Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Trigonometric Embeddings in Polynomial Extended Mode Decomposition—Experimental Application to an Inverted Pendulum

The extended dynamic mode decomposition algorithm is a tool for accurately approximating the point spectrum of the Koopman operator. This algorithm provides an approximate linear expansion of non-linear discrete-time systems, which can be useful for system analysis and controller design. The accuracy of this algorithm depends heavily on the availability of a set of basis functions that provide the ability to capture the nonlinear dynamics of the underlying system. Recently, the use of orthogonal polynomials, along with reduction techniques for the dimension and maximum order of the polynomial basis, have been successfully used to approximate nonlinear systems with the additional benefit of using smaller datasets. This paper expands the current methods for selecting the set of observables for nonlinear systems with periodic behavior, which is prone to a representation in terms of trigonometric functions. The benefit of working with orthogonal polynomials is preserved by embedding the trigonometric functions into the orthogonal basis. The algorithm is illustrated with the data-driven modelling of an inverted pendulum in simulation and real-life experiments.

Visualization of drug target interactions in the contexts of pathways and networks with ReactomeFIViz

The precision medicine paradigm is centered on therapies targeted to particular molecular entities that will elicit an anticipated and controlled therapeutic response. However, genetic alterations in the drug targets themselves or in genes whose products interact with the targets can affect how well a drug actually works for an individual patient. To better understand the effects of targeted therapies in patients, we need software tools capable of simultaneously visualizing patient-specific variations and drug targets in their biological context. This context can be provided using pathways, which are process-oriented representations of biological reactions, or biological networks, which represent pathway-spanning interactions among genes, proteins, and other biological entities. To address this need, we have recently enhanced the Reactome Cytoscape app, ReactomeFIViz, to assist researchers in visualizing and modeling drug and target interactions. ReactomeFIViz integrates drug-target interaction information with high quality manually curated pathways and a genome-wide human functional interaction network. Both the pathways and the functional interaction network are provided by Reactome, the most comprehensive open source biological pathway knowledgebase. We describe several examples demonstrating the application of these new features to the visualization of drugs in the contexts of pathways and networks. Complementing previous features in ReactomeFIViz, these new features enable researchers to ask focused questions about targeted therapies, such as drug sensitivity for patients with different mutation profiles, using a pathway or network perspective.

Smoldyn: particle-based simulation with rule-based modeling, improved molecular interaction and a library interface

Motivation

Smoldyn is a spatial and stochastic biochemical simulator. It treats each molecule of interest as an individual particle in continuous space, simulating molecular diffusion, molecule-membrane interactions and chemical reactions, all with good accuracy. This article presents several new features.

Results

Smoldyn now supports two types of rule-based modeling. These are a wildcard method, which is very convenient, and the BioNetGen package with extensions for spatial simulation, which is better for complicated models. Smoldyn also includes new algorithms for simulating the diffusion of surface-bound molecules and molecules with excluded volume. Both are exact in the limit of short time steps and reasonably good with longer steps. In addition, Smoldyn supports single-molecule tracking simulations. Finally, the Smoldyn source code can be accessed through a C/C ++ language library interface.

Availability and Implementation

Smoldyn software, documentation, code, and examples are at http://www.smoldyn.org .

Contact

steven.s.andrews@gmail.com.

The (Mathematical) Modeling Process in Biosciences

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.