Exact and efficient calculation of Lagrange multipliers in constrained biological polymers: Proteins and nucleic acids as example cases

In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of Nc equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(Nc) operations, instead of the usual O(Nc3) for generic molecular systems. We develop the formalism, and describe the appropriate indexing for a number of model molecules and also for alkanes, proteins and DNA. Finally, we provide a numerical example of the technique in a series of polyalanine peptides of different lengths using the AMBER molecular dynamics package.Comment: 29 pages, 10 figures, 1 tabl

The canonical equilibrium of constrained molecular models

In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. Since the maximum time step required for the stability of the dynamics is proportional to the shortest period associated with the motions of the system, constraining the fastest vibrations allows to increase it and, assuming that the added numerical cost is not too high, also increase the overall efficiency of the simulation. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a “stiff” approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a constant number. We obtain the different correcting terms associated with the kinetic energy mass-metric tensor determinants, but also with the details of the potential energy in the vicinity of the constrained subspace (encoded in its first and second derivatives). This allows us to directly compare, at the conformational level, how the imposition of constraints changes the thermal equilibrium of molecular systems with respect to the unconstrained case. We also provide an extensive review of the relevant literature, and we show that all models previously reported can be considered special cases of the most general treatments presented in this work. Finally, we numerically analyze a simple methanol molecule in order to illustrate the theoretical concepts in a practical case.This work has been supported by the research projects E24/3 (DGA, Spain), FIS2009- 13364-C02-01 (MICINN, Spain), 200980I064 (CSIC, Spain) and ARAID and Ibercaja grant for young researchers (Spain). P. G.-R. is supported by a JAE PREDOC grant (CSIC, Spain)

A critical assessment on the short-term response of microbial relative composition in a mine tailings soil amended with biochar and manure compost

Phytomanagement of tailings requires the use of soil conditioners to favour plant establishment, but their benefits on soil microbial composition need to be assessed. The goal of this work was to evaluate the effect of two organic amendments, manure compost and biochar, on soil bacterial and fungal composition at metallic mine tailings. The addition of compost caused stronger effects in most of soil parameters and microbial composition than biochar, especially at the initial stage of the experiment. However, the higher dependence on labile organic carbon for some bacterial groups at the treatments containing compost determined their decay along time (Flavobacteriales, Sphingobacteriales) and the appearance of other taxa more dependent on recalcitrant organic matter (Xanthomonadales, Myxococcales). Biochar favoured bacterial decomposers (Actinomycetales) specialised in high lignin and other recalcitrant carbon compounds. Unlike bacteria, only a few fungal orders increased their relative abundances in the treatments containing compost (Sordariales and Microascales) while the rest showed a decrease or remained unaltered. The mix biochar-compost may result the best option to support a more diverse microbial population in terms of soil functionality that is able to decompose both labile and recalcitrant carbon compounds. This may favour the resilience of the system against environmental stressors.Financial support for this research was provided by FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación-Project CGL2017-82264-R. The experiment was performed at the facilities of the Instituto of Biotecnología Vegetal (IBV) of the Universidad Politécnica de Cartagena. We thank Borja Rojas from IBV for its help in bioinformatics processing and Dr. Francisco J. Jiménez from BIOCYMA, Consultora en Calidad y Medio Ambiente (Murcia) for his help in field sampling

How accurate does Newton have to be?

We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. We briefly discuss implications for parallel solvers.Comment: 12 pages, 2 figures, preprint accepted by PPAM 2022, expected to appear in LNCS vol. 13826 during 202

Evaluation of the rhizospheric microbiome of the native colonizer Piptatherum miliaceum in semiarid mine tailings

