Stages in the development of a model organism as a platform for mechanistic models in developmental biology: Zebrafish, 1970-2000

Model organisms became an indispensable part of experimental systems in molecular developmental and cell biology, constructed to investigate physiological and pathological processes. They are thought to play a crucial role for the elucidation of gene function, complementing the sequencing of the genomes of humans and other organisms. Accordingly, historians and philosophers paid considerable attention to various issues concerning this aspect of experimental biology. With respect to the representational features of model organisms, that is, their status as models, the main focus was on generalization of phenomena investigated in such experimental systems. Model organisms have been said to be models for other organisms or a higher taxon. This, however, presupposes a representation of the phenomenon in question. I will argue that prior to generalization, model organisms allow researchers to built generative material models of phenomena - structures, processes or the mechanisms that explain them - through their integration in experimental set-ups that carve out the phenomena from the whole organism and thus represent them. I will use the history of zebrafish biology to show how model organism systems, from around 1970 on, were developed to construct material models of molecular mechanisms explaining developmental or physiological processes.     

Supporting upper-level undergraduate students in building a systems perspective in a botany course

Undergraduate biology majors require biological literacy about the critical and dynamic relationships between plants and ecosystems and the effect human-made processes have on these systems. To support students in understanding systems relationships, we redesigned an undergraduate botany course using an ecological framework and embedded systems modelling to support students in understanding the criticality of plant processes to the global carbon cycle. The class meetings included lectures, opportunities to develop systems models identifying the relationships between plant processes and other systems, reflections on their systems understanding and open-floor discussions about assigned primary and secondary readings that explored the relationships between plant systems, abiotic and biotic processes and global carbon cycling in their systems models. We used the systems models students developed at the beginning and end of the course to examine how their systems understanding grew. Our results suggest that at the beginning of term, students’ ideas about plants were egocentric identifying the purpose of plants was to support human life and they did not consider relationships between plants and global carbon systems. By the end of the term, their models and reflections identified elements of a systems perspective and the students considered human impact on this delicate balance.     

Comparative and Experimental Approaches to the Study of Microbial Food Webs

ABSTRACT The study of microbial food webs is dominated by field measurements of microbial standing stocks and rate processes and to a lesser extent by laboratory studies. These approaches reflect the concerns of microbial ecologists to assess accurately the capabilities of microorganisms and to compare microbial processes to other ecosystem parameters. These approaches have led to enormous advances in understanding microbial food webs. Reconciling our expanding knowledge with general questions about the significance and representation of microbial food webs in ecosystem studies requires additional approaches including comparative studies and field experiments. Comparative studies, analyses of microbial stocks or rates across a wide range of ecosystems, lead to quantitative models of microbial processes. These models facilitate testing of hypotheses at a very general level, allow the comparison of different stocks or rate processes across a gradient of systems, and detect unusual situations or outlier systems. Field experimental manipulations offer the advantages of working with intact natural communities, of direct evaluation of results with statistical methods, and of testing important qualitative hypotheses. Both comparative and field manipulation studies have led to important advances in the study of microbial food webs and should be expanded.     

Multiscale computational models can guide experimentation and targeted measurements for crop improvement

Computational models of plants have identified gaps in our understanding of biological systems, and have revealed ways to optimize cellular processes or organ‐level architecture to increase productivity. Thus, computational models are learning tools that help direct experimentation and measurements. Models are simplifications of complex systems, and often simulate specific processes at single scales (e.g. temporal, spatial, organizational, etc.). Consequently, single‐scale models are unable to capture the critical cross‐scale interactions that result in emergent properties of the system. In this perspective article, we contend that to accurately predict how a plant will respond in an untested environment, it is necessary to integrate mathematical models across biological scales. Computationally mimicking the flow of biological information from the genome to the phenome is an important step in discovering new experimental strategies to improve crops. A key challenge is to connect models across biological, temporal and computational (e.g. CPU versus GPU) scales, and then to visualize and interpret integrated model outputs. We address this challenge by describing the efforts of the international Crops in silico consortium.     

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.     

Biology by numbers: mathematical modelling in developmental biology

In recent years, mathematical modelling of developmental processes has earned new respect. Not only have mathematical models been used to validate hypotheses made from experimental data, but designing and testing these models has led to testable experimental predictions. There are now impressive cases in which mathematical models have provided fresh insight into biological systems, by suggesting, for example, how connections between local interactions among system components relate to their wider biological effects. By examining three developmental processes and corresponding mathematical models, this Review addresses the potential of mathematical modelling to help understand development.     

Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Sampling, defining, characterising and modeling the rhizosphere—the soil science tool box

We review methods and models that help to assess how root activity changes soil properties and affects the fluxes of matter in the soil. Subsections discuss (1) experimental systems including plant treatments in artificial media, studying the interaction of model root and microbial exudates with soil constituents, and microcosms to distinguish between soil compartments differing in root influence, (2) the sampling and characterization of rhizosphere soil and solution, focusing on the separation of soil at different distances from roots and the spatially resolved sampling of soil solution, (3) cutting-edge methodologies to study chemical effects in soil, including the estimation of bioavailable element or ion contents (biosensors, diffusive gradients in thin-films), studying the ultrastructure of soil components, localizing elements and determining their chemical form (microscopy, diffractometry, spectroscopy), tracing the compartmentalization of substances in soils (isotope probing, autoradiography), and imaging gradients in-situ with micro electrodes or gels or filter papers containing dye indicators, (4) spectroscopic and geophysical methods to study the plants influence on the distribution of water in soils, and (5) the modeling of rhizosphere processes. Macroscopic models with a rudimentary depiction of rhizosphere processes are used to predict water or nutrient requirements by crops and forests, to estimate biogeochemical element cycles, to calculate soil water transport on a profile scale, or to simulate the development of root systems. Microscopic or explanatory models are based on mechanistic or empirical relations that describe processes on a single root or root system scale and/or chemical reactions in soil solution. We conclude that in general we have the tools at hand to assess individual processes on the microscale under rather artificial conditions. Microscopic, spectroscopic and tracer methods to look at processes in small “aliquots” of naturally structured soil seem to step out of their infancy and have become promising tools to better understand the complex interactions between plant roots, soil and microorganisms. On the field scale, while there are promising first results on using non-invasive geophysical methods to assess the plant’s influence on soil moisture, there are no such tools in the pipeline to assess the spatial heterogeneity of chemical properties and processes in the field. Here, macroscopic models have to be used, or model results on the microscopic level have to be scaled up to the whole plant or plot scale. Upscaling is recognized as a major challenge.     

The Scale of Successional Models and Restoration Objectives

Successional models are used to predict how restoration projects will achieve their goals. These models have been developed on different spatial and temporal scales and consequently emphasize different types of dynamics. This paper focuses on the restoration goal of self-sustainability, but only in the context of a long-term goal. Because of the temporal scale of this goal, we must consider the impact of processes arising outside of the restoration site as of greater importance than restoration itself. Because ecological systems are open, restoration sites will be subjected to many external influential processes. Depending on the landscape context, the impact of these processes may not be noticeable, or, at the other extreme, they may prevent the achievement of restoration objectives. A second issue is to emphasize the nature of processes in the long term, that they are a complex of characteristics such as magnitude, frequency, and extent. Ecological systems are only adapted to a range of values in each of these characteristics. Restoration often combines goals that are of different scales. Models appropriate to these goals need consideration.     

Elements of a dynamic systems model of canopy photosynthesis

Improving photosynthesis throughout the full canopy rather than photosynthesis of only the top leaves of the canopy is central to improving crop yields. Many canopy photosynthesis models have been developed from physiological and ecological perspectives, however most do not consider heterogeneities of microclimatic factors inside a canopy, canopy dynamics and associated energetics, or competition among different plants, and most models lack a direct linkage to molecular processes. Here we described the rationale, elements, and approaches necessary to build a dynamic systems model of canopy photosynthesis. A systems model should integrate metabolic processes including photosynthesis, respiration, nitrogen metabolism, resource re-mobilization and photosynthate partitioning with canopy level light, CO(2), water vapor distributions and heat exchange processes. In so doing a systems-based canopy photosynthesis model will enable studies of molecular ecology and dramatically improve our insight into engineering crops for improved canopy photosynthetic CO(2) uptake, resource use efficiencies and yields.     

Simulation as experiment: a philosophical reassessment for biological modeling

Some scientific modelers suggest that complex simulation models that mimic biological processes should have a limited place in ecological and evolutionary studies. However, complex simulation models can have a role that is different from that of simpler models that are designed to be fit to data. Simulation can be viewed as another kind of experimental system and should be analyzed as such. Here, I argue that current discussions in the philosophy of science and in the physical sciences fields about the use of simulation as an experimental system have important implications for biology, especially complex sciences such as evolution and ecology. Simulation models can be used to mimic complex systems, but unlike nature, can be manipulated in ways that would be impossible, too costly or unethical to do in natural systems. Simulation can add to theory development and testing, can offer hypotheses about the way the world works and can give guidance as to which data are most important to gather experimentally.     

Animal models and conserved processes

Background

The concept of conserved processes presents unique opportunities for using nonhuman animal models in biomedical research. However, the concept must be examined in the context that humans and nonhuman animals are evolved, complex, adaptive systems. Given that nonhuman animals are examples of living systems that are differently complex from humans, what does the existence of a conserved gene or process imply for inter-species extrapolation?

