Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell–matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices – collagen and fibrin – and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL^?1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.     

Computational ligand-based rational design: Role of conformational sampling and force fields in model development

A significant number of drug discovery efforts are based on natural products or high throughput screens from which compounds showing potential therapeutic effects are identified without knowledge of the target molecule or its 3D structure. In such cases computational ligand-based drug design (LBDD) can accelerate the drug discovery processes. LBDD is a general approach to elucidate the relationship of a compound's structure and physicochemical attributes to its biological activity. The resulting structure-activity relationship (SAR) may then act as the basis for the prediction of compounds with improved biological attributes. LBDD methods range from pharmacophore models identifying essential features of ligands responsible for their activity, quantitative structure-activity relationships (QSAR) yielding quantitative estimates of activities based on physiochemical properties, and to similarity searching, which explores compounds with similar properties as well as various combinations of the above. A number of recent LBDD approaches involve the use of multiple conformations of the ligands being studied. One of the basic components to generate multiple conformations in LBDD is molecular mechanics (MM), which apply an empirical energy function to relate conformation to energies and forces. The collection of conformations for ligands is then combined with functional data using methods ranging from regression analysis to neural networks, from which the SAR is determined. Accordingly, for effective application of LBDD for SAR determinations it is important that the compounds be accurately modelled such that the appropriate range of conformations accessible to the ligands is identified. Such accurate modelling is largely based on use of the appropriate empirical force field for the molecules being investigated and the approaches used to generate the conformations. The present chapter includes a brief overview of currently used SAR methods in LBDD followed by a more detailed presentation of issues and limitations associated with empirical energy functions and conformational sampling methods.     

Biochemical processing of E-cadherin under cellular stress

The proteolytic cleavage pathways of E-cadherin endogenously expressed in MDCK (Madin-Darby canine kidney) cells were characterized in cells treated with antimycin A and deoxyglucose to examine transmembrane protein processing under cellular stress. E-cadherin is a type I transmembrane protein which operates as the cell adhesion molecule component of the adherens junction, a complex of proteins involved in epithelial tissue development and integrity. We now demonstrate that treatment of MDCK cells with antimycin A and deoxyglucose activates caspase mediated pathways that cleave E-cadherin. E-cadherin is cleaved into two major fragments, with the sizes predicted by the location of a caspase-3 cleavage consensus sequence. Cleavage of E-cadherin and deposition of the C-terminal fragment into the cytoplasm are inhibited by the caspase inhibitor DEVD-CHO. Thus, a major mechanism for E-cadherin cleavage and dissolution of the adherens junction under antimycin/deoxyglucose treatment is caspase mediated, initiated by activation of an apoptosis pathway.     

Individualization as driving force of clustering phenomena in humans

One of the most intriguing dynamics in biological systems is the emergence of clustering, in the sense that individuals self-organize into separate agglomerations in physical or behavioral space. Several theories have been developed to explain clustering in, for instance, multi-cellular organisms, ant colonies, bee hives, flocks of birds, schools of fish, and animal herds. A persistent puzzle, however, is the clustering of opinions in human populations, particularly when opinions vary continuously, such as the degree to which citizens are in favor of or against a vaccination program. Existing continuous opinion formation models predict "monoculture" in the long run, unless subsets of the population are perfectly separated from each other. Yet, social diversity is a robust empirical phenomenon, although perfect separation is hardly possible in an increasingly connected world. Considering randomness has not overcome the theoretical shortcomings so far. Small perturbations of individual opinions trigger social influence cascades that inevitably lead to monoculture, while larger noise disrupts opinion clusters and results in rampant individualism without any social structure. Our solution to the puzzle builds on recent empirical research, combining the integrative tendencies of social influence with the disintegrative effects of individualization. A key element of the new computational model is an adaptive kind of noise. We conduct computer simulation experiments demonstrating that with this kind of noise a third phase besides individualism and monoculture becomes possible, characterized by the formation of metastable clusters with diversity between and consensus within clusters. When clusters are small, individualization tendencies are too weak to prohibit a fusion of clusters. When clusters grow too large, however, individualization increases in strength, which promotes their splitting. In summary, the new model can explain cultural clustering in human societies. Strikingly, model predictions are not only robust to "noise"-randomness is actually the central mechanism that sustains pluralism and clustering.     

Computational reconstruction of multidomain proteins using atomic force microscopy data

Classical structural biology techniques face a great challenge to determine the structure at the atomic level of large and flexible macromolecules. We present a novel methodology that combines high-resolution AFM topographic images with atomic coordinates of proteins to assemble very large macromolecules or particles. Our method uses a two-step protocol: atomic coordinates of individual domains are docked beneath the molecular surface of the large macromolecule, and then each domain is assembled using a combinatorial search. The protocol was validated on three test cases: a simulated system of antibody structures; and two experimentally based test cases: Tobacco mosaic virus, a rod-shaped virus; and Aquaporin Z, a bacterial membrane protein. We have shown that AFM-intermediate resolution topography and partial surface data are useful constraints for building macromolecular assemblies. The protocol is applicable to multicomponent structures connected in the polypeptide chain or as disjoint molecules. The approach effectively increases the resolution of AFM beyond topographical information down to atomic-detail structures.     

