clinical practice, the therapeutic agent is administered repeatedly, and doses are adjusted in each patient based on repeatedly measured continuous responses, to maintain the response levels in a target range. Because a lower dose tends to be selected for patients with a better outcome, simple summarizations may wrongly show a better outcome for the lower dose, producing an incorrect dose–response relationship. In this study, we consider the dose–response relationship under these situations. We show that maximum‐likelihood estimates are consistent without modeling the dose‐modification mechanisms when the selection of the dose as a time‐dependent covariate is based only on observed, but not on unobserved, responses, and measurements are generated based on administered doses. We confirmed this property by performing simulation studies under several dose‐modification mechanisms. We examined an autoregressive linear mixed effects model. The model represents profiles approaching each patient's asymptote when identical doses are repeatedly administered. The model takes into account the previous dose history and provides a dose–response relationship of the asymptote as a summary measure. We also examined a linear mixed effects model assuming all responses are measured at steady state. In the simulation studies, the estimates of both the models were unbiased under the dose modification based on observed responses, but biased under the dose modification based on unobserved responses. In conclusion, the maximum‐likelihood estimates of the dose–response relationship are consistent under the dose modification based only on observed responses.     

Interferon-alpha acutely impairs sleep in healthy humans

We investigated the effects of two low doses of interferon-alpha (IFN-alpha) on nocturnal sleep in 18 healthy men by means of polysomnographic sleep recordings. At 1900h, human recombinant IFN-alpha (1000 or 10000 U/kg body weight) or placebo was administered subcutaneously. Between 2300h and 0700h subjects were allowed to sleep. In general effects were stronger at the dose of 10000 than 1000 U/kg body weight of IFN-alpha. Although, after IFN-alpha subjects experienced increased fatigue, the cytokine impaired the quality of nocturnal sleep. The higher dose of IFN-alpha suppressed slow wave sleep (17.8 +/- 2.0% vs 25.2 +/- 2.6% following placebo, P<0.003) but increased time spent in shallow sleep (P<0.05) during the first half of sleep time. Rapid eye movement (REM) sleep latency was postponed (P<0.02) and time spent in REM sleep was significantly decreased after IFN-alpha (P<0.04). The impairing influence of IFN-alpha on sleep in humans is in contrast with findings of sleep promoting effects of this cytokine in animals. Our data suggest that endogenous IFN-alpha may be a factor responsible for alterations of sleep, e.g. in the course of viral infections.     

A Single Compartment Quantal Response Model with a Renewal Type Input Process and IID Releases

We deal with a single compartment quantal response model, where unlike the previous models, which do not have any input after the administration of a single dose Z(0)=z at time t=0, we allow inputs of doses after time t=0. More precisely, the system uses the (s, S) input policy as in inventory models, and has IID releases. Also when the amount of dose in the subject reaches 0, there is a probability p to stop having input thereafter. Among other results, the probability that the subject never responds and the expressions for some quantities of interest are obtained.     

A three-oscillator model of the human circadian system controlling the core temperature rhythm and the sleep-wake cycle

Even during “free-running” experiments, in which subjects lived in caves or cellars without any time cues, various circadian rhythms such as core body temperature and the sleep-wake cycle remained for a long time mutually synchronized in one group of subjects. In another group of subjects, or later in the same subjects, a number of unusually long sleep-wake cycles occurred while body temperature persisted in a near-24 hr rhythm. This has been termed “internal desynchronization” by Aschoff & Wever (1962) to emphasize the uncoupling of rhythms. Zulley (1980) and Czeisler et al. (1980) found that the duration of sleep depends regularly on the phase of the sleep onset in the body temperature rhythm, even in the apparently “random and irregular” sleep-wake pattern. The graph which plots, the sleep duration against the sleep onset phase is called sleep duration in this paper. We develop a quantitative, multi-oscillator model of human circadian system following Wever (1979) and Kronauer et al. (1982). Because the simplest model, which describes the state of each component oscillator by only one variable (ptlase) was adopted for each component oscillator, we can determine the intFraction between oscillators using sleep duration. It is found that a three-oscillator model can simulate several qualitative features of human circadian rhythms, such as an irregular free-running pattern and sleep duration. Moreover we find that the model reproduces the mysterious phenomenon of “forbidden wake up”, although we do not incorporate a priori any mechanism to explain it.     

A Novel,Open Access Method to Assess Sleep Duration Using a Wrist-Worn Accelerometer

Wrist-worn accelerometers are increasingly being used for the assessment of physical activity in population studies, but little is known about their value for sleep assessment. We developed a novel method of assessing sleep duration using data from 4,094 Whitehall II Study (United Kingdom, 2012–2013) participants aged 60–83 who wore the accelerometer for 9 consecutive days, filled in a sleep log and reported sleep duration via questionnaire. Our sleep detection algorithm defined (nocturnal) sleep as a period of sustained inactivity, itself detected as the absence of change in arm angle greater than 5 degrees for 5 minutes or more, during a period recorded as sleep by the participant in their sleep log. The resulting estimate of sleep duration had a moderate (but similar to previous findings) agreement with questionnaire based measures for time in bed, defined as the difference between sleep onset and waking time (kappa = 0.32, 95%CI:0.29,0.34) and total sleep duration (kappa = 0.39, 0.36,0.42). This estimate was lower for time in bed for women, depressed participants, those reporting more insomnia symptoms, and on weekend days. No such group differences were found for total sleep duration. Our algorithm was validated against data from a polysomnography study on 28 persons which found a longer time window and lower angle threshold to have better sensitivity to wakefulness, while the reverse was true for sensitivity to sleep. The novelty of our method is the use of a generic algorithm that will allow comparison between studies rather than a “count” based, device specific method.     

