A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

A Method to Identify and Analyze Biological Programs through Automated Reasoning.

Predictive biology is elusive because rigorous, data-constrained, mechanistic models of complex biological systems are difficult to derive and validate. Current approaches tend to construct and examine static interaction network models, which are descriptively rich but often lack explanatory and predictive power, or dynamic models that can be simulated to reproduce known behavior. However, in such approaches implicit assumptions are introduced as typically only one mechanism is considered, and exhaustively investigating all scenarios is impractical using simulation. To address these limitations, we present a methodology based on automated formal reasoning, which permits the synthesis and analysis of the complete set of logical models consistent with experimental observations. We test hypotheses against all candidate models, and remove the need for simulation by characterizing and simultaneously analyzing all mechanistic explanations of observed behavior. Our methodology transforms knowledge of complex biological processes from sets of possible interactions and experimental observations to precise, predictive biological programs governing cell function

A temporal logic approach to modular design of synthetic biological circuits

We present a new approach for the design of a synthetic biological circuit whose behaviour is specified in terms of signal temporal logic (STL) formulae. We first show how to characterise with STL formulae the input/output behaviour of biological modules miming the classical logical gates (AND, NOT, OR). Hence, we provide the regions of the parameter space for which these specifications are satisfied. Given a STL specification of the target circuit to be designed and the networks of its constituent components, we propose a methodology to constrain the behaviour of each module, then identifying the subset of the parameter space in which those constraints are satisfied, providing also a measure of the robustness for the target circuit design. This approach, which leverages recent results on the quantitative semantics of Signal Temporal Logic, is illustrated by synthesising a biological implementation of an half-adder

Dominant Vertices in Regulatory Networks Dynamics

Discrete-time regulatory networks are dynamical systems on directed graphs, with a structure inspired on natural systems of interacting units. There is a natural notion of determination amongst vertices, which we use to classify the nodes of the network, and to determine what we call "sets of dominant vertices". In this paper we prove that in the asymptotic regime, the projection of the dynamics on a dominant set allows us to determine the state of the whole system at all times. We provide an algorithm to find sets of dominant vertices, and we test its accuracy on three families of theoretical examples. Then, by using the same algorithm, we study the relation between the structure of the underlying network and the corresponding dominant set of vertices. We also present a result concerning the inheritability of the dominance between strongly connected networks

Detection of regulator genes and eQTLs in gene networks

Genetic differences between individuals associated to quantitative phenotypic traits, including disease states, are usually found in non-coding genomic regions. These genetic variants are often also associated to differences in expression levels of nearby genes (they are "expression quantitative trait loci" or eQTLs for short) and presumably play a gene regulatory role, affecting the status of molecular networks of interacting genes, proteins and metabolites. Computational systems biology approaches to reconstruct causal gene networks from large-scale omics data have therefore become essential to understand the structure of networks controlled by eQTLs together with other regulatory genes, and to generate detailed hypotheses about the molecular mechanisms that lead from genotype to phenotype. Here we review the main analytical methods and softwares to identify eQTLs and their associated genes, to reconstruct co-expression networks and modules, to reconstruct causal Bayesian gene and module networks, and to validate predicted networks in silico.Comment: minor revision with typos corrected; review article; 24 pages, 2 figure

Linear fuzzy gene network models obtained from microarray data by exhaustive search

BACKGROUND: Recent technological advances in high-throughput data collection allow for experimental study of increasingly complex systems on the scale of the whole cellular genome and proteome. Gene network models are needed to interpret the resulting large and complex data sets. Rationally designed perturbations (e.g., gene knock-outs) can be used to iteratively refine hypothetical models, suggesting an approach for high-throughput biological system analysis. We introduce an approach to gene network modeling based on a scalable linear variant of fuzzy logic: a framework with greater resolution than Boolean logic models, but which, while still semi-quantitative, does not require the precise parameter measurement needed for chemical kinetics-based modeling. RESULTS: We demonstrated our approach with exhaustive search for fuzzy gene interaction models that best fit transcription measurements by microarray of twelve selected genes regulating the yeast cell cycle. Applying an efficient, universally applicable data normalization and fuzzification scheme, the search converged to a small number of models that individually predict experimental data within an error tolerance. Because only gene transcription levels are used to develop the models, they include both direct and indirect regulation of genes. CONCLUSION: Biological relationships in the best-fitting fuzzy gene network models successfully recover direct and indirect interactions predicted from previous knowledge to result in transcriptional correlation. Fuzzy models fit on one yeast cell cycle data set robustly predict another experimental data set for the same system. Linear fuzzy gene networks and exhaustive rule search are the first steps towards a framework for an integrated modeling and experiment approach to high-throughput "reverse engineering" of complex biological systems

Synthetic biology: new engineering rules for an emerging discipline

Synthetic biologists engineer complex artificial biological systems to investigate natural biological phenomena and for a variety of applications. We outline the basic features of synthetic biology as a new engineering discipline, covering examples from the latest literature and reflecting on the features that make it unique among all other existing engineering fields. We discuss methods for designing and constructing engineered cells with novel functions in a framework of an abstract hierarchy of biological devices, modules, cells, and multicellular systems. The classical engineering strategies of standardization, decoupling, and abstraction will have to be extended to take into account the inherent characteristics of biological devices and modules. To achieve predictability and reliability, strategies for engineering biology must include the notion of cellular context in the functional definition of devices and modules, use rational redesign and directed evolution for system optimization, and focus on accomplishing tasks using cell populations rather than individual cells. The discussion brings to light issues at the heart of designing complex living systems and provides a trajectory for future development

