Subject-specific geometry affects acetabular contact pressure during gait more than subject-specific loading patterns

Abstract

Finite element modeling (FEM) can predict hip cartilage contact mechanics. This study investigated how subject-specific boundary conditions and joint geometry affect acetabular cartilage contact mechanics using a multi-scale workflow. For two healthy subjects, musculoskeletal models calculated subject-specific hip kinematics and loading, which were used as boundary conditions for FEM. Cartilage contact mechanics were predicted using either generic or subject-specific FEM and boundary conditions. A subject-specific mesh resulted in a more lateral contact. Effects of subject-specific boundary conditions varied between both subjects. Results highlight the complex interplay between loading and kinematics and their effect on cartilage contact mechanics.     

Loopholes and missing links in protein modeling

This paper provides an unbiased comparison of four commercially available programs for loop sampling, Prime, Modeler, ICM, and Sybyl, each of which uses a different modeling protocol. The study assesses the quality of results and examines the relative strengths and weaknesses of each method. The set of loops to be modeled varied in length from 4-12 amino acids. The approaches used for loop modeling can be classified into two methodologies: ab initio loop generation (Modeler and Prime) and database searches (Sybyl and ICM). Comparison of the modeled loops to the native structures was used to determine the accuracy of each method. All of the protocols returned similar results for short loop lengths (four to six residues), but as loop length increased, the quality of the results varied among the programs. Prime generated loops with RMSDs <2.5 A for loops up to 10 residues, while the other three methods met the 2.5 A criteria at seven-residue loops. Additionally, the ability of the software to utilize disulfide bonds and X-ray crystal packing influenced the quality of the results. In the final analysis, the top-ranking loop from each program was rarely the loop with the lowest RMSD with respect to the native template, revealing a weakness in all programs to correctly rank the modeled loops.     

A kinetic model of Escherichia coli core metabolism satisfying multiple sets of mutant flux data

In contrast to stoichiometric-based models, the development of large-scale kinetic models of metabolism has been hindered by the challenge of identifying kinetic parameter values and kinetic rate laws applicable to a wide range of environmental and/or genetic perturbations. The recently introduced ensemble modeling (EM) procedure provides a promising remedy to address these challenges by decomposing metabolic reactions into elementary reaction steps and incorporating all phenotypic observations, upon perturbation, in its model parameterization scheme. Here, we present a kinetic model of Escherichia coli core metabolism that satisfies the fluxomic data for wild-type and seven mutant strains by making use of the EM concepts. This model encompasses 138 reactions, 93 metabolites and 60 substrate-level regulatory interactions accounting for glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, major pyruvate metabolism, anaplerotic reactions and a number of reactions in other parts of the metabolism. Parameterization is performed using a formal optimization approach that minimizes the discrepancies between model predictions and flux measurements. The predicted fluxes by the model are within the uncertainty range of experimental flux data for 78% of the reactions (with measured fluxes) for both the wild-type and seven mutant strains. The remaining flux predictions are mostly within three standard deviations of reported ranges. Converting the EM-based parameters into a Michaelis–Menten equivalent formalism revealed that 35% of K_m and 77% of k_cat parameters are within uncertainty range of the literature-reported values. The predicted metabolite concentrations by the model are also within uncertainty ranges of metabolomic data for 68% of the metabolites. A leave-one-out cross-validation test to evaluate the flux prediction performance of the model showed that metabolic fluxes for the mutants located in the proximity of mutations used for training the model can be predicted more accurately. The constructed model and the parameterization procedure presented in this study pave the way for the construction of larger-scale kinetic models with more narrowly distributed parameter values as new metabolomic/fluxomic data sets are becoming available for E. coli and other organisms.     

Network Development in Biological Gels: Role in Lymphatic Vessel Development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model. This work was supported by the Royal Society (London) by the award of a University Research Fellowship.     

