On foundations of discrete element analysis of contact in diarthrodial joints

Information about the stress distribution on contact surfaces of adjacent bones is indispensable for analysis of arthritis, bone fracture and remodeling. Numerical solution of the contact problem based on the classical approaches of solid mechanics is sophisticated and time-consuming. However, the solution can be essentially simplified on the following physical grounds. The bone contact surfaces are covered with a layer of articular cartilage, which is a soft tissue as compared to the hard bone. The latter allows ignoring the bone compliance in analysis of the contact problem, i.e. rigid bones are considered to interact through a compliant cartilage. Moreover, cartilage shear stresses and strains can be ignored because of the negligible friction between contacting cartilage layers. Thus, the cartilage can be approximated by a set of unilateral compressive springs normal to the bone surface. The forces in the springs can be computed from the equilibrium equations iteratively accounting for the changing contact area. This is the essence of the discrete element analysis (DEA). Despite the success in applications of DEA to various bone contact problems, its classical formulation required experimental validation because the springs approximating the cartilage were assumed linear while the real articular cartilage exhibited non-linear mechanical response in reported tests. Recent experimental results of Ateshian and his co-workers allow for revisiting the classical DEA formulation and establishing the limits of its applicability. In the present work, it is shown that the linear spring model is remarkably valid within a wide range of large deformations of the cartilage. It is also shown how to extend the classical DEA to the case of strong nonlinearity if necessary.     

The ideal and the feasible: physical constraints on evolution

The laws of physics and the properties of the physical environment impose constraints on evolution. Structures and processes that may be imagined cannot in some cases be evolved, because they are physically impossible. This paper explores the consequences of the particulate nature of matter and of light; of the wave nature of light and sound; of the laws of diffusion and heat exchange; of the mechanical properties of materials; of limits to aerodynamic and hydrodynamic performance; and of the behaviour of electricity.     

The challenges and scope of theoretical biology

Scientific theories seek to provide simple explanations for significant empirical regularities based on fundamental physical and mechanistic constraints. Biological theories have rarely reached a level of generality and predictive power comparable to physical theories. This discrepancy is explained through a combination of frozen accidents, environmental heterogeneity, and widespread non-linearities observed in adaptive processes. At the same time, model building has proven to be very successful when it comes to explaining and predicting the behavior of particular biological systems. In this respect biology resembles alternative model-rich frameworks, such as economics and engineering. In this paper we explore the prospects for general theories in biology, and suggest that these take inspiration not only from physics, but also from the information sciences. Future theoretical biology is likely to represent a hybrid of parsimonious reasoning and algorithmic or rule-based explanation. An open question is whether these new frameworks will remain transparent to human reason. In this context, we discuss the role of machine learning in the early stages of scientific discovery. We argue that evolutionary history is not only a source of uncertainty, but also provides the basis, through conserved traits, for very general explanations for biological regularities, and the prospect of unified theories of life.     

Human cortical bone: the SiNuPrOs model

Many models that have been developed for cortical bone oversimplify much of the architectural and physical complexity. With SiNuPrOs model, a more complete approach is investigated: it is multiscale because it contains five structural levels and multi physic because it takes into account simultaneously structure (with various properties: elasticity, piezoelectricity, porous medium), fluid and mineralization process modelization. The multiscale aspect is modeled by using 18 structural parameters in a specific application of the mathematical theory of homogenization and 10 other physical parameters are necessary for the multi physic aspect. The modelization of collagen as a piezoelectric medium has needed the development of a new behaviour law allowing a better simulation of the effect of a medium considered as evolving during a mineralization process.

Then the main interest of SiNuPrOs deals with the possibility to study, at each level of the cortical architecture, either the elastic properties or the fluid motion or the piezoelectric effects or both of them. All these possibilities constitute a very large work and all this mass of information (fluid aspects, even at the nanoscopic scale, piezoelectric phenomena and simulations) will be presented in several papers. This first one is only devoted to the presentation of this model with an application to the computation of elastic properties at the macroscopic scale.

The computational methods have been packed into software also called SiNuPrOs and allowing a large number of predictive simulations corresponding to various different configurations.     