Computational model of particle deposition in the nasal cavity under steady and dynamic flow

A computational model for flow and particle deposition in a three-dimensional representation of the human nasal cavity is developed. Simulations of steady state and dynamic airflow during inhalation are performed at flow rates of 9–60 l/min. Depositions for particles of size 0.5–20 μm are determined and compared with experimental and simulation results from the literature in terms of deposition efficiencies. The nasal model is validated by comparison with experimental and simulation results from the literature for particle deposition under steady-state flow. The distribution of deposited particles in the nasal cavity is presented in terms of an axial deposition distribution as well as a bivariate axial deposition and particle size distribution. Simulations of dynamic airflow and particle deposition during an inhalation cycle are performed for different nasal cavity outlet pressure variations and different particle injections. The total particle deposition efficiency under dynamic flow is found to depend strongly on the dynamics of airflow as well as the type of particle injection.     

Computational model of dot-pattern selective cells

A computational model of a dot-pattern selective neuron is proposed. This type of neuron is found in the inferotemporal cortex of monkeys. It responds strongly to groups of dots and spots of light intensity variation but very weakly or not at all to single dots and spots that are not part of a pattern. This non-linear behaviour is quite different from the spatial frequency filtering behaviour exhibited by other neurons that react to spot-shaped stimuli, such as neurons with centre-surround receptive field profiles found in the lateral geniculate nuclei and layer 4Cβ of V1. It is implemented in the proposed computational model by using an AND-type non-linearity to combine the responses of centre-surround cells. The proposed model is capable of explaining the results of neurophysiological experiments as well as certain psychophysical observations. Received: 20 December 1999 / Accepted in revised form: 3 March 2000     

A micromechanical muscle model for determining the impact of motor unit fiber clustering on force transmission in aging skeletal muscle

This study used a micromechanical finite element muscle model to investigate the effects of the redistribution of spatial activation patterns in young and old muscle. The geometry consisted of a bundle of 19 active muscle fibers encased in endomysium sheets, surrounded by passive tissue to model a fascicle. Force was induced by activating combinations of the 19 active muscle fibers. The spacial clustering of muscle fibers modeled in this study showed unbalanced strains suggesting tissue damage at higher strain levels may occur during higher levels of activation and/or during dynamic conditions. These patterns of motor unit remodeling are one of the consequences of motor unit loss and reinnervation associated with aging. The results did not reveal evident quantitative changes in force transmission between old and young adults, but the patterns of stress and strain distribution were affected, suggesting an uneven distribution of the forces may occur within the fascicle that could provide a mechanism for muscle injury in older muscle.

     

Computational modeling of healing: an application of the material force method

The basic aim of the present contribution is the qualitative simulation of healing phenomena typically encountered in hard and soft tissue mechanics. The mechanical framework is provided by the theory of open system thermodynamics, which will be formulated in the spatial as well as in the material motion context. While the former typically aims at deriving the density and the spatial motion deformation field in response to given spatial forces, the latter will be applied to determine the material forces in response to a given density and material deformation field. We derive a general computational framework within the finite element context that will serve to evaluate both the spatial and the material motion problem. However, once the spatial motion problem has been solved, the solution of the material motion problem represents a mere post-processing step and is thus extremely cheap from a computational point of view. The underlying algorithm will be elaborated systematically by means of two prototype geometries subjected to three different representative loading scenarios, tension, torsion, and bending. Particular focus will be dedicated to the discussion of the additional information provided by the material force method. Since the discrete material node point forces typically point in the direction of potential material deposition, they can be interpreted as a driving force for the healing mechanism.Blues the healer, John Lee Hooker [1989]     

Computational model for monitoring cholesterol metabolism

A non-deterministic finite automaton is designed to observe the cholesterol metabolism with the states of acceptance and rejection. The acceptance state of the automaton depicts the normal level of metabolism and production of good cholesterol as an end product. The rejection state of this machine shows the inhibition of enzymatic activity in cholesterol synthesis and removal of free fatty acids. The deficiency in human cholesterol metabolism pathway results in abnormal accumulation of cholesterol in plasma, arterial tissues leading to diseases such as hypercholesterolemia, atherosclerosis respectively and formation of gallstones. The designed machine can be used to monitor the cholesterol metabolism at molecular level through regulation of enzymes involved in the biosynthesis and metabolism of cholesterol for the treatment of diseases incident due to the respective metabolic disorder. In addition, an algorithm for this machine has been developed to compare the programmed string with the given string. This study demonstrates the construction of a machine that is used for the development of molecular targeted therapy for the disorders in cholesterol metabolism.     

Computational model of a synovial joint morphogenesis

Biomechanics and Modeling in Mechanobiology - Joints enable the relative movement between the connected bones. The shape of the joint is important for the joint movements since they facilitate and...     