Knee Pain and Low Back Pain Additively Disturb Sleep in the General Population: A Cross-Sectional Analysis of the Nagahama Study

Introduction

Association of knee and low back pain with sleep disturbance is poorly understood. We aimed to clarify the independent and combined effects of these orthopedic symptoms on sleep in a large-scale general population.

Methods

Cross-sectional data about sleep and knee/low back pain were collected for 9,611 community residents (53±14 years old) by a structured questionnaire. Sleep duration less than 6 h/d was defined as short sleep. Sleep quality and the presence of knee and low back pain were evaluated by dichotomous questions. Subjects who complained about knee or low back pains were graded by tertiles of a numerical response scale (NRS) score and a Roland-Morris disability questionnaire (RDQ) score respectively. Multivariate regression analyses were performed to determine the correlates of short sleep duration and poor sleep quality.

Results

Frequency of participants who complained of the orthopedic symptoms was as follows; knee pain, 29.0%; low back pain, 42.0% and both knee and low back pain 17.6%. Both knee and low back pain were significantly and independently associated with short sleep duration (knee pain: odds ratio (OR) = 1.19, p<0.01; low back pain: OR = 1.13, p = 0.01) and poor sleep quality (knee pain: OR = 1.22, p<0.01; low back pain; OR = 1.57, p<0.01). The group in the highest tertile of the NRS or RDQ score had the highest risk for short sleep duration and poor sleep quality except for the relationship between the highest tertile of the RDQ score and short sleep duration.(the highest tertile of the NRS: OR for short sleep duration = 1.31, p<0.01; OR for poor sleep quality = 1.47, p<0.01; the highest tertile of the RDQ: OR for short sleep duration = 1.11, p = 0.12; OR for poor sleep quality = 1.81, p<0.01) Further, coincident knee and low back pain raised the odds ratios for short sleep duration (either of knee or low back pain: OR = 1.10, p = 0.06; both knee and low back pain: OR = 1.40, p<0.01) and poor sleep quality (either of knee or low back pain: OR = 1.61, p<0.01; both knee and low back pain: OR = 2.17, p<0.01).

Conclusion

Knee and low back pains were independently associated with short sleep duration and poor sleep quality. Further, they additively increased the correlation with these sleep problems in the general population.     

Clinical and Statistical Evaluation of Six Hypnotic Agents

Six hypnotic drugs and a placebo were coded and administered at random, one dose at 8 p.m., to 20 patients in a Toronto hospital. A special evaluation scale was used, studying average duration of sleep, time of onset of sleep, quality of sleep and side effects. Secobarbital sodium and methyprylon were statistically significantly more effective than the placebo. The other drugs, glutethimide and three quinozolinone derivatives, were not statistically different from the placebo in their effects. The placebo effect itself was studied. A particular feature of this report is the detailed statistical treatment of the data collected.     

Rod sensitivity and visual pigment concentration in Xenopus

Xenopus larvae were raised on a vitamin A-free diet under constant illumination until their visual pigment content had decreased to between 8% of normal and an undetectably low level. After the intramuscular injection of 2.1 X 10(13-2.1 X 10(16) molecules of [3H]vitamin A, ocular tissue showed a rapid rate of uptake of label which reached a maximum level of incorporation by 48 h. Light- microscopic autoradiography revealed that the retinal uptake of label was concentrated within the receptor outer segments. Spectral transmissivity measurements at various times after injection were made upon intact retinas and upon digitonin extracts. They showed that visual pigment with a lambdamax of 504 nm was formed in the retina and that the amount formed was a function of incubation time and the magnitude of the dose administered. Electrophysiological measures of photoreceptor light responses were obtained from the PIII component of the electroretinogram, isolated with aspartate. The quantal flux required to elicit a criterion response was determined and related to the fraction of visual pigment present. The results showed that rod sensitivity varied linearly with the probability of quantal absorption.     

