The semiotics of control and modeling relations in complex systems

We provide a conceptual analysis of ideas and principles from the systems theory discourse which underlie Pattee's semantic or semiotic closure, which is itself foundational for a school of theoretical biology derived from systems theory and cybernetics, and is now being related to biological semiotics and explicated in the relational biological school of Rashevsky and Rosen. Atomic control systems and models are described as the canonical forms of semiotic organization, sharing measurement relations, but differing topologically in that control systems are circularly and models linearly related to their environments. Computation in control systems is introduced, motivating hierarchical decomposition, hybrid modeling and control systems, and anticipatory or model-based control. The semiotic relations in complex control systems are described in terms of relational constraints, and rules and laws are distinguished as contingent and necessary functional entailments, respectively. Finally, selection as a meta-level of constraint is introduced as the necessary condition for semantic relations in control systems and models.     

Computer simulation of biological systems

The current status of mathematical models of biological systems is reviewed. Advances in supercomputer hardware allows more complex models to be constructed. The new generation of microcomputers are quite adequate for many computer simulations of biological systems. A theory of modeling is being developed to improve the relationship between the real biological system and the model. Deterministic models, stochastic models and applications of control theory and optimization methods are discussed. Examples given include models of molecular structure, of experimental techniques, and of biochemical reactions. It is recommended that experimental biologists consider the use of microcomputers to model the system under study as a part of their research program.     

Biological information processing: the use of information for the support of function

In biological systems, the processing and use of information has evolved out of the need for survival in the face of an uncertain environment. As a consequence, the information-function relationship in these systems is shaped by their adaptability characteristics. In contrast, the information-function relationship in man-designed, goal-oriented organizational systems depends on the ability of the information processing system to support the achievement of the organization's goals. In this paper we use results from adaptability theory in the analysis of control-related aspects of the information-function relationship in man-designed organizational systems. In particular, we use a conceptual model of organizational control to characterize features of functional and control structures and their effect on the adaptability of these systems. The concept of implicit control and a design principle for adaptability-enhancing information systems are derived for this analysis.     

Adjusting phenotypes by noise control

Genetically identical cells can show phenotypic variability. This is often caused by stochastic events that originate from randomness in biochemical processes involving in gene expression and other extrinsic cellular processes. From an engineering perspective, there have been efforts focused on theory and experiments to control noise levels by perturbing and replacing gene network components. However, systematic methods for noise control are lacking mainly due to the intractable mathematical structure of noise propagation through reaction networks. Here, we provide a numerical analysis method by quantifying the parametric sensitivity of noise characteristics at the level of the linear noise approximation. Our analysis is readily applicable to various types of noise control and to different types of system; for example, we can orthogonally control the mean and noise levels and can control system dynamics such as noisy oscillations. As an illustration we applied our method to HIV and yeast gene expression systems and metabolic networks. The oscillatory signal control was applied to p53 oscillations from DNA damage. Furthermore, we showed that the efficiency of orthogonal control can be enhanced by applying extrinsic noise and feedback. Our noise control analysis can be applied to any stochastic model belonging to continuous time Markovian systems such as biological and chemical reaction systems, and even computer and social networks. We anticipate the proposed analysis to be a useful tool for designing and controlling synthetic gene networks.     

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.     

Diversified Control Paths: A Significant Way Disease Genes Perturb the Human Regulatory Network

Background

The complexity of biological systems motivates us to use the underlying networks to provide deep understanding of disease etiology and the human diseases are viewed as perturbations of dynamic properties of networks. Control theory that deals with dynamic systems has been successfully used to capture systems-level knowledge in large amount of quantitative biological interactions. But from the perspective of system control, the ways by which multiple genetic factors jointly perturb a disease phenotype still remain.

