Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions.
Scope
In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding.
Conclusions
We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes.
Cardiac arrhythmias are becoming one of the major health care problem in the world, causing numerous serious disease conditions including stroke and sudden cardiac death. Furthermore, cardiac arrhythmias are intimately related to the signaling ability of cardiac cells, and are caused by signaling defects. Consequently, modeling the electrical activity of the heart, and the complex signaling models that subtend dangerous arrhythmias such as tachycardia and fibrillation, necessitates a quantitative model of action potential (AP) propagation. Yet, many electrophysiological models, which accurately reproduce dynamical characteristic of the action potential in cells, have been introduced. However, these models are very complex and are very time consuming computationally. Consequently, a large amount of research is consecrated to design models with less computational complexity.
Results
This paper is presenting a new model for analyzing the propagation of ionic concentrations and electrical potential in space and time. In this model, the transport of ions is governed by Nernst-Planck flux equation (NP), and the electrical interaction of the species is described by a new cable equation. These set of equations form a system of coupled partial nonlinear differential equations that is solved numerically. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretization and then we choose an appropriate resolution algorithm.
Conclusions
We give numerical simulations obtained for different input scenarios in the case of suicide substrate reaction which were compared to those obtained in literature. These input scenarios have been chosen so as to provide an intuitive understanding of dynamics of the model. By accessing time and space domains, it is shown that interpreting the electrical potential of cell membrane at steady state is incorrect. This model is general and applies to ions of any charge in space and time domains. The results obtained show a complete agreement with literature findings and also with the physical interpretation of the phenomenon. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is second-order accurate in space.
The numerical simulation of spiking neural networks requires particular attention. On the one hand, time-stepping methods
are generic but they are prone to numerical errors and need specific treatments to deal with the discontinuities of integrate-and-fire
models. On the other hand, event-driven methods are more precise but they are restricted to a limited class of neuron models.
We present here a voltage-stepping scheme that combines the advantages of these two approaches and consists of a discretization
of the voltage state-space. The numerical simulation is reduced to a local event-driven method that induces an implicit activity-dependent time discretization (time-steps automatically increase when
the neuron is slowly varying). We show analytically that such a scheme leads to a high-order algorithm so that it accurately
approximates the neuronal dynamics. The voltage-stepping method is generic and can be used to simulate any kind of neuron
models. We illustrate it on nonlinear integrate-and-fire models and show that it outperforms time-stepping schemes of Runge-Kutta
type in terms of simulation time and accuracy.
We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature. 相似文献
All-atomistic (AA) molecular dynamics (MD) is considered as one of the desirable methods for studying glass transition temperatures (Tg) of specific polymers. However, heavy computational efforts are generally required, and the simulated Tg values are not always in good agreement with the experimental data. In this work, a multiscale scheme is proposed: first, the structural and volumetric properties based multiscale modeling is employed to parameterize the coarse-grained (CG) potentials against the AA simulations of an oligomeric melt; with the CG potentials, MD simulations are then carried out on a serial of oligomer bulks and polymer systems of interests, for which the dynamical Tg values are determined. With poly(ethylene oxide) and poly(methyl methacrylate) as typical examples, the simulated dynamical Tg values of the oligomeric bulks exhibit a linear relation with the empirical values, which is used to determine the “actual Tg” for the polymer bulk. The so-obtained Tg is found to compare very well with the experimental data. Such a computational framework can be quite promising in investigating the effects of various complex factors on polymer Tg.
In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391–401, 2015; Merelli et al. in Entropy 17(10):6872–6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117–128, 2016), a special resolution parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. It is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range. Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140–162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the “regularity” of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the “regularity” information in any systems. 相似文献
Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012). 相似文献
Multiscale approaches for integrating submodels of various levels of biological organization into a single model became the major tool of systems biology. In this paper, we have constructed and simulated a set of multiscale models of spatially distributed microbial communities and study an influence of unevenly distributed environmental factors on the genetic diversity and evolution of the community members.
Results
Haploid Evolutionary Constructor software http://evol-constructor.bionet.nsc.ru/ was expanded by adding the tool for the spatial modeling of a microbial community (1D, 2D and 3D versions). A set of the models of spatially distributed communities was built to demonstrate that the spatial distribution of cells affects both intensity of selection and evolution rate.
Conclusion
In spatially heterogeneous communities, the change in the direction of the environmental flow might be reflected in local irregular population dynamics, while the genetic structure of populations (frequencies of the alleles) remains stable. Furthermore, in spatially heterogeneous communities, the chemotaxis might dramatically affect the evolution of community members.
Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca
cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues). 相似文献
Electron dynamics and acceleration in an electromagnetic field configuration modeling the current sheet configuration of the Earth’s magnetotail region is investigated. A focus is made on the role of the dawn?dusk magnetic field component By in the convection electron heating by an electric field Ey. For numerical integration of a large number of test particle trajectories over long time intervals, the equations of motion written in the guiding center approximation are used. It is shown that the presence of a By ≠ 0 magnetic field significantly changes the electron heating and allows electrons with small pitch angles to gain energy much more efficiently than the equatorial electrons. As a result, the convection heating in the current sheet with By ≠ 0 leads to the formation of an accelerated anisotropic population of particles with energies higher than a few hundred electronvolts. The obtained results and spacecraft observations in the Earth’s magnetotail are compared, and possible limitations in the proposed model approaches are discussed. 相似文献
Rule-based modeling has become a powerful approach for modeling intracellular networks, which are characterized by rich molecular diversity. Truly comprehensive models of cell behavior, however, must address spatial complexity at both the intracellular level and at the level of interacting populations of cells, and will require richer modeling languages and tools. A recent paper in BMC Systems Biology represents a signifcant step toward the development of a unified modeling language and software platform for the development of multi-level, multiscale biological models. See research article: http://www.biomedcentral.com/1752-0509/5/166相似文献
Root-specific responses to stress are not well-known, and have been largely based on indirect measurements of bulk soil water extraction, which limits mechanistic modeling of root function.
Methods
Here, we used neutron radiography to examine in situ root-soil water dynamics of a previously droughted black cottonwood (Populus trichocarpa) seedling, contrasting water uptake by the two major components of the root system that differed in initial recovery rate as apparent by ‘new’ (whiter, thinner), or ‘old’ (darker, thicker) parts of the fine root system.
Results
The smaller diameter ‘new’ roots had greater water uptake per unit surface area than the larger diameter ‘old’ roots, but they had less total surface area leading to less total water extraction; rates ranged from 0.0027–0.0116 g cm?2 h?1. The finest most-active roots were not visible in the radiographs, indicating the need to include destructive sampling. Analysis based on root-free bulk soil hydraulic properties indicated substantial redistribution of water via saturated/unsaturated flow and capillary wicking across the layers - suggesting water uptake dynamics following an infiltration event may be more complex than approximated by common soil hydraulic or root surface area modeling approaches.
Conclusions
Our results highlight the need for continued exploration of root-trait specific water uptake rates in situ, and impacts of roots on soil hydraulic properties – both critical components for mechanistic modeling of root function.
Existing software for quantitative trait mapping is either not able to model polygenic variation or does not allow incorporation of more than one genetic variance component. Improperly modeling the genetic relatedness among subjects can result in excessive false positives. We have developed an R package, QTLRel, to enable more flexible modeling of genetic relatedness as well as covariates and non-genetic variance components.
Results
We have successfully used the package to analyze many datasets, including F34 body weight data that contains 688 individuals genotyped at 3105 SNP markers and identified 11 QTL. It took 295 seconds to estimate variance components and 70 seconds to perform the genome scan on an Linux machine equipped with a 2.40GHz Intel(R) Core(TM)2 Quad CPU.
Conclusions
QTLRel provides a toolkit for genome-wide association studies that is capable of calculating genetic incidence matrices from pedigrees, estimating variance components, performing genome scans, incorporating interactive covariates and genetic and non-genetic variance components, as well as other functionalities such as multiple-QTL mapping and genome-wide epistasis. 相似文献
In the present paper, we propose and study by numerical simulations a multiscale model for plant invasion based on allelopathic suppression in a homogeneous environment. The negative effects on seed production and germination, establishment and mortality of native plants generated by the root-secreted alien phytotoxin constitute the basic mechanism contributing to invasiveness. We obtained the invasion patterns, their success probabilities, the time evolution of plant populations, the gyration radius and the border roughness of the invaded region. As an important result, it was observed that, in addition to the phytotoxin nature (synthesis and degradation rates, diffusivity and phytotoxic threshold), invasive patterns and invasion success depend on the kind of native plants present in the area. In fact, both success and invasion speed decrease in the presence of resistant native plants. Also, self-affine invasion fronts are smooth (Hurst exponent H = 1) in the absence of resistant plants, but are rough (H ≠ 1) on the contrary. Furthermore, if the resistant native species are randomly distributed on the landscape, the invasion front exhibits long-range correlations (H ～ 0.76), while its border is anti-correlated (H ～ 0.20), if resistant plants are distributed in patches. Finally, the cluster size distribution functions of resistant plants are exponentials with characteristic cluster sizes increasing in time. 相似文献
Neuromusculoskeletal modeling and simulation enable investigation of the neuromusculoskeletal system and its role in human movement dynamics. These methods are progressively introduced into daily clinical practice. However, a major factor limiting this translation is the lack of robust tools for the pre-processing of experimental movement data for their use in neuromusculoskeletal modeling software.
Results
This paper presents MOtoNMS (matlab MOtion data elaboration TOolbox for NeuroMusculoSkeletal applications), a toolbox freely available to the community, that aims to fill this lack. MOtoNMS processes experimental data from different motion analysis devices and generates input data for neuromusculoskeletal modeling and simulation software, such as OpenSim and CEINMS (Calibrated EMG-Informed NMS Modelling Toolbox). MOtoNMS implements commonly required processing steps and its generic architecture simplifies the integration of new user-defined processing components. MOtoNMS allows users to setup their laboratory configurations and processing procedures through user-friendly graphical interfaces, without requiring advanced computer skills. Finally, configuration choices can be stored enabling the full reproduction of the processing steps. MOtoNMS is released under GNU General Public License and it is available at the SimTK website and from the GitHub repository. Motion data collected at four institutions demonstrate that, despite differences in laboratory instrumentation and procedures, MOtoNMS succeeds in processing data and producing consistent inputs for OpenSim and CEINMS.
