The linear framework: using graph theory to reveal the algebra and thermodynamics of biomolecular systems

KM Nam, R Martinez-Corral… - Interface …, 2022‏ - royalsocietypublishing.org
The linear framework uses finite, directed graphs with labelled edges to model biomolecular
systems. Graph vertices represent biochemical species or molecular states, edges represent …

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 …

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 …

The structure of MESSI biological systems

M Pérez Millán, A Dickenstein - SIAM Journal on Applied Dynamical Systems, 2018‏ - SIAM
We introduce a general framework for biological systems, called MESSI systems, that
describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove …

Joining and decomposing reaction networks

E Gross, H Harrington, N Meshkat, A Shiu - Journal of mathematical …, 2020‏ - Springer
In systems and synthetic biology, much research has focused on the behavior and design of
single pathways, while, more recently, experimental efforts have focused on how cross-talk …

The multistationarity structure of networks with intermediates and a binomial core network

AH Sadeghimanesh, E Feliu - Bulletin of Mathematical Biology, 2019‏ - Springer
This work addresses whether a reaction network, taken with mass-action kinetics, is
multistationary, that is, admits more than one positive steady state in some stoichiometric …

Statistical and computational challenges for whole cell modelling

MPH Stumpf - Current Opinion in Systems Biology, 2021‏ - Elsevier
Mathematical modelling of whole biological cells opens up new opportunities for
fundamental and applied biology. In particular in the context of synthetic biology, it opens up …

A proof of unlimited multistability for phosphorylation cycles

E Feliu, AD Rendall, C Wiuf - Nonlinearity, 2020‏ - iopscience.iop.org
The multiple futile cycle is a phosphorylation system in which a molecular substrate might be
phosphorylated sequentially n times by means of an enzymatic mechanism. The system has …

A structural property for reduction of biochemical networks

A Küken, P Wendering, D Langary, Z Nikoloski - Scientific Reports, 2021‏ - nature.com
Large-scale biochemical models are of increasing sizes due to the consideration of
interacting organisms and tissues. Model reduction approaches that preserve the flux …

Stochastically modeled weakly reversible reaction networks with a single linkage class

DF Anderson, D Cappelletti, J Kim - Journal of Applied Probability, 2020‏ - cambridge.org
It has been known for nearly a decade that deterministically modeled reaction networks that
are weakly reversible and consist of a single linkage class have trajectories that are …