Neural mechanisms underlying the evolvability of behaviour

The complexity of nervous systems alters the evolvability of behaviour. Complex nervous systems are phylogenetically constrained; nevertheless particular species-specific behaviours have repeatedly evolved, suggesting a predisposition towards those behaviours. Independently evolved behaviours in animals that share a common neural architecture are generally produced by homologous neural structures, homologous neural pathways and even in the case of some invertebrates, homologous identified neurons. Such parallel evolution has been documented in the chromatic sensitivity of visual systems, motor behaviours and complex social behaviours such as pair-bonding. The appearance of homoplasious behaviours produced by homologous neural substrates suggests that there might be features of these nervous systems that favoured the repeated evolution of particular behaviours. Neuromodulation may be one such feature because it allows anatomically defined neural circuitry to be re-purposed. The developmental, genetic and physiological mechanisms that contribute to nervous system complexity may also bias the evolution of behaviour, thereby affecting the evolvability of species-specific behaviour.     

Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber

MOTIVATION: Because of the complexity of metabolic networks and their regulation, formal modelling is a useful method to improve the understanding of these systems. An essential step in network modelling is to validate the network model. Petri net theory provides algorithms and methods, which can be applied directly to metabolic network modelling and analysis in order to validate the model. The metabolism between sucrose and starch in the potato tuber is of great research interest. Even if the metabolism is one of the best studied in sink organs, it is not yet fully understood. RESULTS: We provide an approach for model validation of metabolic networks using Petri net theory, which we demonstrate for the sucrose breakdown pathway in the potato tuber. We start with hierarchical modelling of the metabolic network as a Petri net and continue with the analysis of qualitative properties of the network. The results characterize the net structure and give insights into the complex net behaviour.     

Simplicity and complexity in MIRROR universes

The scientific simplicity principle (OCCAM's razor) has always been strongly enforced by the available modelling tools. Moreover, the concept of simplicity itself is shaped by these (classical) tools. Computer models are less subject to simplicity constraints than other models are. It may be argued that complexity is the preeminent property for biological systems to study. In this paper we discuss our MIRROR modelling methodology in which (a concept of) simplicity is reconciled with biological complexity. Simplicity resides in the simple "TODO" ("do what there is to do") of the "individuals" (molecules, cells, organisms) which inhabit the model universe. The complexity appears in the multiple (levels of) individuals and the multiple levels of observable behavior of the universe. Examples are given of the development of complex, self-regulating social structures by simple interactions of individuals, and the adaptability of TODO based entities is compared to that of evolving entities. On the basis of these examples we sketch a slightly unconventional image of the evolution of complexity in biotic systems and discuss observations on the molecular record of biotic evolution which seem to fit this image.     

A framework for models of biological behaviour

Modelling is most clearly understood as a adjunct in the process of deriving predictions from hypotheses. By representing a hypothesised mechanism in a model we hope by manipulating the model to understand the hypotheses' consequences. Eight dimensions on which models of biological behaviour can vary are described: the degree of realism with which they apply to biology; the level of biology they represent; the generality or range of systems the model is supposed to cover; the abstraction or amount of biological detail represented; the accuracy of representation of the mechanisms; the medium in which the model is built; the match of the model behaviour to biological behaviour; and the utility of the model in providing biological understanding and/or technical insight. It is hoped this framework will help to clarify debates over different approaches to modelling, particularly by pointing out how the above dimensions are relatively independent and should not be conflated.     

Processing of complex stimuli and natural scenes in the visual cortex

A major part of vision research builds on the assumption that processing of visual stimuli can be understood on the basis of knowledge about the processing of simplified, artificial stimuli. Recent experimental advances, however, show that a combination of responses to simplified stimuli does not adequately describe responses to natural visual scenes. The systems performance exceeds the performance predicted from understanding its basic constituents. This highlights the fact that the visual system is specifically adapted to the properties of its everyday input and can only fully be understood when probed with naturalistic stimuli.     

Visual flight control in naturalistic and artificial environments

Although the visual flight control strategies of flying insects have evolved to cope with the complexity of the natural world, studies investigating this behaviour have typically been performed indoors using simplified two-dimensional artificial visual stimuli. How well do the results from these studies reflect the natural behaviour of flying insects considering the radical differences in contrast, spatial composition, colour and dimensionality between these visual environments? Here, we aim to answer this question by investigating the effect of three- and two-dimensional naturalistic and artificial scenes on bumblebee flight control in an outdoor setting and compare the results with those of similar experiments performed in an indoor setting. In particular, we focus on investigating the effect of axial (front-to-back) visual motion cues on ground speed and centring behaviour. Our results suggest that, in general, ground speed control and centring behaviour in bumblebees is not affected by whether the visual scene is two- or three dimensional, naturalistic or artificial, or whether the experiment is conducted indoors or outdoors. The only effect that we observe between naturalistic and artificial scenes on flight control is that when the visual scene is three-dimensional and the visual information on the floor is minimised, bumblebees fly further from the midline of the tunnel. The findings presented here have implications not only for understanding the mechanisms of visual flight control in bumblebees, but also for the results of past and future investigations into visually guided flight control in other insects.     