Aging, evolvability, and the individual benefit requirement; medical implications of aging theory controversies

There is a class of theories of aging (variously termed adaptive aging, aging by design, aging selected for its own sake, or programmed death theories) that hold that an organism design that limits life span conveys benefits and was selected specifically because it limits life span. These theories have enjoyed a resurgence of popularity because of the discovery of genes that promote aging in various organisms.However, traditional evolution theory has a core tenet that excludes the possibility of evolving and retaining an individually adverse organism design, i.e. a design characteristic that reduces the ability of individual organisms to survive or reproduce without any compensating individual benefit. Various theories of aging dating from the 1950s and based on traditional evolution theory enjoy substantial popularity. Therefore, any theorist proposing an adaptive theory of aging must necessarily also propose some adjustment to traditional evolution theory that specifically addresses the individual benefit issue. This paper describes an adaptive theory of aging and describes how one of the proposed adjustments (evolvability theory) supports adaptive aging.This issue is important because adaptive theories are generally more optimistic regarding prospects for medical intervention in the aging process and also suggest different approaches in achieving such intervention.     

Microbiology of the phyllosphere: a playground for testing ecological concepts

Many concepts and theories in ecology are highly debated, because it is often difficult to design decisive tests with sufficient replicates. Examples include biodiversity theories, succession concepts, invasion theories, coexistence theories, and concepts of life history strategies. Microbiological tests of ecological concepts are rapidly accumulating, but have yet to tap into their full potential to complement traditional macroecological theories. Taking the example of microbial communities on leaf surfaces (i.e. the phyllosphere), we show that most explorations of ecological concepts in this field of microbiology focus on autecology and population ecology, while community ecology remains understudied. Notable exceptions are first tests of the island biogeography theory and of biodiversity theories. Here, the phyllosphere provides the unique opportunity to set up replicated experiments, potentially moving fields such as biogeography, macroecology, and landscape ecology beyond theoretical and observational evidence. Future approaches should take advantage of the great range of spatial scales offered by the leaf surface by iteratively linking laboratory experiments with spatial simulation models.     

Blind Prediction of Charged Ligand Binding Affinities in a Model Binding Site

Predicting absolute protein–ligand binding affinities remains a frontier challenge in ligand discovery and design. This becomes more difficult when ionic interactions are involved because of the large opposing solvation and electrostatic attraction energies. In a blind test, we examined whether alchemical free-energy calculations could predict binding affinities of 14 charged and 5 neutral compounds previously untested as ligands for a cavity binding site in cytochrome c peroxidase. In this simplified site, polar and cationic ligands compete with solvent to interact with a buried aspartate. Predictions were tested by calorimetry, spectroscopy, and crystallography. Of the 15 compounds predicted to bind, 13 were experimentally confirmed, while 4 compounds were false negative predictions. Predictions had a root-mean-square error of 1.95 kcal/mol to the experimental affinities, and predicted poses had an average RMSD of 1.7 Å to the crystallographic poses. This test serves as a benchmark for these thermodynamically rigorous calculations at predicting binding affinities for charged compounds and gives insights into the existing sources of error, which are primarily electrostatic interactions inside proteins. Our experiments also provide a useful set of ionic binding affinities in a simplified system for testing new affinity prediction methods.     

A numerically validated probabilistic model of a simplified total hip replacement construct

Hip replacement constructs are paradigms of uncertain systems, and as such are suited to the application of probabilistic methods to assess their structural integrity. In order to gain confidence in a probabilistic model, it would be useful to verify the findings with experimental data; however, this is difficult to achieve in practice because of the exhaustive number of parameter combinations that need to be tested. As an alternative to experimental testing, benchmarking can be carried out provided a known analytical solution is available. To this end, a simplified 2D two-beam model of the femoral part of a total hip replacement construct was utilised to analyse uncertainties and variability in the construct as it is subjected to load. The use of a simplified model enabled geometric parameters to be investigated; these are commonly not considered in probabilistic models due to the increased complexity involved. Analytical and finite element representations of the model were developed and compared. The probabilistic study used the Monte Carlo simulation technique and the first-order reliability method to look at the inducible displacement of a hip implant, a phenomenon that has been linked to the most common cause of hip implant failure, aseptic loosening. Excellent correlation was observed between the analytical and probabilistic solutions, and it was shown that probabilistic approaches could efficiently predict the response of the simplified beam model while readily identifying the parameters most likely to compromise the structural integrity of the construct.     

