Molecular Dynamics as a Mathematical Mapping. II. Partial Derivatives in the Microcanonical Ensemble

Abstract

Performing molecular dynamics in a fully continuous and differentiable framework can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and input macroscopic conditions, and, on the other, the calculated corresponding macroscopic properties of the bulk molecular system.

Within this framework, it is possible to apply standard methods of variational calculus for the computation of the partial derivatives of the molecular dynamics mapping based on the integration of either the adjoint equations or the sensitivity equations of the classical Newtonian equations of motion. We present procedures for these computations in the standard microcanonical (N, V, E) ensemble, and compare the computational efficiency of the two approaches. The general formulations developed are applied to the specific example of bulk ethane fluid.

With these procedures in place, it is now possible to compute the partial derivatives of any property determined by molecular dynamics with respect to any input property and any potential parameter. Moreover, these derivatives are computed to essentially the same level of numerical accuracy as the output properties themselves.     

Molecular Dynamics as a Mathematical Mapping. I. Differentiable Force Functions

Abstract

The molecular dynamics technique can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and the input macroscopic conditions, and, on the other, the calculated macroscopic properties of the bulk molecular system.

The differentiability of such a mapping in the conventional molecular dynamics calculations is affected by the discontinuities in particle positions introduced by the periodic boundary conditions and the discontinuities introduced by the minimum image convention and other methods commonly employed to approximate the calculation of interparticle potential and force.

This paper proposes an alternative molecular dynamics framework based on modified force functions which are almost everywhere continuous and differentiable, and exhibit a natural periodicity. These characteristics obviate the need for both the periodic boundary conditions and the minimum image convention, as well as for any corrections for long-range interactions. They also make it possible to apply standard methods of variational calculus for the computation of partial derivatives of the molecular dynamics mapping.

The modified framework is first introduced for the case of simple monoatomic fluids where the nature of the forces exerted between any pair of two particles is identical. A more general model describing the interactions of flexible molecules is then developed. We describe the application of this approach to mixtures of alkane molecules interacting via the NERD force field.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.     

Lipid lowering activity of novel N-(benzoylphenyl)pyridine-3-carboxamide derivatives in Triton WR-1339-induced hyperlipidemic rats

Abstract

Context: Dyslipidemia is a major risk factor for the development of cardiovascular diseases. Many dyslipidemic patients do not achieve their target lipid levels with the currently available medications, and most of them may experience many side effects.

Objective: The present work aimed toward identifying a new class of novel nicotinic acid-carboxamide derivatives as promising antihyperlipidemic compounds.

Materials and methods: Six novel N-(benzoylphenyl)pyridine-3-carboxamide derivatives were synthesized using acid chloride pathways. All structures were confirmed using ¹H-NMR, ¹³C-NMR, IR, and HRMS. The evaluation of biological activity was conducted using Triton WR-1339-induced hyperlipidemic rats model.

Results: This study revealed that some of the newly synthesized novel N-(benzoylphenyl)pyridine-3-carboxamide derivatives mainly C4 and C6 possessed significant antihyperlipidemic activities on lipid components TG and TC (p value?<0.05).

Discussion and conclusion: This research opens the door for new potential antihyperlipidemic compounds derived from nicotinic acid that need further optimization of their biological activities.     

Testing methods to estimate abundance of Magellanic Penguins Spheniscus magellanicus

Capsule Using simulations in a geographical information system our results showed that systematic sampling with quadrats was the most accurate, precise and cost-effective method to survey Magellanic Penguin colonies.

Aims To determine which sampling method gives better estimations of penguin abundance.

Methods A virtual colony was generated deriving spatial parameters from a real survey and applying Kriging interpolation. Three sampling methods were then applied on this virtual colony: random sampling with quadrats; systematic sampling with quadrats; systematic sampling with fixed-width transects. The estimated abundance for each trial was compared to the abundance of the virtual colony to have a measure of accuracy and precision.

Results Systematic sampling with quadrats estimated penguin abundance better than random or systematic sampling with transects since it achieved 100% accuracy and great precision after sampling only 2.1% of the virtual colony.

Conclusion The use of a simulated colony allowed the comparison of several sampling methods traditionally used in Magellanic Penguin surveys. The results of this study are important in order to standardize sampling protocols for Magellanic Penguins and to have more comparable estimations to detect trends over time. Also, the methodological approach used here could be used to assess sampling methods for other colonial bird species.     

The discriminant power of biometrics for sex determination in European Bee-eaters Merops apiaster

ABSTRACT

Capsule A combination of several biometric measures enables the reliable sexing of the European Bee-eater Merops apiaster, a species with subtle sex differences in plumage and morphometry.

Aims To explore variation in biometrics and their suitability to discriminate sex in adult European Bee-eaters Merops apiaster.

