Strategies for building criticism skills in undergraduate biochemists

This paper describes an easy method for empowering biochemistry students to think critically about research data. The technique encourages students to formulate their own opinions by removing the usually dominant 'expert' commentary. The exercise can be done individually or in very large groups, requires no specialist materials and confirmation that articulation and criticism skills have been learnt can be assessed under standard examination conditions. The skills learnt are not discipline specific and, as well as learning how best to read research papers, students also learn something about the research process.     

A circadian oscillator model based on empirical data

A model based on the van der Pol equation has been developed to predict the pattern of adaptation of aircrew and other travellers to rapid time-zone transitions, when the exposure to light cannot be quantified. The parameters of the model include the stiffness (mu) and the intrinsic period (T0), which together define the free-running period, and the external force (F). The parameter values were estimated by using a simplex minimization technique to fit the output from the model to body temperature data from 12 individuals before, and over a 12-day period immediately after, a 10-h eastward transition between London and Sydney. Data were collected at three equally spaced points during each sleep period and at the end of four 45-min rest periods during the day. The fitting procedure enabled the parameters of the temperature rhythm to be estimated after correcting for the masking effect of sleep. The average estimates of mu (0.38 h) and T0 (24.24 h) were close to earlier estimates based on forced desynchronization experiments, and the mean free-running period, calculated from these, was 24.50 h. The mean value of the external force F (0.54) was surprisingly high, and this may reflect the strong outdoor light levels during the days in Sydney. Estimates of phase, based on the model solutions, suggested that 11 subjects adapted by a phase delay and 1 by a phase advance. However, the amplitude of the rhythms was much reduced at times when the phase was changing rapidly. Simulations using the range of the model parameters for the 12 individuals predicted that adaptation to within 1 h after a 10-h eastward transition would be achieved within between 3 and 11 days. However, since these predictions are dependent on the choice of external force, estimates may need to be more conservative in real-life situations when light exposure cannot be measured.     

A phase dynamics model of human circadian rhythms

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker-driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.     

A simpler model of the human circadian pacemaker

Numerous studies have used the classic van der Pol oscillator, which contains a cubic nonlinearity, to model the effect of light on the human circadian pacemaker. Jewett and Kronauer demonstrated that Aschoff's rule could be incorporated into van der Pol type models and used a van der Pol type oscillator with higher order nonlinearities. Kronauer, Forger, and Jewett have proposed a model for light preprocessing, Process L, representing a biochemical process that converts a light signal into an effective drive on the circadian pacemaker. In the paper presented here, the authors use the classic van der Pol oscillator with Process L and Jewett and Kronauer's model of Aschoff's rule to model the human circadian pacemaker. This simpler cubic model predicts the results of a three-pulse human phase response curve experiment and a two-pulse amplitude reduction study with as much, or more, accuracy as the models of Jewett and Kronauer and Kronauer, Forger, and Jewett, which both employ a nonlinearity of degree 7. This suggests that this simpler cubic model should be considered as a potential alternative to other models of the human circadian system currently available.     

A model for circadian clocks

An extension of an earlier model simulating the effects of light on the drosophila eclosion rhythm is presented. The effects of variable light intensity are described. This allows not only the simulation of certain experiments not covered by the earlier model, but also it permits an extension of the model to other organisms. By changing only its sensitivity to light the model simulates the phase response curves of certain mammals as well as Aschoff’srule.     

Revised limit cycle oscillator model of human circadian pacemaker

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.     

A statistical model of the human core-temperature circadian rhythm

We formulate a statistical model of the human core-temperature circadian rhythm in which the circadian signal is modeled as a van der Pol oscillator, the thermoregulatory response is represented as a first-order autoregressive process, and the evoked effect of activity is modeled with a function specific for each circadian protocol. The new model directly links differential equation-based simulation models and harmonic regression analysis methods and permits statistical analysis of both static and dynamical properties of the circadian pacemaker from experimental data. We estimate the model parameters by using numerically efficient maximum likelihood algorithms and analyze human core-temperature data from forced desynchrony, free-run, and constant-routine protocols. By representing explicitly the dynamical effects of ambient light input to the human circadian pacemaker, the new model can estimate with high precision the correct intrinsic period of this oscillator ( approximately 24 h) from both free-run and forced desynchrony studies. Although the van der Pol model approximates well the dynamical features of the circadian pacemaker, the optimal dynamical model of the human biological clock may have a harmonic structure different from that of the van der Pol oscillator.     

Statistical considerations for high throughput screening data

High throughput screening (HTS) is a widely used effective approach in genome-wide association and large scale protein expression studies, drug discovery, and biomedical imaging research. How to accurately identify candidate ‘targets’ or biologically meaningful features with a high degree of confidence has led to extensive statistical research in an effort to minimize both false-positive and false-negative rates. A large body of literature on this topic with in-depth statistical contents is available. We examine currently available statistical methods on HTS and aim to summarize some selected methods into a concise, easy-tofollow introduction for experimental biologists.     

Statistical inference for serial dilution assay data

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.     

Accuracy of human circadian entrainment under natural light conditions: model simulations

The patterns of light intensity to which humans expose their circadian pacemakers in daily life are very irregular and vary greatly from day to day. The circadian pacemaker can adjust to such irregular exposure patterns by daily phase shifts, such as summarized in a phase response curve. It is demonstrated in this paper on the basis of computer simulations applying actually recorded human light exposure patterns that the pacemaker can substantially improve its accuracy by an additional response to light: For that purpose, it should additionally change its angular velocity (and consequently its period tau) in response to light. Reductions of tau in response to light in the morning and increases of tau in response to light in the evening can lead to an increase in entrained pacemaker accuracy with about 25%. Circadian pacemakers have evolved as accurate internal representations of external time, and investigated diurnal mammals all seem to respond to light by changing the period of their circadian pacemaker (in addition to shifting phase). The authors suggest that also human circadian systems take advantage of this possibility and that their pacemakers respond to light by shifting phase and changing period. As a consequence of this postulated mechanism, the simulations demonstrate that the period of the pacemaker under normally entrained conditions is 24 h. The maximum accuracy corresponds to a day-to-day standard deviation of the time of phase 0 of circa 15 min. This is considerably more accurate than the light signal humans usually perceive.     

Automatic data recording of circadian rhythms

This paper illustrates a method for automatic data recording using the printer port of personal computer and software designed ad hoc. The system was tested by measuring circadian rhythms of activity in the subterranean rodent Ctenomys talarum. Data is recorded in a text-only comma-delimited file, and displayed on screen.     

The human circadian clock and aging

The suprachiasmatic nucleus (SCN) of the hypothalamus is implicated in the timing of a wide variety of circadian processes. Since the environmental light-dark cycle is the main zeitgeber for many of the rhythms, photic information may have a synchronizing effect on the endogenous clock of the SCN by inducing periodic changes in the biological activity of certain groups of neurons. By studying the brains obtained at autopsy of human subjects, marked diurnal oscillations were observed in the neuropeptide content of the SCN. Vasopressin, for example, one of the most abundant peptides in the human SCN, exhibited a diurnal rhythm, with low values at night and peak values during the early morning. However, with advancing age, these diurnal fluctuations deteriorated, leading to a disrupted cycle with a reduced amplitude in elderly people. These findings suggest that the synthesis of some peptides in the human SCN exhibits an endogenous circadian rhythmicity, and that the temporal organization of these rhythms becomes progressively disturbed in senescence. (Chronobiology International, 17(3), 245-259, 2000)     

Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.