Biochemical systems theory: a review

EO Voit - International Scholarly Research Notices, 2013 - Wiley Online Library
Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools
that facilitate the analysis of dynamic biological systems. This paper depicts major …

Foundations of chemical reaction network theory

M Feinberg - 2019 - Springer
When I am called upon to teach fluid mechanics, I always show students a copy of Newton's
Principia. I do this for a number of reasons, not least of which is the connection I hope they …

Dynamics of posttranslational modification systems: Recent progress and future directions

C Conradi, A Shiu - Biophysical journal, 2018 - cell.com
Posttranslational modification of proteins is important for signal transduction, and hence
significant effort has gone toward understanding how posttranslational modification …

Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph

G Craciun, M Feinberg - SIAM Journal on Applied Mathematics, 2006 - SIAM
For mass action kinetics, the capacity for multiple equilibria in an isothermal homogeneous
continuous flow stirred tank reactor is determined by the structure of the underlying network …

Identifying parameter regions for multistationarity

C Conradi, E Feliu, M Mincheva… - PLoS computational …, 2017 - journals.plos.org
Mathematical modelling has become an established tool for studying the dynamics of
biological systems. Current applications range from building models that reproduce …

Identifiability of chemical reaction networks

G Craciun, C Pantea - Journal of Mathematical Chemistry, 2008 - Springer
We consider the dynamics of chemical reaction networks under the assumption of mass-
action kinetics. We show that there exist reaction networks R for which the reaction rate …

Sign conditions for injectivity of generalized polynomial maps with applications to chemical reaction networks and real algebraic geometry

S Müller, E Feliu, G Regensburger, C Conradi… - Foundations of …, 2016 - Springer
We give necessary and sufficient conditions in terms of sign vectors for the injectivity of
families of polynomial maps with arbitrary real exponents defined on the positive orthant …

Atoms of multistationarity in chemical reaction networks

B Joshi, A Shiu - Journal of Mathematical Chemistry, 2013 - Springer
Chemical reaction systems are dynamical systems that arise in chemical engineering and
systems biology. In this work, we consider the question of whether the minimal (in a precise …

A new necessary condition on interaction graphs for multistationarity

M Kaufman, C Soule, R Thomas - Journal of theoretical biology, 2007 - Elsevier
We consider a dynamical system, described by a system of ordinary differential equations,
and the associated interaction graphs, which are defined using the matrix of signs of the …

Simplifying biochemical models with intermediate species

E Feliu, C Wiuf - Journal of the royal society interface, 2013 - royalsocietypublishing.org
Mathematical models are increasingly being used to understand complex biochemical
systems, to analyse experimental data and make predictions about unobserved quantities …