A composite micromechanical model for connective tissues: Part I--Theory.

A micromechanical model has been developed to study and predict the mechanical behavior of fibrous soft tissues. The model uses the theorems of least work and minimum potential energy to predict upper and lower bounds on material behavior based on the structure and properties of tissue components. The basic model consists of a composite of crimped collagen fibers embedded in an elastic glycosaminoglycan matrix. Upper and lower bound aggregation rules predict composite material behavior under the assumptions of uniform strain and uniform stress, respectively. Input parameters consist of the component material properties and the geometric configuration of the fibers. The model may be applied to a variety of connective tissue structures and is valuable in giving insight into material behavior and the nature of interactions between tissue components in various structures. Application of the model to rat tail tendon and cat knee joint capsule is described in a companion paper [2].     

A differential adhesion approach to the patterning of nerve connections

A model for the ordering of neuronal connections encompassing many facets of previous models is developed and tested against a wide range of data on the visual system of lower vertebrates (amphibia and fish). The goal of this paper is to establish that such a synthetic model can accommodate a wide range of data and reliably predict experimental results. This model makes two advances over previous efforts: (i) It predicts both minority and majority results for many of the experiments in which mixed results are obtained, and (ii) it reduces to behave as many of the previous models in some experimental settings. In addition, the model predicts different biochemical properties for cell-cell recognition than previously considered (i.e., homophilic adhesion). The model thus brings apparently disparate experimental results into a unified conceptual framework.     

A microstructurally driven model for pulmonary artery tissue

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the total crimped fiber model. This model is based on the material and microstructural properties of the two main, passive, load-bearing components of the artery wall, elastin, and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a microstructural total crimped fiber model of pulmonary artery tissue mechanics, which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.     

Model of aggregation of pigments in the chlorosomal antenna of the green bacteria Chloroflexus aurantiacus

Independent experimental and theoretical evaluation was performed for the adequacy of our previously proposed general molecular model of structural organization of light-harvesting pigments in chlorosomal bacteriochlorophyll (BChl) c/d/e-containing superantenna of different green bacteria. Simultaneous measurement of hole burning in the optical spectra of chlorosomal BChl c and temperature dependence of steady-state fluorescence spectra of BChl c was accomplished in intact cells of photosynthetic green bacterium Chloroflexus aurantiacus; this allows unambiguous determination of the structure of exciton levels of BChl c oligomers in this natural antenna, which is a fundamental criterion for adequacy of any molecular model for in vivo aggregation of antenna pigments. Experimental data were shown to confirm our model of organization of oligometric pigments in chlorosomal BChl c antenna of green bacterium Chloroflexus aurantiacus. This model, which is based on experimental data and our theory of spectroscopy of oligomeric pigments, implies that the unit building block of BChl c antenna is a cylindrical assembly containing six excitonically coupled linear pigment chains whose exciton structure with intense upper levels provides for the optimal spectral properties of the light-harvesting antenna.     

The Role of Cell Contraction and Adhesion in Dictyostelium Motility

The crawling motion of Dictyostelium discoideum on substrata involves a number of coordinated events including cell contractions and cell protrusions. The mechanical forces exerted on the substratum during these contractions have recently been quantified using traction force experiments. Based on the results from these experiments, we present a biomechanical model of the contraction phase of Dictyostelium discoideum motility with an emphasis on the adhesive properties of the cell-substratum contact. Our model assumes that the cell contracts at a constant rate and is bound to the substratum by adhesive bridges that are modeled as elastic springs. These bridges are established at a spatially uniform rate while detachment occurs at a spatially varying, load-dependent rate. Using Monte Carlo simulations and assuming a rigid substratum, we find that the cell speed depends only weakly on the detachment kinetics of the cell-substratum interface, in agreement with experimental data. By varying the parameters that control the adhesive and contractile properties of the cell, we are able to make testable predictions. We also extend our model to include a flexible substrate and show that our model is able to produce substratum deformations and force patterns that are quantitatively and qualitatively in agreement with experimental data.     