Rat C6 glioma as experimental model system for the study of glioblastoma growth and invasion

Infiltration of the central nervous system by neoplastic cells in patients with glioblastoma multiforme (GBM) leads to neurological dysfunction and eventually to death. The elucidation of the mechanisms underlying the aggressive nature of GBM aims at improving radio-, chemo- and gene therapy. This review is focused on the use of rat C6 glioma as an experimental model system for GBM and provides an overview of the experimental data published in the literature using this cell line in elucidating the mechanism of tumor growth, angiogenesis and invasion, and in the design and evaluation of anticancer therapies. Understanding the stages of malignant brain tumor progression requires a series of experimental approaches with a varying degree of complexity. Implantation of malignant cells into animal brain tissue closely resembles in vivo tumor growth and has the advantage over simplified models that inflammatory and vascular mechanisms are activated. However, the complexity of these models makes it difficult to identify the individual processes involved in sustained tumor growth, angiogenesis and invasion. In cell culture models, the effect of growth factors, extracellular matrix components, proteases and adhesion molecules can be investigated. The secretion of tumor-derived factors into the medium can also be analyzed when simplified models are used. This review is a compilation of experimental data focused on the characterization of tumor-related processes and on the evaluation of new therapies for the treatment of malignant glial neoplasms using rat C6 glioma as a model system.     

A numerically validated probabilistic model of a simplified total hip replacement construct

Hip replacement constructs are paradigms of uncertain systems, and as such are suited to the application of probabilistic methods to assess their structural integrity. In order to gain confidence in a probabilistic model, it would be useful to verify the findings with experimental data; however, this is difficult to achieve in practice because of the exhaustive number of parameter combinations that need to be tested. As an alternative to experimental testing, benchmarking can be carried out provided a known analytical solution is available. To this end, a simplified 2D two-beam model of the femoral part of a total hip replacement construct was utilised to analyse uncertainties and variability in the construct as it is subjected to load. The use of a simplified model enabled geometric parameters to be investigated; these are commonly not considered in probabilistic models due to the increased complexity involved. Analytical and finite element representations of the model were developed and compared. The probabilistic study used the Monte Carlo simulation technique and the first-order reliability method to look at the inducible displacement of a hip implant, a phenomenon that has been linked to the most common cause of hip implant failure, aseptic loosening. Excellent correlation was observed between the analytical and probabilistic solutions, and it was shown that probabilistic approaches could efficiently predict the response of the simplified beam model while readily identifying the parameters most likely to compromise the structural integrity of the construct.     

Transformation of DNA sequence data into geometric symbols

Comparative analysis of related DNA sequences has been simplified by the transformation of data in the standard A, G, C, T format into a set of geometric symbols that promote pattern recognition. Previously, comparing more than 2 or 3 sequences simultaneously has been difficult because of the monotonous patterns established by letters. Here 33 sequences are simultaneously compared to demonstrate the ease with which nucleotide substitutions are accurately identified. This has been accomplished by writing a Word-Perfect macro program to facilitate this transformation. Since this word processing program is widely used, performing this kind of analysis is readily achievable in most laboratories involved in DNA sequence analysis.     

Integrated function of a kinetic proofreading mechanism: steady-state analysis testing internal consistency of data obtained in vivo and in vitro and predicting parameter values

Experimental measurements of the kinetic mechanism involving isoleucyl-tRNA synthetase proofreading valyl-tRNAIle in Escherichia coli have been incorporated into the conventional Michaelis-Menten model for this system. The model was subjected to a detailed mathematical analysis in the steady state. The results of this analysis provide an excellent illustration of the value of integrating fragmentary data into a model of the intact system. (1) Such integration provides a rigorous test for consistency of the individual measurements. For the above synthetase system, the published experimental data were found to be internally inconsistent. (2) Such integration predicts which experimental data are most suspect. In this case, one of the three most questionable measurements, the isoleucine pool size in vivo, was found upon reexamination to be in error by 10-15-fold. Correction of this error produced a self-consistent set of parameter values. (3) The integrated analysis provides predictions for various parameter values. In many cases, these predictions provide estimates for parameter values that are difficult to determine directly or that have yet to be measured experimentally. (4) A sensitivity analysis provides an indication of the relative importance of various parameter values and, hence, an indication of where future experimental effort might be focused most profitably.     

Numerical studies of unreactive contractile networks.

