Subject-specific planning of femoroplasty: A combined evolutionary optimization and particle diffusion model approach

A potential effective treatment for prevention of osteoporotic hip fractures is augmentation of the mechanical properties of the femur by injecting it with agents such as (PMMA) bone cement – femoroplasty. The operation, however, is only in research stage and can benefit substantially from computer planning and optimization. We report the results of computational planning and optimization of the procedure for biomechanical evaluation. An evolutionary optimization method was used to optimally place the cement in finite element (FE) models of seven osteoporotic bone specimens. The optimization, with some inter-specimen variations, suggested that areas close to the cortex in the superior and inferior of the neck and supero-lateral aspect of the greater trochanter will benefit from augmentation. We then used a particle-based model for bone cement diffusion simulation to match the optimized pattern, taking into account the limitations of the actual surgery, including limited volume of injection to prevent thermal necrosis. Simulations showed that the yield load can be significantly increased by more than 30%, using only 9 ml of bone cement. This increase is comparable to previous literature reports where gross filling of the bone was employed instead, using more than 40 ml of cement. These findings, along with the differences in the optimized plans between specimens, emphasize the need for subject-specific models for effective planning of femoral augmentation.     

RNA based evolutionary optimization

The notion of an RNA world has been introduced for a prebiotic scenario that is dominated by RNA molecules and their properties, in particular their capabilities to act as templates for reproduction and as catalysts for several cleavage and ligation reactions of polynucleotides and polypeptides. This notion is used here also for simple experimental assays which are well suited to study evolution in the test tube. In molecular evolution experiments fitness is determined in essence by the molecular structures of RNA molecules. Evidence is presented for adaptation to environment in cell-free media. RNA based molecular evolution experiments have led to interesting spin-offs in biotechnology, commonly called applied molecular evolution, which make use of Darwinian trial-and-error strategies in order to synthesize new pharmacological compounds and other advanced materials on a biological basis.Error-propagation in RNA replication leads to formation of mutant spectra called quasispecies. An increase in the error rate broadens the mutant spectrum. There exists a sharply defined threshold beyond which heredity breaks down and evolutionary adaptation becomes impossible. Almost all RNA viruses studied so far operate at conditions close to this error threshold. Quasispecies and error thresholds are important for an understanding of RNA virus evolution, and they may help to develop novel antiviral strategies.Evolution of RNA molecules can be studied and interpreted by considering secondary structures. The notion of sequence space introduces a distance between pairs of RNA sequences which is tantamount to counting the minimal number of point mutations required to convert the sequences into each other. The mean sensitivity of RNA secondary structures to mutation depends strongly on the base pairing alphabet: structures from sequences which contain only one base pair (GC or AU are much less stable against mutation than those derived from the natural (AUGC) sequences. Evolutionary optimization of two-letter sequences in thus more difficult than optimization in the world of natural RNA sequences with four bases. This fact might explain the usage of four bases in the genetic language of nature.Finally we study the mapping from RNA sequences into secondary structures and explore the topology of RNA shape space. We find that neutral paths connecting neighbouring sequences with identical structures go very frequently through entire sequence space. Sequences folding into common structures are found everywhere in sequence space. Hence, evolution can migrate to almost every part of sequence space without hill climbing and only small fractions of the entire number of sequences have to be searched in order to find suitable structures.     

An evolutionary optimization principle

Characteristics of evolutionarily stable strategies, or ESS's, are investigated for a general class of evolutionary models. Both differential equation and difference equation models are considered. At an ESS, species that exhibit negative density dependence maximize population size; those that show positive density dependence minimize population size.     

Gnarled-trunk evolutionary model of influenza A virus hemagglutinin

Human influenza A viruses undergo antigenic changes with gradual accumulation of amino acid substitutions on the hemagglutinin (HA) molecule. A strong antigenic mismatch between vaccine and epidemic strains often requires the replacement of influenza vaccines worldwide. To establish a practical model enabling us to predict the future direction of the influenza virus evolution, relative distances of amino acid sequences among past epidemic strains were analyzed by multidimensional scaling (MDS). We found that human influenza viruses have evolved along a gnarled evolutionary pathway with an approximately constant curvature in the MDS-constructed 3D space. The gnarled pathway indicated that evolution on the trunk favored multiple substitutions at the same amino acid positions on HA. The constant curvature was reasonably explained by assuming that the rate of amino acid substitutions varied from one position to another according to a gamma distribution. Furthermore, we utilized the estimated parameters of the gamma distribution to predict the amino acid substitutions on HA in subsequent years. Retrospective prediction tests for 12 years from 1997 to 2009 showed that 70% of actual amino acid substitutions were correctly predicted, and that 45% of predicted amino acid substitutions have been actually observed. Although it remains unsolved how to predict the exact timing of antigenic changes, the present results suggest that our model may have the potential to recognize emerging epidemic strains.     

A stochastic evolutionary model of molecular sequences.

