Analytic approaches to twin data using structural equation models

The classical twin study is the most popular design in behavioural genetics. It has strong roots in biometrical genetic theory, which allows predictions to be made about the correlations between observed traits of identical and fraternal twins in terms of underlying genetic and environmental components. One can infer the relative importance of these 'latent' factors (model parameters) by structural equation modelling (SEM) of observed covariances of both twin types. SEM programs estimate model parameters by minimising a goodness-of-fit function between observed and predicted covariance matrices, usually by the maximum-likelihood criterion. Likelihood ratio statistics also allow the comparison of fit of different competing models. The program Mx, specifically developed to model genetically sensitive data, is now widely used in twin analyses. The flexibility of Mx allows the modelling of multivariate data to examine the genetic and environmental relations between two or more phenotypes and the modelling to categorical traits under liability-threshold models.     

Towards mechanistic models of plant organ growth

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.     

Maximum likelihood estimation of oncogenetic tree models

We present a new approach for modelling the dependences between genetic changes in human tumours. In solid tumours, data on genetic alterations are usually only available at a single point in time, allowing no direct insight into the sequential order of genetic events. In our approach, genetic tumour development and progression is assumed to follow a probabilistic tree model. We show how maximum likelihood estimation can be used to reconstruct a tree model for the dependences between genetic alterations in a given tumour type. We illustrate the use of the proposed method by applying it to cytogenetic data from 173 cases of clear cell renal cell carcinoma, arriving at a model for the karyotypic evolution of this tumour.     

Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modelling and simulation

We reconstruct the regulatory network controlling commitment and sporulation of Physarum polycephalum from experimental results using a hierarchical Petri Net-based modelling and simulation framework. The stochastic Petri Net consistently describes the structure and simulates the dynamics of the molecular network as analysed by genetic, biochemical and physiological experiments within a single coherent model. The Petri Net then is extended to simulate time-resolved somatic complementation experiments performed by mixing the cytoplasms of mutants altered in the sporulation response, to systematically explore the network structure and to probe its dynamics. This reverse engineering approach presumably can be employed to explore other molecular or genetic signalling systems where the activity of genes or their products can be experimentally controlled in a time-resolved manner.     

Global parameter estimation methods for stochastic biochemical systems

Background  

The importance of stochasticity in cellular processes having low number of molecules has resulted in the development of stochastic models such as chemical master equation. As in other modelling frameworks, the accompanying rate constants are important for the end-applications like analyzing system properties (e.g. robustness) or predicting the effects of genetic perturbations. Prior knowledge of kinetic constants is usually limited and the model identification routine typically includes parameter estimation from experimental data. Although the subject of parameter estimation is well-established for deterministic models, it is not yet routine for the chemical master equation. In addition, recent advances in measurement technology have made the quantification of genetic substrates possible to single molecular levels. Thus, the purpose of this work is to develop practical and effective methods for estimating kinetic model parameters in the chemical master equation and other stochastic models from single cell and cell population experimental data.     

Genetic patchiness in European eel adults evidenced by molecular genetics and population dynamics modelling

Disentangling the demographic processes that determine the genetic structure of a given species is a fundamental question in conservation and management. In the present study, the population structure of the European eel was examined with a multidisciplinary approach combining the fields of molecular genetics and population dynamics modelling. First, we analyzed a total of 346 adult specimens of known age collected in three separate sample sites using a large panel of 22 EST-linked microsatellite loci. Second, we developed a European eel-specific model to unravel the demographic mechanisms that can produce the level of genetic differentiation estimated by molecular markers. This is the first study that reveals a pattern of genetic patchiness in maturing adults of the European eel. A highly significant genetic differentiation was observed among samples that did not follow an Isolation-by-Distance or Isolation-by-Time pattern. The observation of genetic patchiness in adults is likely to result from a limited parental contribution to each spawning event as suggested by our modelling approach. The value of genetic differentiation found is predicted by the model when reproduction occurs in a limited number of spawning events isolated from each other in time or space, with an average of 130-375 breeders in each spawning event. Unpredictability in spawning success may have important consequences for the life-history evolution of the European eel, including a bet-hedging strategy (distributing reproductive efforts over time) which could in turn guarantee successful reproduction of some adults.     

