Statistical Measures to Quantify Similarity between Molecular Dynamics Simulation Trajectories.

Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by Cα-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between Cα-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.

Variation in carbon and nitrogen concentrations among peatland categories at the global scale.

Peatlands account for 15 to 30% of the world's soil carbon (C) stock and are important controls over global nitrogen (N) cycles. However, C and N concentrations are known to vary among peatlands contributing to the uncertainty of global C inventories, but there are few global studies that relate peatland classification to peat chemistry. We analyzed 436 peat cores sampled in 24 countries across six continents and measured C, N, and organic matter (OM) content at three depths down to 70 cm. Sites were distinguished between northern (387) and tropical (49) peatlands and assigned to one of six distinct broadly recognized peatland categories that vary primarily along a pH gradient. Peat C and N concentrations, OM content, and C:N ratios differed significantly among peatland categories, but few differences in chemistry with depth were found within each category. Across all peatlands C and N concentrations in the 10-20 cm layer, were 440 ± 85.1 g kg-1 and 13.9 ± 7.4 g kg-1, with an average C:N ratio of 30.1 ± 20.8. Among peatland categories, median C concentrations were highest in bogs, poor fens and tropical swamps (446-532 g kg-1) and lowest in intermediate and extremely rich fens (375-414 g kg-1). The C:OM ratio in peat was similar across most peatland categories, except in deeper samples from ombrotrophic tropical peat swamps that were higher than other peatlands categories. Peat N concentrations and C:N ratios varied approximately two-fold among peatland categories and N concentrations tended to be higher (and C:N lower) in intermediate fens compared with other peatland types. This study reports on a unique data set and demonstrates that differences in peat C and OM concentrations among broadly classified peatland categories are predictable, which can aid future studies that use land cover assessments to refine global peatland C and N stocks.

The role of soils in provision of energy.

Soils have both direct and indirect impacts on available energy, but energy provision, in itself, has direct and indirect impacts on soils. Burning peats provides only approximately 0.02% of global energy supply yet emits approximately 0.7-0.8% of carbon losses from land-use change and forestry (LUCF). Bioenergy crops provide approximately 0.3% of energy supply and occupy approximately 0.2-0.6% of harvested area. Increased bioenergy demand is likely to encourage switching from forests and pastures to rotational energy cropping, resulting in soil carbon loss. However, with protective policies, incorporation of residues from energy provision could sequester approximately 0.4% of LUCF carbon losses. All organic wastes available in 2018 could provide approximately 10% of global energy supply, but at a cost to soils of approximately 5% of LUCF carbon losses; not using manures avoids soil degradation but reduces energy provision to approximately 9%. Wind farms, hydroelectric solar and geothermal schemes provide approximately 3.66% of energy supply and occupy less than approximately 0.3% of harvested area, but if sited on peatlands could result in carbon losses that exceed reductions in fossil fuel emissions. To ensure renewable energy provision does not damage our soils, comprehensive policies and management guidelines are needed that (i) avoid peats, (ii) avoid converting permanent land uses (such as perennial grassland or forestry) to energy cropping, and (iii) return residues remaining from energy conversion processes to the soil. This article is part of the theme issue 'The role of soils in delivering Nature's Contributions to People'.

High throughput nonparametric probability density estimation.

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

Systems approaches in global change and biogeochemistry research.

Systems approaches have great potential for application in predictive ecology. In this paper, we present a range of examples, where systems approaches are being developed and applied at a range of scales in the field of global change and biogeochemical cycling. Systems approaches range from Bayesian calibration techniques at plot scale, through data assimilation methods at regional to continental scales, to multi-disciplinary numerical model applications at country to global scales. We provide examples from a range of studies and show how these approaches are being used to address current topics in global change and biogeochemical research, such as the interaction between carbon and nitrogen cycles, terrestrial carbon feedbacks to climate change and the attribution of observed global changes to various drivers of change. We examine how transferable the methods and techniques might be to other areas of ecosystem science and ecology.