A stochastic evolutionary model of molecular sequences is proposed. The basic forces in evolution are supposed to be mutation and selection. The concept is somewhat similar to Kauffman-Levin's concept of adaptive walks and corresponding analytical expressions have been developed. The selective force is divided into two parts: a slowly-varying part and a rapidly-changing fluctuation. The latter influences the distribution of sequences and results in an equation of motion along the flow line. The former plays a more important role in the emergence of evolutionary order. It is demonstrated that the asymmetry of selective forces would lead to a definite order of the system.     

A model for the evolutionary diversification of religions

We address the problem of cultural diversification by studying selection on cultural ideas that colonize human hosts and using diversification of religions as a conceptual example. In analogy to studying the evolution of pathogens or symbionts colonizing animal hosts, we use models for host-pathogen dynamics known from theoretical epidemiology. In these models, religious content colonizes individual humans. Rates of transmission of ideas between humans, i.e., transmission of cultural content, and rates of loss of ideas (loss of belief) are determined by the phenotype of the cultural content, and by interactions between hosts carrying different ideas. In particular, based on the notion that cultural non-conformism can be negative frequency-dependent (for example, religion can lead to oppression of lower classes and emergence of non-conformism and dissent once a religious belief has reached dominance), we assume that the rate of loss of belief increases as the number of humans colonized by a particular religious phenotype increases. This generates frequency-dependent selection on cultural content, and we use evolutionary theory to show that this frequency dependence can lead to the emergence of coexisting clusters of different cultural types. The different clusters correspond to different cultural traditions, and hence our model describes the emergence of distinct descendant cultures from a single ancestral culture in the absence of any geographical isolation.     

A computer model of the house-environment system

An energy-flow computer model of a house is developed which can be made to simulate the changes in temperature of a simple physical model during the 24-hr day. By adjusting parameters (albedo, sun's angles, conduction coefficients, wall dimensions, window dimensions, house orientation, internal heating or air-conditioning, insolation) the computer model is easily altered. It is presumably an easier model to experiment with than physical models. Experimentation with the computer model by architects should help them to maximize useful and minimize detrimental aspects of the external climate in the design of houses.

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Zusammenfassung Ein Energiefluss Computer-Modell eines Hauses wird beschrieben, das zur Simulierung der Veränderungen in der Temperatur eines einfachen physikalischen Models während eines 24-Stunden Tages benutzt werden kann. Das Computer-Modell lässt sich leicht durch Anpassung der Parameter (Albedo, Sonnenstand, Leitungskoeffizient, Dimensionen der Wände und Fenster, Stellung des Hauses, Heizung oder Luftkonditionierung) verändern. Man kann damit vermutlich leichter experimentieren als mit physikalischen Modellen. Es sollte Architekten beim Entwurf von Häusern helfen, um wertvolle Aspekte des äusseren Klimas maximal auszunutzen und nachteilige auszuschalten.

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Resume On décrit ici un modèle, utilisable sur ordinateur, du flux d'énergie à l'intérieur d'une maison. Ce modèle permet de simuler les modifications de température d'un immeuble aux conditions physiques simples pendant les 24 heures de la journée. Ce modèle peut être modifié facilement en adaptant les paramètres (albédo, hauteur du soleil, coefficient de conductibilité, dimensions des parois et des fenêtres, orientation de l'immeuble, chauffage ou conditionnement de l'air). Il est plus facile d'expérimenter par cette méthode qu'en utilisant des modèles uniquement physiques. Cette nouvelle méthode devrait aider les architectes dans l'établissement de plans de maisons, en leur apportant de précieuses valeurs provenant du climat extérieur et en leur évitant par là même bien des déboires.

     

Stationary mutant distributions and evolutionary optimization

Molecular evolution is modelled by erroneous replication of binary sequences. We show how the selection of two species of equal or almost equal selective value is influenced by its nearest neighbours in sequence space. In the case of perfect neutrality and sufficiently small error rates we find that the Hamming distance between the species determines selection. As the error rate increases the fitness parameters of neighbouring species become more and more important. In the case of almost neutral sequences we observe a critical replication accuracy at which a drastic change in the “quasispecies”, in the stationary mutant distribution occurs. Thus, in frequently mutating populations fitness turns out to be an ensemble property rather than an attribute of the individual. In addition we investigate the time dependence of the mean excess production as a function of initial conditions. Although it is optimized under most conditions, cases can be found which are characterized by decrease or non-monotonous change in mean excess productions.     

A computer model of pancreatic islet glycolysis

We have modeled an experiment with perifused pancreatic islet cells using our BIOSSIM language. The experiment and the resulting model are concerned with glucose uptake and glycolysis by the beta-cells of pancreatic islets. Although glycolysis appears to be involved in insulin release, we do not have enough information to represent insulin release in detail. The rapid entry of glucose into the beta-cell is promoted by a carrier having a very high tissue capacity. Phosphorylation of glucose by the low affinity enzyme glucokinase appears to be limiting for glycolysis. The effects of several hexose diphosphate activators of phosphofructokinase are modeled. Model behavior is described. The kinetic parameters of the enzyme submodels are given. Because of the difficulties of preparing large amounts of experimental material, information on pancreatic islet metabolism is limited. This model is a plausible explanation of the experimental results. Recent work on the genetically engineered glucose transporter and glucokinase is discussed.     

