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Über dieses Buch

This book constitutes the thoroughly refereed proceedings of the 6th International Workshop on Hybrid Systems Biology, HSB 2019, held in Prague, Czech Republic, in April 2019.
The 8 full papers presented in this book together with 1 short paper and 3 invited papers were carefully reviewed and selected from 13 submissions. They cover topics such as: modeling and analysis of metabolic, signaling, and genetic regulatory networks in living cells; models of tissues, organs, physiological models; models and methods coping with incomplete, uncertain and heterogeneous information including learning for biological systems, parametric synthesis and inference; stochastic and hybrid models in biology; hierarchical systems for multi-scale, multi-domain analysis; abstraction, approximation, discretization, and model reduction techniques; modeling, analysis and design for synthetic biology, cyber-biological systems and biomedical studies (e.g. therapies, teleoperation); game-theoretical frameworks and population models in biology (e.g. mixed-effects and Bayesian modeling); biological applications of quantitative and formal analysis techniques (e.g. reachability computation, model checking, abstract interpretation, bifurcation theory, stability and sensitivity analysis); efficient techniques for combined and heterogeneous (stochastic/deterministic, spatial/non-spatial) simulations for biological models; modeling languages and logics for biological systems with related analysis and simulation tools; and control architectures of biological systems including biology-in-the-loop systems and bio-robotics.

Inhaltsverzeichnis

Frontmatter

Invited Papers

Frontmatter

A Multimodular System to Study the Impact of a Focal Lesion in Neuronal Cell Cultures

Abstract
Characterizing neuronal networks activity and their dynamical changes due to endogenous and exogenous causes is a key issue of computational neuroscience and constitutes a fundamental contribution towards the development of innovative intervention strategies in case of brain damage. We address this challenge by making use of a multimodular system able to confine the growth of cells on substrate-embedded microelectrode arrays to investigate the interactions between networks of neurons. We observed their spontaneous and electrically induced network activity before and after a laser cut disconnecting one of the modules from all the others. We found that laser dissection induced de-synchronized activity among different modules during spontaneous activity, and prevented the propagation of evoked responses among modules during electrical stimulation. This reproducible experimental model constitutes a test-bed for the design and development of innovative computational tools for characterizing neural damage, and of novel neuro-prostheses aimed at restoring lost neuronal functionality between distinct brain areas.
Alberto Averna, Marta Carè, Stefano Buccelli, Marianna Semprini, Francesco Difato, Michela Chiappalone

Reachability Analysis and Hybrid Systems Biology - In Memoriam Oded Maler

Abstract
In this note we present some influential contributions of Oded Maler in hybrid systems research, with a focus on his pioneering results in reachability analysis and applications to systems biology. We also give a brief discussion of the evolution of the reachability computation techniques which have greatly progressed in recent years. This discussion is not intended to include an exhaustive survey of the existing results (The reader is referred to the recent proceedings of the conferences Hybrid Systems: Computation and Control.) but to show the strong impact of his foundational work.
Thao Dang

Reaction Networks, Oscillatory Motifs and Parameter Estimation in Biochemical Systems

Abstract
We outline an approach to analysis of dynamics of biosystems formulated as reaction networks. In particular, we discuss stability analysis provided that stoichiometric equations are given for each reaction step together with power law rate expressions. Based on stoichiometry alone, the network at stationary state can be decomposed into elementary subnetworks (elementary modes, extreme currents, fluxes). Assuming power law kinetics, the capacity of the elementary subnetworks for displaying dynamical instabilities, such as bistability and oscillations, is evaluated. These subnetworks are then suitably combined to form the entire network satisfying certain stability constraints implied by experiments. Specifically, we assume that an experimentally measured biosystem represented by a reaction network displays an experimentally observed change from a steady state to oscillations. For the assumed reaction mechanism only a limited set kinetic parameters is known. In contrast, input/output parameters are known from the experiment. The set of unknown kinetic parameters may be estimated by finding a suitable linear combination of elementary modes via linear optimization so that the dynamics displayed by the model fits the experimentally observed behavior. Moreover, reaction network theory is useful in identifying subnetworks that are destabilizing the steady state to yield oscillations. Such subnetworks are called oscillatory motifs and possess a characteristic topology. As an example, we analyze a carbon-nitrogen metabolism of cyanobacteria and examine its oscillatory dynamics.
Igor Schreiber, František Muzika, Jan Červený