Effect of post-exposure administration of keratinocyte growth factor (Palifermin) on radiation effects in oral mucosa in mice

Oral mucositis is a severe component of the acute radiation syndrome. The present study was initiated to determine the potential of recombinant human keratinocyte growth factor (rHuKGF, Palifermin) to ameliorate oral mucositis in a mouse model after a single radiation exposure. A 3 × 3 mm² area in the center of the lower tongue surface of C3H/Neu mice was irradiated with graded single doses of 25 kV X-rays. Acute mucosal ulceration was used as the quantal end-point for dose–response analyses. Palifermin was applied at a dose of 15 mg/kg on days 0, 1, 2, 3, 4 or 5. For comparison, three injections of 5 or 15 mg/kg on days 1–3 were administered. The ED₅₀ (dose at which ulceration is expected in 50% of the animals) for irradiation alone was 11.6 ± 1.2 Gy. Mean latent time was 9.4 ± 0.2 days; mean ulcer duration was 2.8 ± 0.2 days. Single injections of rHuKGF did not result in a significant increase in isoeffective radiation doses at any of the administration days. However, the latent time to ulceration was significantly shortened by 1–2 days in all protocols. Repeated administration of rHuKGF (15 mg/kg) resulted a significant increase in ED50 to 16.8 ± 4.0 Gy (P = 0.0047); the mean latent time was 4.4 ± 0.9 days. Three injections of 5 mg/kg of Palifermin on days 1–3 yielded an ED50 of 19.4 ± 1.7 Gy. In this protocol, mean latent time was 6.6 ± 0.6 days. In conclusion, Palifermin has a potential to reduce the mucositis burden in patients after a single radiation exposure. Repeated injections are required. For three injections, a negative dose-effect of rHuKGF was observed. The optimum dose, number and timing of the administration require further investigation.     

Revisiting the relationship between wages and sleep duration: The role of insomnia

This paper uses the 2005 and 2010 Canadian General Social Surveys (Time Use) to investigate the effect of wages on the sleep duration of individuals in the labour force. The endogeneity of wages is taken into account with an instrumental variables approach; we find that the wage rate affects sleeping time in general, corroborating Biddle and Hamermesh’s (1990) main conclusion. A ten percent increase in the wage rate leads to an 11–12 min decrease in sleep per week. But this number masks several effects. The responsiveness of sleep time to wage rate changes depends upon the sex of the individual, whether or not sleep problems are present and general economic conditions. By far the largest adjustment is found for insomniacs in 2010, a year of general economic downturn in Canada. We also investigate the non-randomness of insomnia in the population by using a Heckman procedure, and find that the sleep time of female non-insomniacs is even more responsive to wage rate changes once account is taken of this selection bias, but otherwise selection was not a problem in our samples.     

Dose-response time modelling for highly pathogenic avian influenza A (H5N1) virus infection

Aims: To develop time‐dependent dose–response models for highly pathogenic avian influenza A (HPAI) of the H5N1 subtype virus. Methods and Results: A total of four candidate time‐dependent dose–response models were fitted to four survival data sets for animals (mice or ferrets) exposed to graded doses of HPAI H5N1 virus using the maximum‐likelihood estimation. A beta‐Poisson dose–response model with the N₅₀ parameter modified by an exponential‐inverse‐power time dependency or an exponential dose–response model with the k parameter modified by an exponential‐inverse time dependency provided a statistically adequate fit to the observed survival data. Conclusions: We have successfully developed the time‐dependent dose–response models to describe the mortality of animals exposed to an HPAI H5N1 virus. The developed model describes the mortality over time and represents observed experimental responses accurately. Significance and Impact of the Study: This is the first study describing time‐dependent dose–response models for HPAI H5N1 virus. The developed models will be a useful tool for estimating the mortality of HPAI H5N1 virus, which may depend on time postexposure, for the preparation of a future influenza pandemic caused by this lethal virus.     

A dose-response model for teratological experiments involving quantal responses

This paper introduces a dose-response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size. The maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm. Two methods of low-dose extrapolation are presented, one based on the litter size distribution and the other a conservative method. The resulting procedures are then applied to a teratological data set from the literature.     

Habitual sleep and human plasma metabolomics

Introduction

Sleep plays an important role in cardiometabolic health. The sleep-wake cycle is partially driven by the endogenous circadian clock, which governs a range of metabolic pathways. The association between sleep and cardiometabolic health may be mediated by alterations of the human metabolome.

Objectives

To better understand the biological mechanism underlying the association between sleep and health, we examined human plasma metabolites in relation to sleep duration and sleep timing.

Methods

Using an untargeted approach, 329 fasting plasma metabolites were measured in 277 Chinese participants. We measured sleep timing (midpoint between bedtime and wake up time) using repeated time-use surveys (4 weeks during 1 year) and previous night sleep duration from questionnaires completed before sample donation.

Results

We found 64 metabolites that were associated with sleep timing with a false discovery rate of 0.2 or lower, after adjusting for potential confounders. Notably, we found that later sleep timing was associated with higher levels of multiple metabolites in amino acid metabolism, including branched chain amino acids and their gamma-glutamyl dipeptides. We also found widespread associations between sleep timing and numerous metabolites in lipid metabolism, including bile acids, carnitines and fatty acids. In contrast, previous night sleep duration was not associated with plasma metabolites in our study.

Conclusion

Sleep timing was associated with a large number of metabolites across a variety of biochemical pathways. Some metabolite associations are consistent with a relationship between late chronotype and adverse effects on cardiometabolic health.