A computer simulation of evolutionary forces controlling the size of a multigene family

Summary A Monte Carlo-type simulation of the evolution of a multigene family was performed. The model was designed to study the selective forces which may control the size of a multigene family. As expected, we find that direct selection on the size of the multigene family can control its size. More important, we find that selection acting upon the family as a single functional unit, in conjunction with homologous but unequal crossing over, can also control the size of a multigene family.     

The evolutionary forces maintaining a wild polymorphism of Littorina saxatilis: model selection by computer simulations

Two rocky shore ecotypes of Littorina saxatilis from north-west Spain live at different shore levels and habitats and have developed an incomplete reproductive isolation through size assortative mating. The system is regarded as an example of sympatric ecological speciation. Several experiments have indicated that different evolutionary forces (migration, assortative mating and habitat-dependent selection) play a role in maintaining the polymorphism. However, an assessment of the combined contributions of these forces supporting the observed pattern in the wild is absent. A model selection procedure using computer simulations was used to investigate the contribution of the different evolutionary forces towards the maintenance of the polymorphism. The agreement between alternative models and experimental estimates for a number of parameters was quantified by a least square method. The results of the analysis show that the fittest evolutionary model for the observed polymorphism is characterized by a high gene flow, intermediate-high reproductive isolation between ecotypes, and a moderate to strong selection against the nonresident ecotypes on each shore level. In addition, a substantial number of additive loci contributing to the selected trait and a narrow hybrid definition with respect to the phenotype are scenarios that better explain the polymorphism, whereas the ecotype fitnesses at the mid-shore, the level of phenotypic plasticity, and environmental effects are not key parameters.     

An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Numerical optimization is the key to estimate the values of kinetic parameters so that the dynamic model reproduces the behaviors of the existing experimental data. It is required to develop general strategies for the optimization of complex biochemical networks with a huge space of search parameters, under the condition that kinetic and quantitative data are hardly available. We propose an integrative and practical strategy for optimizing a complex dynamic model by using qualitative and incomplete experimental data. The key technologies are the divide and conquer method for reducing the search space, handling of multiple objective functions representing different types of biological behaviors, and design of rule-based objective functions that are suitable for qualitative and error-prone experimental data. This strategy is applied to optimizing a dynamic model of the yeast cell cycle to demonstrate the feasibility of it.     

A stability pattern of protein hydrophobic mutations that reflects evolutionary structural optimization

We have determined the effect of mutations involving isoleucine and valine (i.e., mutations I-->V and V-->I) on the stability of Escherichia coli thioredoxin. Despite the similarity in chemical structure (V and I differ only in a methyl group), we find that many environments are optimized to a significant extent for either V or I. We find, furthermore, that a plot of effect of hydrophobic mutations on stability versus packing density shows a strikingly simple pattern that clearly reflects evolutionary structural optimization. The existence of such patterns suggests the possibility of rationalizing (and perhaps even predicting) mutation effects on protein stability on the basis of evolutionary models. By "evolutionary model" we specifically refer in this context to a model for mutation effects on stability in which certain physical features of the mutated residue environments are evaluated from an assumption regarding how such environments have been selected during protein evolution (as opposed to a purely "physical model" in which those features would be derived from some kind of energetics analysis of the protein structural characteristics). To illustrate this novel approach and provide general guidelines for its application, we develop here a simple evolutionary model that successfully explains the effect of the I<-->V mutations on thioredoxin stability.     

A computational model of symbiotic composition in evolutionary transitions

Several of the major transitions in evolutionary history, such as the symbiogenic origin of eukaryotes from prokaryotes, share the feature that existing entities became the components of composite entities at a higher-level of organization. This composition of pre-adapted extant entities into a new whole is a fundamentally different source of variation from the gradual accumulation of small random variations, and it has some interesting consequences for issues of evolvability. Intuitively, the pre-adaptation of sets of features in reproductively independent specialists suggests a form of 'divide and conquer' decomposition of the adaptive domain. Moreover, the compositions resulting from one level may become the components for compositions at the next level, thus scaling-up the variation mechanism. In this paper, we explore and develop these concepts using a simple abstract model of symbiotic composition to examine its impact on evolvability. To exemplify the adaptive capacity of the composition model, we employ a scale-invariant fitness landscape exhibiting significant ruggedness at all scales. Whilst innovation by mutation and by conventional evolutionary algorithms becomes increasingly more difficult as evolution continues in this landscape, innovation by composition is not impeded as it discovers and assembles component entities through successive hierarchical levels.     

A computer model for epidermal cellular interactions

A model has been constructed of an assembly of mammalian epidermal cells. The model, simulated by computer, has served as a framework by which experiments can be performed “in machina”. Relationships between the various parameters considered have been established. Hypotheses referring to the time at which cells leave the basal layer, and to the simultaneous occurrence of folded basal layer and of a significant number of vertical mitosis in some hyperplastic conditions have been implemented and examined.     

On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism’s traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of vital success of an individual. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environment (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R _L , as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R _L . In terms of adaptive dynamics, the maximum R _L corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.