Results

In this work, we combine tools from control theory and network science to address the diversified control paths in complex networks. Then the ways by which the disease genes perturb biological systems are identified and quantified by the control paths in a human regulatory network. Furthermore, as an application, prioritization of candidate genes is presented by use of control path analysis and gene ontology annotation for definition of similarities. We use leave-one-out cross-validation to evaluate the ability of finding the gene-disease relationship. Results have shown compatible performance with previous sophisticated works, especially in directed systems.

Conclusions

Our results inspire a deeper understanding of molecular mechanisms that drive pathological processes. Diversified control paths offer a basis for integrated intervention techniques which will ultimately lead to the development of novel therapeutic strategies.     

Theoretical contributions to biological control success

Ecologists have long tried, with little success, to develop ecological theory for biological control. Biological control illustrates how science often follows, rather than precedes, technological advances. A scientific theory of biological control remains a worthy and achievable goal. We need to (1) combine deductions from mathematical models with rigorous empiricism measuring and modeling the effects of abiotic and biotic environmental drivers on demography and population dynamics of real biological control systems in the field, (2) use a wider range of model systems to explore how population structure, movement, spatial heterogeneity, and external environmental conditions influence population and community dynamics, and (3) combine deductive and inductive approaches to address the day-to-day concerns of biocontrol scientists including how to rear and release a control organism, suppress the target organism, and minimize harm to non-target organisms. Further progress will require more fundamental research in population and community ecology directly relevant to biological control.     

Stochastic analysis of a nonlinear model for selection of biological macromolecules

A stochastic analysis of a nonlinear selection model is presented. The model, based on Eigen and Schuster's theory of selection and evolution of biological macromolecules, considers the effects of fluctuations on the individual concentrations of macromolecules as well as the total population numbers in constrained systems. Our analysis shows that one of the models most often treated deterministically (referred to as constant organization in the literature) becomes unstable when fluctuations in the total population number are considered. An alternative model which apparently has built in self-regulating properties is analyzed and proves to be stable except for some special cases of degeneracy.     

Biocomplexity: adaptive behavior in complex stochastic dynamical systems

Existing methods of complexity research are capable of describing certain specifics of bio systems over a given narrow range of parameters but often they cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes-abrupt state transitions. Chaos tools have the potential of reaching to the essential driving mechanisms that organize matter into living substances. Our basic thesis is that while established chaos tools are useful in describing complexity in physical systems, they lack the power of grasping the essence of the complexity of life. This thesis illustrates sensory perception of vertebrates and the operation of the vertebrate brain. The study of complexity, at the level of biological systems, cannot be completed by the analytical tools, which have been developed for non-living systems. We propose a new approach to chaos research that has the potential of characterizing biological complexity. Our study is biologically motivated and solidly based in the biodynamics of higher brain function. Our biocomplexity model has the following features, (1) it is high-dimensional, but the dimensionality is not rigid, rather it changes dynamically; (2) it is not autonomous and continuously interacts and communicates with individual environments that are selected by the model from the infinitely complex world; (3) as a result, it is adaptive and modifies its internal organization in response to environmental factors by changing them to meet its own goals; (4) it is a distributed object that evolves both in space and time towards goals that is continually re-shaping in the light of cumulative experience stored in memory; (5) it is driven and stabilized by noise of internal origin through self-organizing dynamics. The resulting theory of stochastic dynamical systems is a mathematical field at the interface of dynamical system theory and stochastic differential equations. This paper outlines several possible avenues to analyze these systems. Of special interest are input-induced and noise-generated, or spontaneous state-transitions and related stability issues.     

Modelling Malaria Control by Introduction of Larvivorous Fish

Malaria creates serious health and economic problems which call for integrated management strategies to disrupt interactions among mosquitoes, the parasite and humans. In order to reduce the intensity of malaria transmission, malaria vector control may be implemented to protect individuals against infective mosquito bites. As a sustainable larval control method, the use of larvivorous fish is promoted in some circumstances. To evaluate the potential impacts of this biological control measure on malaria transmission, we propose and investigate a mathematical model describing the linked dynamics between the host–vector interaction and the predator–prey interaction. The model, which consists of five ordinary differential equations, is rigorously analysed via theories and methods of dynamical systems. We derive four biologically plausible and insightful quantities (reproduction numbers) that completely determine the community composition. Our results suggest that the introduction of larvivorous fish can, in principle, have important consequences for malaria dynamics, but also indicate that this would require strong predators on larval mosquitoes. Integrated strategies of malaria control are analysed to demonstrate the biological application of our developed theory.     