Predictive models in spatially and temporally variable freshwater systems

Abstract This paper discusses the relationships between scaling and predictability in ecosystems. The logical basis of ecosystem modelling is explored using ideas first developed in complexity theory and analogies with the behaviour of complex adaptive systems. Any ecological model is a scale-dependent entity and both empirical and dynamic models of freshwater systems have their strengths and weaknesses. The logical basis of modelling using functional groups is explored. I conclude that such an approach can be justified and that such models have predictive power. Any predictive model of freshwater systems must take the major scales of external (atmospheric and catchment) forcing into account as well as the scales of key processes in the ecosystem itself. The importance of so-called ‘pink noise’ spectra, which arise both from external forcing and the internal dynamics of dynamic systems, is noted. The key scales of pattern and process in freshwater ecosystems are discussed in relation to the properties of the major functional groups. In order to have predictive power, I conclude that models of freshwater systems must include sediment exchanges and the properties of aquatic macrophytes as well as water column interactions and the pelagic components. When viewed at the scale of functional groups and the major biogeochemical processes, freshwater ecosystems may not be as complex as is often assumed.     

Measuring collective behaviour of multicellular ensembles: role of space-time scales

Living systems are spectacular examples of spatiotemporally organized structures. During the development of complex organization there is dynamic equilibrium between the local and global processes acting at the intra-and intercellular levels in multiple space and time scales. Although in modelling studies such spatiotemporal systems can be described by different space-time scales and at many organizational levels, the experimental quantities measured and predictions useful for practical applications are at a macroscopic (coarser or averaged) level/scale; these are limited by the resolution of the measuring method and experimental protocol. In this work, we address whether the spatiotemporal collective dynamics exhibited by a multiscale system can discriminate between, or be borne out by, the coarse-grained and averaged measurements done at different spatial and temporal scales. Using a simple model of a ring of cells, we show that measurements of both spatial and spatiotemporal average behaviour in this multicellular ensemble can mask the variety of collective dynamics observed at other space-time scales, and exhibit completely different behaviours. Such outcomes of measurements can lead to incomplete and incorrect understanding of physiological functions and pathogenesis in multicell ensembles.     

Positive and negative feedback: striking a balance between necessary antagonists

Most biological regulation systems comprise feedback circuits as crucial components. Negative feedback circuits have been well understood for a very long time; indeed, their understanding has been the basis for the engineering of cybernetic machines exhibiting stable behaviour. The importance of positive feedback circuits, considered as "vicious circles", has however been underestimated. In this article, we give a demonstration based on degree theory for vector fields of the conjecture, made by René Thomas, that the presence of positive feedback circuits is a necessary condition for autonomous differential systems, covering a wide class of biologically relevant systems, to possess multiple steady states. We also show ways to derive constraints on the weights of positive and negative feedback circuits. These qualitative and quantitative results provide, respectively, structural constraints (i.e. related to the interaction graph) and numerical constraints (i.e. related to the magnitudes of the interactions) on systems exhibiting complex behaviours, and should make it easier to reverse-engineer the interaction networks animating those systems on the basis of partial, sometimes unreliable, experimental data. We illustrate these concepts on a model multistable switch, in the context of cellular differentiation, showing a requirement for sufficient cooperativity. Further developments are expected in the discovery and modelling of regulatory networks in general, and in the interpretation of bio-array hybridization and proteomics experiments in particular.     

Systematic modelling in nutrition]

Live organisms can be considered as open complex systems in a steady state through which passes a flow of matter which undergoes a series of transformations which constitutes the nutritional process. The systemic approach and modelling procedure can be applied to nutrition as it can to other scientific areas, although examples of this particular application are few. This review describes the complexity of components in nutritional systems and presents a means of simplifying this. A section is given over to a comparative study of the main types of models (empirical vs mechanistic, static vs dynamic) which can be applied to nutrition. The other topics covered concern the modelling of the regulating systems in nutrition (homeostasis, homeorhesis), model validation and comments on application models and research.     

A general reaction–diffusion model of acidity in cancer invasion

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction–diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system—a special case of our generalised system—allows us to comment on the structural stability and predictive power of the modelling framework.     