A comparative study of available software for high-accuracy homology modeling: from sequence alignments to structural models

An open question in protein homology modeling is, how well do current modeling packages satisfy the dual criteria of quality of results and practical ease of use? To address this question objectively, we examined homology‐built models of a variety of therapeutically relevant proteins. The sequence identities across these proteins range from 19% to 76%. A novel metric, the difference alignment index (DAI), is developed to aid in quantifying the quality of local sequence alignments. The DAI is also used to construct the relative sequence alignment (RSA), a new representation of global sequence alignment that facilitates comparison of sequence alignments from different methods. Comparisons of the sequence alignments in terms of the RSA and alignment methodologies are made to better understand the advantages and caveats of each method. All sequence alignments and corresponding 3D models are compared to their respective structure‐based alignments and crystal structures. A variety of protein modeling software was used. We find that at sequence identities >40%, all packages give similar (and satisfactory) results; at lower sequence identities (<25%), the sequence alignments generated by Profit and Prime, which incorporate structural information in their sequence alignment, stand out from the rest. Moreover, the model generated by Prime in this low sequence identity region is noted to be superior to the rest. Additionally, we note that DSModeler and MOE, which generate reasonable models for sequence identities >25%, are significantly more functional and easier to use when compared with the other structure‐building software.     

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

Guidelines for a priori grouping of species in hierarchical community models

Recent methodological advances permit the estimation of species richness and occurrences for rare species by linking species‐level occurrence models at the community level. The value of such methods is underscored by the ability to examine the influence of landscape heterogeneity on species assemblages at large spatial scales. A salient advantage of community‐level approaches is that parameter estimates for data‐poor species are more precise as the estimation process “borrows” from data‐rich species. However, this analytical benefit raises a question about the degree to which inferences are dependent on the implicit assumption of relatedness among species. Here, we assess the sensitivity of community/group‐level metrics, and individual‐level species inferences given various classification schemes for grouping species assemblages using multispecies occurrence models. We explore the implications of these groupings on parameter estimates for avian communities in two ecosystems: tropical forests in Puerto Rico and temperate forests in northeastern United States. We report on the classification performance and extent of variability in occurrence probabilities and species richness estimates that can be observed depending on the classification scheme used. We found estimates of species richness to be most precise and to have the best predictive performance when all of the data were grouped at a single community level. Community/group‐level parameters appear to be heavily influenced by the grouping criteria, but were not driven strictly by total number of detections for species. We found different grouping schemes can provide an opportunity to identify unique assemblage responses that would not have been found if all of the species were analyzed together. We suggest three guidelines: (1) classification schemes should be determined based on study objectives; (2) model selection should be used to quantitatively compare different classification approaches; and (3) sensitivity of results to different classification approaches should be assessed. These guidelines should help researchers apply hierarchical community models in the most effective manner.     

蛋白质结构与功能研究中的分子模拟技术

分子模拟技术为蛋白质的研究提供了一种崭新的手段,在理论上解决了结构预测和功能分析以及蛋白质工程实施方面所面临的难题。它在蛋白质的结构预测和模建工作中占有举足轻重的地位,实现了生物技术与计算机技术的完美结合。本文简要阐述了该技术的基本步骤和工作原理,并以目前应用最广的生物大分子领域的商品化分子模拟软件Accelrys公司基于Linux系统开发的InsightII为例,介绍了相关程序模块的功能和作用,同时结合该技术在蛋白质的结构预测和模建、结构与功能关系分析、分子设计等过程中的开发与应用,加以具体说明和展望。     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis II: Bacterial Populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.     

Combined finite-element and rigid-body analysis of human jaw joint dynamics

The jaw joint plays a crucial role in human mastication. It acts as a guidance for jaw movements and as a fulcrum for force generation. The joint is subjected to loading which causes tensions and deformations in its cartilaginous structures. These are assumed to be a major determinant for development, maintenance and also degeneration of the joint. To analyze the distribution of tensions and deformations in the cartilaginous structures of the jaw joint during jaw movement, a dynamical model of the human masticatory system has been constructed. Its movements are controlled by muscle activation. The articular cartilage layers and articular disc were included as finite-element (FE) models. As this combination of rigid-body and FE modeling had not been applied to musculoskeletal systems yet, its benefits and limitations were assessed by simulating both unloaded and loaded jaw movements. It was demonstrated that joint loads increase with muscle activation, irrespective of the external loads. With increasing joint load, the size of the stressed area of the articular surfaces was enlarged, whereas the peak stresses were much less affected. The results suggest that the articular disc enables distribution of local contact stresses over a much wider area of the very incongruent articular surfaces by transforming compressive principal stress into shear stress.     