The study of the rhizospheric microbiome in native plants should be a prerequisite before carrying out the phytomanagement of mine tailings. The goal of this work was to evaluate the rhizospheric microbiome of Piptatherum miliaceum in semiarid mine tailings. A comprehensive edaphic characterization was performed including the description of soil microbial composition in the rhizosphere of P. miliaceum growing at a mine tailings pile and at a control site. Plant nutritional and isotopic compositions were also determined. Neutral pH of the tailings (7.3) determined low metal extractability in 0.01 M CaCl2 (e.g. < 1 mg/kg for Zn). In spite of the contrasting edaphic fertility conditions of both sites, N (~ 15 g kg−1) and P (~ 400 mg kg−1) leaf concentrations were similar. The lower δ15N at the tailings plants (− 4.50‰) compared to the control (6.42‰) indicated greater efficiency of P. miliaceum for uptaking N under the low fertility conditions of the tailings (0.1% total soil nitrogen). The presence at the tailings of bacterial orders related to the cycling of N, such as Rhizobiales, could have contributed to enhance N acquisition. The lower leaf δ13C values at the tailings (− 30.22‰) compared to the control (− 28.47‰) indicated lower water use efficiency of the tailing plants. Some organotrophic bacterial and fungal groups in the tailings’ rhizospheres were also found in the control site (e.g. Cytophagales, Sphingobacteriales for bacteria; Hypocreales, Pleosporales for fungi). This may indicate that P. miliaceum is able to shape its own specific microbiome at the tailings independently from the initial microbial composition of the tailings.Grant CTM2017-82264-R funded by MCIN/AEI/10.13039/501100011033 and ERDF “A way of making Europe”. We also thank Mr Francisco Crispín Fuentes Narváez for facilitating the access to the sampling area. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Financial support for this research was provided by FEDER and the Ministerio de Ciencia e Innovación of Spain (Project CTM2017-82264-R)

Sperm quality parameters of Iberian toothcarp (Aphanius iberus) and Valencia toothcarp (Valencia hispanica): new conservation tools from a gamete perspective

[EN] The sensitive state of conservation of several endemic fish species such as Iberian toothcarp (Aphanius iberus) and Valencia toothcarp (Valencia hispanica) has led governments to consider the implementation of conservation measures to preserve their populations. However, limited knowledge about the reproductive biology of these species makes it necessary to investigate different aspects of their reproductive cycle. In this sense, the main objectives of this work were i) to advance knowledge of the breeding biology of both species, and ii) to develop protocols for the conservation of gametes for the future management and conservation. During the spring of 2019 a temporal series of samplings were carried out in different places in the Comunitat Valenciana. Sperm samples were collected and sperm motion parameters were assessed for the first time in both species. Kinetic patterns were similar showing high motility and velocity values during the first 30 s, and a rapid decrease from that point. At the same time, an in-depth morphometric analysis was carried out using computer-assisted sperm analysis software. Spermatozoa from A. iberus and V. hispanica showed similar sizes and shapes to other external fertilizers belonging to Cyprinodontiformes, with small spherical heads, uniflagellated and without acrosomes. In addition, a new cryopreservation protocol was designed for cryobanking the sperm of these threatened species. Cryopreserved samples showed lower motility than fresh samples but reaching acceptable percentages of motile cells after thawing of around 20 and 25% (A. iberus and V. hispanica, respectively). This study is the first of its kind to successfully achieve gamete cryopreservation of these two endemic and endangered species from the Iberian Peninsula, providing new and useful tools to complement the management and conservation programs that are being developed for both species.This project has received funding from the Generalitat Valenciana (GV; Valencia, Spain) under the "Subvenciones para la realizacion de proyectos de I+D+I desarrollados por grupos de investigacion emergentes (GV/2019/130)". VG has a postdoc grant from the Ministerio de Economia, Industria y Competitividad (MINECO; Madrid, Spain) under the project IJCI-2017-34200. We would like to thank all the technicians of the CCEDCV for their work and effort during the samplings, specially to J. Velazquez, J. Hernandez and A. Pradillo.Blanes-García, M.; Risueño, P.; Pérez Igualada, LM.; Asturiano, JF.; Gallego Albiach, V. (2021). Sperm quality parameters of Iberian toothcarp (Aphanius iberus) and Valencia toothcarp (Valencia hispanica): new conservation tools from a gamete perspective. Aquaculture. 530:1-9. https://doi.org/10.1016/j.aquaculture.2020.735819S1953

A review of High Performance Computing foundations for scientists

The increase of existing computational capabilities has made simulation emerge as a third discipline of Science, lying midway between experimental and purely theoretical branches [1, 2]. Simulation enables the evaluation of quantities which otherwise would not be accessible, helps to improve experiments and provides new insights on systems which are analysed [3-6]. Knowing the fundamentals of computation can be very useful for scientists, for it can help them to improve the performance of their theoretical models and simulations. This review includes some technical essentials that can be useful to this end, and it is devised as a complement for researchers whose education is focused on scientific issues and not on technological respects. In this document we attempt to discuss the fundamentals of High Performance Computing (HPC) [7] in a way which is easy to understand without much previous background. We sketch the way standard computers and supercomputers work, as well as discuss distributed computing and discuss essential aspects to take into account when running scientific calculations in computers.Comment: 33 page