Optimal adjustment of the human circadian clock in the real world

Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body’s internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock’s primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain. We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings.     

Optimal loading dose for the initiation of warfarin: a systematic review

Background

Selection of the right warfarin dose at the outset of treatment is not straightforward, and current evidence is lacking to determine the optimal strategy for initiation of therapy.

Methods

We included randomized controlled trials in patients commencing anticoagulation with warfarin, comparing different loading dose or different regimens. We searched Medline, EMBASE, the Cochrane Library and the NHS Health Economics Database up to June 2009. Primary outcomes were time to stable INR and adverse events. We summarised results as proportion of INRs in range from date of initiation and compared dichotomous outcomes using relative risks (RR) and calculated 95% confidence intervals (CIs).

Results

We included 11 studies of 1,340 patients newly initiated on warfarin. In two studies that used single INR measures, a loading dose of 10 mg compared to 5 mg led to more patients in range on day five. However, in two studies which measured two consecutive INRs, a loading dose of 10 mg compared to 5 mg did not lead to more patients in range on day five (RR = 0.86, 95% CI, 0.62 to 1.19, p = 0.37). Patients receiving a 2.5 mg initiation does took longer to achieve the therapeutic range, whilst those receiving a calculated initiation dose achieved target range 0.8 days quicker (4.2 days vs. 5 days, p = 0.007). More elderly patients receiving an age adjusted dose achieved a stable INR compared to the Fennerty protocol (48% vs. 22% p = 0.02) and significantly fewer patients on the age adjusted regimens had high out-of-range INRs. Two studies report no significant differences between genotype guided and 5 mg or 10 mg initiation doses and in the one significant genotype study the control group INRs were significantly lower than expected.

Conclusion

Our review findings suggest there is still considerable uncertainty between a 10 mg and a 5 mg loading dose for initiation of warfarin. In the elderly, lower initiation doses or age adjusted doses are more appropriate, leading to less higher INRs. Currently there is insufficient evidence to warrant genotype guided initiation, and adequately powered trials to detect effects on adverse events are currently warranted.     

Conformation of beta-hairpins in protein structures. A systematic classification with applications to modelling by homology, electron density fitting and protein engineering

A systematic classification of beta-hairpin structures which takes into account the polypeptide chain length and hydrogen bonding between the two antiparallel beta-strands is described. We have used this classification of beta-hairpin structures and their specific sequence pattern to derive rules which demonstrate its usefulness in assisting modelling beta-hairpins. These rules can be applied to comparative model building, modelling into electron density and in the prediction of conformation of beta-hairpins to aid protein engineering.     

Chick growth in albatrosses: curve fitting with a twist

We present a new type of equation to describe the growth patterns of procellariiform seabirds and other species whose chicks characteristically lose mass towards the end of the rearing period. Our equation is based on the Gompertz curve; our principles are also applicable to logistic and von Bertalanffy curves. From our model, five coefficients can be derived to characterise the patterns of growth. These are: growth rate, peak mass and age at which it is attained, loss rate and an index describing the overall shape of the curve. We illustrate the use of this new equation with data collected, using automated weighing platforms, on six years of chick growth of Black-browed Diomedea melanophris and Grey-headed D. chrysostoma albatrosses at Bird Island, South Georgia. In comparison with Grey-headed Albatross, Black-browed Albatross chicks grow at a faster rate and to a higher peak mass; they also reach their peak mass at an earlier age, and lose mass at a faster rate in the mass recession period. However, in both species, chicks reached peak mass when 72% of the rearing period had elapsed; within species, only this did not vary between years. This new equation not only enables the period of mass recession to be incorporated into growth analysis, but, because it does not require assumptions about asymptotic mass, greatly facilitates inter-species comparisons.     