Self versus Environment Motion in Postural Control

To stabilize our position in space we use visual information as well as non-visual physical motion cues. However, visual cues can be ambiguous: visually perceived motion may be caused by self-movement, movement of the environment, or both. The nervous system must combine the ambiguous visual cues with noisy physical motion cues to resolve this ambiguity and control our body posture. Here we have developed a Bayesian model that formalizes how the nervous system could solve this problem. In this model, the nervous system combines the sensory cues to estimate the movement of the body. We analytically demonstrate that, as long as visual stimulation is fast in comparison to the uncertainty in our perception of body movement, the optimal strategy is to weight visually perceived movement velocities proportional to a power law. We find that this model accounts for the nonlinear influence of experimentally induced visual motion on human postural behavior both in our data and in previously published results.     

Analysing scientific workflows with Computational Tree Logic

Motivated by the widespread use of workflow systems in e-Science applications, this article introduces a formal analysis framework for the verification and profiling of the control flow aspects of scientific workflows. The framework relies on process algebras that characterise each workflow component with a process behaviour, which is then used to build a CTL state model that can be reasoned about. We demonstrate the benefits of the approach by modelling the control flow behaviour of the Discovery Net system, one of the earliest workflow-based e-Science systems, and present how some key properties of workflows and individual service utilisation can be queried at design time. Our approach is generic and can be applied easily to modelling workflows developed in any other system. It also provides a formal basis for the comparison of control aspects of e-Science workflow systems and a design method for future systems.     

An open source simulation model for soil and sediment bioturbation

Bioturbation is one of the most widespread forms of ecological engineering and has significant implications for the structure and functioning of ecosystems, yet our understanding of the processes involved in biotic mixing remains incomplete. One reason is that, despite their value and utility, most mathematical models currently applied to bioturbation data tend to neglect aspects of the natural complexity of bioturbation in favour of mathematical simplicity. At the same time, the abstract nature of these approaches limits the application of such models to a limited range of users. Here, we contend that a movement towards process-based modelling can improve both the representation of the mechanistic basis of bioturbation and the intuitiveness of modelling approaches. In support of this initiative, we present an open source modelling framework that explicitly simulates particle displacement and a worked example to facilitate application and further development. The framework combines the advantages of rule-based lattice models with the application of parameterisable probability density functions to generate mixing on the lattice. Model parameters can be fitted by experimental data and describe particle displacement at the spatial and temporal scales at which bioturbation data is routinely collected. By using the same model structure across species, but generating species-specific parameters, a generic understanding of species-specific bioturbation behaviour can be achieved. An application to a case study and comparison with a commonly used model attest the predictive power of the approach.     

Simulating complex intracellular processes using object-oriented computational modelling

The aim of this paper is to give an overview of computer modelling and simulation in cellular biology, in particular as applied to complex biochemical processes within the cell. This is illustrated by the use of the techniques of object-oriented modelling, where the computer is used to construct abstractions of objects in the domain being modelled, and these objects then interact within the computer to simulate the system and allow emergent properties to be observed. The paper also discusses the role of computer simulation in understanding complexity in biological systems, and the kinds of information which can be obtained about biology via simulation.     

Evolutionarily conserved concepts in glial cell biology

The evolutionary conservation of glial cells has been appreciated since Ramon y Cajal and Del Rio Hortega first described the morphological features of cells in the nervous system. We now appreciate that glial cells have essential roles throughout life in most nervous systems. The field of glial cell biology has grown exponentially in the last ten years. This new wealth of knowledge has been aided by seminal findings in non-mammalian model systems. Ultimately, such concepts help us to understand glia in mammalian nervous systems. Rather than summarizing the field of glial biology, I will first briefly introduce glia in non-mammalian models systems. Then, highlight seminal findings across the glial field that utilized non-mammalian model systems to advance our understanding of the mammalian nervous system. Finally, I will call attention to some recent findings that introduce new questions about glial cell biology that will be investigated for years to come.     

Metabolic response to exogenous ethanol in yeast: an in vivo NMR and mathematical modelling approach

The understanding of the metabolic behaviour of complex systems such as eukaryotic cells needs the development of new approaches that are able to deal with the complexity due to a large number of interactions within the system. In this paper, we applied an approach based on the combined use of in vivo NMR experiments and mathematical modelling in order to analyze the metabolic response to ethanol stress in a wild-strain of Saccharomyces cerevisiae. Considering the cellular metabolic processes resulting from activation, inhibition, and feed-back activities, we developed a model able to describe the modulation of the whole system induced by an external stress due to increasing concentrations of exogenous ethanol. This approach was able to interpret the experimental results in terms of metabolic response to exogenous ethanol in the yeast. The robustness and flexibility of the model enables it to work correctly at different initial exogenous ethanol concentrations.