The layer-oriented approach to declarative languages for biological modeling

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.     

Multilocus genomics of outcrossing plant populations

The structure and organization of natural plant populations can be understood by estimating the genetic parameters related to mating behavior, recombination frequency, and gene associations with DNA-based markers typed throughout the genome. We developed a statistical and computational model for estimating and testing these parameters from multilocus data collected in a natural population. This model, constructed by a maximum likelihood approach and implemented within the EM algorithm, is shown to be robust for simultaneously estimating the outcrossing rate, recombination frequencies and linkage disequilibria. The algorithm built with three or more markers allows the characterization of crossover interference in meiosis and high-order disequilibria among different genes, thus providing a powerful tool for illustrating a detailed picture of genetic diversity and organization in natural populations. Computer simulations demonstrate the statistical properties of the proposed model. This multilocus model will be useful for studying the pattern and amount of genetic variation within and among populations to further infer the evolutionary history of a plant species.     

Effects of Homology, Size and Exchange on the Meiotic Segregation of Model Chromosomes in Saccharomyces Cerevisiae

In most eukaryotic organisms, chiasmata, the connections formed between homologous chromosomes as a consequence of crossing over, are important for ensuring that the homologues move away from each other at meiosis I. Some organisms have the capacity to partition the rare homologues that have failed to experience reciprocal recombination. The yeast Saccharomyces cerevisiae is able to correctly partition achiasmate homologues with low fidelity by a mechanism that is largely unknown. It is possible to test which parameters affect the ability of achiasmate chromosomes to segregate by constructing strains that will have three achiasmate chromosomes at the time of meiosis. The meiotic partitioning of these chromosomes can be monitored to determine which ones segregate away from each other at meiosis I. This approach was used to test the influence of homologous yeast DNA sequences, recombination intiation sites, chromosome size and crossing over on the meiotic segregation of the model chromosomes. Chromosome size had no effect on achiasmate segregation. The influence of homologous yeast sequences on the segregation of noncrossover model chromosomes was negligible. In meioses in which two of the three model chromosomes experienced a crossover, they nearly always disjoined at meiosis I.     

Computational modeling to predict mechanical function of joints: application to the lower leg with simulation of two cadaver studies

Computational models of musculoskeletal joints and limbs can provide useful information about joint mechanics. Validated models can be used as predictive devices for understanding joint function and serve as clinical tools for predicting the outcome of surgical procedures. A new computational modeling approach was developed for simulating joint kinematics that are dictated by bone/joint anatomy, ligamentous constraints, and applied loading. Three-dimensional computational models of the lower leg were created to illustrate the application of this new approach. Model development began with generating three-dimensional surfaces of each bone from CT images and then importing into the three-dimensional solid modeling software SOLIDWORKS and motion simulation package COSMOSMOTION. Through SOLIDWORKS and COSMOSMOTION, each bone surface file was filled to create a solid object and positioned necessary components added, and simulations executed. Three-dimensional contacts were added to inhibit intersection of the bones during motion. Ligaments were represented as linear springs. Model predictions were then validated by comparison to two different cadaver studies, syndesmotic injury and repair and ankle inversion following ligament transection. The syndesmotic injury model was able to predict tibial rotation, fibular rotation, and anterior/posterior displacement. In the inversion simulation, calcaneofibular ligament extension and angles of inversion compared well. Some experimental data proved harder to simulate accurately, due to certain software limitations and lack of complete experimental data. Other parameters that could not be easily obtained experimentally can be predicted and analyzed by the computational simulations. In the syndesmotic injury study, the force generated in the tibionavicular and calcaneofibular ligaments reduced with the insertion of the staple, indicating how this repair technique changes joint function. After transection of the calcaneofibular ligament in the inversion stability study, a major increase in force was seen in several of the ligaments on the lateral aspect of the foot and ankle, indicating the recruitment of other structures to permit function after injury. Overall, the computational models were able to predict joint kinematics of the lower leg with particular focus on the ankle complex. This same approach can be taken to create models of other limb segments such as the elbow and wrist. Additional parameters can be calculated in the models that are not easily obtained experimentally such as ligament forces, force transmission across joints, and three-dimensional movement of all bones. Muscle activation can be incorporated in the model through the action of applied forces within the software for future studies.     