The analysis of distributed control and information processing in adaptive systems: a biologically motivated approach.

Biological systems have evolved hierarchical, distributed control structures that greatly enhance their adaptability. Two important determinants of biological adaptability considered here are: (i) the pattern of distribution of self-control capabilities; (ii) the degree of programmability of information processing. In this paper we model organizations as goal-oriented, adaptive systems, possessing properties similar to those of biological systems. We use the notion of implicit control (defined as the capability of self-control that is embedded in a system's own dynamics) in the analysis of the impact of specific patterns of distribution of control and information processing on the adaptability of organizations. A principle of design of organizational information systems, that captures important aspects of adaptability-preserving strategies of information processing in biological systems, is stated in terms of the implicit control concept.     

Proteomic tools for biomedicine

Proteomic tools measure gene expression, protein activity and interactions of biological events at the protein level. Proteins are the major catalysts of biological functions and contain several dimensions of information that collectively indicate the actual rather than the potential functional state as indicated by mRNA analysis. Measurements can be made in terms of protein quantity, location, and time-point. For the future we see a further integration of existing and new technologies for proteomics from a wide range of areas of biochemistry, chemistry, physics, computing science and molecular biology. This will further advance our knowledge of how biological systems are built up and what mechanisms control these systems. However, the potential of proteomics to comprehensively answer all biological questions is limited as only protein activity is measured. A unification of genomics, proteomics, and other technologies is needed if we are to start to understand the complexity of biological function in the context of disease and health.     

Population biology and biological control of nematodes.

We studied the population biology of the nematophagous fungus Hirsutella rhossiliensis to understand its potential as a biological control agent. Because the fungus is an infectious and transmissible parasite, we framed our study within an epidemiological context. Field observations, theory, and experiments demonstrated that (i) parasitism of nematodes by H. rhossiliensis is dependent on nematode density, (ii) local populations of the fungus will go extinct unless supplied with some minimum number of nematodes (the host threshold density), and (iii) natural epidemics of this fungus in populations of nematodes develop slowly and only after long periods of high host density. Additional in-depth research on population biology is needed to explain other biological control systems and to guide future research. The most effective research will combine field observation, theory, and experimentation.     

Robustness analysis of biochemical network models

Biological systems that have been experimentally verified to be robust to significant changes in their environments require mathematical models that are themselves robust. In this context, a necessary condition for model robustness is that the model dynamics should not be sensitive to small variations in the model's parameters. Robustness analysis problems of this type have been extensively studied in the field of robust control theory and have been found to be very difficult to solve in general. The authors describe how some tools from robust control theory and nonlinear optimisation can be used to analyse the robustness of a recently proposed model of the molecular network underlying adenosine 3',5'-cyclic monophosphate (cAMP) oscillations observed in fields of chemotactic Dictyostelium cells. The network model, which consists of a system of seven coupled nonlinear differential equations, accurately reproduces the spontaneous oscillations in cAMP observed during the early development of D. discoideum. The analysis by the authors reveals, however, that very small variations in the model parameters can effectively destroy the required oscillatory dynamics. A biological interpretation of the analysis results is that correct functioning of a particular positive feedback loop in the proposed model is crucial to maintaining the required oscillatory dynamics.     

