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.     

Prospects for advancing the understanding of complex biochemical systems

The application of mathematical theories to understanding the behaviour of complex biochemical systems is reviewed. Key aspects of behaviour are identified as the flux through particular pathways in a steady state, the nature and stability of dynamical states, and the thermodynamic properties of systems. The first of these is dealt primarily in theories of metabolic control, and metabolic control analysis (MCA) is an important example. The valid application of this theory is limited to steady-state systems, and the cases where the essential features of control can be derived from calibration experiments which perturb the state of the system by a sufficiently small amount from its operating point. In practice, time-dependent systems exist, it is not always possible to know a priori whether applied perturbations are sufficiently small, and important features of control may lie farther from the operating point than the application of the theory permits. The nature and stability of dynamical and thermodynamical states is beyond the scope of MCA. To understand the significance of these limitations fully, and to address the dynamical and thermodynamical properties, more complete theories are required. Non-linear systems theory offers the possibility of studying important questions regarding control of steady and dynamical states. It can also link to thermodynamic properties of the system including the energetic efficiency of particular pathways. However, its application requires a more detailed characterisation of the system under study. This extra detail may be an essential feature of the study of non-equilibrium states in general, and non-ideal pathways in particular. Progress requires considerably more widespread integration of theoretical and experimental approaches than currently exists.     

Multi-layered representation for cell signaling pathways

To understand complex signaling pathways and networks, it is necessary to develop a formal and structured representation of the available information in a format suitable for analysis by software tools. Due to the complexity and incompleteness of the current biological knowledge about cell signaling, such a device must be able to represent cellular pathways at differing levels of details, one level of information abstract enough to convey an essential signaling flow while hiding its details and another level of information detailed enough to explain the underlying mechanisms that account for the signaling flow described at a more abstract level. We have defined a formal ontology for cell-signaling events that allows us to describe these cellular pathways at various levels of abstraction. Using this formal representation, ROSPath (reactive oxygen species-mediated signaling pathway) database system has been implemented and made available on the web (rospath.ewha.ac.kr). ROSPath is a database system for reactive oxygen species (ROS)-mediated cell signaling pathways and signaling processes in molecular detail, which facilitates a comprehensive understanding of the regulatory mechanisms in signaling pathways. ROSPath includes growth factor-, stress-, and cytokine-induced signaling pathways containing about 500 unique proteins (mostly mammalian) and their related protein states, protein complexes, protein complex states, signaling interactions, signaling steps, and pathways. It is a web-based structured repository of information on the signaling pathways of interest and provides a means for managing data produced by large-scale and high-throughput techniques such as proteomics. Also, software tools are provided for querying, displaying, and analyzing pathways, thus furnishing an integrated web environment for visualizing and manipulating ROS-mediated cell-signaling events.     

Relax with CouchDB--into the non-relational DBMS era of bioinformatics

With the proliferation of high-throughput technologies, genome-level data analysis has become common in molecular biology. Bioinformaticians are developing extensive resources to annotate and mine biological features from high-throughput data. The underlying database management systems for most bioinformatics software are based on a relational model. Modern non-relational databases offer an alternative that has flexibility, scalability, and a non-rigid design schema. Moreover, with an accelerated development pace, non-relational databases like CouchDB can be ideal tools to construct bioinformatics utilities. We describe CouchDB by presenting three new bioinformatics resources: (a) geneSmash, which collates data from bioinformatics resources and provides automated gene-centric annotations, (b) drugBase, a database of drug-target interactions with a web interface powered by geneSmash, and (c) HapMap-CN, which provides a web interface to query copy number variations from three SNP-chip HapMap datasets. In addition to the web sites, all three systems can be accessed programmatically via web services.     

On Circuit Functionality in Boolean Networks

It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it “generates” several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of “generates.” Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.     

How structure determines correlations in neuronal networks

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

Mathematical approaches to differentiation and gene regulation

We consider some mathematical issues raised by the modelling of gene networks. The expression of genes is governed by a complex set of regulations, which is often described symbolically by interaction graphs. These are finite oriented graphs where vertices are the genes involved in the biological system of interest and arrows describe their interactions: a positive (resp. negative) arrow from a gene to another represents an activation (resp. inhibition) of the expression of the latter gene by some product of the former. Once such an interaction graph has been established, there remains the difficult task to decide which dynamical properties of the gene network can be inferred from it, in the absence of precise quantitative data about their regulation. There mathematical tools, among others, can be of some help. In this paper we discuss a rule proposed by Thomas according to which the possibility for the network to have several stationary states implies the existence of a positive circuit in the corresponding interaction graph. We prove that, when properly formulated in rigorous terms, this rule becomes a theorem valid for several different types of formal models of gene networks. This result is already known for models of differential [C. Soulé, Graphic requirements for multistationarity, ComPlexUs 1 (2003) 123-133] or Boolean [E. Rémy, P. Ruet, D. Thieffry, Graphic requirements for multistability and attractive cycles in a boolean dynamical framework, 2005, Preprint] type. We show here that a stronger version of it holds in the differential setup when the decay of protein concentrations is taken into account. This allows us to verify also the validity of Thomas' rule in the context of piecewise-linear models. We then discuss open problems.     