A thermodynamic model for receptor clustering

Intracellular signaling often arises from ligand-induced oligomerization of cell surface receptors. This oligomerization or clustering process is fundamentally a cooperative behavior between near-neighbor receptor molecules; the properties of this cooperative process clearly affect the signal transduction. Recent investigations have revealed the molecular basis of receptor-receptor interactions, but a simple theoretical framework for using these data to predict cluster formation has been lacking. Here, we propose a simple, coarse-grained, phenomenological model for ligand-modulated receptor interactions and discuss its equilibrium properties via mean-field theory. The existence of a first-order transition for this model has immediate implications for the robustness of the cellular signaling response.     

A computational model of transmembrane integrin clustering

The presented work describes a structural model for integrin homooligomerization, focusing on the transmembrane domains. The two noncovalently linked integrin subunits, alpha and beta, were previously shown to homodimerize or homotrimerize, respectively. Our work is based on published mutational work that induced homotrimerization of beta3 integrins. The mutations provided structural restraints for the creation of a structural model of the beta3 homotrimer by a computational search of the conformational space of homomeric interactions of the beta3 integrin. Additionally, we explored possible conformations of the alphaIIb integrin homodimer, for which no unique solution was found. Two possible models of signal transduction, involving two different alphaIIb conformations, are discussed. One of the possible homodimeric alphaIIb conformations is GpA like, which is in line with experimental evidence. Based on our here-presented structural models and on recent experiments, we will argue that most probably the heteromeric alpha/beta transmembrane complex separates in the course of clustering.     

Computational modeling of axonal microtubule bundles under tension

Microtubule bundles cross-linked by tau protein serve a variety of neurological functions including maintaining mechanical integrity of the axon, promoting axonal growth, and facilitating cargo transport. It has been observed that axonal damage in traumatic brain injury leads to bundle disorientation, loss of axonal viability, and cognitive impairment. This study investigates the initial mechanical response of axonal microtubule bundles under uniaxial tension using a discrete bead-spring representation. Mechanisms of failure due to traumatic stretch loading and their impact on the mechanical response and stability are also characterized. This study indicates that cross-linked axonal microtubule bundles in tension display stiffening behavior similar to a power-law relationship from nonaffine network deformations. Stretching of cross-links and microtubule bending were the primary deformation modes at low stresses. Microtubule stretch was negligible up to tensile stresses of ～1 MPa. Bundle failure occurred by failure of cross-links leading to pull-out of microtubules and loss of bundle integrity. This may explain the elongation, undulation, and delayed elasticity of axons following traumatic stretch loading. More extensively cross-linked bundles withstood higher tensile stresses before failing. The bundle mechanical behavior uncovered by these computational techniques should guide future experiments on stretch-injured axons.     

A kinetic molecular model of the reversible unfolding and refolding of titin under force extension.

Molecular elasticity is a physicomechanical property that is associated with a select number of polypeptides and proteins, such as the giant muscle protein, titin, and the extracellular matrix protein, tenascin. Both proteins have been the subject of atomic force microscopy (AFM), laser tweezer, and other in vitro methods for examining the effects of force extension on the globular (FNIII/Ig-like) domains that comprise each protein. In this report we present a time-dependent method for simulating AFM force extension and its effect on FNIII/Ig domain unfolding and refolding. This method treats the unfolding and refolding process as a standard three-state protein folding model (U right arrow over left arrow T right arrow over left arrow F, where U is the unfolded state, T is the transition or intermediate state, and F is the fully folded state), and integrates this approach within the wormlike chain (WLC) concept. We simulated the effect of AFM tip extension on a hypothetical titin molecule comprised of 30 globular domains (Ig or FNIII) and 25% Pro-Glu-Val-Lys (PEVK) content, and analyzed the unfolding and refolding processes as a function of AFM tip extension, extension rate, and variation in PEVK content. In general, we find that the use of a three-state protein-folding kinetic-based model and the implicit inclusion of PEVK domains can accurately reproduce the experimental force-extension curves observed for both titin and tenascin proteins. Furthermore, our simulation data indicate that PEVK domains exhibit extensibility behavior, assist in the unfolding and refolding of FNIII/Ig domains in the titin molecule, and act as a force "buffer" for the FNIII/Ig domains, particularly at low and moderate extension forces.     

Computational model of motor learning and perceptual change

Motor learning in the context of arm reaching movements has been frequently investigated using the paradigm of force-field learning. It has been recently shown that changes to somatosensory perception are likewise associated with motor learning. Changes in perceptual function may be the reason that when the perturbation is removed following motor learning, the hand trajectory does not return to a straight line path even after several dozen trials. To explain the computational mechanisms that produce these characteristics, we propose a motor control and learning scheme using a simplified two-link system in the horizontal plane: We represent learning as the adjustment of desired joint-angular trajectories so as to achieve the reference trajectory of the hand. The convergence of the actual hand movement to the reference trajectory is proved by using a Lyapunov-like lemma, and the result is confirmed using computer simulations. The model assumes that changes in the desired hand trajectory influence the perception of hand position and this in turn affects movement control. Our computer simulations support the idea that perceptual change may come as a result of adjustments to movement planning with motor learning.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.