Modeling HIV-1 integrase complexes based on their hydrodynamic properties

We present a model structure of a candidate tetramer for HIV-1 integrase. The model was built in three steps using data from fluorescence anisotropy, structures of the individual integrase domains, cross-linking data, and other biochemical data. First, the structure of the full-length integrase monomer was modeled using the individual domain structures and the hydrodynamic properties of the full-length protein that were recently measured by fluorescence depolarization. We calculated the rotational correlation times for different arrangements of three integrase domains, revealing that only structures with close proximity among the domains satisfied the experimental data. The orientations of the domains were constrained by iterative tests against the data on cross-linking and footprinting in integrase-DNA complexes. Second, the structure of an integrase dimer was obtained by joining the model monomers in accordance with the available dimeric crystal structures of the catalytic core. The hydrodynamic properties of the dimer were in agreement with the experimental values. Third, the active sites of the two model dimers were placed in agreement with the spacing between the sites of integration on target DNA as well as the integrase-DNA cross-linking data, resulting in twofold symmetry of a tetrameric complex. The model is consistent with the experimental data indicating that the F185K substitution, which is found in the model at a tetramerization interface, selectively disrupts correct complex formation in vitro and HIV replication in vivo. Our model of the integrase tetramer bound to DNA may help to design anti-integrase inhibitors.     

Fission–fusion social systems as a strategy for coping with ecological constraints: a primate case

Fission–fusion social systems, in which members of a social community form frequently changing subgroups, occur in a number of mammalian taxa. Such systems are assumed to be a response to the costs of grouping, but evidence to support this hypothesis is limited. We use a linear programming approach to build a time budget model that predicts the upper bound on group size in order to test the hypothesis that fission–fusion social systems are the outcome of time constraints. Comparative data from 14 wild chimpanzee (Pan spp.) populations are used to derive a set of equations defining the relationship between climatic variables and time budget components, which are then used to calculate the upper limits on group size that can be maintained in different habitats. We validate the model by showing that it correctly predicts the presence/absence of chimpanzees across sub-Saharan Africa and the group sizes observed in natural populations. The model suggests that the costs of travel are limiting for chimpanzees. Chimpanzees can reduce these costs dramatically by fissioning their bonded communities into small foraging parties. If they did not, they would be unable to live in any habitats where they currently occur.     

Modeling the interaction between aldolase and the thrombospondin-related anonymous protein, a key connection of the malaria parasite invasion machinery

A complex molecular motor empowers substrate-dependent motility and host cell invasion in malaria parasites. The interaction between aldolase and the transmembrane adhesin thrombospondin-related anonymous protein (TRAP) transduces the motor force across the parasite surface. Here, we analyzed this interaction by using state-of-the-art flexible docking. Besides algorithms to account for induced fit in the side-chains of the Plasmodium falciparum aldolase (PfAldo) structure, we used additional in silico receptors modeled upon crystallographic structures of evolutionarily related aldolases to incorporate enzyme backbone flexibility, and to overcome structure inaccuracies due to the relatively low resolution (3.0 A) of the genuine PfAldo structure. Our results indicate that, in spite of multiple intermolecular contacts, only the six C-terminal residues of the TRAP cytoplasmic tail bind in an ordered manner to PfAldo. This portion of TRAP targets the PfAldo active site, with its n-1 Trp residue, which is essential for this interaction, buried within the PfAldo catalytic pocket. Docking of a TRAP peptide bearing a Trp to Ala mutation rendered the lower energy configurations either bound weakly outside the active site or not bound to PfAldo at all. The position of the bound TRAP peptide, and particularly the close proximity between the carbonyl of its n-2 Asp residue and the experimentally determined position of the phosphate-6 group of fructose 1,6-phosphate bound to mammalian aldolases, predicts an inhibitory effect of TRAP on catalysis. Enzymatic and TRAP-binding assays using mutant PfAldo molecules strongly support the overall structural model. These results might provide the initial framework for the identification of novel antiparasitic compounds.     

Prediction of the structure of the complex between the 30S ribosomal subunit and colicin E3 via weighted-geometric docking

Colicin E3 kills Escherichia coli cells by ribonucleolytic cleavage in the 16S rRNA. The cleavage occurs at the ribosomal decoding A-site between nucleotides A1493 and G1494. The breaking of this single phosphodiester bond results in a complete termination of protein biosynthesis leading to cell death. A model structure of the complex of the ribosomal subunit 30S and colicin E3 was constructed by means of a new weighted-geometric docking algorithm, in which interactions involving specified parts of the molecular surface can be up-weighted, allowing incorporation of experimental data in the docking search. Our model, together with available experimental data, predicts the role of the catalytic residues of colicin E3. In addition, it suggests that bound acidic immunity protein inhibits the enzymatic activity of colicin E3 by electrostatic repulsion of the negatively charged substrate.     

