Finite element models predict cancellous apparent modulus when tissue modulus is scaled from specimen CT-attenuation

High-resolution architecture-based finite element models are commonly used for characterizing the mechanical behavior of cancellous bone. The vast majority of studies use homogeneous material properties to model trabecular tissue. The objectives of this study were to demonstrate that inhomogeneous finite element models that account for microcomputed tomography-measured tissue modulus variability more accurately predict the apparent stiffness of cancellous bone than homogeneous models, and to examine the sensitivity of an inhomogeneous model to the degree of tissue property variability. We tested five different material cases in finite element models of ten cancellous cubes in simulated uniaxial compression. Three of these cases were inhomogeneous and two were homogeneous. Four of these cases were unique to each specimen, and the remaining case had the same tissue modulus for all specimens. Results from all simulations were compared with measured elastic moduli from previous experiments. Tissue modulus variability for the most accurate of the three inhomogeneous models was then artificially increased to simulate the effects of non-linear CT-attenuation-modulus relationships. Uniqueness of individual models was more critical for model accuracy than level of inhomogeneity. Both homogeneous and inhomogeneous models that were unique to each specimen had at least 8% greater explanatory power for apparent modulus than models that applied the same material properties to all specimens. The explanatory power for apparent modulus of models with a tissue modulus coefficient of variation (COV) range of 21-31% was 13% greater than homogeneous models (COV=0). The results of this study indicate that inhomogenous finite element models that have tissue moduli unique to each specimen more accurately predict the elastic behavior of cancellous cubic specimens than models that have common tissue moduli between all specimens.     

Evaluating scaling models in biology using hierarchical Bayesian approaches

Theoretical models for allometric relationships between organismal form and function are typically tested by comparing a single predicted relationship with empirical data. Several prominent models, however, predict more than one allometric relationship, and comparisons among alternative models have not taken this into account. Here we evaluate several different scaling models of plant morphology within a hierarchical Bayesian framework that simultaneously fits multiple scaling relationships to three large allometric datasets. The scaling models include: inflexible universal models derived from biophysical assumptions (e.g. elastic similarity or fractal networks), a flexible variation of a fractal network model, and a highly flexible model constrained only by basic algebraic relationships. We demonstrate that variation in intraspecific allometric scaling exponents is inconsistent with the universal models, and that more flexible approaches that allow for biological variability at the species level outperform universal models, even when accounting for relative increases in model complexity.     

What are the dielectric “constants” of proteins and how to validate electrostatic models?

Implicit models for evaluation of electrostatic energies in proteins include dielectric constants that represent effect of the protein environment. Unfortunately, the results obtained by such models are very sensitive to the value used for the dielectric constant. Furthermore, the factors that determine the optimal value of these constants are far from being obvious. This review considers the meaning of the protein dielectric constants and the ways to determine their optimal values. It is pointed out that typical benchmarks for validation of electrostatic models cannot discriminate between consistent and inconsistent models. In particular, the observed pK(a) values of surface groups can be reproduced correctly by models with entirely incorrect physical features. Thus, we introduce a discriminative benchmark that only includes residues whose pK(a) values are shifted significantly from their values in water. We also use the semimacroscopic version of the protein dipole Langevin dipole (PDLD/S) formulation to generate a series of models that move gradually from microscopic to fully macroscopic models. These include the linear response version of the PDLD/S models, Poisson Boltzmann (PB)-type models, and Tanford Kirkwwod (TK)-type models. Using our different models and the discriminative benchmark, we show that the protein dielectric constant, epsilon(p), is not a universal constant but simply a parameter that depends on the model used. It is also shown in agreement with our previous works that epsilon(p) represents the factors that are not considered explicitly. The use of a discriminative benchmark appears to help not only in identifying nonphysical models but also in analyzing effects that are not reproduced in an accurate way by consistent models. These include the effect of water penetration and the effect of the protein reorganization. Finally, we show that the optimal dielectric constant for self-energies is not the optimal constant for charge-charge interactions.     

Dynamic conditionally linear mixed models for longitudinal data

We develop a new class of models, dynamic conditionally linear mixed models, for longitudinal data by decomposing the within-subject covariance matrix using a special Cholesky decomposition. Here 'dynamic' means using past responses as covariates and 'conditional linearity' means that parameters entering the model linearly may be random, but nonlinear parameters are nonrandom. This setup offers several advantages and is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models. First, it allows for flexible and computationally tractable models that include a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, e.g., all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and motivate the usefulness of these models using a series of longitudinal depression studies for which the features of these new models are well suited.     