Regular Papers

Frontmatter

Fixed-Point Computation of Equilibria in Biochemical Regulatory Networks

Abstract
The analysis of equilibria of ordinary differential equations (ODEs) that represent biochemical reaction networks is crucial in order to understand various functional properties of regulation in systems biology. In this paper, we develop a numerical algorithm to compute equilibria under the assumption that the regulatory network satisfies certain graph-theoretic conditions which lead to fixed-point iterations over an anti-monotonic function. Unlike generic approaches based on Netwon’s method, our algorithm does not require the availability of the Jacobian of the ODE vector field, which may be expensive when the dimensionality of the system is large. More important, it produces an estimation (through over-approximation) of the entire set of equilibria, with the guarantee of yielding the unique equilibrium of the ODE in the case that the returned set is a singleton. We demonstrate the applicability of our algorithm to two signaling pathways of MAPK and EGFR.
Isabel Cristina Pérez-Verona, Mirco Tribastone, Max Tschaikowski

Rejection-Based Simulation of Stochastic Spreading Processes on Complex Networks

Abstract
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or compartments). Nodes change their state randomly after an exponentially distributed waiting time and according to a given set of rules. For networks of realistic size, even the generation of only a single stochastic trajectory of a spreading process is computationally very expensive.
Here, we propose a novel simulation approach, which combines the advantages of event-based simulation and rejection sampling. Our method outperforms state-of-the-art methods in terms of absolute runtime and scales significantly better while being statistically equivalent.
Gerrit Großmann, Verena Wolf

Controlling Noisy Expression Through Auto Regulation of Burst Frequency and Protein Stability

Abstract
Protein levels can be controlled by regulating protein synthesis or half life. The aim of this paper is to investigate how introducing feedback in burst frequency or protein decay rate affects the stochastic distribution of protein level. Using a tractable hybrid mathematical framework, we show that the two feedback pathways lead to the same mean and noise predictions in the small-noise regime. Away from the small-noise regime, feedback in decay rate outperforms feedback in burst frequency in terms of noise control. The difference is particularly conspicuous in the strong-feedback regime. We also formulate a fine-grained discrete model which reduces to the hybrid model in the large system-size limit. We show how to approximate the discrete protein copy-number distribution and its Fano factor using hybrid theory. We also demonstrate that the hybrid model reduces to an ordinary differential equation in the limit of small noise. Our study thus contains a comparative evaluation of feedback in burst frequency and decay rate, and provides additional results on model reduction and approximation.
Pavol Bokes, Abhyudai Singh

Extracting Landscape Features from Single Particle Trajectories

Abstract
The predictive power of dynamical models of cell signaling is often limited due to the difficulty in estimating the relevant kinetic parameters. Super-resolution microscopy techniques can provide in vivo trajectories of individual receptors, and serve as a direct source of quantitative information on molecular processes. Single particle tracking (SPT) has been used to extract reaction kinetic parameters such as dimer lifetimes and diffusion rates. However, signaling models aim to characterize kinetics relevant to the entire cell while SPT follows individual molecules in a small fraction of the cell. The gap in resolution can be bridged with spatial simulations of molecular movement, validated at SPT resolution, which are used to infer effective kinetics on larger spatial scales.
Our focus is on processes that involve receptors bound to the cell membrane. Extrapolating kinetics observed at SPT resolution must take into account the spatial structures that interferes with the free movement of molecules of interest. This is reflected in patterns of movement that deviate from standard Brownian motion. Ideally, simulations at SPT resolution should reproduce observed movement patterns, which reflect the properties and transformation of the molecules as well as those of the underlying cell membrane.
We first sought to identify general signatures of the underlying membrane landscape in jump size distributions extracted from SPT data. We found that Brownian motion simulations in the presence of a pattern of obstacles could provide a good qualitative match. The next step is to infer the underlying landscape structures. We discuss our method used to identify such structures from long single particle trajectories that are obtained at low density. Our approach is based on deviations from ideal Brownian motion and identifies likely regions that trap receptors. We discuss the details of the method in its current form and outline a framework aimed at refinement using simulated motion in a known landscape.
Ádám M. Halász, Brandon L. Clark, Ouri Maler, Jeremy S. Edwards