A quantitative model of cellular elasticity based on tensegrity

A tensegrity structure composed of six struts interconnected with 24 elastic cables is used as a quantitative model of the steady-state elastic response of cells, with the struts and cables representing microtubules and actin filaments, respectively. The model is stretched uniaxially and the Young's modulus (E0) is obtained from the initial slope of the stress versus strain curve of an equivalent continuum. It is found that E0 is directly proportional to the pre-existing tension in the cables (or compression in the struts) and inversely proportional to the cable (or strut) length square. This relationship is used to predict the upper and lower bounds of E0 of cells, assuming that the cable tension equals the yield force of actin (approximately 400 pN) for the upper bound, and that the strut compression equals the critical buckling force of microtubules for the lower bound. The cable (or strut) length is determined from the assumption that model dimensions match the diameter of probes used in standard mechanical tests on cells. Predicted values are compared to reported data for the Young's modulus of various cells. If the probe diameter is greater than or equal to 3 microns, these data are closer to the lower bound than to the upper bound. This, in turn, suggests that microtubules of the CSK carry initial compression that exceeds their critical buckling force (order of 10(0)-10(1) pN), but is much smaller than the yield force of actin. If the probe diameter is less than or equal to 2 microns, experimental data fall outside the region defined by the upper and lower bounds.     

Measures and limits of models of fixation selection

Models of fixation selection are a central tool in the quest to understand how the human mind selects relevant information. Using this tool in the evaluation of competing claims often requires comparing different models' relative performance in predicting eye movements. However, studies use a wide variety of performance measures with markedly different properties, which makes a comparison difficult. We make three main contributions to this line of research: First we argue for a set of desirable properties, review commonly used measures, and conclude that no single measure unites all desirable properties. However the area under the ROC curve (a classification measure) and the KL-divergence (a distance measure of probability distributions) combine many desirable properties and allow a meaningful comparison of critical model performance. We give an analytical proof of the linearity of the ROC measure with respect to averaging over subjects and demonstrate an appropriate correction of entropy-based measures like KL-divergence for small sample sizes in the context of eye-tracking data. Second, we provide a lower bound and an upper bound of these measures, based on image-independent properties of fixation data and between subject consistency respectively. Based on these bounds it is possible to give a reference frame to judge the predictive power of a model of fixation selection. We provide open-source python code to compute the reference frame. Third, we show that the upper, between subject consistency bound holds only for models that predict averages of subject populations. Departing from this we show that incorporating subject-specific viewing behavior can generate predictions which surpass that upper bound. Taken together, these findings lay out the required information that allow a well-founded judgment of the quality of any model of fixation selection and should therefore be reported when a new model is introduced.     

Couple-stress moduli of a trabecular bone idealized as a 3D periodic cellular network

Trabecular bone is modeled as a cellular material with an idealized periodic structure made of open cubic cells, which is effectively orthotropic. We evaluate apparent couple-stress moduli of such a periodic material; apparent moduli refer to the moduli obtained using a domain smaller than a Representative Volume Element and they depend on boundary conditions. We conduct this analysis computationally (using ANSYS) by subjecting a unit cell of this periodic cellular material to either displacement or traction boundary conditions. Cell walls, representing bone tissue, and void space, representing bone marrow, are both modeled and they are assumed to be linear elastic. The applied loadings include a uniaxial extension (or uniaxial stress), a hydrostatic deformation (or hydrostatic stress) and a shear deformation (or shear stress) to evaluate the first stiffness (or compliance) tensor, and an applied curvature (or bending moment), a uniaxial twist (or torsion), and a triaxial twist (or triaxial torsion) to evaluate the second couple-stress stiffness (or compliance) tensor. Apparent couple-stress moduli are computed by equating the total strain energy stored in the unit cell with the energy of an equivalent homogeneous orthotropic couple-stress material for each applied loading. The moduli computed using displacement boundary conditions give upper bound, while those obtained using traction boundary conditions give lower bound on effective couple-stress moduli. These bounds are very wide due to a large mismatch in elastic moduli of bone tissue and bone marrow. These results are in agreement with our studies on composite materials with very stiff or very compliant inclusions.     