Combining Boolean Networks and Ordinary Differential Equations for Analysis and Comparison of Gene Regulatory Networks

This thesis is concerned with different groups of qualitative models of gene regulatory networks. Four types of models will be considered: interaction graphs, Boolean networks, models based on differential equations and discrete abstractions of differential equations. We will investigate the relations between these modeling frameworks and how they can be used in the analysis of individual models. The focus lies on the mathematical analysis of these models. This thesis makes several contributions in relating these different modeling frameworks. The first approach concerns individual Boolean models and parametrized families of ordinary differential equations (ODEs). To construct ODE models systematically from Boolean models several automatic conversion algorithms have been proposed. In Chapter 2 several such closely related algorithms will be considered. It will be proven that certain invariant sets are preserved during the conversion from a Boolean network to a model based on ODEs. In the second approach the idea of abstracting the dynamics of individual models to relate structure and dynamics will be introduced. This approach will be applied to Boolean models and models based on differential equations. This allows to compare groups of models in these modeling frameworks which have the same structure. We demonstrate that this constitutes an approach to link the interaction graph to the dynamics of certain sets of Boolean networks and models based on differential equations. The abstracted dynamics – or more precisely the restrictions on the abstracted behavior – of such sets of Boolean networks or models based on differential equations will be represented as Boolean state transitions graphs themselves. We will show that these state transition graphs can be considered as asynchronous Boolean networks. Despite the rather theoretical question this thesis tries to answer there are many potential applications of the results. The results in Chapter 2 can be applied to network reduction of ODE models based on Hill kinetics. The results of the second approach in Chapter 4 can be applied to network inference and analysis of Boolean model sets. Furthermore, in the last chapter of this thesis several ideas for applications with respect to experiment design will be considered. This leads to the question how different asynchronous Boolean networks or different behaviours of a single asynchronous Boolean network can be distinguishedDiese Arbeit beschäftigt sich mit unterschiedlichen Typen von qualitativen Modellen genregulatorischer Netzwerke. Vier Typen von Modellen werden betrachtet: Interaktionsgraphen, Boolesche Netzwerke, Modelle, die auf Differentialgleichungen basieren und diskrete Abstraktionen von Differentialgleichungen. Wir werden mehr über die Beziehungen zwischen diesen Modellgruppen lernen und wie diese Beziehungen genutzt werden können, um einzelne Modelle zu analysieren. Der Schwerpunkt liegt hierbei auf der mathematischen Analyse dieser Modellgruppen. In dieser Hinsicht leistet diese Arbeit mehrere Beiträge. Zunächst betrachten wir Boolesche Netzwerke und parametrisierte Familien von gewöhnlichen Differentialgleichungen (ODEs). Um solche ODE-Modelle systematisch aus Booleschen Modellen abzuleiten, wurden in der Vergangenheit verschiedene automatische Konvertierungsalgorithmen vorgeschlagen. In Kapitel 2 werden einige dieser Algorithmen näher untersucht. Wir werden beweisen, dass bestimmte invariante Mengen bei der Konvertierung eines Booleschen Modells in ein ODE-Modell erhalten bleiben. Der zweite Ansatz, der in dieser Arbeit verfolgt wird, beschäftigt sich mit diskreten Abstraktionen der Dynamik von Modellen. Mit Hilfe dieser Abstraktionen ist es möglich, die Struktur – den Interaktionsgraphen – und die Dynamik der zugehörigen Modelle in Bezug zu setzen. Diese Methode wird sowohl auf Boolesche Modelle als auch auf ODE-Modelle angewandt. Gleichzeitig erlaubt dieser Ansatz Mengen von Modellen in unterschiedlichen Modellgruppen zu vergleichen, die dieselbe Struktur haben. Die abstrahierten Dynamiken (genauer die Einschränkungen der abstrahierten Dynamiken) der Booleschen Modellmengen oder ODE-Modellmengen können als Boolesche Zustandsübergangsgraphen repräsentiert werden. Wir werden zeigen, dass diese Zustandsübergangsgraphen wiederum selber als (asynchrone) Boolesche Netzwerke aufgefasst werden können. Trotz der theoretischen Ausgangsfrage werden in dieser Arbeit zahlreiche Anwendungen aufgezeigt. Die Ergebnisse aus Kapitel 2 können zur Modellreduktion benutzt werden, indem die Dynamik der ODE-Modelle auf den zu den Booleschen Netzwerken gehörigen “trap spaces” betrachtet wird. Die Resultate aus Kapitel 4 können zur Netzwerkinferenz oder zur Analyse von Modellmengen genutzt werden. Weiterhin werden im letzten Kapitel dieser Arbeit einige Anwendungsideen im Bezug auf Experimentdesign eingeführt. Dies führt zu der Fragestellung, wie verschiedene asynchrone Boolesche Netzwerke oder unterschiedliche Dynamiken, die mit einem einzelnen Modell vereinbar sind, unterschieden werden können