A Hybrid HMM Approach for the Dynamics of DNA Methylation

Abstract
The understanding of mechanisms that control epigenetic changes is an important research area in modern functional biology. Epigenetic modifications such as DNA methylation are in general very stable over many cell divisions. DNA methylation can however be subject to specific and fast changes over a short time scale even in non-dividing (i.e. not-replicating) cells. Such dynamic DNA methylation changes are caused by a combination of active demethylation and de novo methylation processes which have not been investigated in integrated models.
Here we present a hybrid (hidden) Markov model to describe the cycle of methylation and demethylation over (short) time scales. Our hybrid model decribes several molecular events either happening at deterministic points (i.e. describing mechanisms that occur only during cell division) and other events occurring at random time points. We test our model on mouse embryonic stem cells using time-resolved data. We predict methylation changes and estimate the efficiencies of the different modification steps related to DNA methylation and demethylation.
Charalampos Kyriakopoulos, Pascal Giehr, Alexander Lück, Jörn Walter, Verena Wolf

Using a Hybrid Approach to Model Central Carbon Metabolism Across the Cell Cycle

Abstract
Metabolism and cell cycle are two central processes in the life of a eukaryote cell. If they have been extensively studied in their own right, their interconnection remains relatively poorly understood. In this paper, we propose to use a differential model of the central carbon metabolism. After verifying the model accurately reproduces known metabolic variations during the cell cycle’s phases, we extend it into a hybrid system reproducing an imposed succession of the phases. This first hybrid approach qualitatively recovers observations made in the literature, providing an interesting first step towards a better understanding of the crosstalks between cell cycle and metabolism.
Cecile Moulin, Laurent Tournier, Sabine Peres

Data-Informed Parameter Synthesis for Population Markov Chains

Abstract
Stochastic population models are widely used to model phenomena in different areas such as chemical kinetics or collective animal behaviour. Quantitative analysis of stochastic population models easily becomes challenging, due to the combinatorial propagation of dependencies across the population. The complexity becomes especially prominent when model’s parameters are not known and available measurements are limited. In this paper, we illustrate this challenge in a concrete scenario: we assume a simple communication scheme among identical individuals, inspired by how social honeybees emit the alarm pheromone to protect the colony in case of danger. Together, n individuals induce a population Markov chain with n parameters. In addition, we assume to be able to experimentally observe the states only after the steady-state is reached. In order to obtain the parameters of the individual’s behaviour, by utilising the data measurements for population, we combine two existing techniques. First, we use the tools for parameter synthesis for Markov chains with respect to temporal logic properties, and then we employ CEGAR-like reasoning to find the viable parameter space up to desired coverage. We report the performance on a number of synthetic data sets.
Matej Hajnal, Morgane Nouvian, David Šafránek, Tatjana Petrov

rPrism – A Software for Reactive Weighted State Transition Models

Abstract
In this work we introduce the software rPrism, as a branch of the software PRISM model checker, in order to be able to study weighted reactive state transition models. This kind of model gathers together the concepts of reactivity – which consists of the capacity of a state transition model to alter its accessibility relation – and weights, which can be seen as costs, rates, etc.. Given a specific model, the tool performs a simulation based on a Continuous Time Markov Chain. In particular, we show an example of its application for biological systems.
Daniel Figueiredo, Eugénio Rocha, Manuel António Martins, Madalena Chaves

Short Paper

Frontmatter

Hybrid Modeling of Metabolic-Regulatory Networks (Extended Abstract)

Abstract
Computational approaches in systems biology have become a powerful tool for understanding the fundamental mechanisms of cellular metabolism and regulation. However, the interplay between the regulatory and the metabolic system is still poorly understood. In particular, there is a need for formal mathematical frameworks that allow analyzing metabolism together with dynamic enzyme resources and regulatory events. Here, we introduce a metabolic-regulatory network model (MRN) that allows integrating metabolism with transcriptional regulation, macromolecule production and enzyme resources. Using this model, we show that the dynamic interplay between these different cellular processes can be formalized by a hybrid system, combining continuous dynamics and discrete control.
Lin Liu, Alexander Bockmayr

Backmatter

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