Generalizability of neotropical bird abundance and richness models

Predicting the consequences of land-cover change on tropical biotas is a pressing task. However, testing the applicability of models developed with data from one region to another region has rarely been done. Bird faunas were sampled along 3.0-km routes in southern Costa Rica (Coto Brus) to develop statistical models to describe the abundance and richness of groups as a function of land-cover characteristics. The relative value of the land-cover models was assessed by comparing them with null models. The generalizability of the models was tested with data from north-western Costa Rica (Monteverde) to determine whether the models were applicable to another area that has undergone significant land-cover change in the last 60 years. The richness and abundance of understory, open-country and edge non-insectivore groups showed clear relationships with land-cover variables, and the land-cover models had lower prediction errors than the null models for Coto Brus. With one exception, useful models for canopy birds, edge insectivores and hummingbirds could not be developed. The land-cover models of abundance of canopy insectivores, understory insectivores and non-insectivores, and edge non-insectivores were generalizable to Monteverde whereas the land-cover models of abundance of open-country birds and species richness for any of the groups were not better than null models for Monteverde. The results indicate that land-cover models that describe the abundance or richness of various bird groups provide useful predictions in the area where the data were collected and that models of abundance of some canopy, understory and edge birds may perform well in areas that are similar in elevation, life zones and land use to the area from which data were collected. Land-cover models of the abundance of other groups, and of the richness of the majority of groups, may be less generalizable to other areas, or it may be difficult to develop models at all.     

Multiscale modeling of biomolecular systems: in serial and in parallel

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.     

杉木人工林生物量估算模型的选择

采用11种形式的生物量模型,分别对杉木幼龄林（7年生）、中龄林(16年生)、成熟林(28年生)和不分林龄的单木各器官和全株生物量进行拟合,共得到生物量估算模型308个.结果表明: 11种生物量模型均能较好地模拟杉木单木生物量,其中幂函数模型的拟合效果最优,其次为指数模型,然后为多项式模型;共选出估算杉木幼龄林、中龄林和成熟林各器官和全株生物量的最优模型21个（包括18个器官模型、3个全株模型）,不分林龄的杉木单木各生物量的最优模型7个（包括6个器官模型、1个全株模型）,均为幂函数模型;不同林龄的杉木单木生物量最优模型的通用性较差,而不分龄林的杉木单木生物量最优模型具有一定的通用性,精度较高,可用于估算不同林龄的杉木单木生物量.应用福建邵武杉木单木生物量模型对江西28年生的杉木成熟林单木各生物量的预测结果显示,不分林龄的大样本生物量模型精度较高,可在较大范围内应用,而区域小样本模型仅限于在区域小范围内应用.     

The relationship between count-location and stationary renewal models for the chiasma process

It is often convenient to define models for the process of chiasma formation at meiosis as stationary renewal models. However, count-location models are also useful, particularly to capture the biological requirement of at least one chiasma per chromosome. The Sturt model and truncated Poisson model are both count-location models with this feature. We show that the truncated Poisson model can also be expressed as a stationary renewal model, while the Sturt model cannot. More generally, we show that there is only one family of count-location models for the chiasma process that can also be expressed as stationary renewal models. The models in this family can exhibit either positive or negative interference.     

Interpretable pairwise distillations for generative protein sequence models

Many different types of generative models for protein sequences have been proposed in literature. Their uses include the prediction of mutational effects, protein design and the prediction of structural properties. Neural network (NN) architectures have shown great performances, commonly attributed to the capacity to extract non-trivial higher-order interactions from the data. In this work, we analyze two different NN models and assess how close they are to simple pairwise distributions, which have been used in the past for similar problems. We present an approach for extracting pairwise models from more complex ones using an energy-based modeling framework. We show that for the tested models the extracted pairwise models can replicate the energies of the original models and are also close in performance in tasks like mutational effect prediction. In addition, we show that even simpler, factorized models often come close in performance to the original models.     

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.     

土壤-植物-大气连续体水热、CO2通量估算模型研究进展

土壤-植物-大气连续体(SPAC)水热、CO2通量的准确估算对理解陆地和大气的物质和能量交换过程有着重要意义.重点阐述了基于过程的土壤-植物-大气连续体水热、CO2通量模型,综述了统计模型、综合模型及基于遥感的模型的发展过程.其中水热通量统计模型包括基于温度和湿度以及基于温度和辐射的方法;CO2通量统计模型包括基于气候因子或蒸散因子以及基于光能利用率的方法.水热通量过程模型包括大叶、双源、多源和多层的水热传输物理模型;CO2通量过程模型包括叶片尺度及由大叶、双叶和多层方法扩展到冠层尺度的生理生态模型以及光合-蒸腾耦合模型.综合模型包括生物物理模型、生物化学模型和生物地理模型.统计模型形式简单,资料易得,对大范围的水热通量模拟具有指导意义;过程模型准确的揭示了水热和CO2通量传输的物理和生理过程,是大尺度综合模型的基础.未来生态系统水热、CO2通量估算模型将集成各种技术手段进行多尺度网络观测和大尺度机理模拟.     

Density-based score for selecting near-native atomic models of unknown structures

We present a low-resolution density-based scoring scheme for selecting high-quality models from a large pool of lesser quality models. We use pre-configured decoy data sets that contain large numbers of models with different degrees of correctness to evaluate the performance of the strategy. We find that the scoring scheme consistently identifies one of the highest quality models for a wide variety of target structures, resolution ranges, and noise models. Tests with experimental data yield similar results.     

Model reduction of genome-scale metabolic models as a basis for targeted kinetic models

Constraint-based, genome-scale metabolic models are an essential tool to guide metabolic engineering. However, they lack the detail and time dimension that kinetic models with enzyme dynamics offer. Model reduction can be used to bridge the gap between the two methods and allow for the integration of kinetic models into the Design-Built-Test-Learn cycle. Here we show that these reduced size models can be representative of the dynamics of the original model and demonstrate the automated generation and parameterisation of such models. Using these minimal models of metabolism could allow for further exploration of dynamic responses in metabolic networks.     

Integration of kinetic information on yeast sphingolipid metabolism in dynamical pathway models

For the first time, kinetic information from the literature was collected and used to construct integrative dynamical mathematical models of sphingolipid metabolism. One model was designed primarily with kinetic equations in the tradition of Michaelis and Menten whereas the other two models were designed as alternative power-law models within the framework of Biochemical Systems Theory. Each model contains about 50 variables, about a quarter of which are dependent (state) variables, while the others are independent inputs and enzyme activities that are considered constant. The models account for known regulatory signals that exert control over the pathway. Standard mathematical testing, repeated revisiting of the literature, and numerous rounds of amendments and refinements resulted in models that are stable and rather insensitive to perturbations in inputs or parameter values. The models also appear to be compatible with the modest amount of experimental experience that lends itself to direct comparisons. Even though the three models are based on different mathematical representations, they show dynamic responses to a variety of perturbations and changes in conditions that are essentially equivalent for small perturbations and similar for large perturbations. The kinetic information used for model construction and the models themselves can serve as a starting point for future analyses and refinements.     

Metapopulation theory, its use and misuse

Baguette (2004) has criticized the use of patch-occupancy metapopulation models in conservation. I discuss the relative strengths and weaknesses of different types of metapopulation models, taking for granted that there is a need to develop both general theory and predictive models. I conclude that the classical metapopulation theory is most appropriate for species living in highly fragmented landscapes. For these situations, the patch-occupancy metapopulation models provide a modelling approach that has been helpful also for conservation.     

Spatial heterogeneity and critical patch size: Area effects via diffusion in closed environments

We describe a class of mathematical models for critical patch size in which the mechanisms inducing area effects are based on source-sink population dynamics arising from dispersal throughout a closed, finite, but spatially heterogeneous environment. Our models are reaction-diffusion equations, but unlike classical KISS models for area effects they do not assume that there is dispersal across the boundary of the environment into a hostile exterior. We observe that simple rescaling has the same effects in our models as in KISS models and hence predicts the same sort of area effects, but that other sorts of rescaling may not predict area effects. The models considered here provide an alternative to the KISS models used in our previous work on species-area relationships in island biogeography.     

Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences

Although phylogenetic inference of protein-coding sequences continues to dominate the literature, few analyses incorporate evolutionary models that consider the genetic code. This problem is exacerbated by the exclusion of codon-based models from commonly employed model selection techniques, presumably due to the computational cost associated with codon models. We investigated an efficient alternative to standard nucleotide substitution models, in which codon position (CP) is incorporated into the model. We determined the most appropriate model for alignments of 177 RNA virus genes and 106 yeast genes, using 11 substitution models including one codon model and four CP models. The majority of analyzed gene alignments are best described by CP substitution models, rather than by standard nucleotide models, and without the computational cost of full codon models. These results have significant implications for phylogenetic inference of coding sequences as they make it clear that substitution models incorporating CPs not only are a computationally realistic alternative to standard models but may also frequently be statistically superior.