The biomechanical model of the long finger extensor mechanism and its parametric identification

The extensor mechanism of the finger is a structure transmitting the forces from several muscles to the finger joints. Force transmission in the extensor mechanism is usually modeled by equations with constant coefficients which are determined experimentally only for finger extension posture. However, the coefficient values change with finger flexion because of the extensor mechanism deformation. This induces inaccurate results for any other finger postures. We proposed a biomechanical model of the extensor mechanism represented as elastic strings. The model includes the main tendons and ligaments. The parametric identification of the model in extension posture was performed to match the distribution of the forces among the tendons to experimental data. The parametrized model was used to simulate three degrees of flexion. Furthermore, the ability of the model to reproduce how the force distribution in simulated extensor mechanism changes according to the muscle forces was also demonstrated. The proposed model could be used to simulate the extensor mechanism for any physiological finger posture for which the coefficients involved in the equations are unknown.     

Modeling the structure of Pyrococcus furiosus rubredoxin by homology to other X-ray structures.

The three-dimensional structure of rubredoxin from the hyperthermophilic archaebacterium, Pyrococcus furiosus, has been modeled from the X-ray crystal structures of three homologous proteins from Clostridium pasteurianum, Desulfovibrio gigas, and Desulfovibrio vulgaris. All three homology models are similar. When comparing the positions of all heavy atoms and essential hydrogen atoms to the recently solved crystal structure (Day, M. W., et al., 1992, Protein Sci. 1, 1494-1507) of the same protein, the homology model differ from the X-ray structure by 2.09 A root mean square (RMS). The X-ray and the zinc-substituted NMR structures (Blake, P. R., et al., 1992b, Protein Sci. 1, 1508-1521) show a similar level of difference (2.05 A RMS). On average, the homology models are closer to the X-ray structure than to the NMR structures (2.09 vs. 2.42 A RMS).     

UML应用建模研究

介绍了UML产生的背景、基本内容、应用机制及其扩展性。在此基础上,对UML建模的一般过程做了概述,并以商业管理信息系统(MIS)的开发过程为例,具体介绍了UML的建模过程。     

Refinement of unreliable local regions in template-based protein models

Contemporary template-based modeling techniques allow applications of modeling methods to vast biological problems. However, they tend to fail to provide accurate structures for less-conserved local regions in sequence even when the overall structure can be modeled reliably. We call these regions unreliable local regions (ULRs). Accurate modeling of ULRs is of enormous value because they are frequently involved in functional specificity. In this article, we introduce a new method for modeling ULRs in template-based models by employing a sophisticated loop modeling technique. Combined with our previous study on protein termini, the method is applicable to refinement of both loop and terminus ULRs. A large-scale test carried out in a blind fashion in CASP9 (the 9th Critical Assessment of techniques for protein structure prediction) shows that ULR structures are improved over initial template-based models by refinement in more than 70% of the successfully detected ULRs. It is also notable that successful modeling of several long ULRs over 12 residues is achieved. Overall, the current results show that a careful application of loop and terminus modeling can be a promising tool for model refinement in template-based modeling.     

Pattern formation during vasculogenesis

Vasculogenesis, the assembly of the first vascular network, is an intriguing developmental process that yields the first functional organ system of the embryo. In addition to being a fundamental part of embryonic development, vasculogenic processes also have medical importance. To explain the organizational principles behind vascular patterning, we must understand how morphogenesis of tissue level structures can be controlled through cell behavior patterns that, in turn, are determined by biochemical signal transduction processes. Mathematical analyses and computer simulations can help conceptualize how to bridge organizational levels and thus help in evaluating hypotheses regarding the formation of vascular networks. Here, we discuss the ideas that have been proposed to explain the formation of the first vascular pattern: cell motility guided by extracellular matrix alignment (contact guidance), chemotaxis guided by paracrine and autocrine morphogens, and sprouting guided by cell–cell contacts. Birth Defects Research (Part C) 96:153–162, 2012. © 2012 Wiley Periodicals, Inc.     