Sensitivity of vertebral compressive strength to endplate loading distribution

The sensitivity of vertebral body strength to the distribution of axial forces along the endplate has not been comprehensively evaluated. Using quantitative computed tomography-based finite element models of 13 vertebral bodies, an optimization analysis was performed to determine the endplate force distributions that minimized (lower bound) and maximized (upper bound) vertebral strength for a given set of externally applied axial compressive loads. Vertebral strength was also evaluated for three generic boundary conditions: uniform displacement, uniform force, and a nonuniform force distribution in which the interior of the endplate was loaded with a force that was 1.5 times greater than the periphery. Our results showed that the relative difference between the upper and lower bounds on vertebral strength was 14.2 +/- 7.0% (mean +/- SD). While there was a weak trend for the magnitude of the strength bounds to be inversely proportional to bone mineral density (R2 = 0.32, p = 0.02), both upper and lower bound vertebral strength measures were well predicted by the strength response under uniform displacement loading conditions (R2 = 0.91 and R2 = 0.99, respectively). All three generic boundary conditions resulted in vertebral strength values that were statistically indistinguishable from the loading condition that resulted in an upper bound on strength. The results of this study indicate that the uncertainty in strength arising from the unknown condition of the disc is dependent on the condition of the bone (whether it is osteoporotic or normal). Although bone mineral density is not a good predictor of strength sensitivity, vertebral strength under generic boundary conditions, i.e., uniform displacement or force, was strongly correlated with the relative magnitude of the strength bounds. Thus, explicit disc modeling may not be necessary.     

Torsion of the central pair microtubules in eukaryotic flagella due to bending-driven lateral buckling

Inspired by recent interest in torsion of the central pair microtubules in eukaryotic flagella, a novel thin-walled elastic beam model is suggested to study critical condition under which uniform bending of a flagellum will cause lateral/torsional buckling of the central pair. The model is directed to the central pair itself and the role of all surrounding cross-linkings inside the flagellum is modeled as an equivalent surrounding elastic medium. The model predicts that bending-driven torsion of the central pair does occur when the radius of curvature of the bent flagellum reduces to a moderate critical value typically of tens of microns. In particular, this critical value is almost independent of the flagellum length, and more sensitive to the parameters defining the surrounding elastic medium than the shear modulus of microtubules. The predicted wavelengths of the torsional buckling mode are insensitive to the flagellum length and comparable to some known related experimental data. These results indicate that torsion of the central pair microtubules in flagella is inevitable as a result of bending-driven lateral buckling. This offers an entirely new insight into the ongoing research on the mechanism of the central pair torsion.     

An implementation of reinforcement learning based on spike timing dependent plasticity

An explanatory model is developed to show how synaptic learning mechanisms modeled through spike-timing dependent plasticity (STDP) can result in long-term adaptations consistent with reinforcement learning models. In particular, the reinforcement learning model known as temporal difference (TD) learning has been used to model neuronal behavior in the orbitofrontal cortex (OFC) and ventral tegmental area (VTA) of macaque monkey during reinforcement learning. While some research has observed, empirically, a connection between STDP and TD, there has not been an explanatory model directly connecting TD to STDP. Through analysis of the learning dynamics that results from a general form of a STDP learning rule, the connection between STDP and TD is explained. We further demonstrate that a STDP learning rule drives the spike probability of a reward predicting neuronal population to a stable equilibrium. The equilibrium solution has an increasing slope where the steepness of the slope predicts the probability of the reward, similar to the results from electrophysiological recordings suggesting a different slope that predicts the value of the anticipated reward of Montague and Berns [Neuron 36(2):265–284, 2002]. This connection begins to shed light into more recent data gathered from VTA and OFC which are not well modeled by TD. We suggest that STDP provides the underlying mechanism for explaining reinforcement learning and other higher level perceptual and cognitive function. This material is based upon work supported by the National Science Foundation under Grants No. IOB-0445648 (PDR) and DMS-0408334 (GL) and by a Career Support grant from Portland State University (GL).     

Prediction of the Structure of the Complex Between the 30S Ribosomal Subunit and Colicin E3 via Weighted-Geometric Docking

Abstract

Colicin E3 kills Escherichia coli cells by ribonucleolytic cleavage in the 16S rRNA. The cleavage occurs at the ribosomal decoding A-site between nucleotides A1493 and G1494. The breaking of this single phosphodiester bond results in a complete termination of protein biosynthesis leading to cell death. A model structure of the complex of the ribosomal subunit 30S and colicin E3 was constructed by means of a new weighted-geometric docking algorithm, in which interactions involving specified parts of the molecular surface can be up-weighted, allowing incorporation of experimental data in the docking search. Our model, together with available experimental data, predicts the role of the catalytic residues of colicin E3. In addition, it suggests that bound acidic immunity protein inhibits the enzymatic activity of colicin E3 by electrostatic repulsion of the negatively charged substrate.     