The effects of intraspecific competition and stabilizing selection on a polygenic trait

The equilibrium properties of an additive multilocus model of a quantitative trait under frequency- and density-dependent selection are investigated. Two opposing evolutionary forces are assumed to act: (i) stabilizing selection on the trait, which favors genotypes with an intermediate phenotype, and (ii) intraspecific competition mediated by that trait, which favors genotypes whose effect on the trait deviates most from that of the prevailing genotypes. Accordingly, fitnesses of genotypes have a frequency-independent component describing stabilizing selection and a frequency- and density-dependent component modeling competition. We study how the equilibrium structure, in particular, number, degree of polymorphism, and genetic variance of stable equilibria, is affected by the strength of frequency dependence, and what role the number of loci, the amount of recombination, and the demographic parameters play. To this end, we employ a statistical and numerical approach, complemented by analytical results, and explore how the equilibrium properties averaged over a large number of genetic systems with a given number of loci and average amount of recombination depend on the ecological and demographic parameters. We identify two parameter regions with a transitory region in between, in which the equilibrium properties of genetic systems are distinctively different. These regions depend on the strength of frequency dependence relative to pure stabilizing selection and on the demographic parameters, but not on the number of loci or the amount of recombination. We further study the shape of the fitness function observed at equilibrium and the extent to which the dynamics in this model are adaptive, and we present examples of equilibrium distributions of genotypic values under strong frequency dependence. Consequences for the maintenance of genetic variation, the detection of disruptive selection, and models of sympatric speciation are discussed.     

Genetic control of meiosis in Drozophila

By the beginning of 2000, more than 80 genes specifically controlling meiosis and meiotic recombination in Drosophila melanogaster have been described. Meiosis in Drosophila is different from the classical model. In females, these differences concern cytological features of prophase I, which have no principal genetic significance. Drosophila males lack lateral synapsis of chromosomes, recombination and chiasmata, and their chromosomes segregate in meiosis I following the "touch-and-go" principle. Meiotic genes in Drosophila can be classified according to their functions as affecting prerequisites for recombination and crossing over, controlling chromosome segregation in meiosis I separately in males and females and controlling sister-chromatid segregation in meiosis II in both sexes. Some meiotic genes are pleiotropic. There are meiotic genes controlling mitosis, and vice versa. Some genes for DNA repair in somatic cells are also involved in meiosis. Meiotic genes in Drosophila are compared with their counterparts in other organisms.     

Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to Eikonal-Diffusion models in cardiac electrophysiology

Biophysical models are increasingly used for medical applications at the organ scale. However, model predictions are rarely associated with a confidence measure although there are important sources of uncertainty in computational physiology methods. For instance, the sparsity and noise of the clinical data used to adjust the model parameters (personalization), and the difficulty in modeling accurately soft tissue physiology. The recent theoretical progresses in stochastic models make their use computationally tractable, but there is still a challenge in estimating patient-specific parameters with such models. In this work we propose an efficient Bayesian inference method for model personalization using polynomial chaos and compressed sensing. This method makes Bayesian inference feasible in real 3D modeling problems. We demonstrate our method on cardiac electrophysiology. We first present validation results on synthetic data, then we apply the proposed method to clinical data. We demonstrate how this can help in quantifying the impact of the data characteristics on the personalization (and thus prediction) results. Described method can be beneficial for the clinical use of personalized models as it explicitly takes into account the uncertainties on the data and the model parameters while still enabling simulations that can be used to optimize treatment. Such uncertainty handling can be pivotal for the proper use of modeling as a clinical tool, because there is a crucial requirement to know the confidence one can have in personalized models.     