Bayesian modelling of shared gene function

MOTIVATION: Biological assays are often carried out on tissues that contain many cell lineages and active pathways. Microarray data produced using such material therefore reflect superimpositions of biological processes. Analysing such data for shared gene function by means of well-matched assays may help to provide a better focus on specific cell types and processes. The identification of genes that behave similarly in different biological systems also has the potential to reveal new insights into preserved biological mechanisms. RESULTS: In this article, we propose a hierarchical Bayesian model allowing integrated analysis of several microarray data sets for shared gene function. Each gene is associated with an indicator variable that selects whether binary class labels are predicted from expression values or by a classifier which is common to all genes. Each indicator selects the component models for all involved data sets simultaneously. A quantitative measure of shared gene function is obtained by inferring a probability measure over these indicators. Through experiments on synthetic data, we illustrate potential advantages of this Bayesian approach over a standard method. A shared analysis of matched microarray experiments covering (a) a cycle of mouse mammary gland development and (b) the process of in vitro endothelial cell apoptosis is proposed as a biological gold standard. Several useful sanity checks are introduced during data analysis, and we confirm the prior biological belief that shared apoptosis events occur in both systems. We conclude that a Bayesian analysis for shared gene function has the potential to reveal new biological insights, unobtainable by other means. AVAILABILITY: An online supplement and MatLab code are available at http://www.sykacek.net/research.html#mcabf     

Cellular signaling is potentially regulated by cell density in receptor trafficking networks

Previous work has shown that receptor trafficking is a potential site for the control of signaling pathways. In most biological experiments, the ligand concentration and cell density vary within a wide range among different systems. However, there is less attention to systematically analyze how much cellular signal response is affected by cell densities. Here, we use a quantitative mathematical model to investigate signal responses in different receptor trafficking networks by simultaneous variations of ligand concentration and cell density. Computational analysis of the model revealed that receptor trafficking networks have potential sigmoid responses to ratio between ligand and surface receptor number per cell, which is a key factor to control the signaling responses in receptor trafficking networks. Furthermore, cell density also affects the robustness of dose-response curve upon the variation of binding affinity.     

Information-Theoretic Analysis of the Dynamics of an Executable Biological Model

To facilitate analysis and understanding of biological systems, large-scale data are often integrated into models using a variety of mathematical and computational approaches. Such models describe the dynamics of the biological system and can be used to study the changes in the state of the system over time. For many model classes, such as discrete or continuous dynamical systems, there exist appropriate frameworks and tools for analyzing system dynamics. However, the heterogeneous information that encodes and bridges molecular and cellular dynamics, inherent to fine-grained molecular simulation models, presents significant challenges to the study of system dynamics. In this paper, we present an algorithmic information theory based approach for the analysis and interpretation of the dynamics of such executable models of biological systems. We apply a normalized compression distance (NCD) analysis to the state representations of a model that simulates the immune decision making and immune cell behavior. We show that this analysis successfully captures the essential information in the dynamics of the system, which results from a variety of events including proliferation, differentiation, or perturbations such as gene knock-outs. We demonstrate that this approach can be used for the analysis of executable models, regardless of the modeling framework, and for making experimentally quantifiable predictions.     

A Mathematical Biologist’s Guide to Absolute and Convective Instability

Mathematical models have been highly successful at reproducing the complex spatiotemporal phenomena seen in many biological systems. However, the ability to numerically simulate such phenomena currently far outstrips detailed mathematical understanding. This paper reviews the theory of absolute and convective instability, which has the potential to redress this inbalance in some cases. In spatiotemporal systems, unstable steady states subdivide into two categories. Those that are absolutely unstable are not relevant in applications except as generators of spatial or spatiotemporal patterns, but convectively unstable steady states can occur as persistent features of solutions. The authors explain the concepts of absolute and convective instability, and also the related concepts of remnant and transient instability. They give examples of their use in explaining qualitative transitions in solution behaviour. They then describe how to distinguish different types of instability, focussing on the relatively new approach of the absolute spectrum. They also discuss the use of the theory for making quantitative predictions on how spatiotemporal solutions change with model parameters. The discussion is illustrated throughout by numerical simulations of a model for river-based predator–prey systems.