Structural simplification of chemical reaction networks preserving deterministic semantics

International audienceWe study the structural simplification of chemical reaction networks preserving the deterministic kinetics. We aim at finding simplification rules that can eliminate intermediate molecules while preserving the dynamics of all others. The rules should be valid even though the network is plugged into a bigger context. An example is Michaelis-Menten's simplification rule for enzymatic reactions. In this paper, we present a large class of structural simplification rules for reaction networks that can eliminate intermediate molecules at equilibrium, without assuming that all molecules are at equilibrium, i.e. in a steady state. We prove the correctness of our simplification rules for all contexts that preserve the equilibrium of the eliminated molecules. Finally, we illustrate at a concrete example network from systems biology that our simplification rules may allow to drastically reduce the size of reaction networks in practice

The effects of climatic fluctuations and extreme events on running water ecosystems

Most research on the effects of environmental change in freshwaters has focused on incremental changes in average conditions, rather than fluctuations or extreme events such as heatwaves, cold snaps, droughts, floods or wildfires, which may have even more profound consequences. Such events are commonly predicted to increase in frequency, intensity and duration with global climate change, with many systems being exposed to conditions with no recent historical precedent. We propose a mechanistic framework for predicting potential impacts of environmental fluctuations on running water ecosystems by scaling up effects of fluctuations from individuals to entire ecosystems. This framework requires integration of four key components: effects of the environment on individual metabolism, metabolic and biomechanical constraints on fluctuating species interactions, assembly dynamics of local food webs and mapping the dynamics of the meta-community onto ecosystem function. We illustrate the framework by developing a mathematical model of environmental fluctuations on dynamically assembling food webs. We highlight (currently limited) empirical evidence for emerging insights and theoretical predictions. For example, widely supported predictions about the effects of environmental fluctuations are: high vulnerability of species with high per capita metabolic demands such as large-bodied ones at the top of food webs; simplification of food web network structure and impaired energetic transfer efficiency; reduced resilience and top-down relative to bottom-up regulation of food web and ecosystem processes. We conclude by identifying key questions and challenges that need to be addressed to develop more accurate and predictive bio-assessments of the effects of fluctuations, and implications of fluctuations for management practices in an increasingly uncertain world

Model simplification of signal transduction pathway networks via a hybrid inference strategy

A full-scale mathematical model of cellular networks normally involves a large number of variables and parameters. How to effectively develop manageable and reliable models is crucial for effective computation, analysis and design of such systems. The aim of model simplification is to eliminate parts of a model that are unimportant for the properties of interest. In this work, a model reduction strategy via hybrid inference is proposed for signal pathway networks. It integrates multiple techniques including conservation analysis, local sensitivity analysis, principal component analysis and flux analysis to identify the reactions and variables that can be considered to be eliminated from the full-scale model. Using an I·B-NF-·B signalling pathway model as an example, simulation analysis demonstrates that the simplified model quantitatively predicts the dynamic behaviours of the network

Analytical results for the Sznajd model of opinion formation

The Sznajd model, which describes opinion formation and social influence, is treated analytically on a complete graph. We prove the existence of the phase transition in the original formulation of the model, while for the Ochrombel modification we find smooth behaviour without transition. We calculate the average time to reach the stationary state as well as the exponential tail of its probability distribution. An analytical argument for the observed $1/n$ dependence in the distribution of votes in Brazilian elections is provided.Comment: 10 pages 5 figure

Model reduction of network systems with structure preservation:Graph clustering and balanced truncation

A framework of complex networks can adequately describe a wide class of complex systems composing of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in the high complexity of a network system, which poses intense challenges to system management and operation. The main motivation of this research is to establish suitable model reduction techniques that generate simplified models to capture the essential features of the complex network systems. Two approaches are developed in this thesis to reduce the complexity of a network system with structure preservation. The first one is based on graph clustering, which aims to partition a network into several nonoverlapping clusters and merges all the vertices in each cluster into a single vertex. A reduced-order model is then formulated via the framework of the Petrov-Galerkin projection. This thesis discusses the applications of the clustering-based model reduction methods for second-order networks, controlled power networks, multi-agent systems and directed networks in Part I. The second approach in Part II extends the balanced truncation method for control systems to the simplification of dynamical networks. For networked linear passive systems, the proposed method reduces interconnection structures of a network and the dynamics of each subsystem via a unified framework. Additionally, an approach is developed for the reduction of nonlinear Lur’e networks, showing that the dimension of each nonlinear subsystem can be reduced while preserving the robust synchronization property of the overall network

Store-and-forward based methods for the signal control problem in large-scale congested urban road networks

The problem of designing network-wide traffic signal control strategies for large-scale congested urban road networks is considered. One known and two novel methodologies, all based on the store-and-forward modeling paradigm, are presented and compared. The known methodology is a linear multivariable feedback regulator derived through the formulation of a linear-quadratic optimal control problem. An alternative, novel methodology consists of an open-loop constrained quadratic optimal control problem, whose numerical solution is achieved via quadratic programming. Yet a different formulation leads to an open-loop constrained nonlinear optimal control problem, whose numerical solution is achieved by use of a feasible-direction algorithm. A preliminary simulation-based investigation of the signal control problem for a large-scale urban road network using these methodologies demonstrates the comparative efficiency and real-time feasibility of the developed signal control methods