Model reduction of biochemical reactions networks by tropical analysis methods

We discuss a method of approximate model reduction for networks of biochemical reactions. This method can be applied to networks with polynomial or rational reaction rates and whose parameters are given by their orders of magnitude. In order to obtain reduced models we solve the problem of tropical equilibration that is a system of equations in max-plus algebra. In the case of networks with nonlinear fast cycles we have to solve the problem of tropical equilibration at least twice, once for the initial system and a second time for an extended system obtained by adding to the initial system the differential equations satisfied by the conservation laws of the fast subsystem. The two steps can be reiterated until the fast subsystem has no conservation laws different from the ones of the full model. Our method can be used for formal model reduction in computational systems biology

Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided

Symbolic Methods for Chemical Reaction Networks (Dagstuhl Seminar 12462)

During 11-16 November 2012, the Dagstuhl Seminar 12462 "Symbolic Methods for Chemical Reaction Networks" was held in Schloss Dagstuhl - Leibneiz Center for Informatics. The seminar brought together researchers in symbolic computation, chemical engineering, and systems biology. During the seminar, participants presented five-minute talks introducing their research interests, five participants gave longer talks, and all participants had the opportunity to take part in various discussion groups. Abstracts of presentations and summaries of the discussion groups are compiled in this report

Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience

Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.Comment: Darwinian Neurodynamics. Submitted as a two part paper to Living Machines 2013 Natural History Museum, Londo

The Activity of Abstraction in Physical Chemistry Problem Solving and Instruction

Productive problem solving, concept construction, and sense making occur through the core process of abstraction. Although the capacity for domain-general abstraction is developed at a young age, the role of abstraction in increasingly complex and disciplinary environments, such as those encountered in undergraduate STEM education, is not well understood. Undergraduate physical chemistry relies particularly heavily on abstraction because it uses many overlapping and imperfect mathematical models to represent and interpret phenomena occurring on multiple scales. To reconcile these models, extract meaning from them, and recognize when to apply them in problem solving requires processes of abstraction. This dissertation aims to develop a framework that can be used to make abstraction in physical chemistry visible to better understand how undergraduate physical chemistry students navigate these processes and abstract in problem solving scenarios. Using an activity theoretical lens, this dissertation has three aims: (1) to operationalize abstraction as a series of epistemic actions, and to use this operationalization to investigate (2) what motivates and influences whether abstraction is realized in the moment, and (3) the role abstraction plays in physical chemistry instruction. First, problem solving teaching interviews with individuals and pairs (n=18) on thermodynamics and kinetics topics are analyzed using a constant comparative approach. The resulting Epistemic Actions of Abstraction framework characterizes eight epistemic actions along two dimensions: increasing abstractness relative to the context (concretizing, manipulating, restructuring, and generalizing) and nature of the object the action operates on (conceptual or symbolic). These teaching interviews are then inductively analyzed to identify what sparks abstraction and the influence of interaction on abstraction. Three types of needs (task-directed, situational-insufficient, and situational-emergent), and three major themes (framing, interviewer intervention, and peer interaction) are found. Finally, a multiple-case study of physical chemistry instructors (n=2) at two different institutions is conducted to investigate how and why instructors model abstraction. Analysis of classroom video and video-stimulated recall interviews yields two identified roles abstraction plays in physical chemistry instruction: developing mathematical tools grounded in conceptual understanding, and developing conceptual understanding grounded in mathematics. Implications for research and teaching are discussed

Towards an automated reduction method for polynomial ODE models in cellular biology

International audienceThis paper presents the first version of an algorithmic scheme dedicated to the model reduction problem, in the context of polynomial ODE models derived from generalized chemical reaction systems. This scheme, which relies on computer algebra, is implemented within a new MAPLE package. It is applied over an example. The qualitative analysis of the reduced model is afterwards completely carried out, proving the practical relevance of our methods