Modeling the interaction of gametes and embryos with the maternal genital tract: From in vivo to in silico

Understanding the complex interaction between gametes or embryos and the maternal genital tract requires the use of experimental models. The selection of the right model is an important task to undertake, and despite many new developments in this area, an ideal model system has not yet been developed. In this review article, we focus on how the most appropriate model species and model system can be selected, each with its particular advantages and disadvantages. Selection criteria need to be based on the evaluation of the aim of the experiment, the tools that are available to the scientist, and the ethics that are involved in working with particular animal species and model systems. Society and politics direct scientists to “Refine, Reduce, and Replace” the use of experimental animals, which means that the use of in vivo models is increasingly being discouraged. An in vivo model allows experimentation in the full biological environment of a living organism. In contrast with in vivo models, in vitro models are less complex and are abstracts of in vivo systems, leading often to results that are different from the in vivo situation. If an investigator could understand all the components of a complex biological system and re-create them as individual smaller models in a computer, he or she could create in silico models that would completely represent the complexity of in vivo models. We predict that in the future, in silico modeling will be the natural departure from in vivo, in situ, and in vitro modeling approaches. In addition to numerous advantages that this modeling approach can bring to studying maternal interaction with gametes and embryo, it is perhaps the only true alternative method to animal experimentation.     

On the Relationship of Steady States of Continuous and Discrete Models Arising from Biology

For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.     

Improving real-time forecasting of water quality indicators with combination of process-based models and data assimilation technique

Water quality indicators can be used to characterize the status and quantify and qualify the change of aquatic ecosystems under different disturbance regimes. Although many studies have been done to develop and assess indicators and discuss interactions among them, few studies have focused on how to improve the predicted indicators and explore their variations in receiving water bodies. Accurate and effective predictions of ecological indictors are critical to better understand changes of water quality in aquatic ecosystems, especially for the real-time forecasting. Process-based water quality models can predict the spatiotemporal variations of the water quality indicators and provide useful information for policy-makers on sound management of water resources. Given their inherent constraints, however, such process models alone cannot actually guarantee perfect results since water quality models generally have a large number of parameters and involve many processes which are too complex to be efficiently calibrated. To overcome these limitations and explore a fast and efficient forecasting method for the change of water quality indictors, we proposed a new framework which combines the process-based models and data assimilation technique. Unlike most traditional approaches in which only the model parameters or initial conditions are updated or corrected and the models are run online, this framework allows the information extracted from observations and outputs of process models to be directly used in a data-driven local/modified local model. The results from the data-driven model are then assimilated into the original process model to further improve its forecasting ability. This approach can be efficiently run offline to directly correct and update the output of water quality models. We applied this framework in a real case study in Singapore. Two of the water quality indicators, namely salinity and oxygen were selected and tested against the observations, suggesting that a good performance of improving the model results and reducing computation time can be obtained. This approach is simple and efficient, especially suitable for real-time forecasting systems. Thus, it can enhance forecasting of water quality indictors and thereby facilitate the effective management of water resources.     

Computational modeling of the EGF-receptor system: a paradigm for systems biology

Computational models have rarely been used as tools by biologists but, when models provide experimentally testable predictions, they can be extremely useful. The epidermal growth factor receptor (EGFR) is probably the best-understood receptor system, and computational models have played a significant part in its elucidation. For many years, models have been used to analyze EGFR dynamics and to interpret mutational studies, and are now being used to understand processes including signal transduction, autocrine loops and developmental patterning. The success of EGFR modeling can be a guide to combining models and experiments productively to understand complex biological processes as integrated systems.     

The Edinburgh Mouse Atlas: using the CD

This paper provides a simple introduction to the reconstructions and data-handling tools stored on the Edinburgh Mouse Atlas CD, together with some of the ways in which the viewers and software can be used to understand mouse development and analyse data. The key aspect of the Mouse Atlas is that the underlying models are a complete representation of the histology, which has not been constrained to a particular interpretation. This means, for example, that the current anatomy domains can be further subdivided as required to any resolution up to the resolution of the models (2-7 microm). In the CD of the early embryos described here, virtually all tissues that can be usefully distinguished either by the histology or morphologically have been delineated.     

Plenty more fish in the sea: comparative and functional genomics using teleost models.

Biology has collaborated with evolution to create an enormous repertoire of animal variation. This in turn has provided experimental biologists with models that can be used in the lab to simulate more complex systems. Amongst the organisms that have been used in this way are fish, where a large number of species have been utilised in a variety of different ways. Fish possess the smallest genomes of any vertebrate, making them ideal as models for genome analysis and gene discovery. Fish are also easy to maintain in a laboratory environment and can be bred easily. Fish often have well-defined physiology and respond well to many experimental procedures. Finally, fish are of great economic importance in their own right, as one of the world's largest sources of protein. In this review, the relationship between fish species is examined along with the role of different fish models in a wide range of biological disciplines.     

