Subgroup Contributed Talks

Archana Hari

UMBC, United States, archh1@umbc.edu

"A novel methodology and web application for computing, visualizing and analyzing genome-scale metabolic flux networks"

Genome-scale metabolic models not only represent the biochemical circuits within cells but can also be used to simulate and analyze cellular phenotypes. However, there is a lack of methodologies and user-friendly tools to visualize the complex reaction graphs within these genome-scale metabolic models and simulate their flux behaviors. For this, we have developed a novel methodology and implemented it in a freely-available web application called Fluxer ( https://fluxer.umbc.edu ) that streamlines the simulation and visualization of genome-scale metabolic flux networks with an easy-to-use interface. The application can take as input any metabolic model encoded with the Systems Biology Markup Language format, automatically perform Flux Balance Analysis using linear programming and apply different methods to compute flux graphs. The flux networks can be visualized as spanning trees and complete graphs with different layouts. The interactive graphs can be used to study major pathways contributing to any metabolic reaction or biosynthesis of any metabolite as well as to simulate reaction knockouts. In addition, Fluxer can compute the k-shortest paths between two reaction or metabolites within the model. Nodes can display detailed metabolic and reaction information, including molecular weights, reaction fluxes, and molecular structures. Over 80 whole-genome metabolic reconstructions are readily available for visualization and analysis. The proposed methodology enables efficient analysis and visualization of genome-scale metabolic models towards the discovery of key metabolic pathways.

Peter Stechlinski

University of Maine, United States, peter.stechlinski@maine.edu

"Sensitivity analysis of nonsmooth biological models"

Nonsmooth dynamical systems are an appropriate modeling framework for a variety of problems in mathematical biology, ranging from glucose-insulin kinetics to rioting activity. The presence of nonsmoothness in these models arises from switching phenomena, such as a biochemical threshold signaling sudden insulin release, or a bandwagon effect in rioting behavior corresponding to an outburst of social activity. Nonsmooth modeling frameworks now possess a sensitivity theory that is relevant for nonsmooth ODEs, nonsmooth differential-algebraic equations, optimization-constrained ODEs, and complementarity systems, among others. In this talk, the nonsmooth sensitivity theory is presented, including the generalized derivatives theory upon which it is built. The theory yields an auxiliary, nonsmooth system whose unique solution characterizes (local) sensitivity information. The theory is highlighted using examples from mathematical biology, with numerical implementations that give nonsmooth sensitivity indices. The results can be used to help inform policy decisions (e.g., in rioting) or for design purposes (e.g., in the intravenous glucose tolerance test for type 2 diabetes) by uncovering the mechanisms driving the dynamics.

Ivo Siekmann

Liverpool John Moores University, United Kingdom, i.siekmann@ljmu.ac.uk

"Data-driven modelling of ion channels incorporating uncertainty using hierarchical Markov models"

Ion channels are proteins that regulate the flow of ions across the cell membrane. Patch clamp recordings enable us to watch a single ion channel in action by detecting the electrical current flowing through the channel over time. At first glance we only see that the channel opens and closes stochastically but often a closer look reveals that it also alternates between two or more levels of activity – highly active modes where the channel opens and closes frequently, nearly inactive modes in which the channel is mostly closed, as well as intermediate levels of activity. The striking differences in the dynamics the channel exhibits in the different modes suggest that each mode is associated with a distinct three-dimensional configuration (conformation) of the channel protein. Applying statistical change point analysis to a large single channel data set collected from the inositol-triphosphate receptor (IP3R) highlights the importance of this observation: We find that the dynamics of the IP3R is entirely regulated by switching between two modes. In order to build a mathematical model that takes this into account we develop a novel model, the hierarchical Markov model, which enables us to separate modelling the slower dynamics of mode switching from the faster dynamics of opening and closing characteristic of each mode. We will illustrate this approach by fitting a hierarchical Markov model to type 1 and type 2 IP3R data for a wide range of concentrations of IP3R, Ca2+ and ATP. In contrast to most other ion channel models currently available we account for uncertainty by calculating probability distributions for the parameters of our model following a Bayesian Markov chain Monte Carlo (MCMC) approach.