Methods We sampled populations of a long-distance migratory species with low sexual size dimorphism, the European Bee-eater Merops apiaster, from colonies in western Iberia (Portugal) and Central Europe (Germany) to investigate body size variation and derive population-specific and general sex discriminant functions.

Results Overall, male Bee-eaters were larger than females while Bee-eaters from Germany and Portugal did not differ in size, except for primary length and tail length. The best single measurement to discriminate sex was wing length for Portuguese birds and tail tip length for German birds, as in the combined dataset. Multivariate discriminant functions of head-bill, wing and tail tip lengths provided the highest discriminant accuracy, discriminating sex for 91% of the birds from Portugal, 96% from Germany and 94% when using the combined dataset. Nonetheless, the discriminant accuracy remained high in the functions using only two variables for Portugal (head-bill and tail tip 91%, head-bill and wing 88%, wing and tail tip 88%), Germany (head-bill and tail tip 95%, wing and tail tip 97%) and in the combined dataset (head-bill and tail tip 92%, wing and tail tip 93%).

Conclusions Population specific discriminant functions allow sexing of European Bee-eaters by morphometry with high degree of accuracy at least for Iberia and Central European populations. Such discriminant functions can be used to assign the sex of adult Bee-eaters reliably and swiftly while the bird is still in the hand, highlighting the potential of these functions for rapidly sexing species with low degrees of sexual size and plumage dimorphism.     

Reorientational Correlation Functions,Quaternions and Wigner Rotation Matrices

Abstract

The main results of this paper are tabulations of Wigner rotation matrix elements in terms of quaternion parameters and direction cosines. These will be useful for the calculation of orientational probability functions or reorientational correlation functions from simulations of molecular systems using programs based either on quaternions or constraints. We review the relationship between quaternions and the L = ½ Wigner rotation matrix, give some useful properties of quaternions and Wigner rotation matrices and show how the Lth Wigner rotation matrix can be constructed from the quaternion parameters without first obtaining the Euler angles.     

Accuracy and precision of a wrist movement when vibrotactile prompts inform movement speed

Abstract

Purpose: This study investigated the effect of movement speed on task accuracy and precision when participants were provided temporally oriented vibrotactile prompts. Materials and methods: Participants recreated a simple wrist flexion/extension movement at fast and slow speeds based on target patterns conveyed via vibrating motors affixed to the forearm. Each participant was given five performance-blinded trials to complete the task at each speed. Movement accuracy (root mean square error) and precision (standard deviation) were calculated for each trial in both the spatial and temporal domains. Results: 28 participants completed the study. Results showed temporal accuracy and precision improved with movement speed (both: fast?>?slow, p?<?0.01), while all measures improved across trials (temporal accuracy and precision: trial 1?<?all other trials, p?<?0.05; spatial accuracy: trial 1 and 2?<?all other trials, p?<?0.05; spatial precision: trial 1?<?all other trials, p?<?0.05). Conclusions: Overall, temporal and spatial results indicate participants quickly recreated and maintained the desired pattern regardless of speed. Additionally, movement speed seems to influence movement accuracy and precision, particularly within the temporal domain. These results highlight the potential of vibrotactile prompts in rehabilitation paradigms aimed at motor re-education.     

Utilization of Mentha aquatica L. for removal of fecal pathogens and heavy metals from water of Bosna river,Bosnia and Herzegovina

Abstract

The aim of the present study was to investigate the potential of Mentha aquatica L. for phytoremediation of water contaminated with heavy metals and fecal pathogens from Bosna river. The water was treated with M. aquatica for 5, 10, and 15 days consecutively after which it was analyzed for the various physicochemical and microbiological parameters.

The initial concentration of cadmium (Cd) ranged from 3.644 to 6.108?µg/l, while lead (Pb) varied between 0.1 and 1.386?µg/l. After treatment, M. aquatica accumulated significant amounts of cadmium (Cd) and lead (Pb) with the highest removal rates of 96.49% for Cd and 45.72% for Pb. Values of several physicochemical parameters were decreased after 15 days treatment period.

All water samples were analyzed for enumeration of aerobic heterotrophic bacteria, total coliforms, and fecal coliforms by the membrane filtration. Removal efficiency was greater than 80% for microbiological parameters. The concentration of heavy metals was determined in different plant parts and subsequently, the translocation factor was determined. In M. aquatica plant parts, concentrations of Pb and Cd were increased after 15 days of treatment. Our results demonstrated that M. aquatica could be good candidates for the removal of fecal pathogens and heavy metals present in surface water.     

Additions To The Flora Of Shetland

ABSTRACT

Background: Pallenis spinosa (Asteraceae) produces both winged and wingless achenes. Both achene morphs are non-dormant and show a similar embryo size, rendering dispersal ability as their only apparent functional difference.