A Mathematical Model for the Effects of HER2 Overexpression on Cell Proliferation in Breast Cancer

We present a mathematical model to study the effects of HER2 over-expression on cell proliferation in breast cancer. The model illustrates the proliferative behavior of cells as a function of HER2 and EGFR receptors numbers, and the growth factor EGF. This mathematical model comprises kinetic equations describing the cell surface binding of EGF growth factor to EGFR and HER2 receptors, coupled to a model for the dependence of cell proliferation rate on growth factor receptors binding. The simulation results from this model predict: (1) a growth advantage associated with excess HER2 receptors; (2) that HER2-over-expression is an insufficient parameter to predict the proliferation response of cancer cells to epidermal growth factors; and (3) the EGFR receptor expression level in HER2-over-expressing cells plays a key role in mediating the proliferation response to receptor-ligand signaling. This mathematical model also elucidates the interaction and roles of other model parameters in determining cell proliferation rate of HER2-over-expressing cells.     

Predictive reconstruction of the mitochondrial iron-sulfur cluster assembly metabolism: I. The role of the protein pair ferredoxin-ferredoxin reductase (Yah1-Arh1)

Adrenodoxin reductase homologue (Arh1) and yeast adrenodoxin homologue (Yah1) are essential Saccharomyces cerevisiae mitochondrial proteins involved in heme A biosynthesis and in iron-sulfur cluster (FeSC) assembly. Although the role of Arh1 and Yah1 in heme A biosynthesis is fairly well established, their systemic role on FeSC synthesis is not well understood. Also, while it is thought that the reductase Arh1 provides electrons for the ferredoxin Yah1, two hybrid experiments do not show interaction between the two proteins. In the first part of this article, we use structural bioinformatics methods to evaluate the possibility of interaction between Arh1 and Yah1. Using protein model building and docking algorithms, we predict a complex between Arh1 and Yah1 that is similar to that of their bovine homologues (adrenodoxin reductase-adrenodoxin), suggesting that Arh1 can indeed reduce Yah1. The predicted complex allows us to suggest point mutations to either molecule that could hinder Arh1-Yah1 interaction and test the role of Arh1 as the reductase for Yah1. In the second part of this article, we investigate the physiological role of Arh1-Yah1 on FeSC assembly by deriving alternative mathematical models of the process, based on published information. Comparing the dynamical behavior of each model with that observed in reported experiments emphasizes the importance of Arh1-Yah1 providing electrons for in situ FeSC repair. Only when this mode of action of either of the two proteins in FeSC synthesis is considered can previously reported results be reproduced.     

Predictive reconstruction of the mitochondrial iron-sulfur cluster assembly metabolism. II. Role of glutaredoxin Grx5

Grx5 is a Saccharomyces cerevisiae glutaredoxin involved in iron-sulfur cluster (FeSC) biogenesis. Previous work suggests that Grx5 is involved in regulating protein cysteine glutathionylation, prompting several questions about the systemic role of Grx5. First, is the regulation of mixed protein-glutathione disulfide bridges in FeSC biosynthetic proteins by Grx5 sufficient to account for the observed phenotypes of the Δgrx5 mutants? If so, does Grx5 regulate the oxidation state of mixed protein-glutathione disulfide bridges in FeSC biogenesis in general? Alternatively, can the Δgrx5 mutant phenotypes be explained if Grx5 acts on just one or a few of the FeSC biogenesis proteins? In the first part of this article, we address these questions by building and analyzing a mathematical model of FeSC biosynthesis. We show that, independent of the tested parameter values, the dynamic behavior observed in cells depleted of Grx5 can only be qualitatively reproduced if Grx5 acts by regulating the initial assembly of FeSC in scaffold proteins. This can be achieved by acting on the cysteine desulfurase (Nfs1) activity and/or on scaffold functionality. In the second part of this article, we use structural bioinformatics methods to evaluate the possibility of interaction between Grx5 and proteins involved in FeSC biogenesis. Based on such methods, our results indicate that the proteins with which Grx5 is more likely to interact are consistent with the kinetic modeling results. Thus, our theoretical studies, combined with known Grx5 biochemistry, suggest that Grx5 acts on FeSC biosynthesis by regulating the redox state of important cysteine residues in Nfs1 and/or in the scaffold proteins where FeSC initially assemble. Proteins 2004. © 2004 Wiley-Liss, Inc.