Single Holliday junctions are intermediates of meiotic recombination

Crossing-over between homologous chromosomes facilitates their accurate segregation at the first division of meiosis. Current models for crossing-over invoke an intermediate in which homologs are connected by two crossed-strand structures called Holliday junctions. Such double Holliday junctions are a prominent intermediate in Saccharomyces cerevisiae meiosis, where they form preferentially between homologs rather than between sister chromatids. In sharp contrast, we find that single Holliday junctions are the predominant intermediate in Schizosaccharomyces pombe meiosis. Furthermore, these single Holliday junctions arise preferentially between sister chromatids rather than between homologs. We show that Mus81 is required for Holliday junction resolution, providing further in vivo evidence that the structure-specific endonuclease Mus81-Eme1 is a Holliday junction resolvase. To reconcile these observations, we present a unifying recombination model applicable for both meiosis and mitosis in which single Holliday junctions arise from single- or double-strand breaks, lesions postulated by previous models to initiate recombination.     

Steady state analysis of influx and transbilayer distribution of ergosterol in the yeast plasma membrane

Mathematical modeling is now frequently used in outbreak investigations to understand underlying mechanisms of infectious disease dynamics, assess patterns in epidemiological data, and forecast the trajectory of epidemics. However, the successful application of mathematical models to guide public health interventions lies in the ability to reliably estimate model parameters and their corresponding uncertainty. Here, we present and illustrate a simple computational method for assessing parameter identifiability in compartmental epidemic models. We describe a parametric bootstrap approach to generate simulated data from dynamical systems to quantify parameter uncertainty and identifiability. We calculate confidence intervals and mean squared error of estimated parameter distributions to assess parameter identifiability. To demonstrate this approach, we begin with a low-complexity SEIR model and work through examples of increasingly more complex compartmental models that correspond with applications to pandemic influenza, Ebola, and Zika. Overall, parameter identifiability issues are more likely to arise with more complex models (based on number of equations/states and parameters). As the number of parameters being jointly estimated increases, the uncertainty surrounding estimated parameters tends to increase, on average, as well. We found that, in most cases, R0 is often robust to parameter identifiability issues affecting individual parameters in the model. Despite large confidence intervals and higher mean squared error of other individual model parameters, R0 can still be estimated with precision and accuracy. Because public health policies can be influenced by results of mathematical modeling studies, it is important to conduct parameter identifiability analyses prior to fitting the models to available data and to report parameter estimates with quantified uncertainty. The method described is helpful in these regards and enhances the essential toolkit for conducting model-based inferences using compartmental dynamic models.     

A whole-cell computational model predicts phenotype from genotype

Understanding how complex phenotypes arise from individual molecules and their interactions is a primary challenge in biology that computational approaches are poised to tackle. We report a whole-cell computational model of the life cycle of the human pathogen Mycoplasma genitalium that includes all of its molecular components and their interactions. An integrative approach to modeling that combines diverse mathematics enabled the simultaneous inclusion of fundamentally different cellular processes and experimental measurements. Our whole-cell model accounts for all annotated gene functions and was validated against a broad range of data. The model provides insights into many previously unobserved cellular behaviors, including in vivo rates of protein-DNA association and an inverse relationship between the durations of DNA replication initiation and replication. In addition, experimental analysis directed by model predictions identified previously undetected kinetic parameters and biological functions. We conclude that comprehensive whole-cell models can be used to facilitate biological discovery.     

Tendency modeling: a new approach to obtain simplified kinetic models of metabolism applied to Saccharomyces cerevisiae

A novel approach to construct kinetic models of metabolic pathways, to be used in metabolic engineering, is presented: the tendency modeling approach. This approach greatly facilitates the construction of these models and can easily be applied to complex metabolic networks. The resulting models contain a minimal number of parameters; identification of their values is straightforward. Use of in vitro obtained information in the identification of the kinetic equations is minimized. The tendency modeling approach has been used to derive a dynamic model of primary metabolism for aerobic growth of Saccharomyces cerevisiae on glucose, in which compartmentation is included. Simulation results obtained with the derived model are satisfying for most of the carbon metabolites that have been measured. Compared to a more detailed model, the simulations of our model are less accurate, but taking into account the much smaller number of kinetic parameters (35 instead of 84), the tendency the modeling approach is considered promising.     