Measurement of interrater agreement with adjustment for covariates

The kappa coefficient measures chance-corrected agreement between two observers in the dichotomous classification of subjects. The marginal probability of classification by each rater may depend on one or more confounding variables, however. Failure to account for these confounders may lead to inflated estimates of agreement. A multinomial model is used that assumes both raters have the same marginal probability of classification, but this probability may depend on one or more covariates. The model may be fit using software for conditional logistic regression. Additionally, likelihood-based confidence intervals for the parameter representing agreement may be computed. A simple example is discussed to illustrate model-fitting and application of the technique.     

Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta‐analysis

Females can benefit from mate choice for male traits (e.g. sexual ornaments or body condition) that reliably signal the effect that mating will have on mean offspring fitness. These male‐derived benefits can be due to material and/or genetic effects. The latter include an increase in the attractiveness, hence likely mating success, of sons. Females can potentially enhance any sex‐biased benefits of mating with certain males by adjusting the offspring sex ratio depending on their mate's phenotype. One hypothesis is that females should produce mainly sons when mating with more attractive or higher quality males. Here we perform a meta‐analysis of the empirical literature that has accumulated to test this hypothesis. The mean effect size was small (r = 0.064–0.095; i.e. explaining <1% of variation in offspring sex ratios) but statistically significant in the predicted direction. It was, however, not robust to correction for an apparent publication bias towards significantly positive results. We also examined the strength of the relationship using different indices of male attractiveness/quality that have been invoked by researchers (ornaments, behavioural displays, female preference scores, body condition, male age, body size, and whether a male is a within‐pair or extra‐pair mate). Only ornamentation and body size significantly predicted the proportion of sons produced. We obtained similar results regardless of whether we ran a standard random‐effects meta‐analysis, or a multi‐level, Bayesian model that included a correction for phylogenetic non‐independence. A moderate proportion of the variance in effect sizes (51.6–56.2%) was due to variation that was not attributable to sampling error (i.e. sample size). Much of this non‐sampling error variance was not attributable to phylogenetic effects or high repeatability of effect sizes among species. It was approximately equally attributable to differences (occurring for unknown reasons) in effect sizes among and within studies (25.3, 22.9% of the total variance). There were no significant effects of year of publication or two aspects of study design (experimental/observational or field/laboratory) on reported effect sizes. We discuss various practical reasons and theoretical arguments as to why small effect sizes should be expected, and why there might be relatively high variation among studies. Currently, there are no species where replicated, experimental studies show that mothers adjust the offspring sex ratio in response to a generally preferred male phenotype. Ultimately, we need more experimental studies that test directly whether females produce more sons when mated to relatively more attractive males, and that provide the requisite evidence that their sons have higher mean fitness than their daughters.     

Optimal photosynthetic use of light by tropical tree crowns achieved by adjustment of individual leaf angles and nitrogen content

Background and Aims

Theory for optimal allocation of foliar nitrogen (ONA) predicts that both nitrogen concentration and photosynthetic capacity will scale linearly with gradients of insolation within plant canopies. ONA is expected to allow plants to efficiently use both light and nitrogen. However, empirical data generally do not exhibit perfect ONA, and light-use optimization per se is little explored. The aim was to examine to what degree partitioning of nitrogen or light is optimized in the crowns of three tropical canopy tree species.

Methods

Instantaneous photosynthetic photon flux density (PPFD) incident on the adaxial surface of individual leaves was measured along vertical PPFD gradients in tree canopies at a frequency of 0·5 Hz over 9–17 d, and summed to obtain the average daily integral of PPFD for each leaf to characterize its insolation regime. Also measured were leaf N per area (N_area), leaf mass per area (LMA), the cosine of leaf inclination and the parameters of the photosynthetic light response curve [photosynthetic capacity (A_max), dark respiration (R_d), apparent quantum yield (ϕ) and curvature (θ)]. The instantaneous PPFD measurements and light response curves were used to estimate leaf daily photosynthesis (A_daily) for each leaf.