Dynamic searching in the brain

Cognitive functions rely on the extensive use of information stored in the brain, and the searching for the relevant information for solving some problem is a very complex task. Human cognition largely uses biological search engines, and we assume that to study cognitive function we need to understand the way these brain search engines work. The approach we favor is to study multi-modular network models, able to solve particular problems that involve searching for information. The building blocks of these multimodular networks are the context dependent memory models we have been using for almost 20 years. These models work by associating an output to the Kronecker product of an input and a context. Input, context and output are vectors that represent cognitive variables. Our models constitute a natural extension of the traditional linear associator. We show that coding the information in vectors that are processed through association matrices, allows for a direct contact between these memory models and some procedures that are now classical in the Information Retrieval field. One essential feature of context-dependent models is that they are based on the thematic packing of information, whereby each context points to a particular set of related concepts. The thematic packing can be extended to multimodular networks involving input-output contexts, in order to accomplish more complex tasks. Contexts act as passwords that elicit the appropriate memory to deal with a query. We also show toy versions of several ‘neuromimetic’ devices that solve cognitive tasks as diverse as decision making or word sense disambiguation. The functioning of these multimodular networks can be described as dynamical systems at the level of cognitive variables.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Pattern, process and prediction in aquatic ecology. A limnological view of some general ecological problems

1. New scientific concepts such as models of chaos, complex dynamics and non-linear interactions have the potential to contribute to an improved understanding of ecological patterns and processes. This paper discusses some of the known dynamics of phytoplankton, pelagic food chains and nutrient cycles in the light of some of these new concepts. The paper brings these new conceptual models together with data from a wide range of sources in an attempt to produce a synthesis of system behaviour which allows us to understand why some things are inherently more predictable than others. In particular it looks at the limnological management tools of empirical biomass models and biomanipulation and at the need for prediction of species composition. 2. The structures observed in ecosystems (nutrient pools, sizes, species, temporal/spatial patterns) show properties at a spectrum of scales, as do the processes (fluxes, grazing, competition). Both respond to a spectrum of external perturbations that may be climatologically or anthropogenically induced. Empirical biomass models work because of the annual averaging of pattern and process and because of some inherent properties of the functioning of pelagic ecosystems. Many aspects of ecosystem pattern and process vary in a regular way with trophic state. Examination of empirical data sets can lead to an improved understanding of system behaviour if questions are asked about why things happen the way they do. 3. Feedbacks between pattern, process and periodicity are seen to be an inherent property of the system. Understanding the fundamental dynamics of non-linear interactions in ecosystems may make it possible to exploit the external spectrum of environmental perturbations and to control system function. For example, by imposing external physical perturbations on pelagic systems it may be possible to manipulate the species composition of the phytoplankton community. Because of the complexity of possible interactions both ‘horizontally’ between species and ‘vertically’ within the food chain, any prediction of species composition will necessarily be probabilistic.     

Cellular models to investigate biochemical pathways in Parkinson's disease

Cellular models are instrumental in dissecting a complex pathological process into simpler molecular events. Parkinson's disease is multifactorial and clinically heterogeneous; the aetiology of the sporadic (and most common) form is still unclear and only a few molecular mechanisms have been clarified so far in the neurodegenerative cascade. In such a multifaceted picture, it is particularly important to identify experimental models that simplify the study of the different networks of proteins/genes involved. Cellular models that reproduce some of the features of the neurons that degenerate in Parkinson's disease have contributed to many advances in our comprehension of the pathogenic flow of the disease. In particular, the pivotal biochemical pathways (i.e. apoptosis and oxidative stress, mitochondrial impairment and dysfunctional mitophagy, unfolded protein stress and improper removal of misfolded proteins) have been widely explored in cell lines, challenged with toxic insults or genetically modified. The central role of α-synuclein has generated many models aiming to elucidate its contribution to the dysregulation of various cellular processes. In conclusion, classical cellular models appear to be the correct choice for preliminary studies on the molecular action of new drugs or potential toxins and for understanding the role of single genetic factors. Moreover, the availability of novel cellular systems, such as cybrids or induced pluripotent stem cells, offers the chance to exploit the advantages of an in vitro investigation, although mirroring more closely the cell population being affected.     

A formal language for computational systems biology

The post-genomic era has opened new insights into the complex biochemical reaction systems present in the cell and has generated huge amount of information. The biological systems are highly complex and can overwhelm the numerically computable models. Therefore, models employing symbolical techniques might provide a faster insight. This paper presents some preliminary results and recent trends in the above direction. Specifically, it presents an overview of the main features of some formalisms and techniques from the field of specification languages for concurrency and mobility, which have been proposed to model and simulate the dynamics of the interaction of complex biological systems. The ultimate goal of these symbolic approaches is the modeling, analysis, simulation, and hopefully prediction of the behavior of biological systems (vs. biological components).     

Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.     