History or ecology? Substrate type as a major driver of patial genetic structure in Alpine plants

Climatic history and ecology are considered the most important factors moulding the spatial pattern of genetic diversity. With the advent of molecular markers, species' historical fates have been widely explored. However, it has remained speculative what role ecological factors have played in shaping spatial genetic structures within species. With an unprecedented, dense large-scale sampling and genome-screening, we tested how ecological factors have influenced the spatial genetic structures in Alpine plants. Here, we show that species growing on similar substrate types, largely determined by the nature of bedrock, displayed highly congruent spatial genetic structures. As the heterogeneous and disjunctive distribution of bedrock types in the Alps, decisive for refugial survival during the ice ages, is temporally stable, concerted post-glacial migration routes emerged. Our multispecies study demonstrates the relevance of particular ecological factors in shaping genetic patterns, which should be considered when modelling species projective distributions under climate change scenarios.     

Mathematical models of cell cycle regulation

The cell division cycle is a fundamental process of cell biology and a detailed understanding of its function, regulation and other underlying mechanisms is critical to many applications in biotechnology and medicine. Since a comprehensive analysis of the molecular mechanisms involved is too complex to be performed intuitively, mathematical and computational modelling techniques are essential. This paper is a review and analysis of recent approaches attempting to model cell cycle regulation by means of protein-protein interaction networks.     

A cell based modelling framework for skeletal tissue engineering applications

In this study, a cell based lattice free modelling framework is proposed to study cell aggregate behaviour in bone tissue engineering applications. The model encompasses cell-to-cell and cell–environment interactions such as adhesion, repulsion and drag forces. Oxygen, nutrients, waste products, growth factors and inhibitors are explicitly represented in the model influencing cellular behaviour. Furthermore, a model for cell metabolism is incorporated representing the basic enzymic reactions of glycolysis and the Krebs cycle. Various types of cell death such as necrosis, apoptosis and anoikis are implemented. Finally, an explicit model of the cell cycle controls the proliferation process, taking into account the presence or absence of various metabolites, sufficient space and mechanical stress. Several examples are presented demonstrating the potential of the modelling framework. The behaviour of a synchronised cell aggregate under ideal circumstances is simulated, clearly showing the different stages of the cell cycle and the resulting growth of the aggregate. Also the difference in aggregate development under ideal (normoxic) and hypoxic conditions is simulated, showing hypoxia induced necrosis mainly in the centre of the aggregate grown under hypoxic conditions. The next step in this research will be the application of this modelling framework to specific experimental set-ups for bone tissue engineering applications.     

Crypt dynamics and colorectal cancer: advances in mathematical modelling

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.     

Yeasts make their mark

Budding and fission yeast serve as genetic model organisms for the study of the molecular mechanisms of cell polarity in single cells. Similar to other polarized eukaryotic cells, yeast cells have polarity programmes that regulate where they grow and divide. Here, we describe recent advances in defining the proteins that establish cell polarity and the numerous molecular interactions that may link these factors to the actin cytoskeleton. As many of these components are identified, a comprehensive understanding of complex pathways is beginning to emerge.     

A system architecture for genomic data analysis

MOTIVATION: Most of diseases are caused by a set of gene defects, which occur in a complex association. The association scheme of expressed genes can be modelled by genetic networks. Genetic networks are efficiently facilities to understand the dynamic of pathogenic processes by modelling molecular reality of cell conditions. In this sense a genetic network consists of first, a set of genes of specified cells, tissues or species and second, causal relations between these genes determining the functional condition of the biological system, i. e. under disease. A relation between two genes will exist if they both are directly or indirectly associated with disease [8]. Our goal is to characterize diseases (especially autoimmune diseases like chronic pancreatitis CP, multiple sclerosis MS, rheumatoid arthritis RA) by genetic networks generated by a computer system. We want to introduce this practice as a bioinformatic approach for finding targets.     

A hybrid machine model of rice blast fungus,Magnaporthe grisea

The fungus, Magnaporthe grisea (Rice blast fungus) is a major agricultural problem affecting rice and related food crops. The way that the fungus invades the host plant and propagates itself is a very important scientific problem and recent advances in research into the genetic basis of these processes can be used to build a simple partial model using hybrid computational modelling techniques. The possible potential benefits of doing this include the use of computer simulation and automated analysis through techniques such as model checking to understand the complex behaviour of such systems. The example is a metaphor for the process of trying to integrate and understand much of the vast amounts of genomic and other data that is being produced in current molecular biology research.     

Mouse-based phenogenomics for modelling human disease

The powerful and wide-ranging genetic tools available in the laboratory mouse make it the major experimental model for studying mammalian gene function in vivo and modelling human disease traits. Large-scale random mutagenesis approaches, either gene-driven or phenotype-driven, promise to identify new clinically relevant phenotypes and their associated genes. Development of appropriate tools for assessing clinical phenotypes in mice is a crucial component of these endeavours, as is the establishment of the infrastructure for archiving and distribution of the growing mutant resource to the community. Integrated, multidisciplinary programs will be needed to fully exploit the power of the mouse in molecular medicine.