Aims: We studied morph-specific release and spatial dispersal patterns to ascertain whether the common view of seed dimorphism as a mixed strategy, that is functionally fully differentiated morphs, is appropriate for this system.

Methods: For three years, at the onset of achene release, in early autumn, we placed achene traps at different distances from source plants, censusing achene arrival at 3–4 day intervals. We constructed morph-specific dispersal kernels and related release intensity to prevailing meteorological conditions in census intervals. Selected kernel models were used to describe dispersal effects of observed changes in the proportion of winged achenes (p_w) in successive released fractions.

Results: Achene release extended up to early-mid winter, peaking in rainy, windy intervals. Throughout the season, p_w decreased progressively. Unexpectedly, the wingless morph produced the longest dispersal tails and it only showed ability for fat-tailed dispersal. Consequently, maximum dispersal distances steadily increased throughout the season.

Conclusions: Achene dimorphism in P. spinosa appears to allow a within-season continuous reshaping of the seed-dispersal kernel instead of representing a mixed strategy.     

Spatial relations and population structure of a dominant tree along a treeline ecotone in the Tropical Andes: interactions at gradient and plant-neighbourhood scales

Background: Studies in temperate mountains suggest that plant–plant interactions modulate tree establishment above the forest line. In tropical mountains worldwide this issue remains largely unexplored.

Aims: To analyse the population structure and local spatial relationships of a dominant tree at a species-rich tropical Andean forest line.

Methods: We determined changes in the population structure of Diplostephium venezuelense along an elevation gradient between continuous forest and open páramo and analysed plant community structure and superficial rock cover in the neighbourhood of saplings and adults at the upper forest line.

Results: Sapling and adult densities were highest in low-altitude páramos adjacent to the forest line and at the borders of small forest islands. Saplings showed local spatial aggregation, were positively associated with small boulders and low shrubs, and negatively associated with mosses and lichens. However, no spatial association was found between scattered adults in the páramo and saplings of other forest trees.

Conclusions: Complex species-specific local spatial interactions, suggesting both facilitative and antagonistic effects, seem to modulate the establishment of the dominant tree D. venezuelense at and above the upper forest line. Nevertheless, the establishment of other tree species above continuous forests does not appear to be facilitated by the canopy cover offered by the isolated D. venezuelense individuals established in open páramo environments.     

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

Background

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

Results

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

Conclusions

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-256) contains supplementary material, which is available to authorized users.     

An empirical approach for deriving specific inland water quality parameters from high spatio-spectral resolution image

Inland lake of Vembanad has benefited from continuous monitoring to evaluate water quality which has declined due to increased anthropogenic activities and climate change. Remote sensing techniques can be used to estimate and monitor inland water quality both spatially and temporally. An empirical model is presented in Vemaband lake that retrieves the specific water quality parameters through correlations between various spectral wavelengths of Sentinel-2MSI (S2MSI) with field-measured water quality parameters. This approach includes the combinations of various bands, band ratios, and band arithmetic computation of satellite sensors of spectral datasets. The specific inland water quality parameters such as chlorophyll-a (chl-a), total suspended solids (TSS), turbidity, and secchi disc depth (SDD) were retrieved from the developed water quality model through Sentinel-2A remote sensing reflectance. The result illustrates that Specific Inland Water Quality Parameters (SIWQP) strongly correlated with S2MSI reflection spectral wavelengths. The SIWQP models are constructed for TSS (R²?=?0.8008), Chl-a (R²?=?0.8055), Turbidity (R²?=?0.6329) and SDD (R²?=?0.7174).The spatial distribution of SIWQPs in Vembanad lake for March 2018 is mapped and shows the lake's water quality distribution. The research from Sentinel-2, MSI has potential and is appropriate in high spectral and spatial characteristics for retrieving and continuous monitoring of water quality parameters in the regional scale of inland water bodies.

     

MR microscopy of the human fetal upper extremity – a proof-of-principle study

Background

Bone morphogenetic proteins regulate multiple processes in embryonic development, including early dorso-ventral patterning and neural crest development. BMPs activate heteromeric receptor complexes consisting of type I and type II receptor-serine/threonine kinases. BMP receptors Ia and Ib, also known as ALK3 and ALK6 respectively, are the most common type I receptors that likely mediate most BMP signaling events. Since early expression patterns and functions in Xenopus laevis development have not been described, we have addressed these questions in the present study.

Results

Here we have analyzed the temporal and spatial expression patterns of ALK3 and ALK6; we have also carried out loss-of-function studies to define the function of these receptors in early Xenopus development. We detected both redundant and non-redundant roles of ALK3 and ALK6 in dorso-ventral patterning. From late gastrula stages onwards, their expression patterns diverged, which correlated with a specific, non-redundant requirement of ALK6 in post-gastrula neural crest cells. ALK6 was essential for induction of neural crest cell fate and further development of the neural crest and its derivatives.

