Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or to exploit this multi-scale nature, respectively. In this paper, we propose a jump-diffusion approximation for multi-scale Markov jump processes that couples the two modeling approaches. An error bound of the proposed approximation is derived and used to partition the reactions into fast and slow sets, where the fast set is simulated by a stochastic differential equation and the slow set is modeled by a discrete chain. The error bound leads to a very efficient dynamic partitioning algorithm which has been implemented for several multi-scale reaction systems. The gain in computational efficiency is illustrated by a realistically sized model of a signal transduction cascade coupled to a gene expression dynamics.Comment: 32 pages, 7 figure

Multi-level agent-based modeling - A literature survey

During last decade, multi-level agent-based modeling has received significant and dramatically increasing interest. In this article we present a comprehensive and structured review of literature on the subject. We present the main theoretical contributions and application domains of this concept, with an emphasis on social, flow, biological and biomedical models.Comment: v2. Ref 102 added. v3-4 Many refs and text added v5-6 bibliographic statistics updated. v7 Change of the name of the paper to reflect what it became, many refs and text added, bibliographic statistics update

Anticipating and Coordinating Voltage Control for Interconnected Power Systems

This paper deals with the application of an anticipating and coordinating feedback control scheme in order to mitigate the long-term voltage instability of multi-area power systems. Each local area is uniquely controlled by a control agent (CA) selecting control values based on model predictive control (MPC) and is possibly operated by an independent transmission system operator (TSO). Each MPC-based CA only knows a detailed local hybrid system model of its own area, employing reduced-order quasi steady-state (QSS) hybrid models of its neighboring areas and even simpler PV models for remote areas, to anticipate (and then optimize) the future behavior of its own area. Moreover, the neighboring CAs agree on communicating their planned future control input sequence in order to coordinate their own control actions. The feasibility of the proposed method for real-time applications is explained, and some practical implementation issues are also discussed. The performance of the method, using time-domain simulation of the Nordic32 test system, is compared with the uncoordinated decentralized MPC (no information exchange among CAs), demonstrating the improved behavior achieved by combining anticipation and coordination. The robustness of the control scheme against modeling uncertainties is also illustrated

Kinetic Intersections as a Source of Information on Rate Coefficients

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Setting Parameters for Biological Models With ANIMO

ANIMO (Analysis of Networks with Interactive MOdeling) is a software for modeling biological networks, such as e.g. signaling, metabolic or gene networks. An ANIMO model is essentially the sum of a network topology and a number of interaction parameters. The topology describes the interactions between biological entities in form of a graph, while the parameters determine the speed of occurrence of such interactions. When a mismatch is observed between the behavior of an ANIMO model and experimental data, we want to update the model so that it explains the new data. In general, the topology of a model can be expanded with new (known or hypothetical) nodes, and enables it to match experimental data. However, the unrestrained addition of new parts to a model causes two problems: models can become too complex too fast, to the point of being intractable, and too many parts marked as "hypothetical" or "not known" make a model unrealistic. Even if changing the topology is normally the easier task, these problems push us to try a better parameter fit as a first step, and resort to modifying the model topology only as a last resource. In this paper we show the support added in ANIMO to ease the task of expanding the knowledge on biological networks, concentrating in particular on the parameter settings

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks