On modeling and complexity of developing systems

We consider the general properties of developing systems, the approaches to their modeling, and the question of their complexity. The notion “complex system” is vague; somewhat more distinct is the complexity of the model describing a phenomenon. We propose to discuss two pertinent issues. (i) The complexity of basic models is minimal; in other words, complicated basic models are needless. (ii) Living systems are simpler than inanimate ones. Though developing systems are seen in abiotic as well as in biotic nature, the fundamental difference is that living beings are capable of goal-setting and purposeful development; hence they can be described with simpler basic models.     

The social network and communicative complexity: preface to theme issue

The complex social worlds of many animal species may be linked to complex communicative systems in those species. We now have evidence in diverse taxa and in different communicative modalities suggesting that complexity in social groups can drive complexity in signalling systems. The aim of this theme issue is to develop the theory behind this link between social complexity and communicative complexity, and to provide an overview of the lines of research testing this link.     

Balance between Noise and Information Flow Maximizes Set Complexity of Network Dynamics

Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure of complexity, namely, the statistical complexity. We show that the networks can be tuned to the regime of maximal complexity by adding a suitable amount of noise to the deterministic Boolean dynamics. In fact, we show that for networks with Poisson degree distributions, all networks ranging from subcritical to slightly supercritical can be tuned with noise to reach maximal set complexity in their dynamics. For networks with a fixed number of inputs this is true for near-to-critical networks. This increase in complexity is obtained at the expense of disruption in information flow. For a large ensemble of networks showing maximal complexity, there exists a balance between noise and contracting dynamics in the state space. In networks that are close to critical the intrinsic noise required for the tuning is smaller and thus also has the smallest effect in terms of the information processing in the system. Our results suggest that the maximization of complexity near to the state transition might be a more general phenomenon in physical systems, and that noise present in a system may in fact be useful in retaining the system in a state with high information content.     

RNA self-ligation: from oligonucleotides to full length ribozymes

The RNA-world-theory is one possible explanation of how life on earth has evolved. In this context it is of high interest to search for molecular systems, capable of self-organization into structures with increasing complexity. We have engineered a simple catalytic system in which two short RNA molecules can catalyze their own ligation to form a larger RNA construct. The system is based on the hairpin ribozyme using a 2',3'-cyclophosphate as activated species for ligation. 2',3'-cyclic phosphates can be easily formed and occur in many natural systems, thus being superior candidates for activated building blocks in RNA world scenarios.     

Information transformations in molecular evolution

The prebiotic evolution of chemical systems is characterized by their development of increasingly complex levels of molecular organization. This development is dependent upon the capacity of these systems to acquire and transform chemical information. The informational content of a chemical system can be divided into configurational, energetic, and thermal contributions. The thermal information is specifically related to the number of molecules in the system, and is therefore a function of molecular size or complexity. The molecular complexity of a chemical system can be increased through reactions in which reductions in configurational or energetic information are coupled to increases in thermal information, as limited by the second law of thermodynamics.     

Peptide and protein building blocks for synthetic biology: from programming biomolecules to self-organized biomolecular systems.

There are several approaches to creating synthetic-biological systems. Here, we describe a molecular-design approach. First, we lay out a possible synthetic-biology space, which we define with a plot of complexity of components versus divergence from nature. In this scheme, there are basic units, which range from natural amino acids to totally synthetic small molecules. These are linked together to form programmable tectons, for example, amphipathic alpha-helices. In turn, tectons can interact to give self-assembled units, which can combine and organize further to produce functional assemblies and systems. To illustrate one path through this vast landscape, we focus on protein engineering and design. We describe how, for certain protein-folding motifs, polypeptide chains can be instructed to fold. These folds can be combined to give structured complexes, and function can be incorporated through computational design. Finally, we describe how protein-based systems may be encapsulated to control and investigate their functions.     

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists. When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex. We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.     

Integration of omics data: how well does it work for bacteria?

In the current omics era, innovative high-throughput technologies allow measuring temporal and conditional changes at various cellular levels. Although individual analysis of each of these omics data undoubtedly results into interesting findings, it is only by integrating them that gaining a global insight into cellular behaviour can be aimed at. A systems approach thus is predicated on data integration. However, because of the complexity of biological systems and the specificities of the data-generating technologies (noisiness, heterogeneity, etc.), integrating omics data in an attempt to reconstruct signalling networks is not trivial. Developing its methodologies constitutes a major research challenge. Besides for their intrinsic value towards health care, environment and industry, prokaryotes are ideal model systems to further develop these methods because of their lower regulatory complexity compared with eukaryotes, and the ease with which they can be manipulated. Several successful examples outlined in this review already show the potential of the systems approach for both fundamental and industrial applications, which would be time-consuming or impossible to develop solely through traditional reductionist approaches.     

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.     