We present a finite difference algorithm for integrating the reactive flow model of contractile biological polymer networks on a fixed Eulerian mesh. We discuss the accuracy and limits of the algorithm. To illustrate the application of the algorithm, we carry out a family of computations involving an unreactive contractile network contained in a two-dimensional square reaction vessel. By numerical experiments using different values of the physical parameters of the model, we find that for this simple sort of system two major dynamical modes of contraction are predicted to occur. There is the squeezing type contraction in which the network contracts to a single small clump with gradual expulsion of solution material, and the rending type contraction in which the network tears itself into a number of separate pieces. We find that to a good approximation the transition between the squeezing mode and the rending mode is controlled by a single nondimensional number (the rending number). We discuss the relevance of these results for the analysis of various experimental observations.     

The Structure of Elongated Viral Capsids

There are many viruses whose genetic material is protected by a closed elongated protein shell. Unlike spherical viruses, the structure and construction principles of these elongated capsids are not fully known. In this article, we have developed a general geometrical model to describe the structure of prolate or bacilliform capsids. We show that only a limited set of tubular architectures can be built closed by hemispherical icosahedral caps. In particular, the length and number of proteins adopt a very special set of discrete values dictated by the axial symmetry (fivefold, threefold, or twofold) and the triangulation number of the caps. The results are supported by experimental observations and simulations of simplified physical models. This work brings about a general classification of elongated viruses that will help to predict their structure, and to design viral cages with tailored geometrical properties for biomedical and nanotechnological applications.     

A range-normalization model of context-dependent choice: a new model and evidence

Most utility theories of choice assume that the introduction of an irrelevant option (called the decoy) to a choice set does not change the preference between existing options. On the contrary, a wealth of behavioral data demonstrates the dependence of preference on the decoy and on the context in which the options are presented. Nevertheless, neural mechanisms underlying context-dependent preference are poorly understood. In order to shed light on these mechanisms, we design and perform a novel experiment to measure within-subject decoy effects. We find within-subject decoy effects similar to what have been shown previously with between-subject designs. More importantly, we find that not only are the decoy effects correlated, pointing to similar underlying mechanisms, but also these effects increase with the distance of the decoy from the original options. To explain these observations, we construct a plausible neuronal model that can account for decoy effects based on the trial-by-trial adjustment of neural representations to the set of available options. This adjustment mechanism, which we call range normalization, occurs when the nervous system is required to represent different stimuli distinguishably, while being limited to using bounded neural activity. The proposed model captures our experimental observations and makes new predictions about the influence of the choice set size on the decoy effects, which are in contrast to previous models of context-dependent choice preference. Critically, unlike previous psychological models, the computational resource required by our range-normalization model does not increase exponentially as the set size increases. Our results show that context-dependent choice behavior, which is commonly perceived as an irrational response to the presence of irrelevant options, could be a natural consequence of the biophysical limits of neural representation in the brain.     

From computational quantum chemistry to computational biology: experiments and computations are (full) partners

Computations are being integrated into biological research at an increasingly fast pace. This has not only changed the way in which biological information is managed; it has also changed the way in which experiments are planned in order to obtain information from nature. Can experiments and computations be full partners? Computational chemistry has expanded over the years, proceeding from computations of a hydrogen molecule toward the challenging goal of systems biology, which attempts to handle the entire living cell. Applying theories from ab initio quantum mechanics to simplified models, the virtual worlds explored by computations provide replicas of real-world phenomena. At the same time, the virtual worlds can affect our perception of the real world. Computational biology targets a world of complex organization, for which a unified theory is unlikely to exist. A computational biology model, even if it has a clear physical or chemical basis, may not reduce to physics and chemistry. At the molecular level, computational biology and experimental biology have already been partners, mutually benefiting from each other. For the perception to become reality, computation and experiment should be united as full partners in biological research.     

Decomposition-based qualitative experiment design algorithms for a class of compartmental models.

Qualitative experiment design, to determine experimental input/output configurations that provide identifiability for specific parameters of interest, can be extremely difficult if the number of unknown parameters and the number of compartments are relatively large. However, the problem can be considerably simplified if the parameters can be divided into several groups for separate identification and the model can be decomposed into smaller submodels for separate experiment design. Model decomposition-based experiment design algorithms are proposed for a practical class of large-scale compartmental models representative of biosystems characterized by multiple input sources and unidirectional interconnectivity among subsystems. The model parameters are divided into three types, each of which is identified consecutively, in three stages, using simpler submodel experiment designs. Several practical examples are presented. Necessary and sufficient conditions for identifiability using the algorithm are also discussed.