Key Results

Leaf N_area and A_max changed as a hyperbolic asymptotic function of the PPFD regime, not the linear relationship predicted by ONA. Despite this suboptimal nitrogen partitioning among leaves, A_daily did increase linearly with PPFD regime through co-ordinated adjustments in both leaf angle and physiology along canopy gradients in insolation, exhibiting a strong convergence among the three species.

Conclusions

The results suggest that canopy tree leaves in this tropical forest optimize photosynthetic use of PPFD rather than N per se. Tropical tree canopies then can be considered simple ‘big-leaves’ in which all constituent ‘small leaves’ use PPFD with the same photosynthetic efficiency.Key words: Optimal resource allocation, nitrogen, photosynthetic capacity, leaf mass per area, tropical trees, radiation use efficiency, scaling, leaf angle, canopy architecture, big leaf model     

Real-space refinement with DireX: from global fitting to side-chain improvements

Single-particle cryo-electron microscopy (cryo-EM) has become an important tool to determine the structure of large biomolecules and assemblies thereof. However, the achievable resolution varies considerably over a wide range of about 3.5-20 ?. The interpretation of these intermediate- to low-resolution density maps in terms of atomic models is a big challenge and an area of active research. Here, we present our real-space structure refinement program DireX, which was developed primarily for cryo-EM-derived density maps. The basic principle and its main features are described. DireX employs Deformable Elastic Network (DEN) restraints to reduce overfitting by decreasing the effective number of degrees of freedom used in the refinement. Missing or reduced density due to flexible parts of the protein can lead to artifacts in the structure refinement, which is addressed through the concept of restrained grouped occupancy refinement. Furthermore, we describe the performance of DireX in the 2010 Cryo-EM Modeling Challenge, where we chose six density maps of four different proteins provided by the Modeling Challenge exemplifying typical refinement results at a large resolution range from 3 to 23 ?.     

Flexible fitting to cryo-electron microscopy maps with coarse-grained elastic network models

Cryo-electron microscopy has become an important tool for protein structure determination in recent decades. Since proteins may exist in multiple conformational states, combining high resolution X-ray or NMR structures with cryo-electron microscopy maps is a useful approach to obtain proteins in different functional states. Flexible fitting methods used in cryo-electron microscopy aim to obtain an unknown protein conformation from a high resolution structure and a cryo-electron microscopy map. Since all-atom flexible fitting is computationally expensive, many efficient flexible fitting algorithms that utilize coarse-grained elastic network models have been proposed. In this study, we investigated performance of three coarse-grained elastic network model-based flexible fitting methods (EMFF, iModFit, NMFF) using 25 protein pairs at four resolutions. This study shows that the application of coarse-grained elastic network models to flexible fitting of cryo-electron microscopy maps can provide fast and fruitful models of various conformational states of proteins.     

Flexible fitting in 3D-EM with incomplete data on superfamily variability

We present a substantial improvement of S-flexfit, our recently proposed method for flexible fitting in three dimensional electron microscopy (3D-EM) at a resolution range of 8-12A, together with a comparison of the method capabilities with Normal Mode Analysis (NMA), application examples and a user's guide. S-flexfit uses the evolutionary information contained in protein domain databases like CATH, by means of the structural alignment of the elements of a protein superfamily. The added development is based on a recent extension of the Singular Value Decomposition (SVD) algorithm specifically designed for situations with missing data: Incremental Singular Value Decomposition (ISVD). ISVD can manage gaps and allows considering more aminoacids in the structural alignment of a superfamily, extending the range of application and producing better models for the fitting step of our methodology. Our previous SVD-based flexible fitting approach can only take into account positions with no gaps in the alignment, being appropriate when the superfamily members are relatively similar and there are few gaps. However, with new data coming from structural proteomics works, the later situation is becoming less likely, making ISVD the technique of choice for further works. We present the results of using ISVD in the process of flexible fitting with both simulated and experimental 3D-EM maps (GroEL and Poliovirus 135S cell entry intermediate).