Information Content,Complexity, and Uncertainty in Material Flow Analysis

Material Flow Analysis (MFA) is a useful method for modeling, understanding, and optimizing sociometabolic systems. Among others, MFAs can be distinguished by two general system properties: First, they differ in their complexity, which depends on system structure and size. Second, they differ in their inherent uncertainty, which arises from limited data quality. In this article, uncertainty and complexity in MFA are approached from a systems perspective and expressed as formally linked phenomena. MFAs are, in a graph‐theoretical sense, understood as networks. The uncertainty and complexity of these networks are computed by use of information measures from the field of theoretical ecology. The size of a system is formalized as a function of its number of flows. It defines the potential information content of an MFA system and holds as a reference against which complexity and uncertainty are gauged. Integrating data quality measures, the uncertainty of an MFA before and after balancing is determined. The actual information content of an MFA is measured by relating its uncertainty to its potential information content. The complexity of a system is expressed based on the configuration of each individual flow in relation to its neighboring flows. The proposed metrics enable different material flow systems to be compared to one another and the role of individual flows within a system to be assessed. They provide information useful for the design of MFAs and for the communication of MFA results. For exemplification, the regional MFAs of aluminum and plastics in Austria are analyzed in this article.     

State reduction for network intervention in probabilistic Boolean networks

MOTIVATION: A key goal of studying biological systems is to design therapeutic intervention strategies. Probabilistic Boolean networks (PBNs) constitute a mathematical model which enables modeling, predicting and intervening in their long-run behavior using Markov chain theory. The long-run dynamics of a PBN, as represented by its steady-state distribution (SSD), can guide the design of effective intervention strategies for the modeled systems. A major obstacle for its application is the large state space of the underlying Markov chain, which poses a serious computational challenge. Hence, it is critical to reduce the model complexity of PBNs for practical applications. RESULTS: We propose a strategy to reduce the state space of the underlying Markov chain of a PBN based on a criterion that the reduction least distorts the proportional change of stationary masses for critical states, for instance, the network attractors. In comparison to previous reduction methods, we reduce the state space directly, without deleting genes. We then derive stationary control policies on the reduced network that can be naturally induced back to the original network. Computational experiments study the effects of the reduction on model complexity and the performance of designed control policies which is measured by the shift of stationary mass away from undesirable states, those associated with undesirable phenotypes. We consider randomly generated networks as well as a 17-gene gastrointestinal cancer network, which, if not reduced, has a 2(17) × 2(17) transition probability matrix. Such a dimension is too large for direct application of many previously proposed PBN intervention strategies.     

Circumventing structural uncertainty: A Bayesian perspective on nonlinear forecasting for ecology

As a consequence of the complexity of ecosystems and context-dependence of species interactions, structural uncertainty is pervasive in ecological modeling. This is particularly problematic when ecological models are used to make conservation and management plans whose outcomes may depend strongly on model formulation. Nonlinear time series approaches allow us to circumvent this issue by using the observed dynamics of the system to guide policy development. However, these methods typically require long time series from stationary systems, which are rarely available in ecological settings. Here we present a Bayesian approach to nonlinear forecasting based on Gaussian processes that readily integrates information from several short time series and allows for nonstationary dynamics. We demonstrate the utility of our modeling methods on simulated from a wide range of ecological scenarios. We expect that these models will extend the range of ecological systems to which nonlinear forecasting methods can be usefully applied.     

Optimized submerged batch fermentation strategy for systems scale studies of metabolic switching in Streptomyces coelicolor A3(2)

Background

Given the complex mechanisms underlying biochemical processes systems biology researchers tend to build ever increasing computational models. However, dealing with complex systems entails a variety of problems, e.g. difficult intuitive understanding, variety of time scales or non-identifiable parameters. Therefore, methods are needed that, at least semi-automatically, help to elucidate how the complexity of a model can be reduced such that important behavior is maintained and the predictive capacity of the model is increased. The results should be easily accessible and interpretable. In the best case such methods may also provide insight into fundamental biochemical mechanisms.

Results

We have developed a strategy based on the Computational Singular Perturbation (CSP) method which can be used to perform a "biochemically-driven" model reduction of even large and complex kinetic ODE systems. We provide an implementation of the original CSP algorithm in COPASI (a COmplex PAthway SImulator) and applied the strategy to two example models of different degree of complexity - a simple one-enzyme system and a full-scale model of yeast glycolysis.

Conclusion

The results show the usefulness of the method for model simplification purposes as well as for analyzing fundamental biochemical mechanisms. COPASI is freely available at http://www.copasi.org.     

Characteristics of neuronal systems in the visual cortex

The coupling complexity of cortical areas makes it very difficult to analyse them experimentally. Studies of model systems provide the possibility of adapting the analysis to the available data base and elaborating the fundamental properties that depend on the structure of the system. We propose a model system of variable complexity that is spatially two-dimensional and time-dependent, uses feedback for iteration and smoothing, includes the mapping of the cortical networks and can be nonlinear as the case requires. Combining such elementary systems on the basis of neuroanatomical findings enables us to simulate cortical mappings and to interpret neurophysiological data. The decisive factor is that the dynamics of the system and the neuroanatomically based spatial coupling are closely connected with each other.     