Reaction networks and evolutionary game theory

The powerful mathematical tools developed for the study of large scale reaction networks have given rise to applications of this framework beyond the scope of biochemistry. Recently, reaction networks have been suggested as an alternative way to model social phenomena. In this “socio-chemical metaphor” molecular species play the role of agents’ decisions and their outcomes, and chemical reactions play the role of interactions among these decisions. From here, it is possible to study the dynamical properties of social systems using standard tools of biochemical modelling. In this work we show how to use reaction networks to model systems that are usually studied via evolutionary game theory. We first illustrate our framework by modeling the repeated prisoners’ dilemma. The model is built from the payoff matrix together with assumptions of the agents’ memory and recognizability capacities. The model provides consistent results concerning the performance of the agents, and allows for the examination of the steady states of the system in a simple manner. We further develop a model considering the interaction among Tit for Tat and Defector agents. We produce analytical results concerning the performance of the strategies in different situations of agents’ memory and recognizability. This approach unites two important theories and may produce new insights in classical problems such as the evolution of cooperation in large scale systems.     

Simulation modelling of ecological hierarchies in constructive dynamical systems

Organized complexity is a characteristic feature of ecological systems with heterogeneous components interacting at several spatio-temporal scales. The hierarchy theory is a powerful epistemological framework to describe such systems by decomposing them vertically into levels and horizontally into holons. It was at first developed in a temporal and functional perspective and then, in the context of landscape ecology, extended to a spatial and structural approach. So far, most ecological applications of this theory were restricted to observational purposes, using multi-scale analysis to describe hierarchies. In spite of an increasing attention to dynamics of hierarchically structured ecological systems, current simulation models are still very limited in their representation of self-organization in complex adaptive systems. An ontological conceptualization of the hierarchy theory is outlined, focusing on key concepts, such as levels of organization and the compound and component faces of the holons. Various existing formalisms are currently used in simulation modelling, such as system dynamics, discrete event and agent based paradigms. Their ability to express the hierarchical organization of dynamical ecological systems is discussed. It turns out that a multi-modelling approach linking all these formalisms and oriented toward the specification of a constructive dynamical system would be able to express the dynamical structure of the hierarchy (creation, destruction and change of holons) and the functional and structural links between levels of organization.     

On the robustness of update schedules in Boolean networks

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems.     

Functional brain networks: great expectations,hard times and the big leap forward

Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks has generated great enthusiasm as it allows addressing hitherto non-standard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode.     

Extensible open source content management systems and frameworks: a solution for many needs of a bioinformatics group

A common challenge for bioinformaticians, in either academic or industry laboratory environments, is providing informatic solutions via the Internet or through a web browser. Recently, the open source community began developing tools for building and maintaining web applications for many disciplines. These content management systems (CMS) provide many of the basic needs of an informatics group, whether in a small company, a group within a larger organisation or an academic laboratory. These tools aid in managing software development, website development, document development, course development, datasets, collaborations and customers. Since many of these tools are extensible, they can be developed to support other research-specific activities, such as handling large biomedical datasets or deploying bioanalytic tools. In this review of open source website management tools, the basic features of content management systems are discussed along with commonly used open source software. Additionally, some examples of their use in biomedical research are given.     

Criticality enhances the multilevel reliability of stimulus responses in cortical neural networks

Cortical neural networks exhibit high internal variability in spontaneous dynamic activities and they can robustly and reliably respond to external stimuli with multilevel features–from microscopic irregular spiking of neurons to macroscopic oscillatory local field potential. A comprehensive study integrating these multilevel features in spontaneous and stimulus–evoked dynamics with seemingly distinct mechanisms is still lacking. Here, we study the stimulus–response dynamics of biologically plausible excitation–inhibition (E–I) balanced networks. We confirm that networks around critical synchronous transition states can maintain strong internal variability but are sensitive to external stimuli. In this dynamical region, applying a stimulus to the network can reduce the trial-to-trial variability and shift the network oscillatory frequency while preserving the dynamical criticality. These multilevel features widely observed in different experiments cannot simultaneously occur in non-critical dynamical states. Furthermore, the dynamical mechanisms underlying these multilevel features are revealed using a semi-analytical mean-field theory that derives the macroscopic network field equations from the microscopic neuronal networks, enabling the analysis by nonlinear dynamics theory and linear noise approximation. The generic dynamical principle revealed here contributes to a more integrative understanding of neural systems and brain functions and incorporates multimodal and multilevel experimental observations. The E–I balanced neural network in combination with the effective mean-field theory can serve as a mechanistic modeling framework to study the multilevel neural dynamics underlying neural information and cognitive processes.     

Solitary wave and spatially locked solitary pattern in a chemical reaction system

We investigate the behavior of a one-dimensional two component dynamical system. The dynamical equations are obtained by extracting an essence out of equations which describe the behavior of a biochemical reaction catalyzed by an allosteric protein. The obtained dynamical equations are similar to van der Pol equations. The dynamical equations are solved numerically. In the continuous system, a solitary wave is found to occur in certain ranges of the parameter space. The condition of occurrence of the solitary wave is investigated. The solitary wave can be induced by various initial perturbations, including rectangular ones with space-wise length longer than a certain critical value. The property of the solitary wave is similar to that of the impulses in nervous systems. In the discrete system, a spatially locked solitary pattern is found to occur in certain ranges of the parameter space.