On coding genotypes for genetic markers with multiple alleles in genetic association study of quantitative traits

Background

In genetic association study of quantitative traits using F_∞ models, how to code the marker genotypes and interpret the model parameters appropriately is important for constructing hypothesis tests and making statistical inferences. Currently, the coding of marker genotypes in building F_∞ models has mainly focused on the biallelic case. A thorough work on the coding of marker genotypes and interpretation of model parameters for F_∞ models is needed especially for genetic markers with multiple alleles.

Results

In this study, we will formulate F_∞ genetic models under various regression model frameworks and introduce three genotype coding schemes for genetic markers with multiple alleles. Starting from an allele-based modeling strategy, we first describe a regression framework to model the expected genotypic values at given markers. Then, as extension from the biallelic case, we introduce three coding schemes for constructing fully parameterized one-locus F_∞ models and discuss the relationships between the model parameters and the expected genotypic values. Next, under a simplified modeling framework for the expected genotypic values, we consider several reduced one-locus F_∞ models from the three coding schemes on the estimability and interpretation of their model parameters. Finally, we explore some extensions of the one-locus F_∞ models to two loci. Several fully parameterized as well as reduced two-locus F_∞ models are addressed.

Conclusions

The genotype coding schemes provide different ways to construct F_∞ models for association testing of multi-allele genetic markers with quantitative traits. Which coding scheme should be applied depends on how convenient it can provide the statistical inferences on the parameters of our research interests. Based on these F_∞ models, the standard regression model fitting tools can be used to estimate and test for various genetic effects through statistical contrasts with the adjustment for environmental factors.     

The evolution of meiosis: recruitment and modification of somatic DNA-repair proteins

Several DNA-damage detection and repair mechanisms have evolved to repair double-strand breaks induced by mutagens. Later in evolutionary history, DNA single- and double-strand cuts made possible immune diversity by V(D)J recombination and recombination at meiosis. Such cuts are induced endogenously and are highly regulated and controlled. In meiosis, DNA cuts are essential for the initiation of homologous recombination, and for the formation of joint molecule and crossovers. Many proteins that function during somatic DNA-damage detection and repair are also active during homologous recombination. However, their meiotic functions may be altered from their somatic roles through localization, posttranslational modifications and/or interactions with meiosis-specific proteins. Presumably, somatic repair functions and meiotic recombination diverged during evolution, resulting in adaptations specific to sexual reproduction. (c) 2005 Wiley Periodicals, Inc.     

Stochastic computer model of the cell microtubule dynamics

To study the effect of various factors on the microtubule system, one of the main cytoskeletal elements in the cell, which organizes the intracellular transport of different organelles and is necessary for mitosis and meiosis, a computer model of this system is created. Using a stochastic approach, the model describes the microtubule assembly/disassembly as a set of chemical reactions with certain rate constants. Microtubules are visualized in the computer program field, which makes the model vivid. The program imitates the dynamics and structure of the microtubule system with high reliability. The parameters calculated by the model correlate with the corresponding parameters of microtubules in living cells. This approach to modeling microtubules and similar systems continues to be developed so that the models would better describe living systems and the effect of a still broader range of factors could be studied.     

A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk

Parameter estimation is a critical problem in modeling biological pathways. It is difficult because of the large number of parameters to be estimated and the limited experimental data available. In this paper, we propose a decompositional approach to parameter estimation. It exploits the structure of a large pathway model to break it into smaller components, whose parameters can then be estimated independently. This leads to significant improvements in computational efficiency. We present our approach in the context of Hybrid Functional Petri Net modeling and evolutionary search for parameter value estimation. However, the approach can be easily extended to other modeling frameworks and is independent of the search method used. We have tested our approach on a detailed model of the Akt and MAPK pathways with two known and one hypothesized crosstalk mechanisms. The entire model contains 84 unknown parameters. Our simulation results exhibit good correlation with experimental data, and they yield positive evidence in support of the hypothesized crosstalk between the two pathways.     

Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization

Inverse estimation of model parameters via mathematical modeling route, known as inverse modeling (IM), is an attractive alternative approach to the experimental methods. This approach makes use of efficient optimization techniques in the course of solution of an inverse problem with the aid of measured data. In this study, a novel optimization method based on ant colony optimization (ACO), denoted by ACO-IM, is presented for inverse estimation of kinetic and film thickness parameters of biofilm models that describe an experimental fixed bed anaerobic reactor. The proposed optimization method for parameter estimation emulates the fact that ants are capable of finding the shortest path from a food source to their nest by depositing a trial of pheromone during their walk. The efficacy of the ACO-IM for numerical estimation of bio-kinetic parameters is demonstrated through its application for the anaerobic treatment of industry wastewater in a fixed bed biofilm process. The results explain the rigorousness of mathematical models, the form of kinetic and film thickness models and the type of packing to be used with the biofilm process for accurate determination of kinetic and film thickness parameters so as to ensure reliable predictive performance of the biofilm reactor models.     

A Multi-Paradigm Modeling Framework to Simulate Dynamic Reciprocity in a Bioreactor

Despite numerous technology advances, bioreactors are still mostly utilized as functional black-boxes where trial and error eventually leads to the desirable cellular outcome. Investigators have applied various computational approaches to understand the impact the internal dynamics of such devices has on overall cell growth, but such models cannot provide a comprehensive perspective regarding the system dynamics, due to limitations inherent to the underlying approaches. In this study, a novel multi-paradigm modeling platform capable of simulating the dynamic bidirectional relationship between cells and their microenvironment is presented. Designing the modeling platform entailed combining and coupling fully an agent-based modeling platform with a transport phenomena computational modeling framework. To demonstrate capability, the platform was used to study the impact of bioreactor parameters on the overall cell population behavior and vice versa. In order to achieve this, virtual bioreactors were constructed and seeded. The virtual cells, guided by a set of rules involving the simulated mass transport inside the bioreactor, as well as cell-related probabilistic parameters, were capable of displaying an array of behaviors such as proliferation, migration, chemotaxis and apoptosis. In this way the platform was shown to capture not only the impact of bioreactor transport processes on cellular behavior but also the influence that cellular activity wields on that very same local mass transport, thereby influencing overall cell growth. The platform was validated by simulating cellular chemotaxis in a virtual direct visualization chamber and comparing the simulation with its experimental analogue. The results presented in this paper are in agreement with published models of similar flavor. The modeling platform can be used as a concept selection tool to optimize bioreactor design specifications.     

Examining Variation in Recombination Levels in the Human Female: A Test of the Production-Line Hypothesis

The most important risk factor for human aneuploidy is increasing maternal age, but the basis of this association remains unknown. Indeed, one of the earliest models of the maternal-age effect—the “production-line model” proposed by Henderson and Edwards in 1968—remains one of the most-cited explanations. The model has two key components: (1) that the first oocytes to enter meiosis are the first ovulated and (2) that the first to enter meiosis have more recombination events (crossovers) than those that enter meiosis later in fetal life. Studies in rodents have demonstrated that the first oocytes to enter meiosis are indeed the first to be ovulated, but the association between the timing of meiotic entry and recombination levels has not been tested. We recently initiated molecular cytogenetic studies of second-trimester human fetal ovaries, allowing us to directly examine the number and distribution of crossover-associated proteins in prophase-stage oocytes. Our observations on over 8,000 oocytes from 191 ovarian samples demonstrate extraordinary variation in recombination within and among individuals but provide no evidence of a difference in recombination levels between oocytes entering meiosis early in fetal life and those entering late in fetal life. Thus, our data provide a direct test of the second tenet of the production-line model and suggest that it does not provide a plausible explanation for the human maternal-age effect, meaning that—45 years after its introduction—we can finally conclude that the production-line model is not the basis for the maternal-age effect on trisomy.