Conclusions
MOtoNMS fills the gap between motion analysis and neuromusculoskeletal modeling and simulation. Its support to several devices, a complete implementation of the pre-processing procedures, its simple extensibility, the available user interfaces, and its free availability can boost the translation of neuromusculoskeletal methods in daily and clinical practice.
Predicting complete protein-coding genes in human DNA remains a significant challenge. Though a number of promising approaches have been investigated, an ideal suite of tools has yet to emerge that can provide near perfect levels of sensitivity and specificity at the level of whole genes. As an incremental step in this direction, it is hoped that controlled gene finding experiments in the ENCODE regions will provide a more accurate view of the relative benefits of different strategies for modeling and predicting gene structures.
Results
Here we describe our general-purpose eukaryotic gene finding pipeline and its major components, as well as the methodological adaptations that we found necessary in accommodating human DNA in our pipeline, noting that a similar level of effort may be necessary by ourselves and others with similar pipelines whenever a new class of genomes is presented to the community for analysis. We also describe a number of controlled experiments involving the differential inclusion of various types of evidence and feature states into our models and the resulting impact these variations have had on predictive accuracy.
Conclusion
While in the case of the non-comparative gene finders we found that adding model states to represent specific biological features did little to enhance predictive accuracy, for our evidence-based 'combiner' program the incorporation of additional evidence tracks tended to produce significant gains in accuracy for most evidence types, suggesting that improved modeling efforts at the hidden Markov model level are of relatively little value. We relate these findings to our current plans for future research.
Particle size is a key parameter for drug-delivery nanoparticle design. It is believed that the size of a nanoparticle may have important effects on its ability to overcome the transport barriers in biological tissues. Nonetheless, such effects remain poorly understood. Using a multiscale model, this work investigates particle size effects on the tissue distribution and penetration efficacy of drug-delivery nanoparticles.
Results
We have developed a multiscale spatiotemporal model of nanoparticle transport in biological tissues. The model implements a time-adaptive Brownian Dynamics algorithm that links microscale particle-cell interactions and adhesion dynamics to tissue-scale particle dispersion and penetration. The model accounts for the advection, diffusion, and cellular uptakes of particles. Using the model, we have analyzed how particle size affects the intra-tissue dispersion and penetration of drug delivery nanoparticles. We focused on two published experimental works that investigated particle size effects in in vitro and in vivo tissue conditions. By analyzing experimental data reported in these two studies, we show that particle size effects may appear pronounced in an in vitro cell-free tissue system, such as collagen matrix. In an in vivo tissue system, the effects of particle size could be relatively modest. We provide a detailed analysis on how particle-cell interactions may determine distribution and penetration of nanoparticles in a biological tissue.
Conclusion
Our work suggests that the size of a nanoparticle may play a less significant role in its ability to overcome the intra-tissue transport barriers. We show that experiments involving cell-free tissue systems may yield misleading observations of particle size effects due to the absence of advective transport and particle-cell interactions.
Syphilis continues to be a major global health threat with 11 million new infections each year, and a global burden of 36 million cases. The causative agent of syphilis, Treponema pallidum subspecies pallidum, is a highly virulent bacterium, however the molecular mechanisms underlying T. pallidum pathogenesis remain to be definitively identified. This is due to the fact that T. pallidum is currently uncultivatable, inherently fragile and thus difficult to work with, and phylogenetically distinct with no conventional virulence factor homologs found in other pathogens. In fact, approximately 30% of its predicted protein-coding genes have no known orthologs or assigned functions. Here we employed a structural bioinformatics approach using Phyre2-based tertiary structure modeling to improve our understanding of T. pallidum protein function on a proteome-wide scale.
Results
Phyre2-based tertiary structure modeling generated high-confidence predictions for 80% of the T. pallidum proteome (780/978 predicted proteins). Tertiary structure modeling also inferred the same function as primary structure-based annotations from genome sequencing pipelines for 525/605 proteins (87%), which represents 54% (525/978) of all T. pallidum proteins. Of the 175 T. pallidum proteins modeled with high confidence that were not assigned functions in the previously annotated published proteome, 167 (95%) were able to be assigned predicted functions. Twenty-one of the 175 hypothetical proteins modeled with high confidence were also predicted to exhibit significant structural similarity with proteins experimentally confirmed to be required for virulence in other pathogens.
Conclusions
Phyre2-based structural modeling is a powerful bioinformatics tool that has provided insight into the potential structure and function of the majority of T. pallidum proteins and helped validate the primary structure-based annotation of more than 50% of all T. pallidum proteins with high confidence. This work represents the first T. pallidum proteome-wide structural modeling study and is one of few studies to apply this approach for the functional annotation of a whole proteome.
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