Hannes Klarner

Parameter Identification and Model Ranking of Thomas Networks

We propose a new methodology for identification and analysis of discrete gene networks as defined by Rene Thomas, supported by a tool chain: (i) given a Thomas network with partially known kinetic parameters, we reduce the number of acceptable parametrizations to those that fit time-series measurements and reflect other known constraints by an improved technique of coloured LTL model checking performing efficiently on Thomas networks in distributed environment; (ii) we introduce classification of acceptable parametrizations to identify most optimal ones; (iii) we propose two ways of visualising parametrizations dynamics wrt time-series data. Finally, computational efficiency is evaluated and the methodology is validated on bacteriophage λ case study.

Computing maximal and minimal trap spaces of Boolean networks

AbstractAsymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called trap spaces, can be exploited to investigate attractor properties as well as for model reduction techniques. In this paper, we propose a novel optimization-based method for computing all minimal and maximal trap spaces and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a study of a MAPK pathway model. To test the efficiency and scalability of the method, we compare the performance of the ILP solver gurobi with the ASP solver potassco in a benchmark of random networks.

Time Series Dependent Analysis of Unparametrized Thomas Networks

This paper is concerned with the analysis of labeled Thomas networks using discrete time series. It focuses on refining the given edge labels and on assessing the data quality. The results are aimed at being exploitable for experimental design and include the prediction of new activatory or inhibitory effects of given interactions and yet unobserved oscillations of specific components in between specific sampling intervals. On the formal side, we generalize the concept of edge labels and introduce a discrete time series interpretation. This interpretation features two original concepts: 1) Incomplete measurements are admissible, and 2) it allows qualitative assumptions about the changes in gene expression by means of monotonicity. On the computational side, we provide a Python script, erda.py, that automates the suggested workflow by model checking and constraint satisfaction. We illustrate the workflow by investigating the yeast network IRMA.

Computing Symbolic Steady States of Boolean Networks

Asymptotic behavior is often of particular interest when analyzing asynchronous Boolean networks representing biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called symbolic steady states, can be exploited to investigate attractor properties as well as for model reduction techniques conserving attractors. In this paper, we propose a novel optimization-based method for computing all maximal symbolic steady states and motivate their use. n particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a short study of a MAPK pathway model.

PyBoolNet: a python package for the generation, analysis and visualization of boolean networks

Motivation: The goal of this project is to provide a simple interface to working with Boolean networks. Emphasis is put on easy access to a large number of common tasks including the generation and manipulation of networks, attractor and basin computation, model checking and trap space computation, execution of established graph algorithms as well as graph drawing and layouts. Results: PyBoolNet is a Python package for working with Boolean networks that supports simple access to model checking via NuSMV, standard graph algorithms via NetworkX and visualization via dot. In addition, state of the art attractor computation exploiting Potassco ASP is implemented. The package is function‐based and uses only native Python and NetworkX data types. Availability and Implementation: https://github.com/hklarner/PyBoolNet Contact: hannes.klarner@fu‐berlin.de

Approximating Attractors of Boolean Networks by Iterative CTL Model Checking

This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: “faithfulness” which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, “univocality” which requires that there is a unique attractor in each trap space, and “completeness” which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.

Model Integration and Crosstalk Analysis of Logical Regulatory Networks

Methods for model integration have become increasingly popular for understanding of the interplay between biological processes. In this work, we introduce an approach for coupling models taking uncertainties concerning the crosstalk into account. Using constraintbased modeling and formal verification techniques, a pool of possible integrated models is generated in agreement with previously validated behavior of the isolated models as well as additional experimental observations. Correlation- and causality-based analysis allows us to uncover the importance of particular crosstalk connections for specific functionalities leading to new biological insights and starting points for experimental design. We illustrate our approach studying crosstalk between the MAPK and mTor signaling pathways.

Parameter inference for asynchronous logical networks using discrete time series

This paper is concerned with the dynamics of asynchronous logical models of regulatory networks as introduced by R. Thomas. Available knowledge about the dynamics of a regulatory network is often limited to a sequence of snapshots in the form of a discrete time series. Using CTL formulas together with the concept of partially monotone paths, a methodology is elaborated to investigate the compatibility of a given time series and a Thomas model. The approach can be used to revise the model, but also to evaluate the given data. Additionally, suggestions are made to analyze a model pool for common properties regarding component behavior and interaction types, aiming at results exploitable for experimental design.

Designing miRNA-Based Synthetic Cell Classifier Circuits Using Answer Set Programming

Cell classifier circuits are synthetic biological circuits capable of distinguishing between different cell states depending on specific cellular markers and engendering a state-specific response. An example are classifiers for cancer cells that recognize whether a cell is healthy or diseased based on its miRNA fingerprint and trigger cell apoptosis in the latter case. Binarization of continuous miRNA expression levels allows to formalize a classifier as a Boolean function whose output codes for the cell condition. In this framework, the classifier design problem consists of finding a Boolean function capable of reproducing correct labelings of miRNA profiles. The specifications of such a function can then be used as a blueprint for constructing a corresponding circuit in the lab. To find an optimal classifier both in terms of performance and reliability, however, accuracy, design simplicity and constraints derived from availability of molcular building blocks for the classifiers all need to be taken into account. These complexities translate to computational difficulties, so currently available methods explore only part of the design space and consequently are only capable of calculating locally optimal designs. We present a computational approach for finding globally optimal classifier circuits based on binarized miRNA datasets using Answer Set Programming for efficient scanning of the entire search space. Additionally, the method is capable of computing all optimal solutions, allowing for comparison between optimal classifier designs and identification of key features. Several case studies illustrate the applicability of the approach and highlight the quality of results in comparison with a state of the art method. The method is fully implemented and a comprehensive performance analysis demonstrates its reliability and scalability.

Erratum to: Computing maximal and minimal trap spaces of Boolean networks

Fig. 2 Synchronous and asynchronous transition graphs of the running example. The trap spaces (and the way they are nested) are given as a heat map. Minimal and maximal trap spaces are outlined by a black line and the attractors by a white line. Using the ‘‘H’’ notation, we get the following sets: S! 1⁄4 fHHHH; 00HH; 1HHH; 1H0H; 1H01; 1101g, minðS!Þ 1⁄4 f00HH; 1101g and maxðS!Þ 1⁄4 f00HH; 1HHHg and SF 1⁄4 f1101g