How to build an information gathering and processing system: lessons from naturally and artificially intelligent systems

Imagine a situation in which you had to design a physical agent that could collect information from its environment, then store and process that information to help it respond appropriately to novel situations. What kinds of information should it attend to? How should the information be represented so as to allow efficient use and re-use? What kinds of constraints and trade-offs would there be? There are no unique answers. In this paper, we discuss some of the ways in which the need to be able to address problems of varying kinds and complexity can be met by different information processing systems. We also discuss different ways in which relevant information can be obtained, and how different kinds of information can be processed and used, by both biological organisms and artificial agents. We analyse several constraints and design features, and show how they relate both to biological organisms, and to lessons that can be learned from building artificial systems. Our standpoint overlaps with Karmiloff-Smith (1992) in that we assume that a collection of mechanisms geared to learning and developing in biological environments are available in forms that constrain, but do not determine, what can or will be learnt by individuals.     

Measurable notions of complexity and their relationship to biological complexity

Complexity is often invoked as a motivation for a systems approach to biology. We review three measurable notions of complexity from the areas of computation and data analysis. These measures have each led to mathematical theory and to further insight on the complexity of objects, demonstrating the benefits of having a well-defined measure of complexity. Each measure is applicable in the study of particular biological systems; however, none is satisfactory to serve as a universal measure of biological complexity. The study of biological systems will likely require numerous measures of complexity, each appropriate for analysis in specific settings.     

Can adaptation lead to extinction?

Ever since J.B.S. Haldane proposed the idea, evolutionary biologists are aware that individual level adaptations do not necessarily lead to optimal population performance. A few deeply mathematical models, drawing from a diverse range of systems, even predict that individual selection can lead to the extinction of the whole population, a phenomenon which has become known as evolutionary suicide. Due to the complexity of both following adaptation and determining the exact cause of an extinction, evolutionary suicide has remained untested empirically. However, three recent empirical studies suggest that it may occur, and that suicide should be taken seriously as a potentially important evolutionary phenomenon. Here we ask whether or not evolutionary suicide can occur, briefly reviewing the theoretical and empirical evidence. We further highlight systems which may be used to test whether or not individual level selection can cause extinction.     

Muscle fatigue and contraction intensity modulates the complexity of surface electromyography

Nonlinear dynamical techniques offer a powerful approach for the investigation of physiological time series. Multiscale entropy analyses have shown that pathological and aging systems are less complex than healthy systems and this finding has been attributed to degraded physiological control processes. A similar phenomenon may arise during fatiguing muscle contractions where surface electromyography signals undergo temporal and spectral changes that arise from the impaired regulation of muscle force production. Here we examine the affect of fatigue and contraction intensity on the short and long-term complexity of biceps brachii surface electromyography. To investigate, we used an isometric muscle fatigue protocol (parsed into three windows) and three contraction intensities (% of maximal elbow joint moment: 40%, 70% and 100%). We found that fatigue reduced the short-term complexity of biceps brachii activity during the last third of the fatiguing contraction. We also found that the complexity of surface electromyography is dependent on contraction intensity. Our results show that multiscale entropy is sensitive to muscle fatigue and contraction intensity and we argue it is imperative that both factors be considered when evaluating the complexity of surface electromyography signals. Our data contribute to a converging body of evidence showing that multiscale entropy can quantify subtle information content in physiological time series.     

Analysis of tracer experiments: VII. General multi-compartment systems imbedded in non-homogeneous inaccessible media

An integral equation analysis of generaln compartment steady state systems imbedded in static media of arbitrary complexity has been developed. A set of initial entry functions can be found which serve to determine a corresponding set of partitioned initial entry functions. The partitioned functions, in turn, can be used to predict the probabilities and time courses of various transport histories and to determine all steady state rates of flow between measured compartments. The method is quite general, being completely applicable, for example, to closed systems, to cyclic systems and to systems in which relatively rapid (but finite) exchange between compartments occurs.     

Practical limits for reverse engineering of dynamical systems: a statistical analysis of sensitivity and parameter inferability in systems biology models

The size and complexity of cellular systems make building predictive models an extremely difficult task. In principle dynamical time-course data can be used to elucidate the structure of the underlying molecular mechanisms, but a central and recurring problem is that many and very different models can be fitted to experimental data, especially when the latter are limited and subject to noise. Even given a model, estimating its parameters remains challenging in real-world systems. Here we present a comprehensive analysis of 180 systems biology models, which allows us to classify the parameters with respect to their contribution to the overall dynamical behaviour of the different systems. Our results reveal candidate elements of control in biochemical pathways that differentially contribute to dynamics. We introduce sensitivity profiles that concisely characterize parameter sensitivity and demonstrate how this can be connected to variability in data. Systematically linking data and model sloppiness allows us to extract features of dynamical systems that determine how well parameters can be estimated from time-course measurements, and associates the extent of data required for parameter inference with the model structure, and also with the global dynamical state of the system. The comprehensive analysis of so many systems biology models reaffirms the inability to estimate precisely most model or kinetic parameters as a generic feature of dynamical systems, and provides safe guidelines for performing better inferences and model predictions in the context of reverse engineering of mathematical models for biological systems.