Biomechanics of cranial kinesis in birds: Testing linkage models in the white-throated sparrow (Zonotrichia albicollis)

Cranial kinesis in sparrows refers to the rotation of the upper jaw around its kinetic joint with the braincase. Avian jaw mechanics may involve the coupled motions of upper and lower jaws, in which the postorbital ligament transfers forces from the lower jaw, through the quadrate, pterygoid, and jugal bones, to the upper jaw. Alternatively, jaw motions may be uncoupled, with the upper jaw moving independently of the lower jaw. We tested hypotheses of cranial kinesis through the use of quantitative computer models. We present a biomechanical model of avian jaw kinetics that predicts the motions of the jaws under assumptions of both a coupled and an uncoupled mechanism. In addition, the model predicts jaw motions under conditions of force transfer by either the jugal or the pterygoid bones. Thus four alternative models may be tested using the proposed model (coupled jugal, coupled pterygoid, uncoupled jugal, uncoupled pterygoid). All models are based on the mechanics of four-bar linkages and lever systems and use morphometric data on cranial structure as the basis for predicting cranial movements. Predictions of cranial motions are tested by comparison to kinematics of white-throated sparrows (Zonotrichia albicollis) during singing. The predicted relations between jaw motions for the coupled model are significantly different from video observations. We conclude that the upper and lower jaws are not coupled in white-throated sparrows. The range of jaw motions during song is consistent with a model in which independent contractions of upper and lower jaw muscles control beak motion. © 1996 Wiley-Liss, Inc.     

Corneal Viscoelastic Properties from Finite-Element Analysis of In Vivo Air-Puff Deformation

Biomechanical properties are an excellent health marker of biological tissues, however they are challenging to be measured in-vivo. Non-invasive approaches to assess tissue biomechanics have been suggested, but there is a clear need for more accurate techniques for diagnosis, surgical guidance and treatment evaluation. Recently air-puff systems have been developed to study the dynamic tissue response, nevertheless the experimental geometrical observations lack from an analysis that addresses specifically the inherent dynamic properties. In this study a viscoelastic finite element model was built that predicts the experimental corneal deformation response to an air-puff for different conditions. A sensitivity analysis reveals significant contributions to corneal deformation of intraocular pressure and corneal thickness, besides corneal biomechanical properties. The results show the capability of dynamic imaging to reveal inherent biomechanical properties in vivo. Estimates of corneal biomechanical parameters will contribute to the basic understanding of corneal structure, shape and integrity and increase the predictability of corneal surgery.     

Aggregation kinetics of well and poorly differentiated human prostate cancer cells

Aggregation of attachment-dependent animal cells represents a series of motility, collision, and adhesion events applicable to such diverse fields as tissue engineering, bioseparations, and drug testing. Aggregation of human prostate cancer cells in liquid-overlay culture was modeled using Smoluchowski's collision theory. Using well (LNCaP) and poorly differentiated (DU 145 and PC 3) cell lines, the biological relevance of the model was assessed by comparing aggregation rates with diffusive and adhesive properties. Diffusion coefficients ranged from 5 to 90 microm(2)/min for single LNCaP and PC 3 cells, respectively. Similar diffusivities were predicted by the persistent random walk model and Einstein relation, indicating random motion. LNCaP cells were the most adhesive in our study with reduced cell shedding, 100% adhesion probability, and enhanced expression of E-cadherin. There was an increase in DU 145 cells staining positive for E-cadherin from nearly 20% of single cells to uniform staining across the surface of all aggregates; under 30% of PC 3 aggregates stained positive. Aggregation rates were more consistent with adhesive properties than with motilities, suggesting that aggregation in our study was reaction-controlled. Relative to other assays employed here, aggregation rates were more sensitive to phenotypic differences in cell lines and described size-dependent changes in aggregation at a finer resolution. In particular, model results suggest similar aggregation rates for two-dimensional DU 145 and PC 3 aggregates and upwards of 4-fold higher rates for larger three-dimensional DU 145 spheroids, consistent with expression of E-cadherin. The kinetic model has application to spheroid production, to cell flocculation and as an adhesion assay.     

苹果园二斑叶螨种群的空间格局

种群空间格局的研究是昆虫生态学的重要内容,它不仅揭示出种群的空间结构特征,而且还是确定抽样技术和资料代换的基础,二斑叶螨是苹果园的重要害螨,应用4种聚集度指标和Iwao法分别考查了该螨在苹果树内的空间格局及动态规律,结果表明,二斑叶螨在树内不同方向和高度上均以个体群的形式存在,个体群的分布为聚集分布,其中上层和南面树冠的聚集度最高,而下层和内部树冠的聚集度最低,造成这种差异与该螨的生物学特性和环境条件的异质性有关,不论螨体在上层,中层或下层树冠,都明显地表现出前期高聚块,6月中旬以后聚集强度逐渐降低的趋势。