Modeling how soluble microbial products (SMP) support heterotrophic bacteria in autotroph-based biofilms

Multi-species biofilm modeling has been used for many years to understand the interactions between species in different biofilm systems, but the complex symbiotic relationship between species is sometimes overlooked, because models do not always include all relevant species and components. In this paper, we develop and use a mathematical model to describe a model biofilm system that includes autotrophic and heterotrophic bacteria and the key products produced by the bacteria. The model combines the methods of earlier multi-species models with a multi-component biofilm model in order to explore the interaction between species via exchange of soluble microbial products (SMP). We show that multiple parameter sets are able to describe the findings of experimental studies, and that heterotrophs growing on autotrophically produced SMP may pursue either r- or K-strategies to sustain themselves when SMP is their only substrate. We also show that heterotrophs can colonize some distance from the autotrophs and still be sustained by autotrophically produced SMP. This work defines the feasible range of parameters for utilization of SMP by heterotrophs and the nature of the interactions between autotrophs and heterotrophs in multi-species, multi-component biofilms.     

Bryophytes as experimental models for the study of environmental stress tolerance: Tortula ruralis and desiccation-tolerance in mosses

The development of a complete understanding of how plants interact with the environment at the cellular level is a crucial step in advancing our ability to unravel the complexities of plant ecology particularly with regard to the role that many of the less complex plants (i.e., algae, lichens, and bryophytes) play in plant communities and in establishing areas for colonization by their more complex brothers. One of the main barriers to the advancement of this area of plant biology has been the paucity of simple and appropriate experimental models that would enable the researcher to biochemically and genetically dissect the response of less complex plants to environmental stress. A number of bryophytes model systems have been developed and they have been powerful experimental tools for the elucidation of complex biological processes in plants. Recently there has been a resurgent interest in bryophytes as models systems due to the discovery and development of homologous recombination technologies in the moss Physcomitrella patens (Hedw.) Brach & Schimp. In this report we introduce the desiccation-tolerant moss Tortula ruralis (Hedw.) Gaert., Meyer, and Scherb, as a model for stress tolerance mechanisms that offers a great deal of promise for advancing our efforts to understand how plants respond to and survive the severest of stressful environments. T. ruralis, a species native to Northern and Western North America, has been the most intensely studied of all bryophytes with respect to its physiological, biochemical, and cellular responses, to the severest of water stresses, desiccation. It is our hope that the research conducted using this bryophyte will lay the foundationfor not only the ecology of bryophytes and other less complex plants but also for the role of desiccation-tolerance in the evolution of land plants and the determination of mechanisms by which plant cells can withstand environmental insults. We will focus the discussion on the research we and others have conducted in an effort to understand the ability of T. ruralis to withstand the complete loss of free water from the protoplasm of its cells.     

Paradigm lost: reconsidering functional form and group hypotheses in marine ecology

Although functional form and functional group models for marine algae have been used extensively, there is little general literature support for these models, and many studies have shown that associated hypotheses are often incorrect. In functional form/group models, a wide range of ecological and physiological functions are assumed to be correlated with general algal form or morphology. In contrast, functional group approaches have been used most successfully in terrestrial and aquatic systems when groupings are based on a particular function rather than overall plant morphology, and when addressing ecosystem-level questions. In this type of functional group approach, a given set of species would likely be grouped differently depending on the function under consideration. Functional groupings are appropriate for many situations and questions, but not all. Certainly, grouping taxa by a particular function can be very useful and often necessary for many ecosystem-level questions and modeling, especially where qualitative results are more important than quantitative predictions, and when there are too many species in a system to consider them all individually. However, when one considers species–species interactions or questions about population biology, the specific responses of individual species must be considered. To make functional group models more useful, we recommend that groupings be based on specific functions (e.g. nutrient uptake rates, photosynthesis rates, herbivore resistance, disturbance resistance, etc.) rather than gross morphology. Explicit testing of performance of a particular function should be made before generalizations can be assumed, and groupings should be used for questions/approaches where they are most appropriate. If models fail when tested, they should be modified using the additional information to generate new hypotheses and models, and then retested.     

Modifier genes and the plasticity of genetic networks in mice

Modifier genes are an integral part of the genetic landscape in both humans and experimental organisms, but have been less well explored in mammals than other systems. A growing number of modifier genes in mouse models of disease nonetheless illustrate the potential for novel findings, while new technical advances promise many more to come. Modifier genes in mouse models include induced mutations and spontaneous or wild-derived variations captured in inbred strains. Identification of modifiers among wild-derived variants in particular should detect disease modifiers that have been shaped by selection and might therefore be compatible with high fitness and function. Here we review selected examples and argue that modifier genes derived from natural variation may provide a bias for nodes in genetic networks that have greater intrinsic plasticity and whose therapeutic manipulation may therefore be more resilient to side effects than conventional targets.     

Parameter inference for an individual based model of chytridiomycosis in frogs

Individual based models (IBMs) and Agent based models (ABMs) have become widely used tools to understand complex biological systems. However, general methods of parameter inference for IBMs are not available. In this paper we show that it is possible to address this problem with a traditional likelihood-based approach, using an example of an IBM developed to describe the spread of chytridiomycosis in a population of frogs as a case study. We show that if the IBM satisfies certain criteria we can find the likelihood (or posterior) analytically, and use standard computational techniques, such as MCMC, for parameter inference.