Conclusions

ALK3 and ALK6 both contribute to the gene regulatory network that regulates dorso-ventral patterning; they play partially overlapping and partially non-redundant roles in this process. ALK3 and ALK6 are independently required for the spatially restricted activation of BMP signaling and msx2 upregulation at the neural plate border, whereas in post-gastrula development ALK6 exerts a highly specific, conserved function in neural crest development.

     

A New Spatial Representation of Amino Acid Residues in Globular Proteins

Abstract

For the globular proteins with known three-dimensional structures, an ellipsoid model of each protein was constructed with least volume and its dimensions were derived. The spatial arrangements were made for the C_α and side chain atoms of that protein within that ellipsoid. This new spatial representation shows the residue position from the centroid, as well as the depth from the surface. The average spatial parameters were then calculated. The correlations between these new spatial parameters and the existing parameters of the amino acid residues were then derived.     

Synthesis of Copper-64 and Technetium-99M Labeled Oligonucleotides with Macrocyclic Ligands

Abstract

An efficient procedure for the preparation of oligonucleotides carrying a mono-N-substituted azamacrocycle and its radiolabeled complex with Cu-64 and Tc-99m is reported. The new derivatives are of potential interest for Positron Emission Tomography and Single Photon Emission Tomography.     

Sexing terns using biometrics: the advantage of within-pair comparisons

Capsule Within-pair comparisons substantially improve the accuracy of sexing from biometrics for two congeneric species of seabird with monomorphic plumage and soft-tissue colouration.

Aims To examine the extent to which statistical limitations of sexing birds from biometrics using sample-level analysis could be overcome by sexing Common and Arctic Terns (Sterna hirundo and S. paradisaea) using measurements obtained from breeding pairs.

Methods Incubating adults were caught at the nest using walk-in traps and wing, tarsus, head-plus-bill, tail length, tail fork, and body mass measured. Each bird was individually colour-ringed and dyed with picric acid, enabling subsequent sexing by behavioural observations of copulation and courtship feeding. Birds were sexed using biometrics and the proportion of birds sexed correctly this way at the sample level was compared with the accuracy achieved if, within a pair, the larger bird was classified as male.

Results Head-plus-bill length was the single most accurate measurement for sexing individuals of both species, and correctly classified 72% of Arctic Terns and 73% of Common Terns. Combinations of measurements derived from discriminant analysis achieved slightly higher accuracy (73% and 78% respectively). Within-pair comparisons were more accurate than sample-level analysis for both single measurements and discriminant functions, and were able to sex 84% of Arctic Terns and 86% of Common Terns correctly.

Conclusion Comparing birds within pairs improves accuracy and can eliminate the need to calculate cut points or discriminant functions from a sample of birds of known sex for each particular study. We strongly advocate such comparisons wherever possible to increase accuracy and simplify computational procedures for predicting sex, thus reducing associated sources of error.     

Stomatal response functions to environmental stress of dominant species in the tropical Andean páramo

ABSTRACT

Background: Stomatal response functions of dominant plant species can provide insights into the behaviour of ecosystems under environmental stress, and provide tools for modelling their response to climate change. However, they remain little studied in tropical Alpine ecosystems.

Aims: Our objective was to formulate and compare stomatal response functions for two dominant páramo species with different adaptive strategies to drought, the stress-tolerant shrub Hypericum laricifolium, and the stress avoiding giant rosette Espeletia schultzii and thus enable making projections as to their future fitness in a changing climate.

Methods: A reanalysis of data found in the literature and new ecophysiological and micrometeorological measurements were used to fit and test new stomatal response functions to environmental variables for these two species.

Results: The response functions of vapour pressure differences between leaf and air showed an exponential decrease for both species, while for photosynthetically active radiation (PAR), peak-form response functions provided the best fit. The response function for leaf water potential was linear for the drought-tolerant shrub and decreased exponentially for the stress avoiding giant rosette. Several thresholds prior to stomatal closure were also included in the functions.

Conclusions: Although stress-avoiding and stress-tolerant strategies are both successful in the Andean páramo, the response functions suggest that the tolerant shrub could be more resistant to more intense drought.     

Synthesis and Anti-HIV Activity of Some S-Acyl-2-thioethyl (SATE) Phosphoramidate Derivatives of 3′-Azido-2′,3′-dideoxythymidine

Abstract

The synthesis and in vitro anti-HIV activity of tBuSATE phosphoramidate derivatives of AZT incorporating several methyl-esterified α-aminoacids are reported. The biological evaluation strongly supports the hypothesis that such compounds exert their anti-HIV effects via intracellular delivery of the corresponding 5′-mononucleotide.