• Corpus ID: 246633937

Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness

  title={Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness},
  author={Badal Joshi and Gheorghe Craciun},
Networks with absolute concentration robustness (ACR) have the property that a translation of a coordinate hyperplane either contains all steady states (static ACR) or attracts all trajectories (dynamic ACR). The implication for the underlying biological system is robustness in the concentration of one of the species independent of the initial conditions as well as independent of the concentration of all other species. Identifying network conditions for dynamic ACR is a challenging problem. We… 
Transition graph decomposition for complex balanced reaction networks with non-mass-action kinetics
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small


Foundations of Static and Dynamic Absolute Concentration Robustness (Part I of Dynamic ACR Quadrilogy)
Dynamical ACR is defined, a property related to dynamics, rather than only to equilibrium behavior, and one that guarantees convergence to a robust value, and precise conditions for presence and absence of dynamic ACR are given in complex balanced systems, which in turn yields a large body of reaction networks withynamic ACR.
Absolute concentration robustness in networks with many conservation laws
A reaction system exhibits “absolute concentration robustness” (ACR) in some species if the positive steady-state value of that species does not depend on initial conditions. Mathematically, this
Which Small Reaction Networks Are Multistationary?
This work analyzes the smallest networks, those with only a few chemical species or reactions, and completely answer the question of multistationarity and, in some cases, multistability too, thereby extending related work of Boros.
Inheritance of oscillation in chemical reaction networks
Structural Sources of Robustness in Biochemical Reaction Networks
A large class of robustness-inducing networks that already embraces two quite different biochemical modules for which concentration robustness has been observed experimentally are described, including the Escherichia coli osmoregulation system EnvZ-OmpR and the glyoxylate bypass control system isocitrate dehydrogenase kinase-phosphatase–isocitrates dehydrogenases.
Complete characterization by multistationarity of fully open networks with one non-flow reaction
Atoms of multistationarity in chemical reaction networks
This work enumerate and classify all 386 bimolecular and reversible two-reaction networks and proves that if a subnetwork admits multiple steady states, then these steady states can be lifted to a larger network, provided that the two networks share the same stoichiometric subspace.
A survey of methods for deciding whether a reaction network is multistationary
This work surveys developments in embedding-minimal multistationary networks, with an emphasis on recent results that connect the capacity forMultistationarity of one network to that of another.
Multistationarity in Cyclic Sequestration-Transmutation Networks.
This work completely characterize the capacity of multistationarity of reaction networks which consist of reactions where either two species can inactivate each other, or some species can be transformed into another in a way that gives rise to a feedback cycle.
Local and global robustness in systems of polynomial equations
In this work we consider systems of polynomial equations and study under what conditions the semi-algebraic set of positive real solutions is contained in a parallel translate of a coordinate