Methods

We surveyed the literature including philosophy of science, biological complexity, conserved processes, evolutionary biology, comparative medicine, anti-neoplastic agents, inhalational anesthetics, and drug development journals in order to determine the value of nonhuman animal models when studying conserved processes.

Results

Evolution through natural selection has employed components and processes both to produce the same outcomes among species but also to generate different functions and traits. Many genes and processes are conserved, but new combinations of these processes or different regulation of the genes involved in these processes have resulted in unique organisms. Further, there is a hierarchy of organization in complex living systems. At some levels, the components are simple systems that can be analyzed by mathematics or the physical sciences, while at other levels the system cannot be fully analyzed by reducing it to a physical system. The study of complex living systems must alternate between focusing on the parts and examining the intact whole organism while taking into account the connections between the two. Systems biology aims for this holism. We examined the actions of inhalational anesthetic agents and anti-neoplastic agents in order to address what the characteristics of complex living systems imply for inter-species extrapolation of traits and responses related to conserved processes.

Conclusion

We conclude that even the presence of conserved processes is insufficient for inter-species extrapolation when the trait or response being studied is located at higher levels of organization, is in a different module, or is influenced by other modules. However, when the examination of the conserved process occurs at the same level of organization or in the same module, and hence is subject to study solely by reductionism, then extrapolation is possible.     

The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

Review of stochastic hybrid systems with applications in biological systems modeling and analysis

Stochastic hybrid systems (SHS) have attracted a lot of research interests in recent years. In this paper, we review some of the recent applications of SHS to biological systems modeling and analysis. Due to the nature of molecular interactions, many biological processes can be conveniently described as a mixture of continuous and discrete phenomena employing SHS models. With the advancement of SHS theory, it is expected that insights can be obtained about biological processes such as drug effects on gene regulation. Furthermore, combining with advanced experimental methods, in silico simulations using SHS modeling techniques can be carried out for massive and rapid verification or falsification of biological hypotheses. The hope is to substitute costly and time-consuming in vitro or in vivo experiments or provide guidance for those experiments and generate better hypotheses.     

An engineering approach to modelling, decision support and control for sustainable systems

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.     

Nearly right or precisely wrong? Natural versus laboratory studies of vector-borne diseases

Recent studies that compare experimental vector-borne disease systems incorporating elements of natural pathogen-vector-host interactions with model systems using unnatural associations have highlighted quantitative, and even qualitative, differences in the results. Here, Sarah Randolph and Pat Nuttall argue that the use of mathematical models to explore epidemiological processes and patterns depends on accurate parameter values obtained from natural systems.     

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.     

Biological nitrogen and phosphorus removal in membrane bioreactors: model development and parameter estimation

Membrane bioreactors (MBR) are being increasingly used for wastewater treatment. Mathematical modeling of MBR systems plays a key role in order to better explain their characteristics. Several MBR models have been presented in the literature focusing on different aspects: biological models, models which include soluble microbial products (SMP), physical models able to describe the membrane fouling and integrated models which couple the SMP models with the physical models. However, only a few integrated models have been developed which take into account the relationships between membrane fouling and biological processes. With respect to biological phosphorus removal in MBR systems, due to the complexity of the process, practical use of the models is still limited. There is a vast knowledge (and consequently vast amount of data) on nutrient removal for conventional-activated sludge systems but only limited information on phosphorus removal for MBRs. Calibration of these complex integrated models still remains the main bottleneck to their employment. The paper presents an integrated mathematical model able to simultaneously describe biological phosphorus removal, SMP formation/degradation and physical processes which also include the removal of organic matter. The model has been calibrated with data collected in a UCT-MBR pilot plant, located at the Palermo wastewater treatment plant, applying a modified version of a recently developed calibration protocol. The calibrated model provides acceptable correspondence with experimental data and can be considered a useful tool for MBR design and operation.     

Linking Molecular and Population Processes in Mathematical Models of Quorum Sensing

Many bacteria alter their behaviors as a function of population density, via a process known as quorum sensing (QS). QS is achieved by the synthesis and detection of diffusible signal molecules, often involving complex signal transduction pathways and regulatory networks. Mathematical models have been developed to investigate a number of aspects of QS, resulting in a wide range of model structures; many have focused on either the molecular or the population scale. In this paper, I show that many published models fail to satisfy physical constraints (such as conservation of matter) or rely on a priori assumptions that may not be valid. I present new, simple models of canonical Gram-negative and Gram-positive QS systems, in both well-mixed and biofilm populations, focusing on the interaction between molecular and population processes. I show that this interaction may be crucial for several important features of QS, including bistability and the localization of QS in space. The results highlight the need to link molecular and population processes carefully in QS models, provide a general framework for understanding the behavior of complex system-specific models, and suggest new directions for both theoretical and experimental work.